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1
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1 // xpow.cc -*- C++ -*- |
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2 /* |
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3 |
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1009
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4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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1315
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20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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21 |
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22 */ |
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23 |
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240
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24 #ifdef HAVE_CONFIG_H |
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1192
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25 #include <config.h> |
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26 #endif |
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27 |
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1343
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28 #include <cassert> |
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29 |
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164
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30 #include <Complex.h> |
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31 |
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1352
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32 #include "CColVector.h" |
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453
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33 #include "CDiagMatrix.h" |
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1352
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34 #include "CMatrix.h" |
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453
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35 #include "EIG.h" |
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1352
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36 #include "dDiagMatrix.h" |
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37 #include "dMatrix.h" |
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38 |
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39 #include "error.h" |
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164
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40 #include "tree-const.h" |
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1352
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41 #include "xpow.h" |
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42 |
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43 // This function also appears in tree-const.cc. Maybe it should be a |
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44 // member function of the Matrix class. |
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45 |
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46 static int |
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47 any_element_is_negative (const Matrix& a) |
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48 { |
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49 int nr = a.rows (); |
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50 int nc = a.columns (); |
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51 for (int j = 0; j < nc; j++) |
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52 for (int i = 0; i < nr; i++) |
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53 if (a.elem (i, j) < 0.0) |
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54 return 1; |
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55 return 0; |
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56 } |
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57 |
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767
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58 // Safer pow functions. |
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59 // |
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60 // op2 \ op1: s m cs cm |
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61 // +-- +---+---+----+----+ |
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62 // scalar | | 1 | 5 | 7 | 11 | |
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63 // +---+---+----+----+ |
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64 // matrix | 2 | E | 8 | E | |
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65 // +---+---+----+----+ |
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66 // complex_scalar | 3 | 6 | 9 | 12 | |
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67 // +---+---+----+----+ |
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68 // complex_matrix | 4 | E | 10 | E | |
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69 // +---+---+----+----+ |
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70 // |
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71 // E -> error, trapped in arith-ops.cc. |
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72 |
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767
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73 // -*- 1 -*- |
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74 tree_constant |
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75 xpow (double a, double b) |
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76 { |
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77 if (a < 0.0 && (int) b != b) |
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78 { |
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79 Complex atmp (a); |
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80 return tree_constant (pow (atmp, b)); |
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81 } |
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82 else |
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83 return tree_constant (pow (a, b)); |
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84 } |
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85 |
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767
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86 // -*- 2 -*- |
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1
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87 tree_constant |
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164
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88 xpow (double a, const Matrix& b) |
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1
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89 { |
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90 tree_constant retval; |
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91 |
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92 int nr = b.rows (); |
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93 int nc = b.columns (); |
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94 |
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95 if (nr == 0 || nc == 0 || nr != nc) |
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96 error ("for x^A, A must be square"); |
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97 else |
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98 { |
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99 EIG b_eig (b); |
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100 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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101 ComplexMatrix Q (b_eig.eigenvectors ()); |
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102 |
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103 for (int i = 0; i < nr; i++) |
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104 { |
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105 Complex elt = lambda.elem (i); |
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106 if (imag (elt) == 0.0) |
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107 lambda.elem (i) = pow (a, real (elt)); |
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108 else |
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109 lambda.elem (i) = pow (a, elt); |
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110 } |
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111 ComplexDiagMatrix D (lambda); |
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112 |
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113 ComplexMatrix result = Q * D * Q.inverse (); |
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114 retval = tree_constant (result); |
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115 } |
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116 |
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117 return retval; |
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118 } |
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119 |
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767
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120 // -*- 3 -*- |
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121 tree_constant |
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122 xpow (double a, const Complex& b) |
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123 { |
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124 Complex result; |
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125 Complex atmp (a); |
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126 result = pow (atmp, b); |
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127 return tree_constant (result); |
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128 } |
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129 |
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767
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130 // -*- 4 -*- |
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131 tree_constant |
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164
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132 xpow (double a, const ComplexMatrix& b) |
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133 { |
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134 tree_constant retval; |
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135 |
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136 int nr = b.rows (); |
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137 int nc = b.columns (); |
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138 |
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139 if (nr == 0 || nc == 0 || nr != nc) |
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140 error ("for x^A, A must be square"); |
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141 else |
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142 { |
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143 EIG b_eig (b); |
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144 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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145 ComplexMatrix Q (b_eig.eigenvectors ()); |
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146 |
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147 for (int i = 0; i < nr; i++) |
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148 { |
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149 Complex elt = lambda.elem (i); |
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150 if (imag (elt) == 0.0) |
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151 lambda.elem (i) = pow (a, real (elt)); |
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152 else |
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153 lambda.elem (i) = pow (a, elt); |
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154 } |
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155 ComplexDiagMatrix D (lambda); |
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156 |
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157 ComplexMatrix result = Q * D * Q.inverse (); |
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158 retval = tree_constant (result); |
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159 } |
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160 |
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161 return retval; |
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162 } |
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163 |
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767
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164 // -*- 5 -*- |
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1
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165 tree_constant |
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164
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166 xpow (const Matrix& a, double b) |
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167 { |
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168 tree_constant retval; |
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169 |
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170 int nr = a.rows (); |
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171 int nc = a.columns (); |
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172 |
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173 if (nr == 0 || nc == 0 || nr != nc) |
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174 { |
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175 error ("for A^b, A must be square"); |
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176 return retval; |
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177 } |
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178 |
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179 if ((int) b == b) |
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180 { |
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181 int btmp = (int) b; |
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182 if (btmp == 0) |
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183 { |
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184 DiagMatrix result (nr, nr, 1.0); |
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185 retval = tree_constant (result); |
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186 } |
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187 else |
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188 { |
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1358
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189 // Too much copying? |
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190 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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191 // large... |
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192 |
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1
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193 Matrix atmp; |
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194 if (btmp < 0) |
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195 { |
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196 btmp = -btmp; |
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197 atmp = a.inverse (); |
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198 } |
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199 else |
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200 atmp = a; |
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201 |
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202 Matrix result (atmp); |
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203 for (int i = 1; i < btmp; i++) |
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204 result = result * atmp; |
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205 |
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206 retval = tree_constant (result); |
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207 } |
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208 } |
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209 else |
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210 { |
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211 EIG a_eig (a); |
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212 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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213 ComplexMatrix Q (a_eig.eigenvectors ()); |
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214 |
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215 for (int i = 0; i < nr; i++) |
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216 lambda.elem (i) = pow (lambda.elem (i), b); |
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217 |
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218 ComplexDiagMatrix D (lambda); |
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219 |
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220 ComplexMatrix result = Q * D * Q.inverse (); |
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221 retval = tree_constant (result); |
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222 } |
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223 |
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224 return retval; |
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225 } |
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226 |
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767
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227 // -*- 6 -*- |
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1
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228 tree_constant |
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229 xpow (const Matrix& a, const Complex& b) |
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1
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230 { |
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231 int nr = a.rows (); |
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232 int nc = a.columns (); |
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233 |
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234 if (nr == 0 || nc == 0 || nr != nc) |
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235 { |
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236 error ("for A^b, A must be square"); |
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237 return tree_constant (); |
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238 } |
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239 |
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240 EIG a_eig (a); |
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241 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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242 ComplexMatrix Q (a_eig.eigenvectors ()); |
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243 |
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244 for (int i = 0; i < nr; i++) |
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245 lambda.elem (i) = pow (lambda.elem (i), b); |
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246 |
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247 ComplexDiagMatrix D (lambda); |
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248 |
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249 ComplexMatrix result = Q * D * Q.inverse (); |
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250 |
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251 return tree_constant (result); |
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252 } |
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253 |
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767
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254 // -*- 7 -*- |
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1
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255 tree_constant |
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256 xpow (const Complex& a, double b) |
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1
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257 { |
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258 Complex result; |
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259 result = pow (a, b); |
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260 return tree_constant (result); |
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261 } |
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262 |
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767
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263 // -*- 8 -*- |
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264 tree_constant |
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265 xpow (const Complex& a, const Matrix& b) |
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266 { |
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267 tree_constant retval; |
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268 |
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269 int nr = b.rows (); |
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270 int nc = b.columns (); |
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271 |
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272 if (nr == 0 || nc == 0 || nr != nc) |
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273 { |
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274 error ("for x^A, A must be square"); |
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275 } |
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276 else |
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277 { |
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278 EIG b_eig (b); |
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279 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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280 ComplexMatrix Q (b_eig.eigenvectors ()); |
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281 |
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282 for (int i = 0; i < nr; i++) |
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283 { |
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284 Complex elt = lambda.elem (i); |
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285 if (imag (elt) == 0.0) |
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286 lambda.elem (i) = pow (a, real (elt)); |
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287 else |
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288 lambda.elem (i) = pow (a, elt); |
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289 } |
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290 ComplexDiagMatrix D (lambda); |
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291 |
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292 ComplexMatrix result = Q * D * Q.inverse (); |
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293 retval = tree_constant (result); |
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294 } |
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295 |
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296 return retval; |
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297 } |
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298 |
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767
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299 // -*- 9 -*- |
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1
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300 tree_constant |
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164
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301 xpow (const Complex& a, const Complex& b) |
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302 { |
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303 Complex result; |
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304 result = pow (a, b); |
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305 return tree_constant (result); |
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306 } |
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307 |
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767
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308 // -*- 10 -*- |
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1
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309 tree_constant |
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164
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310 xpow (const Complex& a, const ComplexMatrix& b) |
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311 { |
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312 tree_constant retval; |
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313 |
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314 int nr = b.rows (); |
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315 int nc = b.columns (); |
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316 |
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317 if (nr == 0 || nc == 0 || nr != nc) |
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318 error ("for x^A, A must be square"); |
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319 else |
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320 { |
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321 EIG b_eig (b); |
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322 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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323 ComplexMatrix Q (b_eig.eigenvectors ()); |
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324 |
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325 for (int i = 0; i < nr; i++) |
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326 { |
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327 Complex elt = lambda.elem (i); |
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328 if (imag (elt) == 0.0) |
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329 lambda.elem (i) = pow (a, real (elt)); |
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330 else |
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331 lambda.elem (i) = pow (a, elt); |
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332 } |
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333 ComplexDiagMatrix D (lambda); |
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334 |
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335 ComplexMatrix result = Q * D * Q.inverse (); |
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336 retval = tree_constant (result); |
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337 } |
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338 |
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339 return retval; |
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340 } |
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341 |
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767
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342 // -*- 11 -*- |
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1
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343 tree_constant |
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164
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344 xpow (const ComplexMatrix& a, double b) |
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1
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345 { |
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346 tree_constant retval; |
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347 |
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348 int nr = a.rows (); |
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349 int nc = a.columns (); |
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350 |
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351 if (nr == 0 || nc == 0 || nr != nc) |
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352 { |
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353 error ("for A^b, A must be square"); |
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354 return retval; |
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355 } |
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356 |
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357 if ((int) b == b) |
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358 { |
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359 int btmp = (int) b; |
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360 if (btmp == 0) |
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361 { |
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362 DiagMatrix result (nr, nr, 1.0); |
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363 retval = tree_constant (result); |
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364 } |
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365 else |
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366 { |
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1358
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367 // Too much copying? |
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368 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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369 // large... |
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370 |
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1
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371 ComplexMatrix atmp; |
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372 if (btmp < 0) |
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373 { |
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374 btmp = -btmp; |
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375 atmp = a.inverse (); |
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376 } |
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377 else |
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378 atmp = a; |
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379 |
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380 ComplexMatrix result (atmp); |
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381 for (int i = 1; i < btmp; i++) |
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382 result = result * atmp; |
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383 |
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384 retval = tree_constant (result); |
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385 } |
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386 } |
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387 else |
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388 { |
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389 EIG a_eig (a); |
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390 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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391 ComplexMatrix Q (a_eig.eigenvectors ()); |
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392 |
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393 for (int i = 0; i < nr; i++) |
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394 lambda.elem (i) = pow (lambda.elem (i), b); |
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395 |
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396 ComplexDiagMatrix D (lambda); |
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397 |
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398 ComplexMatrix result = Q * D * Q.inverse (); |
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399 retval = tree_constant (result); |
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400 } |
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401 |
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402 return retval; |
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403 } |
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404 |
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767
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405 // -*- 12 -*- |
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1
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406 tree_constant |
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164
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407 xpow (const ComplexMatrix& a, const Complex& b) |
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1
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408 { |
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409 int nr = a.rows (); |
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410 int nc = a.columns (); |
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411 |
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412 if (nr == 0 || nc == 0 || nr != nc) |
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413 { |
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414 error ("for A^b, A must be square"); |
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415 return tree_constant (); |
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416 } |
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417 |
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418 EIG a_eig (a); |
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419 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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420 ComplexMatrix Q (a_eig.eigenvectors ()); |
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421 |
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422 for (int i = 0; i < nr; i++) |
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423 lambda.elem (i) = pow (lambda.elem (i), b); |
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424 |
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425 ComplexDiagMatrix D (lambda); |
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426 |
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427 ComplexMatrix result = Q * D * Q.inverse (); |
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428 |
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429 return tree_constant (result); |
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430 } |
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431 |
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767
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432 // Safer pow functions that work elementwise for matrices. |
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433 // |
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434 // op2 \ op1: s m cs cm |
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435 // +-- +---+---+----+----+ |
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436 // scalar | | * | 3 | * | 9 | |
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437 // +---+---+----+----+ |
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438 // matrix | 1 | 4 | 7 | 10 | |
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439 // +---+---+----+----+ |
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440 // complex_scalar | * | 5 | * | 11 | |
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441 // +---+---+----+----+ |
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442 // complex_matrix | 2 | 6 | 8 | 12 | |
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443 // +---+---+----+----+ |
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444 // |
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445 // * -> not needed. |
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1
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446 |
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767
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447 // -*- 1 -*- |
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1
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448 tree_constant |
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164
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449 elem_xpow (double a, const Matrix& b) |
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1
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450 { |
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451 tree_constant retval; |
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452 |
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453 int nr = b.rows (); |
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454 int nc = b.columns (); |
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455 |
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1358
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456 // For now, assume the worst. |
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457 |
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1
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458 if (a < 0.0) |
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459 { |
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460 Complex atmp (a); |
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461 ComplexMatrix result (nr, nc); |
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462 for (int j = 0; j < nc; j++) |
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463 for (int i = 0; i < nr; i++) |
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464 result.elem (i, j) = pow (atmp, b.elem (i, j)); |
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465 |
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466 retval = tree_constant (result); |
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467 } |
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468 else |
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469 { |
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470 Matrix result (nr, nc); |
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471 for (int j = 0; j < nc; j++) |
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472 for (int i = 0; i < nr; i++) |
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473 result.elem (i, j) = pow (a, b.elem (i, j)); |
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474 |
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475 retval = tree_constant (result); |
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476 } |
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477 |
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478 return retval; |
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479 } |
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480 |
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767
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481 // -*- 2 -*- |
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1
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482 tree_constant |
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164
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483 elem_xpow (double a, const ComplexMatrix& b) |
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1
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484 { |
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485 int nr = b.rows (); |
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486 int nc = b.columns (); |
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487 |
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488 ComplexMatrix result (nr, nc); |
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489 for (int j = 0; j < nc; j++) |
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490 for (int i = 0; i < nr; i++) |
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491 result.elem (i, j) = pow (a, b.elem (i, j)); |
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492 |
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493 return tree_constant (result); |
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494 } |
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495 |
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767
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496 // -*- 3 -*- |
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1
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497 tree_constant |
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164
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498 elem_xpow (const Matrix& a, double b) |
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1
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499 { |
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|
500 tree_constant retval; |
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|
501 |
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|
502 int nr = a.rows (); |
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|
503 int nc = a.columns (); |
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504 |
|
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505 if ((int) b != b && any_element_is_negative (a)) |
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|
506 { |
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|
507 ComplexMatrix result (nr, nc); |
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508 for (int j = 0; j < nc; j++) |
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|
509 for (int i = 0; i < nr; i++) |
|
|
510 { |
|
|
511 Complex atmp (a.elem (i, j)); |
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|
512 result.elem (i, j) = pow (atmp, b); |
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|
513 } |
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|
514 |
|
|
515 retval = tree_constant (result); |
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|
516 } |
|
|
517 else |
|
|
518 { |
|
|
519 Matrix result (nr, nc); |
|
|
520 for (int j = 0; j < nc; j++) |
|
|
521 for (int i = 0; i < nr; i++) |
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522 result.elem (i, j) = pow (a.elem (i, j), b); |
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|
523 |
|
|
524 retval = tree_constant (result); |
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|
525 } |
|
|
526 |
|
|
527 return retval; |
|
|
528 } |
|
|
529 |
|
767
|
530 // -*- 4 -*- |
|
1
|
531 tree_constant |
|
164
|
532 elem_xpow (const Matrix& a, const Matrix& b) |
|
1
|
533 { |
|
|
534 int nr = a.rows (); |
|
|
535 int nc = a.columns (); |
|
|
536 |
|
|
537 assert (nr == b.rows () && nc == b.columns ()); |
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|
538 |
|
|
539 int convert_to_complex = 0; |
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|
540 for (int j = 0; j < nc; j++) |
|
1321
|
541 for (int i = 0; i < nr; i++) |
|
1
|
542 { |
|
|
543 double atmp = a.elem (i, j); |
|
|
544 double btmp = b.elem (i, j); |
|
|
545 if (atmp < 0.0 && (int) btmp != btmp) |
|
|
546 { |
|
|
547 convert_to_complex = 1; |
|
|
548 goto done; |
|
|
549 } |
|
|
550 } |
|
|
551 |
|
|
552 done: |
|
|
553 |
|
|
554 if (convert_to_complex) |
|
|
555 { |
|
|
556 ComplexMatrix complex_result (nr, nc); |
|
|
557 |
|
1321
|
558 for (int j = 0; j < nc; j++) |
|
|
559 for (int i = 0; i < nr; i++) |
|
1
|
560 { |
|
|
561 Complex atmp (a.elem (i, j)); |
|
|
562 Complex btmp (b.elem (i, j)); |
|
|
563 complex_result.elem (i, j) = pow (atmp, btmp); |
|
|
564 } |
|
|
565 return tree_constant (complex_result); |
|
|
566 } |
|
|
567 else |
|
|
568 { |
|
|
569 Matrix result (nr, nc); |
|
|
570 |
|
1321
|
571 for (int j = 0; j < nc; j++) |
|
|
572 for (int i = 0; i < nr; i++) |
|
1
|
573 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
574 |
|
|
575 return tree_constant (result); |
|
|
576 } |
|
|
577 } |
|
|
578 |
|
767
|
579 // -*- 5 -*- |
|
1
|
580 tree_constant |
|
164
|
581 elem_xpow (const Matrix& a, const Complex& b) |
|
1
|
582 { |
|
|
583 int nr = a.rows (); |
|
|
584 int nc = a.columns (); |
|
|
585 |
|
|
586 ComplexMatrix result (nr, nc); |
|
|
587 for (int j = 0; j < nc; j++) |
|
|
588 for (int i = 0; i < nr; i++) |
|
|
589 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
590 |
|
|
591 return tree_constant (result); |
|
|
592 } |
|
|
593 |
|
767
|
594 // -*- 6 -*- |
|
1
|
595 tree_constant |
|
164
|
596 elem_xpow (const Matrix& a, const ComplexMatrix& b) |
|
1
|
597 { |
|
|
598 int nr = a.rows (); |
|
|
599 int nc = a.columns (); |
|
|
600 |
|
|
601 assert (nr == b.rows () && nc == b.columns ()); |
|
|
602 |
|
|
603 ComplexMatrix result (nr, nc); |
|
|
604 for (int j = 0; j < nc; j++) |
|
|
605 for (int i = 0; i < nr; i++) |
|
|
606 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
607 |
|
|
608 return tree_constant (result); |
|
|
609 } |
|
|
610 |
|
767
|
611 // -*- 7 -*- |
|
1
|
612 tree_constant |
|
164
|
613 elem_xpow (const Complex& a, const Matrix& b) |
|
1
|
614 { |
|
|
615 int nr = b.rows (); |
|
|
616 int nc = b.columns (); |
|
|
617 |
|
|
618 ComplexMatrix result (nr, nc); |
|
|
619 for (int j = 0; j < nc; j++) |
|
|
620 for (int i = 0; i < nr; i++) |
|
|
621 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
622 |
|
|
623 return tree_constant (result); |
|
|
624 } |
|
|
625 |
|
767
|
626 // -*- 8 -*- |
|
1
|
627 tree_constant |
|
164
|
628 elem_xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
629 { |
|
|
630 int nr = b.rows (); |
|
|
631 int nc = b.columns (); |
|
|
632 |
|
|
633 ComplexMatrix result (nr, nc); |
|
|
634 for (int j = 0; j < nc; j++) |
|
|
635 for (int i = 0; i < nr; i++) |
|
|
636 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
637 |
|
|
638 return tree_constant (result); |
|
|
639 } |
|
|
640 |
|
767
|
641 // -*- 9 -*- |
|
1
|
642 tree_constant |
|
164
|
643 elem_xpow (const ComplexMatrix& a, double b) |
|
1
|
644 { |
|
|
645 int nr = a.rows (); |
|
|
646 int nc = a.columns (); |
|
|
647 |
|
|
648 ComplexMatrix result (nr, nc); |
|
|
649 for (int j = 0; j < nc; j++) |
|
|
650 for (int i = 0; i < nr; i++) |
|
|
651 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
652 |
|
|
653 return tree_constant (result); |
|
|
654 } |
|
|
655 |
|
767
|
656 // -*- 10 -*- |
|
1
|
657 tree_constant |
|
164
|
658 elem_xpow (const ComplexMatrix& a, const Matrix& b) |
|
1
|
659 { |
|
|
660 int nr = a.rows (); |
|
|
661 int nc = a.columns (); |
|
|
662 |
|
|
663 assert (nr == b.rows () && nc == b.columns ()); |
|
|
664 |
|
|
665 ComplexMatrix result (nr, nc); |
|
|
666 for (int j = 0; j < nc; j++) |
|
|
667 for (int i = 0; i < nr; i++) |
|
|
668 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
669 |
|
|
670 return tree_constant (result); |
|
|
671 } |
|
|
672 |
|
767
|
673 // -*- 11 -*- |
|
1
|
674 tree_constant |
|
164
|
675 elem_xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
676 { |
|
|
677 int nr = a.rows (); |
|
|
678 int nc = a.columns (); |
|
|
679 |
|
|
680 ComplexMatrix result (nr, nc); |
|
|
681 for (int j = 0; j < nc; j++) |
|
|
682 for (int i = 0; i < nr; i++) |
|
|
683 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
684 |
|
|
685 return tree_constant (result); |
|
|
686 } |
|
|
687 |
|
767
|
688 // -*- 12 -*- |
|
1
|
689 tree_constant |
|
164
|
690 elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b) |
|
1
|
691 { |
|
|
692 int nr = a.rows (); |
|
|
693 int nc = a.columns (); |
|
|
694 |
|
|
695 ComplexMatrix result (nr, nc); |
|
|
696 |
|
|
697 for (int j = 0; j < nc; j++) |
|
|
698 for (int i = 0; i < nr; i++) |
|
|
699 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
700 |
|
|
701 return tree_constant (result); |
|
|
702 } |
|
|
703 |
|
|
704 /* |
|
|
705 ;;; Local Variables: *** |
|
|
706 ;;; mode: C++ *** |
|
|
707 ;;; page-delimiter: "^/\\*" *** |
|
|
708 ;;; End: *** |
|
|
709 */ |
