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3
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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 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 /* |
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25 |
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26 Should probably say something here about why these classes are not |
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27 represented by some sort of inheritance tree... |
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28 |
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29 */ |
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30 |
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31 #if !defined (_Matrix_h) |
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32 #define _Matrix_h 1 |
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33 |
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34 // I\'m not sure how this is supposed to work if the .h file declares |
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35 // several classes, each of which is defined in a separate file... |
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36 // |
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37 // #ifdef __GNUG__ |
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38 // #pragma interface |
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39 // #endif |
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40 |
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41 #include <stdlib.h> |
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42 #include <stddef.h> |
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43 #include <math.h> |
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44 #include <values.h> |
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45 #include <assert.h> |
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46 #include <iostream.h> |
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47 // #include <iomanip.h> // We don\'t use this yet. |
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48 #include <Complex.h> |
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49 |
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50 #define FAIL assert(0) /* XXX FIXME XXX */ |
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51 |
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52 #ifndef MAPPER_FCN_TYPEDEFS |
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53 #define MAPPER_FCN_TYPEDEFS 1 |
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54 |
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55 typedef double (*d_d_Mapper)(double); |
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56 typedef double (*d_c_Mapper)(const Complex&); |
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57 typedef Complex (*c_c_Mapper)(const Complex&); |
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58 |
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59 #endif |
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60 |
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61 #include "f77-uscore.h" |
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62 |
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63 // Fortran functions we call. |
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64 |
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65 extern "C" |
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66 { |
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67 int F77_FCN (dgemm) (const char*, const char*, const int*, |
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68 const int*, const int*, const double*, |
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69 const double*, const int*, const double*, |
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70 const int*, const double*, double*, const int*, |
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71 long, long); |
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72 |
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73 int F77_FCN (dgemv) (const char*, const int*, const int*, |
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74 const double*, const double*, const int*, |
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75 const double*, const int*, const double*, |
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76 double*, const int*, long); |
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77 |
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78 int F77_FCN (dgeco) (double*, const int*, const int*, int*, double*, |
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79 double*); |
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80 |
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81 int F77_FCN (dgesv) (const int*, const int*, double*, const int*, |
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82 int*, double*, const int*, int*); |
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83 |
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84 int F77_FCN (dgeqrf) (const int*, const int*, double*, const int*, |
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85 double*, double*, const int*, int*); |
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86 |
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87 int F77_FCN (dorgqr) (const int*, const int*, const int*, double*, |
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88 const int*, double*, double*, const int*, int*); |
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89 |
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90 int F77_FCN (dgesl) (const double*, const int*, const int*, |
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91 const int*, double*, const int*); |
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92 |
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93 int F77_FCN (dgedi) (double*, const int*, const int*, const int*, |
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94 double*, double*, const int*); |
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95 |
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96 double F77_FCN (ddot) (const int*, const double*, const int*, |
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97 const double*, const int*); |
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98 |
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99 int F77_FCN (dgeev) (const char*, const char*, const int*, double*, |
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100 const int*, double*, double*, double*, |
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101 const int*, double*, const int*, double*, |
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102 const int*, int*, long, long); |
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103 |
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104 int F77_FCN (dgeesx) (const char*, const char*, int (*)(), const char*, |
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105 const int*, double*, const int*, int*, double*, |
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106 double*, double*, const int*, double*, double*, |
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107 double*, const int*, int*, const int*, int*, |
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108 int*, long, long); |
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109 |
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110 int F77_FCN (dhseqr) (const char*, const char*, const int*, |
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111 const int*, const int*, double*, |
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112 const int*, double*, double*, |
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113 double*, const int*, double*, const int*, |
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114 int*, long, long); |
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115 |
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116 int F77_FCN (dgebal) (const char*, const int*, double*, |
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117 const int*, int*, int*, double*, |
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118 int*, long, long); |
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119 |
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120 int F77_FCN (dgebak) (const char*, const char*, const int*, const int*, |
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121 const int*, double*, const int*, double*, const int*, |
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122 int*, long, long); |
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123 |
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124 int F77_FCN (dgehrd) (const int*, const int*, const int*, |
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125 double*, const int*, double*, double*, |
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126 const int*, int*, long, long); |
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127 |
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128 int F77_FCN (dorghr) (const int*, const int*, const int*, |
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129 double*, const int*, double*, double*, |
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130 const int*, int*, long, long); |
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131 |
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132 int F77_FCN (dgesvd) (const char*, const char*, const int*, |
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133 const int*, double*, const int*, double*, |
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134 double*, const int*, double*, const int*, |
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135 double*, const int*, int*, long, long); |
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136 |
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137 int F77_FCN (dgelss) (const int*, const int*, const int*, double*, |
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138 const int*, double*, const int*, double*, |
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139 const double*, int*, double*, const int*, |
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140 int*); |
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141 |
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142 /* |
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143 * f2c translates complex*16 as |
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144 * |
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145 * typedef struct { doublereal re, im; } doublecomplex; |
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146 * |
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147 * and Complex.h from libg++ uses |
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148 * |
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149 * protected: |
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150 * double re; |
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151 * double im; |
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152 * |
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153 * as the only data members, so this should work (fingers crossed that |
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154 * things don't change). |
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155 */ |
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156 |
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157 int F77_FCN (zgemm) (const char*, const char*, const int*, |
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158 const int*, const int*, const Complex*, |
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159 const Complex*, const int*, const Complex*, |
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160 const int*, const Complex*, Complex*, const int*, |
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161 long, long); |
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162 |
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163 int F77_FCN (zgemv) (const char*, const int*, const int*, |
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164 const Complex*, const Complex*, const int*, |
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165 const Complex*, const int*, const Complex*, |
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166 Complex*, const int*, long); |
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167 |
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168 int F77_FCN (zgeco) (Complex*, const int*, const int*, int*, |
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169 double*, Complex*); |
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170 |
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171 int F77_FCN (zgesv) (const int*, const int*, Complex*, const int*, |
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172 int*, Complex*, const int*, int*); |
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173 |
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174 int F77_FCN (zgeqrf) (const int*, const int*, Complex*, const int*, |
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175 Complex*, Complex*, const int*, int*); |
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176 |
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177 int F77_FCN (zgeesx) (const char*, const char*, int (*)(), const char*, |
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178 const int*, Complex*, const int*, int*, |
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179 Complex*, Complex*, const int*, double*, double*, |
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180 Complex*, const int*, double*, int*, int*, |
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181 long, long); |
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182 |
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183 int F77_FCN (zhseqr) (const char*, const char*, const int*, |
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184 const int*, const int*, Complex*, const int*, |
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185 Complex*, Complex*, const int*, Complex*, |
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186 const int*, int*, long, long); |
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187 |
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188 int F77_FCN (zgebal) (const char*, const int*, Complex*, const int*, |
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189 int*, int*, double*, int*, long, long); |
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190 |
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191 int F77_FCN (zgebak) (const char*, const char*, const int*, const int*, |
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192 const int*, double*, const int*, Complex*, |
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193 const int*, int*, long, long); |
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194 |
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195 int F77_FCN (zgehrd) (const int*, const int*, const int*, Complex*, |
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196 const int*, Complex*, Complex*, const int*, |
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197 int*, long, long); |
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198 |
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199 int F77_FCN (zunghr) (const int*, const int*, const int*, Complex*, |
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200 const int*, Complex*, Complex*, const int*, |
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201 int*, long, long); |
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202 |
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203 int F77_FCN (zungqr) (const int*, const int*, const int*, Complex*, |
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204 const int*, Complex*, Complex*, const int*, int*); |
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205 |
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206 int F77_FCN (zgedi) (Complex*, const int*, const int*, int*, |
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207 Complex*, Complex*, const int*); |
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208 |
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209 int F77_FCN (zgesl) (Complex*, const int*, const int*, int*, |
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210 Complex*, const int*); |
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211 |
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212 int F77_FCN (zgeev) (const char*, const char*, const int*, Complex*, |
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213 const int*, Complex*, Complex*, const int*, |
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214 Complex*, const int*, Complex*, const int*, |
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215 double*, int*, long, long); |
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216 |
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217 int F77_FCN (zgesvd) (const char*, const char*, const int*, |
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218 const int*, Complex*, const int*, double*, |
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219 Complex*, const int*, Complex*, const int*, |
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220 Complex*, const int*, double*, int*, long, long); |
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221 |
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222 int F77_FCN (zgelss) (const int*, const int*, const int*, Complex*, |
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223 const int*, Complex*, const int*, double*, |
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224 const double*, int*, Complex*, const int*, |
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225 double*, int*); |
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226 |
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227 // Note that the original complex fft routines were not written for |
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228 // double complex arguments. They have been modified by adding an |
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229 // implicit double precision (a-h,o-z) statement at the beginning of |
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230 // each subroutine. |
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231 |
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232 int F77_FCN (cffti) (const int*, Complex*); |
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233 |
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234 int F77_FCN (cfftf) (const int*, Complex*, Complex*); |
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235 |
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236 int F77_FCN (cfftb) (const int*, Complex*, Complex*); |
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237 |
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238 } |
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239 |
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240 // Classes we declare. |
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241 |
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242 class Matrix; |
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243 class ColumnVector; |
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244 class RowVector; |
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245 class DiagMatrix; |
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246 class ComplexMatrix; |
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247 class ComplexColumnVector; |
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248 class ComplexRowVector; |
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249 class ComplexDiagMatrix; |
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250 class DET; |
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251 class ComplexDET; |
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252 class EIG; |
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253 class HESS; |
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254 class ComplexHESS; |
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255 class SCHUR; |
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256 class ComplexSCHUR; |
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257 class SVD; |
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258 class ComplexSVD; |
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259 class LU; |
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260 class ComplexLU; |
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261 class QR; |
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262 class ComplexQR; |
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263 |
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264 /* |
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265 * Matrix class |
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266 */ |
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267 |
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268 class Matrix |
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269 { |
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270 friend class RowVector; |
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271 friend class DiagMatrix; |
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272 friend class ComplexMatrix; |
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273 friend class ComplexDiagMatrix; |
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274 friend class EIG; |
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275 friend class HESS; |
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276 friend class SCHUR; |
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277 friend class SVD; |
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278 friend class LU; |
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279 friend class QR; |
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280 |
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281 public: |
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282 Matrix (void); |
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283 Matrix (int r, int c); |
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284 Matrix (int r, int c, double val); |
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285 Matrix (const Matrix& a); |
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286 Matrix (const DiagMatrix& a); |
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287 Matrix (double a); |
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288 ~Matrix (void); |
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289 |
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290 #if defined (MDEBUG) |
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291 void *operator new (size_t size) |
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292 { |
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293 Matrix *p = ::new Matrix; |
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294 cerr << "Matrix::new(): " << p << "\n"; |
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295 return p; |
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296 } |
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297 |
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298 void operator delete (void *p, size_t size) |
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299 { |
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300 cerr << "Matrix::delete(): " << p << "\n"; |
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301 ::delete p; |
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302 } |
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303 #endif |
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304 |
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305 Matrix& operator = (const Matrix& a); |
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306 |
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307 int rows (void) const; |
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308 int cols (void) const; |
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309 int columns (void) const; |
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310 |
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311 double& elem (int r, int c); |
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312 double& checkelem (int r, int c); |
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313 double& operator () (int r, int c); |
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314 |
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315 double elem (int r, int c) const; // const access |
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316 double checkelem (int r, int c) const; |
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317 double operator () (int r, int c) const; |
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318 |
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319 Matrix& resize (int r, int c); |
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320 Matrix& resize (int r, int c, double val); |
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321 |
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322 int operator == (const Matrix& a) const; |
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323 int operator != (const Matrix& a) const; |
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324 |
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325 // destructive insert/delete/reorder operations |
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326 |
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327 Matrix& insert (const Matrix& a, int r, int c); |
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328 Matrix& insert (const RowVector& a, int r, int c); |
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329 Matrix& insert (const ColumnVector& a, int r, int c); |
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330 Matrix& insert (const DiagMatrix& a, int r, int c); |
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331 |
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332 Matrix& fill (double val); |
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333 Matrix& fill (double val, int r1, int c1, int r2, int c2); |
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334 |
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335 Matrix append (const Matrix& a) const; |
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336 Matrix append (const RowVector& a) const; |
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337 Matrix append (const ColumnVector& a) const; |
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338 Matrix append (const DiagMatrix& a) const; |
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339 |
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340 Matrix stack (const Matrix& a) const; |
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341 Matrix stack (const RowVector& a) const; |
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342 Matrix stack (const ColumnVector& a) const; |
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343 Matrix stack (const DiagMatrix& a) const; |
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344 |
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345 Matrix transpose (void) const; |
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346 |
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347 // resize is the destructive equivalent for this one |
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348 |
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349 Matrix extract (int r1, int c1, int r2, int c2) const; |
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350 |
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351 // extract row or column i. |
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352 |
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353 RowVector row (int i) const; |
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354 RowVector row (char *s) const; |
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355 |
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356 ColumnVector column (int i) const; |
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357 ColumnVector column (char *s) const; |
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358 |
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359 Matrix inverse (int& info, double& rcond) const; |
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360 Matrix inverse (int& info) const; |
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361 Matrix inverse (void) const; |
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362 |
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363 ComplexMatrix fourier (void) const; |
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364 ComplexMatrix ifourier (void) const; |
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365 |
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366 DET determinant (void) const; |
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367 DET determinant (int& info) const; |
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368 DET determinant (int& info, double& rcond) const; |
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369 |
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370 Matrix solve (const Matrix& b) const; |
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371 Matrix solve (const Matrix& b, int& info) const; |
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372 Matrix solve (const Matrix& b, int& info, double& rcond) const; |
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373 |
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374 ComplexMatrix solve (const ComplexMatrix& b) const; |
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375 ComplexMatrix solve (const ComplexMatrix& b, int& info) const; |
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376 ComplexMatrix solve (const ComplexMatrix& b, int& info, double& rcond) const; |
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377 |
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378 ColumnVector solve (const ColumnVector& b) const; |
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379 ColumnVector solve (const ColumnVector& b, int& info) const; |
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380 ColumnVector solve (const ColumnVector& b, int& info, double& rcond) const; |
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381 |
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382 ComplexColumnVector solve (const ComplexColumnVector& b) const; |
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383 ComplexColumnVector solve (const ComplexColumnVector& b, int& info) const; |
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384 ComplexColumnVector solve (const ComplexColumnVector& b, int& info, |
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385 double& rcond) const; |
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386 |
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387 Matrix lssolve (const Matrix& b) const; |
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388 Matrix lssolve (const Matrix& b, int& info) const; |
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389 Matrix lssolve (const Matrix& b, int& info, int& rank) const; |
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390 |
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391 ComplexMatrix lssolve (const ComplexMatrix& b) const; |
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392 ComplexMatrix lssolve (const ComplexMatrix& b, int& info) const; |
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393 ComplexMatrix lssolve (const ComplexMatrix& b, int& info, |
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394 int& rank) const; |
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395 |
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396 ColumnVector lssolve (const ColumnVector& b) const; |
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397 ColumnVector lssolve (const ColumnVector& b, int& info) const; |
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398 ColumnVector lssolve (const ColumnVector& b, int& info, int& rank) const; |
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399 |
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400 ComplexColumnVector lssolve (const ComplexColumnVector& b) const; |
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401 ComplexColumnVector lssolve (const ComplexColumnVector& b, int& info) const; |
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402 ComplexColumnVector lssolve (const ComplexColumnVector& b, int& info, |
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403 int& rank) const; |
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404 |
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405 // matrix by scalar -> matrix operations |
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406 |
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407 Matrix operator + (double s) const; |
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408 Matrix operator - (double s) const; |
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409 Matrix operator * (double s) const; |
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410 Matrix operator / (double s) const; |
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411 |
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412 ComplexMatrix operator + (Complex s) const; |
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413 ComplexMatrix operator - (Complex s) const; |
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414 ComplexMatrix operator * (Complex s) const; |
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415 ComplexMatrix operator / (Complex s) const; |
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416 |
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417 // scalar by matrix -> matrix operations |
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418 |
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419 friend Matrix operator + (double s, const Matrix& a); |
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420 friend Matrix operator - (double s, const Matrix& a); |
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421 friend Matrix operator * (double s, const Matrix& a); |
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422 friend Matrix operator / (double s, const Matrix& a); |
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423 |
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424 // matrix by column vector -> column vector operations |
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425 |
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426 ColumnVector operator * (const ColumnVector& a) const; |
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427 |
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428 ComplexColumnVector operator * (const ComplexColumnVector& a) const; |
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429 |
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430 // matrix by diagonal matrix -> matrix operations |
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431 |
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432 Matrix operator + (const DiagMatrix& a) const; |
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433 Matrix operator - (const DiagMatrix& a) const; |
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434 Matrix operator * (const DiagMatrix& a) const; |
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435 |
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436 ComplexMatrix operator + (const ComplexDiagMatrix& a) const; |
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437 ComplexMatrix operator - (const ComplexDiagMatrix& a) const; |
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438 ComplexMatrix operator * (const ComplexDiagMatrix& a) const; |
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439 |
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440 Matrix& operator += (const DiagMatrix& a); |
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441 Matrix& operator -= (const DiagMatrix& a); |
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442 |
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443 // matrix by matrix -> matrix operations |
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444 |
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445 Matrix operator + (const Matrix& a) const; |
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446 Matrix operator - (const Matrix& a) const; |
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447 Matrix operator * (const Matrix& a) const; |
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448 |
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449 ComplexMatrix operator + (const ComplexMatrix& a) const; |
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450 ComplexMatrix operator - (const ComplexMatrix& a) const; |
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451 ComplexMatrix operator * (const ComplexMatrix& a) const; |
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452 |
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453 Matrix product (const Matrix& a) const; // element by element |
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454 Matrix quotient (const Matrix& a) const; // element by element |
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455 |
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|
456 ComplexMatrix product (const ComplexMatrix& a) const; // element by element |
|
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457 ComplexMatrix quotient (const ComplexMatrix& a) const; // element by element |
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|
458 |
|
|
459 Matrix& operator += (const Matrix& a); |
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460 Matrix& operator -= (const Matrix& a); |
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461 |
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462 // unary operations |
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463 |
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464 Matrix operator - (void) const; |
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465 Matrix operator ! (void) const; |
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|
466 |
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467 // other operations |
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468 |
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469 friend Matrix map (d_d_Mapper f, const Matrix& a); |
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|
470 void map (d_d_Mapper f); |
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471 |
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|
472 Matrix all (void) const; |
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|
473 Matrix any (void) const; |
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474 |
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475 Matrix cumprod (void) const; |
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|
476 Matrix cumsum (void) const; |
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|
477 Matrix prod (void) const; |
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|
478 Matrix sum (void) const; |
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|
479 Matrix sumsq (void) const; |
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|
480 |
|
|
481 ColumnVector diag (void) const; |
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|
482 ColumnVector diag (int k) const; |
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483 |
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484 ColumnVector row_min (void) const; |
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|
485 ColumnVector row_max (void) const; |
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486 |
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|
487 RowVector column_min (void) const; |
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|
488 RowVector column_max (void) const; |
|
|
489 |
|
|
490 // i/o |
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491 |
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|
492 friend ostream& operator << (ostream& os, const Matrix& a); |
|
|
493 friend istream& operator >> (istream& is, Matrix& a); |
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|
494 |
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|
495 // conversions |
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|
496 |
|
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497 double *fortran_vec (void); |
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498 |
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499 private: |
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|
500 int nr; |
|
|
501 int nc; |
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502 int len; |
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|
503 double *data; |
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504 |
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|
505 Matrix (double *d, int r, int c); |
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506 }; |
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507 |
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508 inline Matrix::Matrix (void) { nr = 0; nc = 0; len = 0; data = 0; } |
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509 |
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510 inline Matrix::Matrix (double *d, int r, int c) |
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511 { nr = r; nc = c; len = nr*nc; data = d; } |
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512 |
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513 inline Matrix::~Matrix (void) { delete [] data; data = 0; } |
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|
514 |
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|
515 inline int Matrix::rows (void) const { return nr; } |
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516 inline int Matrix::cols (void) const { return nc; } |
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|
517 inline int Matrix::columns (void) const { return nc; } |
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518 |
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|
519 inline double& Matrix::elem (int r, int c) { return data[nr*c+r]; } |
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|
520 |
|
|
521 inline double& Matrix::checkelem (int r, int c) |
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522 { |
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|
523 #ifndef NO_RANGE_CHECK |
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|
524 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
525 FAIL; |
|
|
526 #endif |
|
|
527 |
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|
528 return elem (r, c); |
|
|
529 } |
|
|
530 |
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|
531 inline double& Matrix::operator () (int r, int c) |
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532 { return checkelem (r, c); } |
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|
533 |
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|
534 inline double Matrix::elem (int r, int c) const { return data[nr*c+r]; } |
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|
535 |
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|
536 inline double Matrix::checkelem (int r, int c) const |
|
|
537 { |
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|
538 #ifndef NO_RANGE_CHECK |
|
|
539 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
540 FAIL; |
|
|
541 #endif |
|
|
542 |
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|
543 return elem (r, c); |
|
|
544 } |
|
|
545 |
|
|
546 inline double Matrix::operator () (int r, int c) const |
|
|
547 { return checkelem (r, c); } |
|
|
548 |
|
|
549 inline double *Matrix::fortran_vec (void) { return data; } |
|
|
550 |
|
|
551 /* |
|
|
552 * Column Vector class |
|
|
553 */ |
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|
554 |
|
|
555 class ColumnVector |
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|
556 { |
|
|
557 friend class Matrix; |
|
|
558 friend class RowVector; |
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|
559 friend class DiagMatrix; |
|
|
560 friend class ComplexMatrix; |
|
|
561 friend class ComplexColumnVector; |
|
|
562 friend class ComplexDiagMatrix; |
|
|
563 |
|
|
564 public: |
|
|
565 ColumnVector (void); |
|
|
566 ColumnVector (int n); |
|
|
567 ColumnVector (int n, double val); |
|
|
568 ColumnVector (const ColumnVector& a); |
|
|
569 ColumnVector (double a); |
|
|
570 ~ColumnVector (void); |
|
|
571 |
|
|
572 ColumnVector& operator = (const ColumnVector& a); |
|
|
573 |
|
|
574 int capacity (void) const; |
|
|
575 int length (void) const; |
|
|
576 |
|
|
577 double& elem (int n); |
|
|
578 double& checkelem (int n); |
|
|
579 double& operator () (int n); |
|
|
580 |
|
|
581 double elem (int n) const; // const access |
|
|
582 double checkelem (int n) const; |
|
|
583 double operator () (int n) const; |
|
|
584 |
|
|
585 ColumnVector& resize (int n); |
|
|
586 ColumnVector& resize (int n, double val); |
|
|
587 |
|
|
588 int operator == (const ColumnVector& a) const; |
|
|
589 int operator != (const ColumnVector& a) const; |
|
|
590 |
|
|
591 // destructive insert/delete/reorder operations |
|
|
592 |
|
|
593 ColumnVector& insert (const ColumnVector& a, int r); |
|
|
594 |
|
|
595 ColumnVector& fill (double val); |
|
|
596 ColumnVector& fill (double val, int r1, int r2); |
|
|
597 |
|
|
598 ColumnVector stack (const ColumnVector& a) const; |
|
|
599 |
|
|
600 RowVector transpose (void) const; |
|
|
601 |
|
|
602 // resize is the destructive equivalent for this one |
|
|
603 |
|
|
604 ColumnVector extract (int r1, int r2) const; |
|
|
605 |
|
|
606 // column vector by scalar -> column vector operations |
|
|
607 |
|
|
608 ColumnVector operator + (double s) const; |
|
|
609 ColumnVector operator - (double s) const; |
|
|
610 ColumnVector operator * (double s) const; |
|
|
611 ColumnVector operator / (double s) const; |
|
|
612 |
|
|
613 ComplexColumnVector operator + (Complex s) const; |
|
|
614 ComplexColumnVector operator - (Complex s) const; |
|
|
615 ComplexColumnVector operator * (Complex s) const; |
|
|
616 ComplexColumnVector operator / (Complex s) const; |
|
|
617 |
|
|
618 // scalar by column vector -> column vector operations |
|
|
619 |
|
|
620 friend ColumnVector operator + (double s, const ColumnVector& a); |
|
|
621 friend ColumnVector operator - (double s, const ColumnVector& a); |
|
|
622 friend ColumnVector operator * (double s, const ColumnVector& a); |
|
|
623 friend ColumnVector operator / (double s, const ColumnVector& a); |
|
|
624 |
|
|
625 // column vector by row vector -> matrix operations |
|
|
626 |
|
|
627 Matrix operator * (const RowVector& a) const; |
|
|
628 |
|
|
629 ComplexMatrix operator * (const ComplexRowVector& a) const; |
|
|
630 |
|
|
631 // column vector by column vector -> column vector operations |
|
|
632 |
|
|
633 ColumnVector operator + (const ColumnVector& a) const; |
|
|
634 ColumnVector operator - (const ColumnVector& a) const; |
|
|
635 |
|
|
636 ComplexColumnVector operator + (const ComplexColumnVector& a) const; |
|
|
637 ComplexColumnVector operator - (const ComplexColumnVector& a) const; |
|
|
638 |
|
|
639 ColumnVector product (const ColumnVector& a) const; // element by element |
|
|
640 ColumnVector quotient (const ColumnVector& a) const; // element by element |
|
|
641 |
|
|
642 ComplexColumnVector product (const ComplexColumnVector& a) const; |
|
|
643 ComplexColumnVector quotient (const ComplexColumnVector& a) const; |
|
|
644 |
|
|
645 ColumnVector& operator += (const ColumnVector& a); |
|
|
646 ColumnVector& operator -= (const ColumnVector& a); |
|
|
647 |
|
|
648 // unary operations |
|
|
649 |
|
|
650 ColumnVector operator - (void) const; |
|
|
651 |
|
|
652 friend ColumnVector map (d_d_Mapper f, const ColumnVector& a); |
|
|
653 void map (d_d_Mapper f); |
|
|
654 |
|
|
655 double min (void) const; |
|
|
656 double max (void) const; |
|
|
657 |
|
|
658 // i/o |
|
|
659 |
|
|
660 friend ostream& operator << (ostream& os, const ColumnVector& a); |
|
|
661 |
|
|
662 // conversions |
|
|
663 |
|
|
664 double *fortran_vec (void); |
|
|
665 |
|
|
666 private: |
|
|
667 int len; |
|
|
668 double *data; |
|
|
669 |
|
|
670 ColumnVector (double *d, int l); |
|
|
671 }; |
|
|
672 |
|
|
673 inline ColumnVector::ColumnVector (void) { len = 0; data = 0; } |
|
|
674 inline ColumnVector::ColumnVector (double *d, int l) { len = l; data = d; } |
|
|
675 inline ColumnVector::~ColumnVector (void) { delete [] data; data = 0; } |
|
|
676 |
|
|
677 inline int ColumnVector::capacity (void) const { return len; } |
|
|
678 inline int ColumnVector::length (void) const { return len; } |
|
|
679 |
|
|
680 inline double& ColumnVector::elem (int n) { return data[n]; } |
|
|
681 |
|
|
682 inline double& |
|
|
683 ColumnVector::checkelem (int n) |
|
|
684 { |
|
|
685 #ifndef NO_RANGE_CHECK |
|
|
686 if (n < 0 || n >= len) |
|
|
687 FAIL; |
|
|
688 #endif |
|
|
689 |
|
|
690 return elem (n); |
|
|
691 } |
|
|
692 |
|
|
693 inline double& ColumnVector::operator () (int n) { return checkelem (n); } |
|
|
694 |
|
|
695 inline double ColumnVector::elem (int n) const { return data[n]; } |
|
|
696 |
|
|
697 inline double |
|
|
698 ColumnVector::checkelem (int n) const |
|
|
699 { |
|
|
700 #ifndef NO_RANGE_CHECK |
|
|
701 if (n < 0 || n >= len) |
|
|
702 FAIL; |
|
|
703 #endif |
|
|
704 |
|
|
705 return elem (n); |
|
|
706 } |
|
|
707 |
|
|
708 inline double ColumnVector::operator () (int n) const { return checkelem (n); } |
|
|
709 |
|
|
710 inline double *ColumnVector::fortran_vec (void) { return data; } |
|
|
711 |
|
|
712 /* |
|
|
713 * Row Vector class |
|
|
714 */ |
|
|
715 |
|
|
716 class RowVector |
|
|
717 { |
|
|
718 friend class Matrix; |
|
|
719 friend class DiagMatrix; |
|
|
720 friend class ColumnVector; |
|
|
721 friend class ComplexMatrix; |
|
|
722 friend class ComplexRowVector; |
|
|
723 friend class ComplexDiagMatrix; |
|
|
724 |
|
|
725 public: |
|
|
726 RowVector (void); |
|
|
727 RowVector (int n); |
|
|
728 RowVector (int n, double val); |
|
|
729 RowVector (const RowVector& a); |
|
|
730 RowVector (double a); |
|
|
731 ~RowVector (void); |
|
|
732 |
|
|
733 RowVector& operator = (const RowVector& a); |
|
|
734 |
|
|
735 int capacity (void) const; |
|
|
736 int length (void) const; |
|
|
737 |
|
|
738 double& elem (int n); |
|
|
739 double& checkelem (int n); |
|
|
740 double& operator () (int n); |
|
|
741 |
|
|
742 double elem (int n) const; // const access |
|
|
743 double checkelem (int n) const; |
|
|
744 double operator () (int n) const; |
|
|
745 |
|
|
746 RowVector& resize (int n); |
|
|
747 RowVector& resize (int n, double val); |
|
|
748 |
|
|
749 int operator == (const RowVector& a) const; |
|
|
750 int operator != (const RowVector& a) const; |
|
|
751 |
|
|
752 // destructive insert/delete/reorder operations |
|
|
753 |
|
|
754 RowVector& insert (const RowVector& a, int c); |
|
|
755 |
|
|
756 RowVector& fill (double val); |
|
|
757 RowVector& fill (double val, int c1, int c2); |
|
|
758 |
|
|
759 RowVector append (const RowVector& a) const; |
|
|
760 |
|
|
761 ColumnVector transpose (void) const; |
|
|
762 |
|
|
763 // resize is the destructive equivalent for this one |
|
|
764 |
|
|
765 RowVector extract (int c1, int c2) const; |
|
|
766 |
|
|
767 // row vector by scalar -> row vector operations |
|
|
768 |
|
|
769 RowVector operator + (double s) const; |
|
|
770 RowVector operator - (double s) const; |
|
|
771 RowVector operator * (double s) const; |
|
|
772 RowVector operator / (double s) const; |
|
|
773 |
|
|
774 ComplexRowVector operator + (Complex s) const; |
|
|
775 ComplexRowVector operator - (Complex s) const; |
|
|
776 ComplexRowVector operator * (Complex s) const; |
|
|
777 ComplexRowVector operator / (Complex s) const; |
|
|
778 |
|
|
779 // scalar by row vector -> row vector operations |
|
|
780 |
|
|
781 friend RowVector operator + (double s, const RowVector& a); |
|
|
782 friend RowVector operator - (double s, const RowVector& a); |
|
|
783 friend RowVector operator * (double s, const RowVector& a); |
|
|
784 friend RowVector operator / (double s, const RowVector& a); |
|
|
785 |
|
|
786 // row vector by column vector -> scalar |
|
|
787 |
|
|
788 double operator * (const ColumnVector& a) const; |
|
|
789 |
|
|
790 Complex operator * (const ComplexColumnVector& a) const; |
|
|
791 |
|
|
792 // row vector by matrix -> row vector |
|
|
793 |
|
|
794 RowVector operator * (const Matrix& a) const; |
|
|
795 |
|
|
796 ComplexRowVector operator * (const ComplexMatrix& a) const; |
|
|
797 |
|
|
798 // row vector by row vector -> row vector operations |
|
|
799 |
|
|
800 RowVector operator + (const RowVector& a) const; |
|
|
801 RowVector operator - (const RowVector& a) const; |
|
|
802 |
|
|
803 ComplexRowVector operator + (const ComplexRowVector& a) const; |
|
|
804 ComplexRowVector operator - (const ComplexRowVector& a) const; |
|
|
805 |
|
|
806 RowVector product (const RowVector& a) const; // element by element |
|
|
807 RowVector quotient (const RowVector& a) const; // element by element |
|
|
808 |
|
|
809 ComplexRowVector product (const ComplexRowVector& a) const; // el by el |
|
|
810 ComplexRowVector quotient (const ComplexRowVector& a) const; // el by el |
|
|
811 |
|
|
812 RowVector& operator += (const RowVector& a); |
|
|
813 RowVector& operator -= (const RowVector& a); |
|
|
814 |
|
|
815 // unary operations |
|
|
816 |
|
|
817 RowVector operator - (void) const; |
|
|
818 |
|
|
819 friend RowVector map (d_d_Mapper f, const RowVector& a); |
|
|
820 void map (d_d_Mapper f); |
|
|
821 |
|
|
822 double min (void) const; |
|
|
823 double max (void) const; |
|
|
824 |
|
|
825 // i/o |
|
|
826 |
|
|
827 friend ostream& operator << (ostream& os, const RowVector& a); |
|
|
828 |
|
|
829 // conversions |
|
|
830 |
|
|
831 double *fortran_vec (void); |
|
|
832 |
|
|
833 private: |
|
|
834 int len; |
|
|
835 double *data; |
|
|
836 |
|
|
837 RowVector (double *d, int l); |
|
|
838 }; |
|
|
839 |
|
|
840 inline RowVector::RowVector (void) { len = 0; data = 0; } |
|
|
841 inline RowVector::RowVector (double *d, int l) { len = l; data = d; } |
|
|
842 inline RowVector::~RowVector (void) { delete [] data; data = 0; } |
|
|
843 |
|
|
844 inline int RowVector::capacity (void) const { return len; } |
|
|
845 inline int RowVector::length (void) const { return len; } |
|
|
846 |
|
|
847 inline double& RowVector::elem (int n) { return data[n]; } |
|
|
848 |
|
|
849 inline double& |
|
|
850 RowVector::checkelem (int n) |
|
|
851 { |
|
|
852 #ifndef NO_RANGE_CHECK |
|
|
853 if (n < 0 || n >= len) |
|
|
854 FAIL; |
|
|
855 #endif |
|
|
856 |
|
|
857 return elem (n); |
|
|
858 } |
|
|
859 |
|
|
860 inline double& RowVector::operator () (int n) { return checkelem (n); } |
|
|
861 |
|
|
862 inline double RowVector::elem (int n) const { return data[n]; } |
|
|
863 |
|
|
864 inline double |
|
|
865 RowVector::checkelem (int n) const |
|
|
866 { |
|
|
867 #ifndef NO_RANGE_CHECK |
|
|
868 if (n < 0 || n >= len) |
|
|
869 FAIL; |
|
|
870 #endif |
|
|
871 |
|
|
872 return elem (n); |
|
|
873 } |
|
|
874 |
|
|
875 inline double RowVector::operator () (int n) const { return checkelem (n); } |
|
|
876 |
|
|
877 inline double *RowVector::fortran_vec (void) { return data; } |
|
|
878 |
|
|
879 /* |
|
|
880 * Diagonal Matrix class |
|
|
881 */ |
|
|
882 |
|
|
883 class DiagMatrix |
|
|
884 { |
|
|
885 friend class Matrix; |
|
|
886 friend class ComplexMatrix; |
|
|
887 friend class ComplexDiagMatrix; |
|
|
888 |
|
|
889 public: |
|
|
890 DiagMatrix (void); |
|
|
891 DiagMatrix (int n); |
|
|
892 DiagMatrix (int n, double val); |
|
|
893 DiagMatrix (int r, int c); |
|
|
894 DiagMatrix (int r, int c, double val); |
|
|
895 DiagMatrix (const RowVector& a); |
|
|
896 DiagMatrix (const ColumnVector& a); |
|
|
897 DiagMatrix (const DiagMatrix& a); |
|
|
898 DiagMatrix (double a); |
|
|
899 ~DiagMatrix (void); |
|
|
900 |
|
|
901 DiagMatrix& operator = (const DiagMatrix& a); |
|
|
902 |
|
|
903 int rows (void) const; |
|
|
904 int cols (void) const; |
|
|
905 int columns (void) const; |
|
|
906 |
|
|
907 double& elem (int r, int c); |
|
|
908 double& checkelem (int r, int c); |
|
|
909 double& operator () (int r, int c); |
|
|
910 |
|
|
911 double elem (int r, int c) const; // const access |
|
|
912 double checkelem (int r, int c) const; |
|
|
913 double operator () (int r, int c) const; |
|
|
914 |
|
|
915 DiagMatrix& resize (int r, int c); |
|
|
916 DiagMatrix& resize (int r, int c, double val); |
|
|
917 |
|
|
918 int operator == (const DiagMatrix& a) const; |
|
|
919 int operator != (const DiagMatrix& a) const; |
|
|
920 |
|
|
921 DiagMatrix& fill (double val); |
|
|
922 DiagMatrix& fill (double val, int beg, int end); |
|
|
923 DiagMatrix& fill (const ColumnVector& a); |
|
|
924 DiagMatrix& fill (const RowVector& a); |
|
|
925 DiagMatrix& fill (const ColumnVector& a, int beg); |
|
|
926 DiagMatrix& fill (const RowVector& a, int beg); |
|
|
927 |
|
|
928 DiagMatrix transpose (void) const; |
|
|
929 |
|
|
930 // resize is the destructive analog for this one |
|
|
931 |
|
|
932 Matrix extract (int r1, int c1, int r2, int c2) const; |
|
|
933 |
|
|
934 // extract row or column i. |
|
|
935 |
|
|
936 RowVector row (int i) const; |
|
|
937 RowVector row (char *s) const; |
|
|
938 |
|
|
939 ColumnVector column (int i) const; |
|
|
940 ColumnVector column (char *s) const; |
|
|
941 |
|
|
942 DiagMatrix inverse (int& info) const; |
|
|
943 DiagMatrix inverse (void) const; |
|
|
944 |
|
|
945 // diagonal matrix by scalar -> matrix operations |
|
|
946 |
|
|
947 Matrix operator + (double s) const; |
|
|
948 Matrix operator - (double s) const; |
|
|
949 |
|
|
950 ComplexMatrix operator + (Complex s) const; |
|
|
951 ComplexMatrix operator - (Complex s) const; |
|
|
952 |
|
|
953 // diagonal matrix by scalar -> diagonal matrix operations |
|
|
954 |
|
|
955 DiagMatrix operator * (double s) const; |
|
|
956 DiagMatrix operator / (double s) const; |
|
|
957 |
|
|
958 ComplexDiagMatrix operator * (Complex s) const; |
|
|
959 ComplexDiagMatrix operator / (Complex s) const; |
|
|
960 |
|
|
961 // scalar by diagonal matrix -> matrix operations |
|
|
962 |
|
|
963 friend Matrix operator + (double s, const DiagMatrix& a); |
|
|
964 friend Matrix operator - (double s, const DiagMatrix& a); |
|
|
965 |
|
|
966 // scalar by diagonal matrix -> diagonal matrix operations |
|
|
967 |
|
|
968 friend DiagMatrix operator * (double s, const DiagMatrix& a); |
|
|
969 friend DiagMatrix operator / (double s, const DiagMatrix& a); |
|
|
970 |
|
|
971 // diagonal matrix by column vector -> column vector operations |
|
|
972 |
|
|
973 ColumnVector operator * (const ColumnVector& a) const; |
|
|
974 |
|
|
975 ComplexColumnVector operator * (const ComplexColumnVector& a) const; |
|
|
976 |
|
|
977 // diagonal matrix by diagonal matrix -> diagonal matrix operations |
|
|
978 |
|
|
979 DiagMatrix operator + (const DiagMatrix& a) const; |
|
|
980 DiagMatrix operator - (const DiagMatrix& a) const; |
|
|
981 DiagMatrix operator * (const DiagMatrix& a) const; |
|
|
982 |
|
|
983 ComplexDiagMatrix operator + (const ComplexDiagMatrix& a) const; |
|
|
984 ComplexDiagMatrix operator - (const ComplexDiagMatrix& a) const; |
|
|
985 ComplexDiagMatrix operator * (const ComplexDiagMatrix& a) const; |
|
|
986 |
|
|
987 DiagMatrix product (const DiagMatrix& a) const; // element by element |
|
|
988 DiagMatrix quotient (const DiagMatrix& a) const; // element by element |
|
|
989 |
|
|
990 ComplexDiagMatrix product (const ComplexDiagMatrix& a) const; // el by el |
|
|
991 ComplexDiagMatrix quotient (const ComplexDiagMatrix& a) const; // el by el |
|
|
992 |
|
|
993 DiagMatrix& operator += (const DiagMatrix& a); |
|
|
994 DiagMatrix& operator -= (const DiagMatrix& a); |
|
|
995 |
|
|
996 // diagonal matrix by matrix -> matrix operations |
|
|
997 |
|
|
998 Matrix operator + (const Matrix& a) const; |
|
|
999 Matrix operator - (const Matrix& a) const; |
|
|
1000 Matrix operator * (const Matrix& a) const; |
|
|
1001 |
|
|
1002 ComplexMatrix operator + (const ComplexMatrix& a) const; |
|
|
1003 ComplexMatrix operator - (const ComplexMatrix& a) const; |
|
|
1004 ComplexMatrix operator * (const ComplexMatrix& a) const; |
|
|
1005 |
|
|
1006 // unary operations |
|
|
1007 |
|
|
1008 DiagMatrix operator - (void) const; |
|
|
1009 |
|
|
1010 ColumnVector diag (void) const; |
|
|
1011 ColumnVector diag (int k) const; |
|
|
1012 |
|
|
1013 // i/o |
|
|
1014 |
|
|
1015 friend ostream& operator << (ostream& os, const DiagMatrix& a); |
|
|
1016 |
|
|
1017 private: |
|
|
1018 int nr; |
|
|
1019 int nc; |
|
|
1020 int len; |
|
|
1021 double *data; |
|
|
1022 |
|
|
1023 DiagMatrix (double *d, int nr, int nc); |
|
|
1024 }; |
|
|
1025 |
|
|
1026 inline DiagMatrix::DiagMatrix (void) |
|
|
1027 { nr = 0; nc = 0; len = 0; data = 0; } |
|
|
1028 |
|
|
1029 inline DiagMatrix::DiagMatrix (double *d, int r, int c) |
|
|
1030 { nr = r; nc = c; len = nr < nc ? nr : nc; data = d; } |
|
|
1031 |
|
|
1032 inline DiagMatrix::~DiagMatrix (void) { delete [] data; data = 0; } |
|
|
1033 |
|
|
1034 inline int DiagMatrix::rows (void) const { return len; } |
|
|
1035 inline int DiagMatrix::cols (void) const { return len; } |
|
|
1036 inline int DiagMatrix::columns (void) const { return len; } |
|
|
1037 |
|
|
1038 // Would be nice to be able to avoid compiler warning and make this |
|
|
1039 // fail on assignment. |
|
|
1040 inline double& DiagMatrix::elem (int r, int c) |
|
|
1041 { return (r == c) ? data[r] : 0; } |
|
|
1042 |
|
|
1043 inline double& DiagMatrix::checkelem (int r, int c) |
|
|
1044 { |
|
|
1045 #ifndef NO_RANGE_CHECK |
|
|
1046 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1047 FAIL; |
|
|
1048 #endif |
|
|
1049 |
|
|
1050 return elem (r, c); |
|
|
1051 } |
|
|
1052 |
|
|
1053 inline double& DiagMatrix::operator () (int r, int c) |
|
|
1054 { return checkelem (r, c); } |
|
|
1055 |
|
|
1056 inline double DiagMatrix::elem (int r, int c) const |
|
|
1057 { return (r == c) ? data[r] : 0; } |
|
|
1058 |
|
|
1059 inline double DiagMatrix::checkelem (int r, int c) const |
|
|
1060 { |
|
|
1061 #ifndef NO_RANGE_CHECK |
|
|
1062 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1063 FAIL; |
|
|
1064 #endif |
|
|
1065 |
|
|
1066 return elem (r, c); |
|
|
1067 } |
|
|
1068 |
|
|
1069 inline double DiagMatrix::operator () (int r, int c) const |
|
|
1070 { return checkelem (r, c); } |
|
|
1071 |
|
|
1072 /* |
|
|
1073 * Complex Matrix class |
|
|
1074 */ |
|
|
1075 |
|
|
1076 class ComplexMatrix |
|
|
1077 { |
|
|
1078 friend class Matrix; |
|
|
1079 friend class DiagMatrix; |
|
|
1080 friend class ComplexRowVector; |
|
|
1081 friend class ComplexDiagMatrix; |
|
|
1082 friend class EIG; |
|
|
1083 friend class ComplexHESS; |
|
|
1084 friend class ComplexSVD; |
|
|
1085 friend class ComplexSCHUR; |
|
|
1086 friend class ComplexLU; |
|
|
1087 friend class ComplexQR; |
|
|
1088 |
|
|
1089 public: |
|
|
1090 ComplexMatrix (void); |
|
|
1091 ComplexMatrix (int r, int c); |
|
|
1092 ComplexMatrix (int r, int c, double val); |
|
|
1093 ComplexMatrix (int r, int c, Complex val); |
|
|
1094 ComplexMatrix (const Matrix& a); |
|
|
1095 ComplexMatrix (const ComplexMatrix& a); |
|
|
1096 ComplexMatrix (const DiagMatrix& a); |
|
|
1097 ComplexMatrix (const ComplexDiagMatrix& a); |
|
|
1098 ComplexMatrix (double a); |
|
|
1099 ComplexMatrix (Complex a); |
|
|
1100 ~ComplexMatrix (void); |
|
|
1101 |
|
|
1102 ComplexMatrix& operator = (const Matrix& a); |
|
|
1103 ComplexMatrix& operator = (const ComplexMatrix& a); |
|
|
1104 |
|
|
1105 int rows (void) const; |
|
|
1106 int cols (void) const; |
|
|
1107 int columns (void) const; |
|
|
1108 |
|
|
1109 Complex& elem (int r, int c); |
|
|
1110 Complex& checkelem (int r, int c); |
|
|
1111 Complex& operator () (int r, int c); |
|
|
1112 |
|
|
1113 Complex elem (int r, int c) const; // const access |
|
|
1114 Complex checkelem (int r, int c) const; |
|
|
1115 Complex operator () (int r, int c) const; |
|
|
1116 |
|
|
1117 ComplexMatrix& resize (int r, int c); |
|
|
1118 ComplexMatrix& resize (int r, int c, double val); |
|
|
1119 ComplexMatrix& resize (int r, int c, Complex val); |
|
|
1120 |
|
|
1121 int operator == (const ComplexMatrix& a) const; |
|
|
1122 int operator != (const ComplexMatrix& a) const; |
|
|
1123 |
|
|
1124 // destructive insert/delete/reorder operations |
|
|
1125 |
|
|
1126 ComplexMatrix& insert (const Matrix& a, int r, int c); |
|
|
1127 ComplexMatrix& insert (const RowVector& a, int r, int c); |
|
|
1128 ComplexMatrix& insert (const ColumnVector& a, int r, int c); |
|
|
1129 ComplexMatrix& insert (const DiagMatrix& a, int r, int c); |
|
|
1130 |
|
|
1131 ComplexMatrix& insert (const ComplexMatrix& a, int r, int c); |
|
|
1132 ComplexMatrix& insert (const ComplexRowVector& a, int r, int c); |
|
|
1133 ComplexMatrix& insert (const ComplexColumnVector& a, int r, int c); |
|
|
1134 ComplexMatrix& insert (const ComplexDiagMatrix& a, int r, int c); |
|
|
1135 |
|
|
1136 ComplexMatrix& fill (double val); |
|
|
1137 ComplexMatrix& fill (Complex val); |
|
|
1138 ComplexMatrix& fill (double val, int r1, int c1, int r2, int c2); |
|
|
1139 ComplexMatrix& fill (Complex val, int r1, int c1, int r2, int c2); |
|
|
1140 |
|
|
1141 ComplexMatrix append (const Matrix& a) const; |
|
|
1142 ComplexMatrix append (const RowVector& a) const; |
|
|
1143 ComplexMatrix append (const ColumnVector& a) const; |
|
|
1144 ComplexMatrix append (const DiagMatrix& a) const; |
|
|
1145 |
|
|
1146 ComplexMatrix append (const ComplexMatrix& a) const; |
|
|
1147 ComplexMatrix append (const ComplexRowVector& a) const; |
|
|
1148 ComplexMatrix append (const ComplexColumnVector& a) const; |
|
|
1149 ComplexMatrix append (const ComplexDiagMatrix& a) const; |
|
|
1150 |
|
|
1151 ComplexMatrix stack (const Matrix& a) const; |
|
|
1152 ComplexMatrix stack (const RowVector& a) const; |
|
|
1153 ComplexMatrix stack (const ColumnVector& a) const; |
|
|
1154 ComplexMatrix stack (const DiagMatrix& a) const; |
|
|
1155 |
|
|
1156 ComplexMatrix stack (const ComplexMatrix& a) const; |
|
|
1157 ComplexMatrix stack (const ComplexRowVector& a) const; |
|
|
1158 ComplexMatrix stack (const ComplexColumnVector& a) const; |
|
|
1159 ComplexMatrix stack (const ComplexDiagMatrix& a) const; |
|
|
1160 |
|
|
1161 ComplexMatrix hermitian (void) const; // complex conjugate transpose |
|
|
1162 ComplexMatrix transpose (void) const; |
|
|
1163 |
|
|
1164 friend Matrix real (const ComplexMatrix& a); |
|
|
1165 friend Matrix imag (const ComplexMatrix& a); |
|
|
1166 friend ComplexMatrix conj (const ComplexMatrix& a); |
|
|
1167 |
|
|
1168 // resize is the destructive equivalent for this one |
|
|
1169 |
|
|
1170 ComplexMatrix extract (int r1, int c1, int r2, int c2) const; |
|
|
1171 |
|
|
1172 // extract row or column i. |
|
|
1173 |
|
|
1174 ComplexRowVector row (int i) const; |
|
|
1175 ComplexRowVector row (char *s) const; |
|
|
1176 |
|
|
1177 ComplexColumnVector column (int i) const; |
|
|
1178 ComplexColumnVector column (char *s) const; |
|
|
1179 |
|
|
1180 ComplexMatrix inverse (int& info, double& rcond) const; |
|
|
1181 ComplexMatrix inverse (int& info) const; |
|
|
1182 ComplexMatrix inverse (void) const; |
|
|
1183 |
|
|
1184 ComplexMatrix fourier (void) const; |
|
|
1185 ComplexMatrix ifourier (void) const; |
|
|
1186 |
|
|
1187 ComplexDET determinant (void) const; |
|
|
1188 ComplexDET determinant (int& info) const; |
|
|
1189 ComplexDET determinant (int& info, double& rcond) const; |
|
|
1190 |
|
|
1191 ComplexMatrix solve (const Matrix& b) const; |
|
|
1192 ComplexMatrix solve (const Matrix& b, int& info) const; |
|
|
1193 ComplexMatrix solve (const Matrix& b, int& info, double& rcond) const; |
|
|
1194 |
|
|
1195 ComplexMatrix solve (const ComplexMatrix& b) const; |
|
|
1196 ComplexMatrix solve (const ComplexMatrix& b, int& info) const; |
|
|
1197 ComplexMatrix solve (const ComplexMatrix& b, int& info, double& rcond) const; |
|
|
1198 |
|
|
1199 ComplexColumnVector solve (const ColumnVector& b) const; |
|
|
1200 ComplexColumnVector solve (const ColumnVector& b, int& info) const; |
|
|
1201 ComplexColumnVector solve (const ColumnVector& b, int& info, |
|
|
1202 double& rcond) const; |
|
|
1203 |
|
|
1204 ComplexColumnVector solve (const ComplexColumnVector& b) const; |
|
|
1205 ComplexColumnVector solve (const ComplexColumnVector& b, int& info) const; |
|
|
1206 ComplexColumnVector solve (const ComplexColumnVector& b, int& info, |
|
|
1207 double& rcond) const; |
|
|
1208 |
|
|
1209 ComplexMatrix lssolve (const Matrix& b) const; |
|
|
1210 ComplexMatrix lssolve (const Matrix& b, int& info) const; |
|
|
1211 ComplexMatrix lssolve (const Matrix& b, int& info, int& rank) const; |
|
|
1212 |
|
|
1213 ComplexMatrix lssolve (const ComplexMatrix& b) const; |
|
|
1214 ComplexMatrix lssolve (const ComplexMatrix& b, int& info) const; |
|
|
1215 ComplexMatrix lssolve (const ComplexMatrix& b, int& info, |
|
|
1216 int& rank) const; |
|
|
1217 |
|
|
1218 ComplexColumnVector lssolve (const ColumnVector& b) const; |
|
|
1219 ComplexColumnVector lssolve (const ColumnVector& b, int& info) const; |
|
|
1220 ComplexColumnVector lssolve (const ColumnVector& b, int& info, |
|
|
1221 int& rank) const; |
|
|
1222 |
|
|
1223 ComplexColumnVector lssolve (const ComplexColumnVector& b) const; |
|
|
1224 ComplexColumnVector lssolve (const ComplexColumnVector& b, int& info) const; |
|
|
1225 ComplexColumnVector lssolve (const ComplexColumnVector& b, int& info, |
|
|
1226 int& rank) const; |
|
|
1227 |
|
|
1228 // matrix by scalar -> matrix operations |
|
|
1229 |
|
|
1230 ComplexMatrix operator + (double s) const; |
|
|
1231 ComplexMatrix operator - (double s) const; |
|
|
1232 ComplexMatrix operator * (double s) const; |
|
|
1233 ComplexMatrix operator / (double s) const; |
|
|
1234 |
|
|
1235 ComplexMatrix operator + (Complex s) const; |
|
|
1236 ComplexMatrix operator - (Complex s) const; |
|
|
1237 ComplexMatrix operator * (Complex s) const; |
|
|
1238 ComplexMatrix operator / (Complex s) const; |
|
|
1239 |
|
|
1240 // scalar by matrix -> matrix operations |
|
|
1241 |
|
|
1242 friend ComplexMatrix operator + (double s, const ComplexMatrix& a); |
|
|
1243 friend ComplexMatrix operator - (double s, const ComplexMatrix& a); |
|
|
1244 friend ComplexMatrix operator * (double s, const ComplexMatrix& a); |
|
|
1245 friend ComplexMatrix operator / (double s, const ComplexMatrix& a); |
|
|
1246 |
|
|
1247 friend ComplexMatrix operator + (Complex s, const ComplexMatrix& a); |
|
|
1248 friend ComplexMatrix operator - (Complex s, const ComplexMatrix& a); |
|
|
1249 friend ComplexMatrix operator * (Complex s, const ComplexMatrix& a); |
|
|
1250 friend ComplexMatrix operator / (Complex s, const ComplexMatrix& a); |
|
|
1251 |
|
|
1252 // matrix by column vector -> column vector operations |
|
|
1253 |
|
|
1254 ComplexColumnVector operator * (const ColumnVector& a) const; |
|
|
1255 |
|
|
1256 ComplexColumnVector operator * (const ComplexColumnVector& a) const; |
|
|
1257 |
|
|
1258 // matrix by diagonal matrix -> matrix operations |
|
|
1259 |
|
|
1260 ComplexMatrix operator + (const DiagMatrix& a) const; |
|
|
1261 ComplexMatrix operator - (const DiagMatrix& a) const; |
|
|
1262 ComplexMatrix operator * (const DiagMatrix& a) const; |
|
|
1263 |
|
|
1264 ComplexMatrix operator + (const ComplexDiagMatrix& a) const; |
|
|
1265 ComplexMatrix operator - (const ComplexDiagMatrix& a) const; |
|
|
1266 ComplexMatrix operator * (const ComplexDiagMatrix& a) const; |
|
|
1267 |
|
|
1268 ComplexMatrix& operator += (const DiagMatrix& a); |
|
|
1269 ComplexMatrix& operator -= (const DiagMatrix& a); |
|
|
1270 |
|
|
1271 ComplexMatrix& operator += (const ComplexDiagMatrix& a); |
|
|
1272 ComplexMatrix& operator -= (const ComplexDiagMatrix& a); |
|
|
1273 |
|
|
1274 // matrix by matrix -> matrix operations |
|
|
1275 |
|
|
1276 ComplexMatrix operator + (const Matrix& a) const; |
|
|
1277 ComplexMatrix operator - (const Matrix& a) const; |
|
|
1278 ComplexMatrix operator * (const Matrix& a) const; |
|
|
1279 |
|
|
1280 ComplexMatrix operator + (const ComplexMatrix& a) const; |
|
|
1281 ComplexMatrix operator - (const ComplexMatrix& a) const; |
|
|
1282 ComplexMatrix operator * (const ComplexMatrix& a) const; |
|
|
1283 |
|
|
1284 ComplexMatrix product (const Matrix& a) const; // element by element |
|
|
1285 ComplexMatrix quotient (const Matrix& a) const; // element by element |
|
|
1286 |
|
|
1287 ComplexMatrix product (const ComplexMatrix& a) const; // element by element |
|
|
1288 ComplexMatrix quotient (const ComplexMatrix& a) const; // element by element |
|
|
1289 |
|
|
1290 ComplexMatrix& operator += (const Matrix& a); |
|
|
1291 ComplexMatrix& operator -= (const Matrix& a); |
|
|
1292 |
|
|
1293 ComplexMatrix& operator += (const ComplexMatrix& a); |
|
|
1294 ComplexMatrix& operator -= (const ComplexMatrix& a); |
|
|
1295 |
|
|
1296 // unary operations |
|
|
1297 |
|
|
1298 ComplexMatrix operator - (void) const; |
|
|
1299 Matrix operator ! (void) const; |
|
|
1300 |
|
|
1301 // other operations |
|
|
1302 |
|
|
1303 friend ComplexMatrix map (c_c_Mapper f, const ComplexMatrix& a); |
|
|
1304 friend Matrix map (d_c_Mapper f, const ComplexMatrix& a); |
|
|
1305 void map (c_c_Mapper f); |
|
|
1306 |
|
|
1307 Matrix all (void) const; |
|
|
1308 Matrix any (void) const; |
|
|
1309 |
|
|
1310 ComplexMatrix cumprod (void) const; |
|
|
1311 ComplexMatrix cumsum (void) const; |
|
|
1312 ComplexMatrix prod (void) const; |
|
|
1313 ComplexMatrix sum (void) const; |
|
|
1314 ComplexMatrix sumsq (void) const; |
|
|
1315 |
|
|
1316 ComplexColumnVector diag (void) const; |
|
|
1317 ComplexColumnVector diag (int k) const; |
|
|
1318 |
|
|
1319 ComplexColumnVector row_min (void) const; |
|
|
1320 ComplexColumnVector row_max (void) const; |
|
|
1321 |
|
|
1322 ComplexRowVector column_min (void) const; |
|
|
1323 ComplexRowVector column_max (void) const; |
|
|
1324 |
|
|
1325 // i/o |
|
|
1326 |
|
|
1327 friend ostream& operator << (ostream& os, const ComplexMatrix& a); |
|
|
1328 friend istream& operator >> (istream& is, ComplexMatrix& a); |
|
|
1329 |
|
|
1330 // conversions |
|
|
1331 |
|
|
1332 Complex *fortran_vec (void); |
|
|
1333 |
|
|
1334 private: |
|
|
1335 int nr; |
|
|
1336 int nc; |
|
|
1337 int len; |
|
|
1338 Complex *data; |
|
|
1339 |
|
|
1340 ComplexMatrix (Complex *d, int r, int c); |
|
|
1341 }; |
|
|
1342 |
|
|
1343 inline ComplexMatrix::ComplexMatrix (void) |
|
|
1344 { nr = 0; nc = 0; len = 0; data = 0; } |
|
|
1345 |
|
|
1346 inline ComplexMatrix::ComplexMatrix (Complex *d, int r, int c) |
|
|
1347 { nr = r; nc = c; len = nr*nc; data = d; } |
|
|
1348 |
|
|
1349 inline ComplexMatrix::~ComplexMatrix (void) { delete [] data; data = 0; } |
|
|
1350 |
|
|
1351 inline int ComplexMatrix::rows (void) const { return nr; } |
|
|
1352 inline int ComplexMatrix::cols (void) const { return nc; } |
|
|
1353 inline int ComplexMatrix::columns (void) const { return nc; } |
|
|
1354 |
|
|
1355 inline Complex& ComplexMatrix::elem (int r, int c) { return data[nr*c+r]; } |
|
|
1356 |
|
|
1357 inline Complex& ComplexMatrix::checkelem (int r, int c) |
|
|
1358 { |
|
|
1359 #ifndef NO_RANGE_CHECK |
|
|
1360 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1361 FAIL; |
|
|
1362 #endif |
|
|
1363 |
|
|
1364 return elem (r, c); |
|
|
1365 } |
|
|
1366 |
|
|
1367 inline Complex& ComplexMatrix::operator () (int r, int c) |
|
|
1368 { return checkelem (r, c); } |
|
|
1369 |
|
|
1370 inline Complex ComplexMatrix::elem (int r, int c) const |
|
|
1371 { return data[nr*c+r]; } |
|
|
1372 |
|
|
1373 inline Complex ComplexMatrix::checkelem (int r, int c) const |
|
|
1374 { |
|
|
1375 #ifndef NO_RANGE_CHECK |
|
|
1376 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1377 FAIL; |
|
|
1378 #endif |
|
|
1379 |
|
|
1380 return elem (r, c); |
|
|
1381 } |
|
|
1382 |
|
|
1383 inline Complex ComplexMatrix::operator () (int r, int c) const |
|
|
1384 { return checkelem (r, c); } |
|
|
1385 |
|
|
1386 inline Complex *ComplexMatrix::fortran_vec (void) { return data; } |
|
|
1387 |
|
|
1388 /* |
|
|
1389 * Complex Column Vector class |
|
|
1390 */ |
|
|
1391 |
|
|
1392 class ComplexColumnVector |
|
|
1393 { |
|
|
1394 friend class DiagMatrix; |
|
|
1395 friend class ComplexMatrix; |
|
|
1396 friend class ColumnVector; |
|
|
1397 friend class ComplexDiagMatrix; |
|
|
1398 |
|
|
1399 public: |
|
|
1400 ComplexColumnVector (void); |
|
|
1401 ComplexColumnVector (int n); |
|
|
1402 ComplexColumnVector (int n, double val); |
|
|
1403 ComplexColumnVector (int n, Complex val); |
|
|
1404 ComplexColumnVector (const ColumnVector& a); |
|
|
1405 ComplexColumnVector (const ComplexColumnVector& a); |
|
|
1406 ComplexColumnVector (double a); |
|
|
1407 ComplexColumnVector (Complex a); |
|
|
1408 ~ComplexColumnVector (void); |
|
|
1409 |
|
|
1410 ComplexColumnVector& operator = (const ColumnVector& a); |
|
|
1411 ComplexColumnVector& operator = (const ComplexColumnVector& a); |
|
|
1412 |
|
|
1413 int capacity (void) const; |
|
|
1414 int length (void) const; |
|
|
1415 |
|
|
1416 Complex& elem (int n); |
|
|
1417 Complex& checkelem (int n); |
|
|
1418 Complex& operator () (int n); |
|
|
1419 |
|
|
1420 Complex elem (int n) const; // const access |
|
|
1421 Complex checkelem (int n) const; |
|
|
1422 Complex operator () (int n) const; |
|
|
1423 |
|
|
1424 ComplexColumnVector& resize (int n); |
|
|
1425 ComplexColumnVector& resize (int n, double val); |
|
|
1426 ComplexColumnVector& resize (int n, Complex val); |
|
|
1427 |
|
|
1428 int operator == (const ComplexColumnVector& a) const; |
|
|
1429 int operator != (const ComplexColumnVector& a) const; |
|
|
1430 |
|
|
1431 // destructive insert/delete/reorder operations |
|
|
1432 |
|
|
1433 ComplexColumnVector& insert (const ColumnVector& a, int r); |
|
|
1434 ComplexColumnVector& insert (const ComplexColumnVector& a, int r); |
|
|
1435 |
|
|
1436 ComplexColumnVector& fill (double val); |
|
|
1437 ComplexColumnVector& fill (Complex val); |
|
|
1438 ComplexColumnVector& fill (double val, int r1, int r2); |
|
|
1439 ComplexColumnVector& fill (Complex val, int r1, int r2); |
|
|
1440 |
|
|
1441 ComplexColumnVector stack (const ColumnVector& a) const; |
|
|
1442 ComplexColumnVector stack (const ComplexColumnVector& a) const; |
|
|
1443 |
|
|
1444 ComplexRowVector hermitian (void) const; // complex conjugate transpose. |
|
|
1445 ComplexRowVector transpose (void) const; |
|
|
1446 |
|
|
1447 friend ColumnVector real (const ComplexColumnVector& a); |
|
|
1448 friend ColumnVector imag (const ComplexColumnVector& a); |
|
|
1449 friend ComplexColumnVector conj (const ComplexColumnVector& a); |
|
|
1450 |
|
|
1451 // resize is the destructive equivalent for this one |
|
|
1452 |
|
|
1453 ComplexColumnVector extract (int r1, int r2) const; |
|
|
1454 |
|
|
1455 // column vector by scalar -> column vector operations |
|
|
1456 |
|
|
1457 ComplexColumnVector operator + (double s) const; |
|
|
1458 ComplexColumnVector operator - (double s) const; |
|
|
1459 ComplexColumnVector operator * (double s) const; |
|
|
1460 ComplexColumnVector operator / (double s) const; |
|
|
1461 |
|
|
1462 ComplexColumnVector operator + (Complex s) const; |
|
|
1463 ComplexColumnVector operator - (Complex s) const; |
|
|
1464 ComplexColumnVector operator * (Complex s) const; |
|
|
1465 ComplexColumnVector operator / (Complex s) const; |
|
|
1466 |
|
|
1467 // scalar by column vector -> column vector operations |
|
|
1468 |
|
|
1469 friend ComplexColumnVector operator + (double s, |
|
|
1470 const ComplexColumnVector& a); |
|
|
1471 friend ComplexColumnVector operator - (double s, |
|
|
1472 const ComplexColumnVector& a); |
|
|
1473 friend ComplexColumnVector operator * (double s, |
|
|
1474 const ComplexColumnVector& a); |
|
|
1475 friend ComplexColumnVector operator / (double s, |
|
|
1476 const ComplexColumnVector& a); |
|
|
1477 |
|
|
1478 friend ComplexColumnVector operator + (Complex s, |
|
|
1479 const ComplexColumnVector& a); |
|
|
1480 friend ComplexColumnVector operator - (Complex s, |
|
|
1481 const ComplexColumnVector& a); |
|
|
1482 friend ComplexColumnVector operator * (Complex s, |
|
|
1483 const ComplexColumnVector& a); |
|
|
1484 friend ComplexColumnVector operator / (Complex s, |
|
|
1485 const ComplexColumnVector& a); |
|
|
1486 |
|
|
1487 // column vector by row vector -> matrix operations |
|
|
1488 |
|
|
1489 ComplexMatrix operator * (const RowVector& a) const; |
|
|
1490 |
|
|
1491 ComplexMatrix operator * (const ComplexRowVector& a) const; |
|
|
1492 |
|
|
1493 // column vector by column vector -> column vector operations |
|
|
1494 |
|
|
1495 ComplexColumnVector operator + (const ColumnVector& a) const; |
|
|
1496 ComplexColumnVector operator - (const ColumnVector& a) const; |
|
|
1497 |
|
|
1498 ComplexColumnVector operator + (const ComplexColumnVector& a) const; |
|
|
1499 ComplexColumnVector operator - (const ComplexColumnVector& a) const; |
|
|
1500 |
|
|
1501 ComplexColumnVector product (const ColumnVector& a) const; // el by el |
|
|
1502 ComplexColumnVector quotient (const ColumnVector& a) const; // el by el |
|
|
1503 |
|
|
1504 ComplexColumnVector product (const ComplexColumnVector& a) const; |
|
|
1505 ComplexColumnVector quotient (const ComplexColumnVector& a) const; |
|
|
1506 |
|
|
1507 ComplexColumnVector& operator += (const ColumnVector& a); |
|
|
1508 ComplexColumnVector& operator -= (const ColumnVector& a); |
|
|
1509 |
|
|
1510 ComplexColumnVector& operator += (const ComplexColumnVector& a); |
|
|
1511 ComplexColumnVector& operator -= (const ComplexColumnVector& a); |
|
|
1512 |
|
|
1513 // unary operations |
|
|
1514 |
|
|
1515 ComplexColumnVector operator - (void) const; |
|
|
1516 |
|
|
1517 friend ComplexColumnVector map (c_c_Mapper f, const ComplexColumnVector& a); |
|
|
1518 friend ColumnVector map (d_c_Mapper f, const ComplexColumnVector& a); |
|
|
1519 void map (c_c_Mapper f); |
|
|
1520 |
|
|
1521 Complex min (void) const; |
|
|
1522 Complex max (void) const; |
|
|
1523 |
|
|
1524 // i/o |
|
|
1525 |
|
|
1526 friend ostream& operator << (ostream& os, const ComplexColumnVector& a); |
|
|
1527 |
|
|
1528 // conversions |
|
|
1529 |
|
|
1530 Complex *fortran_vec (void); |
|
|
1531 |
|
|
1532 private: |
|
|
1533 int len; |
|
|
1534 Complex *data; |
|
|
1535 |
|
|
1536 ComplexColumnVector (Complex *d, int l); |
|
|
1537 }; |
|
|
1538 |
|
|
1539 inline ComplexColumnVector::ComplexColumnVector (void) { len = 0; data = 0; } |
|
|
1540 inline ComplexColumnVector::ComplexColumnVector (Complex *d, int l) |
|
|
1541 { len = l; data = d; } |
|
|
1542 inline ComplexColumnVector::~ComplexColumnVector (void) |
|
|
1543 { delete [] data; data = 0; } |
|
|
1544 |
|
|
1545 inline int ComplexColumnVector::capacity (void) const { return len; } |
|
|
1546 inline int ComplexColumnVector::length (void) const { return len; } |
|
|
1547 |
|
|
1548 inline Complex& ComplexColumnVector::elem (int n) { return data[n]; } |
|
|
1549 |
|
|
1550 inline Complex& |
|
|
1551 ComplexColumnVector::checkelem (int n) |
|
|
1552 { |
|
|
1553 #ifndef NO_RANGE_CHECK |
|
|
1554 if (n < 0 || n >= len) |
|
|
1555 FAIL; |
|
|
1556 #endif |
|
|
1557 |
|
|
1558 return elem (n); |
|
|
1559 } |
|
|
1560 |
|
|
1561 inline Complex& ComplexColumnVector::operator () (int n) |
|
|
1562 { return checkelem (n); } |
|
|
1563 |
|
|
1564 inline Complex ComplexColumnVector::elem (int n) const { return data[n]; } |
|
|
1565 |
|
|
1566 inline Complex |
|
|
1567 ComplexColumnVector::checkelem (int n) const |
|
|
1568 { |
|
|
1569 #ifndef NO_RANGE_CHECK |
|
|
1570 if (n < 0 || n >= len) |
|
|
1571 FAIL; |
|
|
1572 #endif |
|
|
1573 |
|
|
1574 return elem (n); |
|
|
1575 } |
|
|
1576 |
|
|
1577 inline Complex ComplexColumnVector::operator () (int n) const |
|
|
1578 { return checkelem (n); } |
|
|
1579 |
|
|
1580 inline Complex *ComplexColumnVector::fortran_vec (void) { return data; } |
|
|
1581 |
|
|
1582 /* |
|
|
1583 * Complex Row Vector class |
|
|
1584 */ |
|
|
1585 |
|
|
1586 class ComplexRowVector |
|
|
1587 { |
|
|
1588 friend class RowVector; |
|
|
1589 friend class ComplexMatrix; |
|
|
1590 friend class ComplexColumnVector; |
|
|
1591 friend class ComplexDiagMatrix; |
|
|
1592 |
|
|
1593 public: |
|
|
1594 ComplexRowVector (void); |
|
|
1595 ComplexRowVector (int n); |
|
|
1596 ComplexRowVector (int n, double val); |
|
|
1597 ComplexRowVector (int n, Complex val); |
|
|
1598 ComplexRowVector (const RowVector& a); |
|
|
1599 ComplexRowVector (const ComplexRowVector& a); |
|
|
1600 ComplexRowVector (double a); |
|
|
1601 ComplexRowVector (Complex a); |
|
|
1602 ~ComplexRowVector (void); |
|
|
1603 |
|
|
1604 ComplexRowVector& operator = (const RowVector& a); |
|
|
1605 ComplexRowVector& operator = (const ComplexRowVector& a); |
|
|
1606 |
|
|
1607 int capacity (void) const; |
|
|
1608 int length (void) const; |
|
|
1609 |
|
|
1610 Complex& checkelem (int n); |
|
|
1611 Complex& elem (int n); |
|
|
1612 Complex& operator () (int n); |
|
|
1613 |
|
|
1614 Complex checkelem (int n) const; // const access |
|
|
1615 Complex elem (int n) const; |
|
|
1616 Complex operator () (int n) const; |
|
|
1617 |
|
|
1618 ComplexRowVector& resize (int n); |
|
|
1619 ComplexRowVector& resize (int n, double val); |
|
|
1620 ComplexRowVector& resize (int n, Complex val); |
|
|
1621 |
|
|
1622 int operator == (const ComplexRowVector& a) const; |
|
|
1623 int operator != (const ComplexRowVector& a) const; |
|
|
1624 |
|
|
1625 // destructive insert/delete/reorder operations |
|
|
1626 |
|
|
1627 ComplexRowVector& insert (const RowVector& a, int c); |
|
|
1628 ComplexRowVector& insert (const ComplexRowVector& a, int c); |
|
|
1629 |
|
|
1630 ComplexRowVector& fill (double val); |
|
|
1631 ComplexRowVector& fill (Complex val); |
|
|
1632 ComplexRowVector& fill (double val, int c1, int c2); |
|
|
1633 ComplexRowVector& fill (Complex val, int c1, int c2); |
|
|
1634 |
|
|
1635 ComplexRowVector append (const RowVector& a) const; |
|
|
1636 ComplexRowVector append (const ComplexRowVector& a) const; |
|
|
1637 |
|
|
1638 ComplexColumnVector hermitian (void) const; // complex conjugate transpose. |
|
|
1639 ComplexColumnVector transpose (void) const; |
|
|
1640 |
|
|
1641 friend RowVector real (const ComplexRowVector& a); |
|
|
1642 friend RowVector imag (const ComplexRowVector& a); |
|
|
1643 friend ComplexRowVector conj (const ComplexRowVector& a); |
|
|
1644 |
|
|
1645 // resize is the destructive equivalent for this one |
|
|
1646 |
|
|
1647 ComplexRowVector extract (int c1, int c2) const; |
|
|
1648 |
|
|
1649 // row vector by scalar -> row vector operations |
|
|
1650 |
|
|
1651 ComplexRowVector operator + (double s) const; |
|
|
1652 ComplexRowVector operator - (double s) const; |
|
|
1653 ComplexRowVector operator * (double s) const; |
|
|
1654 ComplexRowVector operator / (double s) const; |
|
|
1655 |
|
|
1656 ComplexRowVector operator + (Complex s) const; |
|
|
1657 ComplexRowVector operator - (Complex s) const; |
|
|
1658 ComplexRowVector operator * (Complex s) const; |
|
|
1659 ComplexRowVector operator / (Complex s) const; |
|
|
1660 |
|
|
1661 // scalar by row vector -> row vector operations |
|
|
1662 |
|
|
1663 friend ComplexRowVector operator + (double s, const ComplexRowVector& a); |
|
|
1664 friend ComplexRowVector operator - (double s, const ComplexRowVector& a); |
|
|
1665 friend ComplexRowVector operator * (double s, const ComplexRowVector& a); |
|
|
1666 friend ComplexRowVector operator / (double s, const ComplexRowVector& a); |
|
|
1667 |
|
|
1668 friend ComplexRowVector operator + (Complex s, const ComplexRowVector& a); |
|
|
1669 friend ComplexRowVector operator - (Complex s, const ComplexRowVector& a); |
|
|
1670 friend ComplexRowVector operator * (Complex s, const ComplexRowVector& a); |
|
|
1671 friend ComplexRowVector operator / (Complex s, const ComplexRowVector& a); |
|
|
1672 |
|
|
1673 // row vector by column vector -> scalar |
|
|
1674 |
|
|
1675 Complex operator * (const ColumnVector& a) const; |
|
|
1676 |
|
|
1677 Complex operator * (const ComplexColumnVector& a) const; |
|
|
1678 |
|
|
1679 // row vector by matrix -> row vector |
|
|
1680 |
|
|
1681 ComplexRowVector operator * (const Matrix& a) const; |
|
|
1682 |
|
|
1683 ComplexRowVector operator * (const ComplexMatrix& a) const; |
|
|
1684 |
|
|
1685 // row vector by row vector -> row vector operations |
|
|
1686 |
|
|
1687 ComplexRowVector operator + (const RowVector& a) const; |
|
|
1688 ComplexRowVector operator - (const RowVector& a) const; |
|
|
1689 |
|
|
1690 ComplexRowVector operator + (const ComplexRowVector& a) const; |
|
|
1691 ComplexRowVector operator - (const ComplexRowVector& a) const; |
|
|
1692 |
|
|
1693 ComplexRowVector product (const RowVector& a) const; // element by element |
|
|
1694 ComplexRowVector quotient (const RowVector& a) const; // element by element |
|
|
1695 |
|
|
1696 ComplexRowVector product (const ComplexRowVector& a) const; // el by el |
|
|
1697 ComplexRowVector quotient (const ComplexRowVector& a) const; // el by el |
|
|
1698 |
|
|
1699 ComplexRowVector& operator += (const RowVector& a); |
|
|
1700 ComplexRowVector& operator -= (const RowVector& a); |
|
|
1701 |
|
|
1702 ComplexRowVector& operator += (const ComplexRowVector& a); |
|
|
1703 ComplexRowVector& operator -= (const ComplexRowVector& a); |
|
|
1704 |
|
|
1705 // unary operations |
|
|
1706 |
|
|
1707 ComplexRowVector operator - (void) const; |
|
|
1708 |
|
|
1709 friend ComplexRowVector map (c_c_Mapper f, const ComplexRowVector& a); |
|
|
1710 friend RowVector map (d_c_Mapper f, const ComplexRowVector& a); |
|
|
1711 void map (c_c_Mapper f); |
|
|
1712 |
|
|
1713 Complex min (void) const; |
|
|
1714 Complex max (void) const; |
|
|
1715 |
|
|
1716 // i/o |
|
|
1717 |
|
|
1718 friend ostream& operator << (ostream& os, const ComplexRowVector& a); |
|
|
1719 |
|
|
1720 // conversions |
|
|
1721 |
|
|
1722 Complex *fortran_vec (void); |
|
|
1723 |
|
|
1724 private: |
|
|
1725 int len; |
|
|
1726 Complex *data; |
|
|
1727 |
|
|
1728 ComplexRowVector (Complex *d, int l); |
|
|
1729 }; |
|
|
1730 |
|
|
1731 inline ComplexRowVector::ComplexRowVector (void) { len = 0; data = 0; } |
|
|
1732 inline ComplexRowVector::ComplexRowVector (Complex *d, int l) |
|
|
1733 { len = l; data = d; } |
|
|
1734 inline ComplexRowVector::~ComplexRowVector (void) { delete [] data; data = 0; } |
|
|
1735 |
|
|
1736 inline int ComplexRowVector::capacity (void) const { return len; } |
|
|
1737 inline int ComplexRowVector::length (void) const { return len; } |
|
|
1738 |
|
|
1739 inline Complex& ComplexRowVector::elem (int n) { return data[n]; } |
|
|
1740 |
|
|
1741 inline Complex& |
|
|
1742 ComplexRowVector::checkelem (int n) |
|
|
1743 { |
|
|
1744 #ifndef NO_RANGE_CHECK |
|
|
1745 if (n < 0 || n >= len) |
|
|
1746 FAIL; |
|
|
1747 #endif |
|
|
1748 |
|
|
1749 return elem (n); |
|
|
1750 } |
|
|
1751 |
|
|
1752 inline Complex& ComplexRowVector::operator () (int n) { return checkelem (n); } |
|
|
1753 |
|
|
1754 inline Complex ComplexRowVector::elem (int n) const { return data[n]; } |
|
|
1755 |
|
|
1756 inline Complex |
|
|
1757 ComplexRowVector::checkelem (int n) const |
|
|
1758 { |
|
|
1759 #ifndef NO_RANGE_CHECK |
|
|
1760 if (n < 0 || n >= len) |
|
|
1761 FAIL; |
|
|
1762 #endif |
|
|
1763 |
|
|
1764 return elem (n); |
|
|
1765 } |
|
|
1766 |
|
|
1767 inline Complex ComplexRowVector::operator () (int n) const |
|
|
1768 { return checkelem (n); } |
|
|
1769 |
|
|
1770 inline Complex *ComplexRowVector::fortran_vec (void) { return data; } |
|
|
1771 |
|
|
1772 /* |
|
|
1773 * Complex Diagonal Matrix class |
|
|
1774 */ |
|
|
1775 |
|
|
1776 class ComplexDiagMatrix |
|
|
1777 { |
|
|
1778 friend class Matrix; |
|
|
1779 friend class DiagMatrix; |
|
|
1780 friend class ComplexMatrix; |
|
|
1781 |
|
|
1782 public: |
|
|
1783 ComplexDiagMatrix (void); |
|
|
1784 ComplexDiagMatrix (int n); |
|
|
1785 ComplexDiagMatrix (int n, double val); |
|
|
1786 ComplexDiagMatrix (int n, Complex val); |
|
|
1787 ComplexDiagMatrix (int r, int c); |
|
|
1788 ComplexDiagMatrix (int r, int c, double val); |
|
|
1789 ComplexDiagMatrix (int r, int c, Complex val); |
|
|
1790 ComplexDiagMatrix (const RowVector& a); |
|
|
1791 ComplexDiagMatrix (const ComplexRowVector& a); |
|
|
1792 ComplexDiagMatrix (const ColumnVector& a); |
|
|
1793 ComplexDiagMatrix (const ComplexColumnVector& a); |
|
|
1794 ComplexDiagMatrix (const DiagMatrix& a); |
|
|
1795 ComplexDiagMatrix (const ComplexDiagMatrix& a); |
|
|
1796 ComplexDiagMatrix (double a); |
|
|
1797 ComplexDiagMatrix (Complex a); |
|
|
1798 ~ComplexDiagMatrix (void); |
|
|
1799 |
|
|
1800 ComplexDiagMatrix& operator = (const DiagMatrix& a); |
|
|
1801 ComplexDiagMatrix& operator = (const ComplexDiagMatrix& a); |
|
|
1802 |
|
|
1803 int rows (void) const; |
|
|
1804 int cols (void) const; |
|
|
1805 int columns (void) const; |
|
|
1806 |
|
|
1807 Complex& checkelem (int r, int c); |
|
|
1808 Complex& elem (int r, int c); |
|
|
1809 Complex& operator () (int r, int c); |
|
|
1810 |
|
|
1811 Complex checkelem (int r, int c) const; // const access |
|
|
1812 Complex elem (int r, int c) const; |
|
|
1813 Complex operator () (int r, int c) const; |
|
|
1814 |
|
|
1815 ComplexDiagMatrix& resize (int r, int c); |
|
|
1816 ComplexDiagMatrix& resize (int r, int c, double val); |
|
|
1817 ComplexDiagMatrix& resize (int r, int c, Complex val); |
|
|
1818 |
|
|
1819 int operator == (const ComplexDiagMatrix& a) const; |
|
|
1820 int operator != (const ComplexDiagMatrix& a) const; |
|
|
1821 |
|
|
1822 ComplexDiagMatrix& fill (double val); |
|
|
1823 ComplexDiagMatrix& fill (Complex val); |
|
|
1824 ComplexDiagMatrix& fill (double val, int beg, int end); |
|
|
1825 ComplexDiagMatrix& fill (Complex val, int beg, int end); |
|
|
1826 ComplexDiagMatrix& fill (const ColumnVector& a); |
|
|
1827 ComplexDiagMatrix& fill (const ComplexColumnVector& a); |
|
|
1828 ComplexDiagMatrix& fill (const RowVector& a); |
|
|
1829 ComplexDiagMatrix& fill (const ComplexRowVector& a); |
|
|
1830 ComplexDiagMatrix& fill (const ColumnVector& a, int beg); |
|
|
1831 ComplexDiagMatrix& fill (const ComplexColumnVector& a, int beg); |
|
|
1832 ComplexDiagMatrix& fill (const RowVector& a, int beg); |
|
|
1833 ComplexDiagMatrix& fill (const ComplexRowVector& a, int beg); |
|
|
1834 |
|
|
1835 ComplexDiagMatrix hermitian (void) const; // complex conjugate transpose |
|
|
1836 ComplexDiagMatrix transpose (void) const; |
|
|
1837 |
|
|
1838 friend DiagMatrix real (const ComplexDiagMatrix& a); |
|
|
1839 friend DiagMatrix imag (const ComplexDiagMatrix& a); |
|
|
1840 friend ComplexDiagMatrix conj (const ComplexDiagMatrix& a); |
|
|
1841 |
|
|
1842 // resize is the destructive analog for this one |
|
|
1843 |
|
|
1844 ComplexMatrix extract (int r1, int c1, int r2, int c2) const; |
|
|
1845 |
|
|
1846 // extract row or column i. |
|
|
1847 |
|
|
1848 ComplexRowVector row (int i) const; |
|
|
1849 ComplexRowVector row (char *s) const; |
|
|
1850 |
|
|
1851 ComplexColumnVector column (int i) const; |
|
|
1852 ComplexColumnVector column (char *s) const; |
|
|
1853 |
|
|
1854 ComplexDiagMatrix inverse (int& info) const; |
|
|
1855 ComplexDiagMatrix inverse (void) const; |
|
|
1856 |
|
|
1857 // diagonal matrix by scalar -> matrix operations |
|
|
1858 |
|
|
1859 ComplexMatrix operator + (double s) const; |
|
|
1860 ComplexMatrix operator - (double s) const; |
|
|
1861 |
|
|
1862 ComplexMatrix operator + (Complex s) const; |
|
|
1863 ComplexMatrix operator - (Complex s) const; |
|
|
1864 |
|
|
1865 // diagonal matrix by scalar -> diagonal matrix operations |
|
|
1866 |
|
|
1867 ComplexDiagMatrix operator * (double s) const; |
|
|
1868 ComplexDiagMatrix operator / (double s) const; |
|
|
1869 |
|
|
1870 ComplexDiagMatrix operator * (Complex s) const; |
|
|
1871 ComplexDiagMatrix operator / (Complex s) const; |
|
|
1872 |
|
|
1873 // scalar by diagonal matrix -> matrix operations |
|
|
1874 |
|
|
1875 friend ComplexMatrix operator + (double s, const ComplexDiagMatrix& a); |
|
|
1876 friend ComplexMatrix operator - (double s, const ComplexDiagMatrix& a); |
|
|
1877 |
|
|
1878 friend ComplexMatrix operator + (Complex s, const ComplexDiagMatrix& a); |
|
|
1879 friend ComplexMatrix operator - (Complex s, const ComplexDiagMatrix& a); |
|
|
1880 |
|
|
1881 // scalar by diagonal matrix -> diagonal matrix operations |
|
|
1882 |
|
|
1883 friend ComplexDiagMatrix operator * (double s, const ComplexDiagMatrix& a); |
|
|
1884 friend ComplexDiagMatrix operator / (double s, const ComplexDiagMatrix& a); |
|
|
1885 |
|
|
1886 friend ComplexDiagMatrix operator * (Complex s, const ComplexDiagMatrix& a); |
|
|
1887 friend ComplexDiagMatrix operator / (Complex s, const ComplexDiagMatrix& a); |
|
|
1888 |
|
|
1889 // diagonal matrix by column vector -> column vector operations |
|
|
1890 |
|
|
1891 ComplexColumnVector operator * (const ColumnVector& a) const; |
|
|
1892 |
|
|
1893 ComplexColumnVector operator * (const ComplexColumnVector& a) const; |
|
|
1894 |
|
|
1895 // diagonal matrix by diagonal matrix -> diagonal matrix operations |
|
|
1896 |
|
|
1897 ComplexDiagMatrix operator + (const DiagMatrix& a) const; |
|
|
1898 ComplexDiagMatrix operator - (const DiagMatrix& a) const; |
|
|
1899 ComplexDiagMatrix operator * (const DiagMatrix& a) const; |
|
|
1900 |
|
|
1901 ComplexDiagMatrix operator + (const ComplexDiagMatrix& a) const; |
|
|
1902 ComplexDiagMatrix operator - (const ComplexDiagMatrix& a) const; |
|
|
1903 ComplexDiagMatrix operator * (const ComplexDiagMatrix& a) const; |
|
|
1904 |
|
|
1905 ComplexDiagMatrix product (const DiagMatrix& a) const; // element by element |
|
|
1906 ComplexDiagMatrix quotient (const DiagMatrix& a) const; // element by element |
|
|
1907 |
|
|
1908 ComplexDiagMatrix product (const ComplexDiagMatrix& a) const; // el by el |
|
|
1909 ComplexDiagMatrix quotient (const ComplexDiagMatrix& a) const; // el by el |
|
|
1910 |
|
|
1911 ComplexDiagMatrix& operator += (const DiagMatrix& a); |
|
|
1912 ComplexDiagMatrix& operator -= (const DiagMatrix& a); |
|
|
1913 |
|
|
1914 ComplexDiagMatrix& operator += (const ComplexDiagMatrix& a); |
|
|
1915 ComplexDiagMatrix& operator -= (const ComplexDiagMatrix& a); |
|
|
1916 |
|
|
1917 // diagonal matrix by matrix -> matrix operations |
|
|
1918 |
|
|
1919 ComplexMatrix operator + (const Matrix& a) const; |
|
|
1920 ComplexMatrix operator - (const Matrix& a) const; |
|
|
1921 ComplexMatrix operator * (const Matrix& a) const; |
|
|
1922 |
|
|
1923 ComplexMatrix operator + (const ComplexMatrix& a) const; |
|
|
1924 ComplexMatrix operator - (const ComplexMatrix& a) const; |
|
|
1925 ComplexMatrix operator * (const ComplexMatrix& a) const; |
|
|
1926 |
|
|
1927 // unary operations |
|
|
1928 |
|
|
1929 ComplexDiagMatrix operator - (void) const; |
|
|
1930 |
|
|
1931 ComplexColumnVector diag (void) const; |
|
|
1932 ComplexColumnVector diag (int k) const; |
|
|
1933 |
|
|
1934 // i/o |
|
|
1935 |
|
|
1936 friend ostream& operator << (ostream& os, const ComplexDiagMatrix& a); |
|
|
1937 |
|
|
1938 private: |
|
|
1939 int nr; |
|
|
1940 int nc; |
|
|
1941 int len; |
|
|
1942 Complex *data; |
|
|
1943 |
|
|
1944 ComplexDiagMatrix (Complex *d, int nr, int nc); |
|
|
1945 }; |
|
|
1946 |
|
|
1947 inline ComplexDiagMatrix::ComplexDiagMatrix (void) |
|
|
1948 { nr = 0; nc = 0; len = 0; data = 0; } |
|
|
1949 |
|
|
1950 inline ComplexDiagMatrix::ComplexDiagMatrix (Complex *d, int r, int c) |
|
|
1951 { nr = r; nc = c; len = nr < nc ? nr : nc; data = d; } |
|
|
1952 |
|
|
1953 inline ComplexDiagMatrix::~ComplexDiagMatrix (void) |
|
|
1954 { delete [] data; data = 0; } |
|
|
1955 |
|
|
1956 inline int ComplexDiagMatrix::rows (void) const { return len; } |
|
|
1957 inline int ComplexDiagMatrix::cols (void) const { return len; } |
|
|
1958 inline int ComplexDiagMatrix::columns (void) const { return len; } |
|
|
1959 |
|
|
1960 // Would be nice to be able to avoid compiler warning and make this |
|
|
1961 // fail on assignment. |
|
|
1962 inline Complex& ComplexDiagMatrix::elem (int r, int c) |
|
|
1963 { Complex czero (0.0, 0.0); return (r == c) ? data[r] : czero; } |
|
|
1964 |
|
|
1965 inline Complex& ComplexDiagMatrix::checkelem (int r, int c) |
|
|
1966 { |
|
|
1967 #ifndef NO_RANGE_CHECK |
|
|
1968 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1969 FAIL; |
|
|
1970 #endif |
|
|
1971 |
|
|
1972 return elem (r, c); |
|
|
1973 } |
|
|
1974 |
|
|
1975 inline Complex& ComplexDiagMatrix::operator () (int r, int c) |
|
|
1976 { return checkelem (r, c); } |
|
|
1977 |
|
|
1978 inline Complex ComplexDiagMatrix::elem (int r, int c) const |
|
|
1979 { Complex czero (0.0, 0.0); return (r == c) ? data[r] : czero; } |
|
|
1980 |
|
|
1981 inline Complex ComplexDiagMatrix::checkelem (int r, int c) const |
|
|
1982 { |
|
|
1983 #ifndef NO_RANGE_CHECK |
|
|
1984 if (r < 0 || r >= nr || c < 0 || c >= nc) |
|
|
1985 FAIL; |
|
|
1986 #endif |
|
|
1987 |
|
|
1988 return elem (r, c); |
|
|
1989 } |
|
|
1990 |
|
|
1991 inline Complex ComplexDiagMatrix::operator () (int r, int c) const |
|
|
1992 { return checkelem (r, c); } |
|
|
1993 |
|
|
1994 /* |
|
|
1995 * Result of a Determinant calculation. |
|
|
1996 */ |
|
|
1997 |
|
|
1998 class DET |
|
|
1999 { |
|
|
2000 public: |
|
|
2001 DET (void) {} |
|
|
2002 |
|
|
2003 DET (const DET& a); |
|
|
2004 |
|
|
2005 DET& operator = (const DET& a); |
|
|
2006 |
|
|
2007 int value_will_overflow (void) const; |
|
|
2008 int value_will_underflow (void) const; |
|
|
2009 double coefficient (void) const; |
|
|
2010 int exponent (void) const; |
|
|
2011 double value (void) const; |
|
|
2012 |
|
|
2013 friend ostream& operator << (ostream& os, const DET& a); |
|
|
2014 |
|
|
2015 private: |
|
|
2016 DET (const double *d); |
|
|
2017 |
|
|
2018 double det [2]; |
|
|
2019 }; |
|
|
2020 |
|
|
2021 inline DET::DET (const DET& a) { det[0] = a.det[0]; det[1] = a.det[1]; } |
|
|
2022 |
|
|
2023 inline DET& DET::operator = (const DET& a) |
|
|
2024 { det[0] = a.det[0]; det[1] = a.det[1]; return *this; } |
|
|
2025 |
|
|
2026 inline int DET::value_will_overflow (void) const |
|
|
2027 { return det[2] + 1 > log10 (MAXDOUBLE) ? 1 : 0; } |
|
|
2028 |
|
|
2029 inline int DET::value_will_underflow (void) const |
|
|
2030 { return det[2] - 1 < log10 (MINDOUBLE) ? 1 : 0; } |
|
|
2031 |
|
|
2032 inline double DET::coefficient (void) const { return det[0]; } |
|
|
2033 inline int DET::exponent (void) const { return (int) det[1]; } |
|
|
2034 inline double DET::value (void) const { return det[0] * pow (10.0, det[1]); } |
|
|
2035 |
|
|
2036 inline DET::DET (const double *d) { det[0] = d[0]; det[1] = d[1]; } |
|
|
2037 |
|
|
2038 /* |
|
|
2039 * Result of a Determinant calculation. |
|
|
2040 */ |
|
|
2041 |
|
|
2042 class ComplexDET |
|
|
2043 { |
|
|
2044 public: |
|
|
2045 ComplexDET (void) {} |
|
|
2046 |
|
|
2047 ComplexDET (const ComplexDET& a); |
|
|
2048 |
|
|
2049 ComplexDET& operator = (const ComplexDET& a); |
|
|
2050 |
|
|
2051 int value_will_overflow (void) const; |
|
|
2052 int value_will_underflow (void) const; |
|
|
2053 Complex coefficient (void) const; |
|
|
2054 int exponent (void) const; |
|
|
2055 Complex value (void) const; |
|
|
2056 |
|
|
2057 friend ostream& operator << (ostream& os, const ComplexDET& a); |
|
|
2058 |
|
|
2059 private: |
|
|
2060 ComplexDET (const Complex *d); |
|
|
2061 |
|
|
2062 Complex det [2]; |
|
|
2063 }; |
|
|
2064 |
|
|
2065 inline ComplexDET::ComplexDET (const ComplexDET& a) |
|
|
2066 { det[0] = a.det[0]; det[1] = a.det[1]; } |
|
|
2067 |
|
|
2068 inline ComplexDET& ComplexDET::operator = (const ComplexDET& a) |
|
|
2069 { det[0] = a.det[0]; det[1] = a.det[1]; return *this; } |
|
|
2070 |
|
|
2071 inline int ComplexDET::value_will_overflow (void) const |
|
|
2072 { return real (det[2]) + 1 > log10 (MAXDOUBLE) ? 1 : 0; } |
|
|
2073 |
|
|
2074 inline int ComplexDET::value_will_underflow (void) const |
|
|
2075 { return real (det[2]) - 1 < log10 (MINDOUBLE) ? 1 : 0; } |
|
|
2076 |
|
|
2077 inline Complex ComplexDET::coefficient (void) const { return det[0]; } |
|
|
2078 |
|
|
2079 inline int ComplexDET::exponent (void) const { return (int) real (det[1]); } |
|
|
2080 |
|
|
2081 inline Complex ComplexDET::value (void) const |
|
|
2082 { return det[0] * pow (10.0, real (det[1])); } |
|
|
2083 |
|
|
2084 inline ComplexDET::ComplexDET (const Complex *d) |
|
|
2085 { det[0] = d[0]; det[1] = d[1]; } |
|
|
2086 |
|
|
2087 /* |
|
|
2088 * Result of a Hessenbug Decomposition |
|
|
2089 */ |
|
|
2090 |
|
|
2091 class HESS |
|
|
2092 { |
|
|
2093 friend class Matrix; |
|
|
2094 |
|
|
2095 public: |
|
|
2096 HESS (void) {} |
|
|
2097 |
|
|
2098 HESS (const Matrix& a); |
|
|
2099 HESS (const Matrix&a, int& info); |
|
|
2100 |
|
|
2101 HESS (const HESS& a); |
|
|
2102 |
|
|
2103 HESS& operator = (const HESS& a); |
|
|
2104 Matrix hess_matrix (void) const; |
|
|
2105 Matrix unitary_hess_matrix (void) const; |
|
|
2106 friend ostream& operator << (ostream& os, const HESS& a); |
|
|
2107 |
|
|
2108 private: |
|
|
2109 int init (const Matrix& a); |
|
|
2110 |
|
|
2111 Matrix hess_mat; |
|
|
2112 Matrix unitary_hess_mat; |
|
|
2113 }; |
|
|
2114 |
|
|
2115 inline HESS::HESS (const Matrix& a) {init (a); } |
|
|
2116 inline HESS::HESS (const Matrix& a, int& info) { info = init(a); } |
|
|
2117 inline HESS::HESS (const HESS& a) |
|
|
2118 { |
|
|
2119 hess_mat = a.hess_mat; |
|
|
2120 unitary_hess_mat = a.unitary_hess_mat; |
|
|
2121 } |
|
|
2122 inline HESS& |
|
|
2123 HESS::operator = (const HESS& a) |
|
|
2124 { |
|
|
2125 hess_mat = a.hess_mat; |
|
|
2126 unitary_hess_mat = a.unitary_hess_mat; |
|
|
2127 |
|
|
2128 return *this; |
|
|
2129 } |
|
|
2130 inline Matrix HESS::hess_matrix (void) const { return hess_mat; } |
|
|
2131 inline Matrix HESS::unitary_hess_matrix (void) const {return unitary_hess_mat;} |
|
|
2132 |
|
|
2133 /* |
|
|
2134 * Result of a Hessenburg Decomposition |
|
|
2135 */ |
|
|
2136 |
|
|
2137 class ComplexHESS |
|
|
2138 { |
|
|
2139 friend class ComplexMatrix; |
|
|
2140 |
|
|
2141 public: |
|
|
2142 ComplexHESS (void) {} |
|
|
2143 ComplexHESS (const ComplexMatrix& a); |
|
|
2144 ComplexHESS (const ComplexMatrix& a, int& info); |
|
|
2145 ComplexHESS (const ComplexHESS& a); |
|
|
2146 ComplexHESS& operator = (const ComplexHESS& a); |
|
|
2147 ComplexMatrix hess_matrix (void) const; |
|
|
2148 ComplexMatrix unitary_hess_matrix (void) const; |
|
|
2149 |
|
|
2150 friend ostream& operator << (ostream& os, const ComplexHESS& a); |
|
|
2151 |
|
|
2152 private: |
|
|
2153 int init (const ComplexMatrix& a); |
|
|
2154 |
|
|
2155 ComplexMatrix hess_mat; |
|
|
2156 ComplexMatrix unitary_hess_mat; |
|
|
2157 }; |
|
|
2158 |
|
|
2159 inline ComplexHESS::ComplexHESS (const ComplexMatrix& a) { init(a); } |
|
|
2160 inline ComplexHESS::ComplexHESS (const ComplexMatrix& a, int& info) |
|
|
2161 { info = init(a); } |
|
|
2162 |
|
|
2163 inline ComplexHESS::ComplexHESS (const ComplexHESS& a) |
|
|
2164 { |
|
|
2165 hess_mat = a.hess_mat; |
|
|
2166 unitary_hess_mat = a.unitary_hess_mat; |
|
|
2167 } |
|
|
2168 |
|
|
2169 inline ComplexHESS& |
|
|
2170 ComplexHESS::operator = (const ComplexHESS& a) |
|
|
2171 { |
|
|
2172 hess_mat = a.hess_mat; |
|
|
2173 unitary_hess_mat = a.unitary_hess_mat; |
|
|
2174 |
|
|
2175 return *this; |
|
|
2176 } |
|
|
2177 |
|
|
2178 inline ComplexMatrix ComplexHESS::hess_matrix (void) const |
|
|
2179 { return hess_mat; } |
|
|
2180 |
|
|
2181 inline ComplexMatrix ComplexHESS::unitary_hess_matrix (void) const |
|
|
2182 { return unitary_hess_mat; } |
|
|
2183 |
|
|
2184 /* |
|
|
2185 * Result of a Schur Decomposition |
|
|
2186 */ |
|
|
2187 |
|
|
2188 class SCHUR |
|
|
2189 { |
|
|
2190 friend class Matrix; |
|
|
2191 |
|
|
2192 public: |
|
|
2193 SCHUR (void) {} |
|
|
2194 |
|
|
2195 SCHUR (const Matrix& a, const char *ord); |
|
|
2196 SCHUR (const Matrix& a, const char *ord, int& info); |
|
|
2197 |
|
|
2198 SCHUR (const SCHUR& a, const char *ord); |
|
|
2199 |
|
|
2200 SCHUR& operator = (const SCHUR& a, const char *ord); |
|
|
2201 |
|
|
2202 Matrix schur_matrix (void) const; |
|
|
2203 Matrix unitary_matrix (void) const; |
|
|
2204 |
|
|
2205 friend ostream& operator << (ostream& os, const SCHUR& a); |
|
|
2206 |
|
|
2207 private: |
|
|
2208 int init (const Matrix& a, const char *ord); |
|
|
2209 |
|
|
2210 Matrix schur_mat; |
|
|
2211 Matrix unitary_mat; |
|
|
2212 }; |
|
|
2213 |
|
|
2214 inline SCHUR::SCHUR (const Matrix& a, const char *ord) { init (a, ord); } |
|
|
2215 |
|
|
2216 inline SCHUR::SCHUR (const Matrix& a, const char *ord, int& info) |
|
|
2217 { info = init (a, ord); } |
|
|
2218 |
|
|
2219 inline SCHUR::SCHUR (const SCHUR& a, const char *ord) |
|
|
2220 { |
|
|
2221 schur_mat = a.schur_mat; |
|
|
2222 unitary_mat = a.unitary_mat; |
|
|
2223 } |
|
|
2224 |
|
|
2225 inline SCHUR& |
|
|
2226 SCHUR::operator = (const SCHUR& a, const char *ord) |
|
|
2227 { |
|
|
2228 schur_mat = a.schur_mat; |
|
|
2229 unitary_mat = a.unitary_mat; |
|
|
2230 |
|
|
2231 return *this; |
|
|
2232 } |
|
|
2233 |
|
|
2234 inline Matrix SCHUR::schur_matrix (void) const { return schur_mat; } |
|
|
2235 inline Matrix SCHUR::unitary_matrix (void) const { return unitary_mat; } |
|
|
2236 |
|
|
2237 /* |
|
|
2238 * Result of a Schur Decomposition |
|
|
2239 */ |
|
|
2240 |
|
|
2241 class ComplexSCHUR |
|
|
2242 { |
|
|
2243 friend class ComplexMatrix; |
|
|
2244 |
|
|
2245 public: |
|
|
2246 ComplexSCHUR (void) {} |
|
|
2247 |
|
|
2248 ComplexSCHUR (const ComplexMatrix& a, const char *ord); |
|
|
2249 ComplexSCHUR (const ComplexMatrix& a, const char *ord, int& info); |
|
|
2250 |
|
|
2251 ComplexSCHUR (const ComplexSCHUR& a, const char *ord); |
|
|
2252 |
|
|
2253 ComplexSCHUR& operator = (const ComplexSCHUR& a, const char *ord); |
|
|
2254 |
|
|
2255 ComplexMatrix schur_matrix (void) const; |
|
|
2256 ComplexMatrix unitary_matrix (void) const; |
|
|
2257 |
|
|
2258 friend ostream& operator << (ostream& os, const ComplexSCHUR& a); |
|
|
2259 |
|
|
2260 private: |
|
|
2261 int init (const ComplexMatrix& a, const char *ord); |
|
|
2262 |
|
|
2263 ComplexMatrix schur_mat; |
|
|
2264 ComplexMatrix unitary_mat; |
|
|
2265 }; |
|
|
2266 |
|
|
2267 inline ComplexSCHUR::ComplexSCHUR (const ComplexMatrix& a, const char *ord) |
|
|
2268 { init (a,ord); } |
|
|
2269 |
|
|
2270 inline ComplexSCHUR::ComplexSCHUR (const ComplexMatrix& a, const char *ord, |
|
|
2271 int& info) |
|
|
2272 { info = init (a,ord); } |
|
|
2273 |
|
|
2274 inline ComplexSCHUR::ComplexSCHUR (const ComplexSCHUR& a, const char *ord) |
|
|
2275 { |
|
|
2276 schur_mat = a.schur_mat; |
|
|
2277 unitary_mat = a.unitary_mat; |
|
|
2278 } |
|
|
2279 |
|
|
2280 inline ComplexSCHUR& |
|
|
2281 ComplexSCHUR::operator = (const ComplexSCHUR& a, const char *ord) |
|
|
2282 { |
|
|
2283 schur_mat = a.schur_mat; |
|
|
2284 unitary_mat = a.unitary_mat; |
|
|
2285 |
|
|
2286 return *this; |
|
|
2287 } |
|
|
2288 inline ComplexMatrix ComplexSCHUR::schur_matrix (void) const |
|
|
2289 { return schur_mat; } |
|
|
2290 |
|
|
2291 inline ComplexMatrix ComplexSCHUR::unitary_matrix (void) const |
|
|
2292 { return unitary_mat; } |
|
|
2293 |
|
|
2294 |
|
|
2295 /* |
|
|
2296 * Result of a Singular Value Decomposition. |
|
|
2297 */ |
|
|
2298 |
|
|
2299 class SVD |
|
|
2300 { |
|
|
2301 friend class Matrix; |
|
|
2302 |
|
|
2303 public: |
|
|
2304 SVD (void) {} |
|
|
2305 |
|
|
2306 SVD (const Matrix& a); |
|
|
2307 SVD (const Matrix& a, int& info); |
|
|
2308 |
|
|
2309 SVD (const SVD& a); |
|
|
2310 |
|
|
2311 SVD& operator = (const SVD& a); |
|
|
2312 |
|
|
2313 DiagMatrix singular_values (void) const; |
|
|
2314 Matrix left_singular_matrix (void) const; |
|
|
2315 Matrix right_singular_matrix (void) const; |
|
|
2316 |
|
|
2317 friend ostream& operator << (ostream& os, const SVD& a); |
|
|
2318 |
|
|
2319 private: |
|
|
2320 int init (const Matrix& a); |
|
|
2321 |
|
|
2322 DiagMatrix sigma; |
|
|
2323 Matrix left_sm; |
|
|
2324 Matrix right_sm; |
|
|
2325 }; |
|
|
2326 |
|
|
2327 inline SVD::SVD (const Matrix& a) { init (a); } |
|
|
2328 |
|
|
2329 inline SVD::SVD (const Matrix& a, int& info) { info = init (a); } |
|
|
2330 |
|
|
2331 inline SVD::SVD (const SVD& a) |
|
|
2332 { |
|
|
2333 sigma = a.sigma; |
|
|
2334 left_sm = a.left_sm; |
|
|
2335 right_sm = a.right_sm; |
|
|
2336 } |
|
|
2337 |
|
|
2338 inline SVD& |
|
|
2339 SVD::operator = (const SVD& a) |
|
|
2340 { |
|
|
2341 sigma = a.sigma; |
|
|
2342 left_sm = a.left_sm; |
|
|
2343 right_sm = a.right_sm; |
|
|
2344 |
|
|
2345 return *this; |
|
|
2346 } |
|
|
2347 |
|
|
2348 inline DiagMatrix SVD::singular_values (void) const { return sigma; } |
|
|
2349 inline Matrix SVD::left_singular_matrix (void) const { return left_sm; } |
|
|
2350 inline Matrix SVD::right_singular_matrix (void) const { return right_sm; } |
|
|
2351 |
|
|
2352 /* |
|
|
2353 * Result of a Singular Value Decomposition. |
|
|
2354 */ |
|
|
2355 |
|
|
2356 class ComplexSVD |
|
|
2357 { |
|
|
2358 friend class ComplexMatrix; |
|
|
2359 |
|
|
2360 public: |
|
|
2361 ComplexSVD (void) {} |
|
|
2362 |
|
|
2363 ComplexSVD (const ComplexMatrix& a); |
|
|
2364 ComplexSVD (const ComplexMatrix& a, int& info); |
|
|
2365 |
|
|
2366 ComplexSVD (const ComplexSVD& a); |
|
|
2367 |
|
|
2368 ComplexSVD& operator = (const ComplexSVD& a); |
|
|
2369 |
|
|
2370 DiagMatrix singular_values (void) const; |
|
|
2371 ComplexMatrix left_singular_matrix (void) const; |
|
|
2372 ComplexMatrix right_singular_matrix (void) const; |
|
|
2373 |
|
|
2374 friend ostream& operator << (ostream& os, const ComplexSVD& a); |
|
|
2375 |
|
|
2376 private: |
|
|
2377 int init (const ComplexMatrix& a); |
|
|
2378 |
|
|
2379 DiagMatrix sigma; |
|
|
2380 ComplexMatrix left_sm; |
|
|
2381 ComplexMatrix right_sm; |
|
|
2382 }; |
|
|
2383 |
|
|
2384 inline ComplexSVD::ComplexSVD (const ComplexMatrix& a) { init (a); } |
|
|
2385 inline ComplexSVD::ComplexSVD (const ComplexMatrix& a, int& info) |
|
|
2386 { info = init (a); } |
|
|
2387 |
|
|
2388 inline ComplexSVD::ComplexSVD (const ComplexSVD& a) |
|
|
2389 { |
|
|
2390 sigma = a.sigma; |
|
|
2391 left_sm = a.left_sm; |
|
|
2392 right_sm = a.right_sm; |
|
|
2393 } |
|
|
2394 |
|
|
2395 inline ComplexSVD& |
|
|
2396 ComplexSVD::operator = (const ComplexSVD& a) |
|
|
2397 { |
|
|
2398 sigma = a.sigma; |
|
|
2399 left_sm = a.left_sm; |
|
|
2400 right_sm = a.right_sm; |
|
|
2401 |
|
|
2402 return *this; |
|
|
2403 } |
|
|
2404 |
|
|
2405 inline DiagMatrix ComplexSVD::singular_values (void) const |
|
|
2406 { return sigma; } |
|
|
2407 |
|
|
2408 inline ComplexMatrix ComplexSVD::left_singular_matrix (void) const |
|
|
2409 { return left_sm; } |
|
|
2410 |
|
|
2411 inline ComplexMatrix ComplexSVD::right_singular_matrix (void) const |
|
|
2412 { return right_sm; } |
|
|
2413 |
|
|
2414 /* |
|
|
2415 * Result of an Eigenvalue computation. |
|
|
2416 */ |
|
|
2417 |
|
|
2418 class EIG |
|
|
2419 { |
|
|
2420 friend class Matrix; |
|
|
2421 friend class ComplexMatrix; |
|
|
2422 |
|
|
2423 public: |
|
|
2424 EIG (void) {} |
|
|
2425 |
|
|
2426 EIG (const Matrix& a); |
|
|
2427 EIG (const Matrix& a, int& info); |
|
|
2428 |
|
|
2429 EIG (const ComplexMatrix& a); |
|
|
2430 EIG (const ComplexMatrix& a, int& info); |
|
|
2431 |
|
|
2432 EIG (const EIG& a); |
|
|
2433 |
|
|
2434 EIG& operator = (const EIG& a); |
|
|
2435 |
|
|
2436 ComplexColumnVector eigenvalues (void) const; |
|
|
2437 ComplexMatrix eigenvectors (void) const; |
|
|
2438 |
|
|
2439 friend ostream& operator << (ostream& os, const EIG& a); |
|
|
2440 |
|
|
2441 private: |
|
|
2442 int init (const Matrix& a); |
|
|
2443 int init (const ComplexMatrix& a); |
|
|
2444 |
|
|
2445 ComplexColumnVector lambda; |
|
|
2446 ComplexMatrix v; |
|
|
2447 }; |
|
|
2448 |
|
|
2449 inline EIG::EIG (const Matrix& a) { init (a); } |
|
|
2450 inline EIG::EIG (const Matrix& a, int& info) { info = init (a); } |
|
|
2451 |
|
|
2452 inline EIG::EIG (const ComplexMatrix& a) { init (a); } |
|
|
2453 inline EIG::EIG (const ComplexMatrix& a, int& info) { info = init (a); } |
|
|
2454 |
|
|
2455 inline EIG::EIG (const EIG& a) { lambda = a.lambda; v = a.v; } |
|
|
2456 |
|
|
2457 inline EIG& EIG::operator = (const EIG& a) |
|
|
2458 { lambda = a.lambda; v = a.v; return *this; } |
|
|
2459 |
|
|
2460 inline ComplexColumnVector EIG::eigenvalues (void) const { return lambda; } |
|
|
2461 |
|
|
2462 inline ComplexMatrix EIG::eigenvectors (void) const { return v; } |
|
|
2463 |
|
|
2464 /* |
|
|
2465 * Result of an LU decomposition. |
|
|
2466 */ |
|
|
2467 |
|
|
2468 class LU |
|
|
2469 { |
|
|
2470 friend class Matrix; |
|
|
2471 |
|
|
2472 public: |
|
|
2473 LU (void) {} |
|
|
2474 |
|
|
2475 LU (const Matrix& a); |
|
|
2476 |
|
|
2477 LU (const LU& a); |
|
|
2478 |
|
|
2479 LU& operator = (const LU& a); |
|
|
2480 |
|
|
2481 Matrix L (void) const; |
|
|
2482 Matrix U (void) const; |
|
|
2483 Matrix P (void) const; |
|
|
2484 |
|
|
2485 friend ostream& operator << (ostream& os, const LU& a); |
|
|
2486 |
|
|
2487 private: |
|
|
2488 |
|
|
2489 Matrix l; |
|
|
2490 Matrix u; |
|
|
2491 Matrix p; |
|
|
2492 }; |
|
|
2493 |
|
|
2494 inline LU::LU (const LU& a) { l = a.l; u = a.u; p = a.p; } |
|
|
2495 |
|
|
2496 inline LU& LU::operator = (const LU& a) |
|
|
2497 { l = a.l; u = a.u; p = a.p; return *this; } |
|
|
2498 |
|
|
2499 inline Matrix LU::L (void) const { return l; } |
|
|
2500 inline Matrix LU::U (void) const { return u; } |
|
|
2501 inline Matrix LU::P (void) const { return p; } |
|
|
2502 |
|
|
2503 class ComplexLU |
|
|
2504 { |
|
|
2505 friend class ComplexMatrix; |
|
|
2506 |
|
|
2507 public: |
|
|
2508 ComplexLU (void) {} |
|
|
2509 |
|
|
2510 ComplexLU (const ComplexMatrix& a); |
|
|
2511 |
|
|
2512 ComplexLU (const ComplexLU& a); |
|
|
2513 |
|
|
2514 ComplexLU& operator = (const ComplexLU& a); |
|
|
2515 |
|
|
2516 ComplexMatrix L (void) const; |
|
|
2517 ComplexMatrix U (void) const; |
|
|
2518 Matrix P (void) const; |
|
|
2519 |
|
|
2520 friend ostream& operator << (ostream& os, const ComplexLU& a); |
|
|
2521 |
|
|
2522 private: |
|
|
2523 |
|
|
2524 ComplexMatrix l; |
|
|
2525 ComplexMatrix u; |
|
|
2526 Matrix p; |
|
|
2527 }; |
|
|
2528 |
|
|
2529 inline ComplexLU::ComplexLU (const ComplexLU& a) { l = a.l; u = a.u; p = a.p; } |
|
|
2530 |
|
|
2531 inline ComplexLU& ComplexLU::operator = (const ComplexLU& a) |
|
|
2532 { l = a.l; u = a.u; p = a.p; return *this; } |
|
|
2533 |
|
|
2534 inline ComplexMatrix ComplexLU::L (void) const { return l; } |
|
|
2535 inline ComplexMatrix ComplexLU::U (void) const { return u; } |
|
|
2536 inline Matrix ComplexLU::P (void) const { return p; } |
|
|
2537 |
|
|
2538 /* |
|
|
2539 * Result of a QR decomposition. |
|
|
2540 */ |
|
|
2541 |
|
|
2542 class QR |
|
|
2543 { |
|
|
2544 public: |
|
|
2545 QR (void) {} |
|
|
2546 |
|
|
2547 QR (const Matrix& A); |
|
|
2548 |
|
|
2549 QR (const QR& a); |
|
|
2550 |
|
|
2551 QR& operator = (const QR& a); |
|
|
2552 |
|
|
2553 Matrix Q (void) const; |
|
|
2554 Matrix R (void) const; |
|
|
2555 |
|
|
2556 friend ostream& operator << (ostream& os, const QR& a); |
|
|
2557 |
|
|
2558 private: |
|
|
2559 Matrix q; |
|
|
2560 Matrix r; |
|
|
2561 }; |
|
|
2562 |
|
|
2563 inline QR::QR (const QR& a) { q = a.q; r = a.r; } |
|
|
2564 |
|
|
2565 inline QR& QR::operator = (const QR& a) { q = a.q; r = a.r; return *this; } |
|
|
2566 |
|
|
2567 inline Matrix QR::Q (void) const { return q; } |
|
|
2568 inline Matrix QR::R (void) const { return r; } |
|
|
2569 |
|
|
2570 class ComplexQR |
|
|
2571 { |
|
|
2572 public: |
|
|
2573 ComplexQR (void) {} |
|
|
2574 |
|
|
2575 ComplexQR (const ComplexMatrix& A); |
|
|
2576 |
|
|
2577 ComplexQR (const ComplexQR& a); |
|
|
2578 |
|
|
2579 ComplexQR& operator = (const ComplexQR& a); |
|
|
2580 |
|
|
2581 ComplexMatrix Q (void) const; |
|
|
2582 ComplexMatrix R (void) const; |
|
|
2583 |
|
|
2584 friend ostream& operator << (ostream& os, const ComplexQR& a); |
|
|
2585 |
|
|
2586 private: |
|
|
2587 ComplexMatrix q; |
|
|
2588 ComplexMatrix r; |
|
|
2589 }; |
|
|
2590 |
|
|
2591 inline ComplexQR::ComplexQR (const ComplexQR& a) { q = a.q; r = a.r; } |
|
|
2592 |
|
|
2593 inline ComplexQR& ComplexQR::operator = (const ComplexQR& a) |
|
|
2594 { q = a.q; r = a.r; return *this; } |
|
|
2595 |
|
|
2596 inline ComplexMatrix ComplexQR::Q (void) const { return q; } |
|
|
2597 inline ComplexMatrix ComplexQR::R (void) const { return r; } |
|
|
2598 |
|
|
2599 #endif |
|
|
2600 |
|
|
2601 /* |
|
|
2602 ;;; Local Variables: *** |
|
|
2603 ;;; mode: C++ *** |
|
|
2604 ;;; page-delimiter: "^/\\*" *** |
|
|
2605 ;;; End: *** |
|
|
2606 */ |
