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1 // xpow.cc -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 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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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include <cassert> |
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29 #include <climits> |
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30 |
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164
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31 #include <Complex.h> |
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32 |
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1352
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33 #include "CColVector.h" |
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453
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34 #include "CDiagMatrix.h" |
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35 #include "CMatrix.h" |
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453
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36 #include "EIG.h" |
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37 #include "dDiagMatrix.h" |
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38 #include "dMatrix.h" |
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39 |
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40 #include "error.h" |
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164
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41 #include "tree-const.h" |
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1567
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42 #include "utils.h" |
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43 #include "xpow.h" |
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44 |
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45 // This function also appears in tree-const.cc. Maybe it should be a |
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46 // member function of the Matrix class. |
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47 |
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48 static int |
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49 any_element_is_negative (const Matrix& a) |
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50 { |
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51 int nr = a.rows (); |
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52 int nc = a.columns (); |
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53 for (int j = 0; j < nc; j++) |
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54 for (int i = 0; i < nr; i++) |
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55 if (a.elem (i, j) < 0.0) |
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56 return 1; |
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57 return 0; |
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58 } |
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59 |
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60 static inline int |
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61 xisint (double x) |
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62 { |
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63 return (D_NINT (x) == x |
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64 && ((x >= 0 && x < INT_MAX) |
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65 || (x <= 0 && x > INT_MIN))); |
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66 } |
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67 |
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767
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68 // Safer pow functions. |
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69 // |
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70 // op2 \ op1: s m cs cm |
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71 // +-- +---+---+----+----+ |
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72 // scalar | | 1 | 5 | 7 | 11 | |
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73 // +---+---+----+----+ |
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74 // matrix | 2 | E | 8 | E | |
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75 // +---+---+----+----+ |
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76 // complex_scalar | 3 | 6 | 9 | 12 | |
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77 // +---+---+----+----+ |
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78 // complex_matrix | 4 | E | 10 | E | |
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79 // +---+---+----+----+ |
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80 // |
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81 // E -> error, trapped in arith-ops.cc. |
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82 |
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767
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83 // -*- 1 -*- |
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84 tree_constant |
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85 xpow (double a, double b) |
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86 { |
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87 if (a < 0.0 && (int) b != b) |
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88 { |
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89 Complex atmp (a); |
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90 return pow (atmp, b); |
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91 } |
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92 else |
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93 return pow (a, b); |
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94 } |
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95 |
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767
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96 // -*- 2 -*- |
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1
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97 tree_constant |
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164
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98 xpow (double a, const Matrix& b) |
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99 { |
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100 tree_constant retval; |
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101 |
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102 int nr = b.rows (); |
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103 int nc = b.columns (); |
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104 |
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105 if (nr == 0 || nc == 0 || nr != nc) |
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106 error ("for x^A, A must be square"); |
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107 else |
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108 { |
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109 EIG b_eig (b); |
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110 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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111 ComplexMatrix Q (b_eig.eigenvectors ()); |
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112 |
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113 for (int i = 0; i < nr; i++) |
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114 { |
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115 Complex elt = lambda.elem (i); |
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116 if (imag (elt) == 0.0) |
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117 lambda.elem (i) = pow (a, real (elt)); |
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118 else |
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119 lambda.elem (i) = pow (a, elt); |
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120 } |
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121 ComplexDiagMatrix D (lambda); |
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122 |
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123 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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124 } |
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125 |
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126 return retval; |
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127 } |
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128 |
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767
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129 // -*- 3 -*- |
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130 tree_constant |
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164
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131 xpow (double a, const Complex& b) |
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132 { |
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133 Complex result; |
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134 Complex atmp (a); |
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135 result = pow (atmp, b); |
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136 return result; |
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137 } |
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138 |
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767
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139 // -*- 4 -*- |
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140 tree_constant |
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164
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141 xpow (double a, const ComplexMatrix& b) |
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142 { |
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143 tree_constant retval; |
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144 |
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145 int nr = b.rows (); |
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146 int nc = b.columns (); |
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147 |
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148 if (nr == 0 || nc == 0 || nr != nc) |
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149 { |
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150 error ("for x^A, A must be square"); |
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151 } |
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152 else |
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153 { |
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154 EIG b_eig (b); |
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155 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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156 ComplexMatrix Q (b_eig.eigenvectors ()); |
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157 |
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158 for (int i = 0; i < nr; i++) |
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159 { |
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160 Complex elt = lambda.elem (i); |
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161 if (imag (elt) == 0.0) |
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162 lambda.elem (i) = pow (a, real (elt)); |
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163 else |
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164 lambda.elem (i) = pow (a, elt); |
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165 } |
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166 ComplexDiagMatrix D (lambda); |
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167 |
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168 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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169 } |
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170 |
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171 return retval; |
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172 } |
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173 |
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767
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174 // -*- 5 -*- |
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175 tree_constant |
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164
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176 xpow (const Matrix& a, double b) |
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177 { |
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178 tree_constant retval; |
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179 |
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180 int nr = a.rows (); |
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181 int nc = a.columns (); |
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182 |
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183 if (nr == 0 || nc == 0 || nr != nc) |
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184 { |
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185 error ("for A^b, A must be square"); |
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186 } |
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187 else |
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1
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188 { |
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189 if ((int) b == b) |
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190 { |
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191 int btmp = (int) b; |
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192 if (btmp == 0) |
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193 { |
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194 retval = DiagMatrix (nr, nr, 1.0); |
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195 } |
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196 else |
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197 { |
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198 // Too much copying? |
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199 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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200 // large... |
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201 |
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202 Matrix atmp; |
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203 if (btmp < 0) |
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204 { |
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205 btmp = -btmp; |
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206 atmp = a.inverse (); |
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207 } |
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208 else |
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209 atmp = a; |
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210 |
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211 Matrix result (atmp); |
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212 for (int i = 1; i < btmp; i++) |
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213 result = result * atmp; |
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214 |
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215 retval = result; |
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216 } |
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217 } |
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218 else |
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219 { |
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220 EIG a_eig (a); |
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221 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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222 ComplexMatrix Q (a_eig.eigenvectors ()); |
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223 |
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224 for (int i = 0; i < nr; i++) |
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225 lambda.elem (i) = pow (lambda.elem (i), b); |
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226 |
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227 ComplexDiagMatrix D (lambda); |
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228 |
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229 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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230 } |
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231 } |
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232 |
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233 return retval; |
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234 } |
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235 |
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236 // -*- 6 -*- |
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237 tree_constant |
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238 xpow (const Matrix& a, const Complex& b) |
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239 { |
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240 tree_constant retval; |
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241 |
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242 int nr = a.rows (); |
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243 int nc = a.columns (); |
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244 |
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245 if (nr == 0 || nc == 0 || nr != nc) |
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246 { |
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247 error ("for A^b, A must be square"); |
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248 } |
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249 else |
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250 { |
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251 EIG a_eig (a); |
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252 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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253 ComplexMatrix Q (a_eig.eigenvectors ()); |
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254 |
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255 for (int i = 0; i < nr; i++) |
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256 lambda.elem (i) = pow (lambda.elem (i), b); |
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257 |
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258 ComplexDiagMatrix D (lambda); |
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259 |
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260 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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261 } |
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262 |
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263 return retval; |
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264 } |
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265 |
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767
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266 // -*- 7 -*- |
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267 tree_constant |
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268 xpow (const Complex& a, double b) |
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269 { |
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270 Complex result; |
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271 |
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272 if (xisint (b)) |
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273 result = pow (a, (int) b); |
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274 else |
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275 result = pow (a, b); |
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276 |
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277 return result; |
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278 } |
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279 |
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767
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280 // -*- 8 -*- |
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281 tree_constant |
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282 xpow (const Complex& a, const Matrix& b) |
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283 { |
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284 tree_constant retval; |
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285 |
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286 int nr = b.rows (); |
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287 int nc = b.columns (); |
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288 |
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289 if (nr == 0 || nc == 0 || nr != nc) |
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290 { |
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291 error ("for x^A, A must be square"); |
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292 } |
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293 else |
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294 { |
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295 EIG b_eig (b); |
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296 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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297 ComplexMatrix Q (b_eig.eigenvectors ()); |
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298 |
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299 for (int i = 0; i < nr; i++) |
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300 { |
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301 Complex elt = lambda.elem (i); |
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302 if (imag (elt) == 0.0) |
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303 lambda.elem (i) = pow (a, real (elt)); |
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304 else |
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305 lambda.elem (i) = pow (a, elt); |
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306 } |
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307 ComplexDiagMatrix D (lambda); |
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308 |
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309 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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310 } |
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311 |
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312 return retval; |
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313 } |
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314 |
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767
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315 // -*- 9 -*- |
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1
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316 tree_constant |
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164
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317 xpow (const Complex& a, const Complex& b) |
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1
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318 { |
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319 Complex result; |
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320 result = pow (a, b); |
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321 return result; |
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322 } |
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323 |
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767
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324 // -*- 10 -*- |
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1
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325 tree_constant |
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326 xpow (const Complex& a, const ComplexMatrix& b) |
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327 { |
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328 tree_constant retval; |
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329 |
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330 int nr = b.rows (); |
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331 int nc = b.columns (); |
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332 |
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333 if (nr == 0 || nc == 0 || nr != nc) |
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334 { |
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335 error ("for x^A, A must be square"); |
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336 } |
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1
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337 else |
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338 { |
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339 EIG b_eig (b); |
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340 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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341 ComplexMatrix Q (b_eig.eigenvectors ()); |
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342 |
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343 for (int i = 0; i < nr; i++) |
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344 { |
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345 Complex elt = lambda.elem (i); |
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346 if (imag (elt) == 0.0) |
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347 lambda.elem (i) = pow (a, real (elt)); |
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348 else |
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349 lambda.elem (i) = pow (a, elt); |
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350 } |
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351 ComplexDiagMatrix D (lambda); |
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352 |
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353 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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354 } |
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355 |
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356 return retval; |
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357 } |
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358 |
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767
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359 // -*- 11 -*- |
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1
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360 tree_constant |
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164
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361 xpow (const ComplexMatrix& a, double b) |
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1
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362 { |
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363 tree_constant retval; |
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364 |
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365 int nr = a.rows (); |
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366 int nc = a.columns (); |
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367 |
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368 if (nr == 0 || nc == 0 || nr != nc) |
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369 { |
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370 error ("for A^b, A must be square"); |
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371 } |
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1567
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372 else |
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1
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373 { |
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374 if ((int) b == b) |
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1
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375 { |
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376 int btmp = (int) b; |
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377 if (btmp == 0) |
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378 { |
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379 retval = DiagMatrix (nr, nr, 1.0); |
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380 } |
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381 else |
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382 { |
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383 // Too much copying? |
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384 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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385 // large... |
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386 |
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387 ComplexMatrix atmp; |
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388 if (btmp < 0) |
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389 { |
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390 btmp = -btmp; |
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391 atmp = a.inverse (); |
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392 } |
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393 else |
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394 atmp = a; |
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395 |
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396 ComplexMatrix result (atmp); |
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397 for (int i = 1; i < btmp; i++) |
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398 result = result * atmp; |
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399 |
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400 retval = result; |
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401 } |
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1
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402 } |
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403 else |
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404 { |
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405 EIG a_eig (a); |
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406 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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407 ComplexMatrix Q (a_eig.eigenvectors ()); |
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408 |
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409 for (int i = 0; i < nr; i++) |
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410 lambda.elem (i) = pow (lambda.elem (i), b); |
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411 |
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412 ComplexDiagMatrix D (lambda); |
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413 |
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414 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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415 } |
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416 } |
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417 |
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1567
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418 return retval; |
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419 } |
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1
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420 |
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1567
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421 // -*- 12 -*- |
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422 tree_constant |
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423 xpow (const ComplexMatrix& a, const Complex& b) |
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424 { |
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425 tree_constant retval; |
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1
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426 |
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1567
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427 int nr = a.rows (); |
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428 int nc = a.columns (); |
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429 |
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430 if (nr == 0 || nc == 0 || nr != nc) |
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431 { |
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432 error ("for A^b, A must be square"); |
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1
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433 } |
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434 else |
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435 { |
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436 EIG a_eig (a); |
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437 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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438 ComplexMatrix Q (a_eig.eigenvectors ()); |
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439 |
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440 for (int i = 0; i < nr; i++) |
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441 lambda.elem (i) = pow (lambda.elem (i), b); |
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442 |
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443 ComplexDiagMatrix D (lambda); |
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444 |
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445 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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446 } |
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447 |
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448 return retval; |
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449 } |
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450 |
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767
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451 // Safer pow functions that work elementwise for matrices. |
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452 // |
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453 // op2 \ op1: s m cs cm |
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454 // +-- +---+---+----+----+ |
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455 // scalar | | * | 3 | * | 9 | |
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456 // +---+---+----+----+ |
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457 // matrix | 1 | 4 | 7 | 10 | |
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458 // +---+---+----+----+ |
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459 // complex_scalar | * | 5 | * | 11 | |
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460 // +---+---+----+----+ |
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461 // complex_matrix | 2 | 6 | 8 | 12 | |
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462 // +---+---+----+----+ |
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463 // |
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464 // * -> not needed. |
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1
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465 |
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767
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466 // -*- 1 -*- |
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1
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467 tree_constant |
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164
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468 elem_xpow (double a, const Matrix& b) |
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1
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469 { |
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470 tree_constant retval; |
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471 |
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472 int nr = b.rows (); |
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473 int nc = b.columns (); |
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474 |
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1358
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475 // For now, assume the worst. |
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476 |
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1
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477 if (a < 0.0) |
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478 { |
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479 Complex atmp (a); |
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480 ComplexMatrix result (nr, nc); |
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481 for (int j = 0; j < nc; j++) |
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482 for (int i = 0; i < nr; i++) |
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483 result.elem (i, j) = pow (atmp, b.elem (i, j)); |
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484 |
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1567
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485 retval = result; |
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1
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486 } |
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487 else |
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488 { |
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489 Matrix result (nr, nc); |
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490 for (int j = 0; j < nc; j++) |
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491 for (int i = 0; i < nr; i++) |
|
|
492 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
493 |
|
1567
|
494 retval = result; |
|
1
|
495 } |
|
|
496 |
|
|
497 return retval; |
|
|
498 } |
|
|
499 |
|
767
|
500 // -*- 2 -*- |
|
1
|
501 tree_constant |
|
164
|
502 elem_xpow (double a, const ComplexMatrix& b) |
|
1
|
503 { |
|
|
504 int nr = b.rows (); |
|
|
505 int nc = b.columns (); |
|
|
506 |
|
|
507 ComplexMatrix result (nr, nc); |
|
|
508 for (int j = 0; j < nc; j++) |
|
|
509 for (int i = 0; i < nr; i++) |
|
|
510 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
511 |
|
1567
|
512 return result; |
|
1
|
513 } |
|
|
514 |
|
767
|
515 // -*- 3 -*- |
|
1
|
516 tree_constant |
|
164
|
517 elem_xpow (const Matrix& a, double b) |
|
1
|
518 { |
|
|
519 tree_constant retval; |
|
|
520 |
|
|
521 int nr = a.rows (); |
|
|
522 int nc = a.columns (); |
|
|
523 |
|
|
524 if ((int) b != b && any_element_is_negative (a)) |
|
|
525 { |
|
|
526 ComplexMatrix result (nr, nc); |
|
|
527 for (int j = 0; j < nc; j++) |
|
|
528 for (int i = 0; i < nr; i++) |
|
|
529 { |
|
|
530 Complex atmp (a.elem (i, j)); |
|
|
531 result.elem (i, j) = pow (atmp, b); |
|
|
532 } |
|
|
533 |
|
1567
|
534 retval = result; |
|
1
|
535 } |
|
|
536 else |
|
|
537 { |
|
|
538 Matrix result (nr, nc); |
|
|
539 for (int j = 0; j < nc; j++) |
|
|
540 for (int i = 0; i < nr; i++) |
|
|
541 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
542 |
|
1567
|
543 retval = result; |
|
1
|
544 } |
|
|
545 |
|
|
546 return retval; |
|
|
547 } |
|
|
548 |
|
767
|
549 // -*- 4 -*- |
|
1
|
550 tree_constant |
|
164
|
551 elem_xpow (const Matrix& a, const Matrix& b) |
|
1
|
552 { |
|
1567
|
553 tree_constant retval; |
|
|
554 |
|
1
|
555 int nr = a.rows (); |
|
|
556 int nc = a.columns (); |
|
|
557 |
|
|
558 assert (nr == b.rows () && nc == b.columns ()); |
|
|
559 |
|
|
560 int convert_to_complex = 0; |
|
|
561 for (int j = 0; j < nc; j++) |
|
1321
|
562 for (int i = 0; i < nr; i++) |
|
1
|
563 { |
|
|
564 double atmp = a.elem (i, j); |
|
|
565 double btmp = b.elem (i, j); |
|
|
566 if (atmp < 0.0 && (int) btmp != btmp) |
|
|
567 { |
|
|
568 convert_to_complex = 1; |
|
|
569 goto done; |
|
|
570 } |
|
|
571 } |
|
|
572 |
|
|
573 done: |
|
|
574 |
|
|
575 if (convert_to_complex) |
|
|
576 { |
|
|
577 ComplexMatrix complex_result (nr, nc); |
|
|
578 |
|
1321
|
579 for (int j = 0; j < nc; j++) |
|
|
580 for (int i = 0; i < nr; i++) |
|
1
|
581 { |
|
|
582 Complex atmp (a.elem (i, j)); |
|
|
583 Complex btmp (b.elem (i, j)); |
|
|
584 complex_result.elem (i, j) = pow (atmp, btmp); |
|
|
585 } |
|
1567
|
586 |
|
|
587 retval = complex_result; |
|
1
|
588 } |
|
|
589 else |
|
|
590 { |
|
|
591 Matrix result (nr, nc); |
|
|
592 |
|
1321
|
593 for (int j = 0; j < nc; j++) |
|
|
594 for (int i = 0; i < nr; i++) |
|
1
|
595 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
596 |
|
1567
|
597 retval = result; |
|
1
|
598 } |
|
1567
|
599 |
|
|
600 return retval; |
|
1
|
601 } |
|
|
602 |
|
767
|
603 // -*- 5 -*- |
|
1
|
604 tree_constant |
|
164
|
605 elem_xpow (const Matrix& a, const Complex& b) |
|
1
|
606 { |
|
|
607 int nr = a.rows (); |
|
|
608 int nc = a.columns (); |
|
|
609 |
|
|
610 ComplexMatrix result (nr, nc); |
|
|
611 for (int j = 0; j < nc; j++) |
|
|
612 for (int i = 0; i < nr; i++) |
|
|
613 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
614 |
|
1567
|
615 return result; |
|
1
|
616 } |
|
|
617 |
|
767
|
618 // -*- 6 -*- |
|
1
|
619 tree_constant |
|
164
|
620 elem_xpow (const Matrix& a, const ComplexMatrix& b) |
|
1
|
621 { |
|
|
622 int nr = a.rows (); |
|
|
623 int nc = a.columns (); |
|
|
624 |
|
|
625 assert (nr == b.rows () && nc == b.columns ()); |
|
|
626 |
|
|
627 ComplexMatrix result (nr, nc); |
|
|
628 for (int j = 0; j < nc; j++) |
|
|
629 for (int i = 0; i < nr; i++) |
|
|
630 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
631 |
|
1567
|
632 return result; |
|
1
|
633 } |
|
|
634 |
|
767
|
635 // -*- 7 -*- |
|
1
|
636 tree_constant |
|
164
|
637 elem_xpow (const Complex& a, const Matrix& b) |
|
1
|
638 { |
|
|
639 int nr = b.rows (); |
|
|
640 int nc = b.columns (); |
|
|
641 |
|
|
642 ComplexMatrix result (nr, nc); |
|
|
643 for (int j = 0; j < nc; j++) |
|
|
644 for (int i = 0; i < nr; i++) |
|
1567
|
645 { |
|
|
646 double btmp = b.elem (i, j); |
|
|
647 if (xisint (btmp)) |
|
|
648 result.elem (i, j) = pow (a, (int) btmp); |
|
|
649 else |
|
|
650 result.elem (i, j) = pow (a, btmp); |
|
|
651 } |
|
1
|
652 |
|
1567
|
653 return result; |
|
1
|
654 } |
|
|
655 |
|
767
|
656 // -*- 8 -*- |
|
1
|
657 tree_constant |
|
164
|
658 elem_xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
659 { |
|
|
660 int nr = b.rows (); |
|
|
661 int nc = b.columns (); |
|
|
662 |
|
|
663 ComplexMatrix result (nr, nc); |
|
|
664 for (int j = 0; j < nc; j++) |
|
|
665 for (int i = 0; i < nr; i++) |
|
|
666 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
667 |
|
1567
|
668 return result; |
|
1
|
669 } |
|
|
670 |
|
767
|
671 // -*- 9 -*- |
|
1
|
672 tree_constant |
|
164
|
673 elem_xpow (const ComplexMatrix& a, double b) |
|
1
|
674 { |
|
|
675 int nr = a.rows (); |
|
|
676 int nc = a.columns (); |
|
|
677 |
|
|
678 ComplexMatrix result (nr, nc); |
|
|
679 |
|
1567
|
680 if (xisint (b)) |
|
|
681 { |
|
|
682 for (int j = 0; j < nc; j++) |
|
|
683 for (int i = 0; i < nr; i++) |
|
|
684 result.elem (i, j) = pow (a.elem (i, j), (int) b); |
|
|
685 } |
|
|
686 else |
|
|
687 { |
|
|
688 for (int j = 0; j < nc; j++) |
|
|
689 for (int i = 0; i < nr; i++) |
|
|
690 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
691 } |
|
|
692 |
|
|
693 return result; |
|
1
|
694 } |
|
|
695 |
|
767
|
696 // -*- 10 -*- |
|
1
|
697 tree_constant |
|
164
|
698 elem_xpow (const ComplexMatrix& a, const Matrix& b) |
|
1
|
699 { |
|
|
700 int nr = a.rows (); |
|
|
701 int nc = a.columns (); |
|
|
702 |
|
|
703 assert (nr == b.rows () && nc == b.columns ()); |
|
|
704 |
|
|
705 ComplexMatrix result (nr, nc); |
|
|
706 for (int j = 0; j < nc; j++) |
|
|
707 for (int i = 0; i < nr; i++) |
|
1567
|
708 { |
|
|
709 double btmp = b.elem (i, j); |
|
|
710 if (xisint (btmp)) |
|
|
711 result.elem (i, j) = pow (a.elem (i, j), (int) btmp); |
|
|
712 else |
|
|
713 result.elem (i, j) = pow (a.elem (i, j), btmp); |
|
|
714 } |
|
1
|
715 |
|
1567
|
716 return result; |
|
1
|
717 } |
|
|
718 |
|
767
|
719 // -*- 11 -*- |
|
1
|
720 tree_constant |
|
164
|
721 elem_xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
722 { |
|
|
723 int nr = a.rows (); |
|
|
724 int nc = a.columns (); |
|
|
725 |
|
|
726 ComplexMatrix result (nr, nc); |
|
|
727 for (int j = 0; j < nc; j++) |
|
|
728 for (int i = 0; i < nr; i++) |
|
|
729 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
730 |
|
1567
|
731 return result; |
|
1
|
732 } |
|
|
733 |
|
767
|
734 // -*- 12 -*- |
|
1
|
735 tree_constant |
|
164
|
736 elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b) |
|
1
|
737 { |
|
|
738 int nr = a.rows (); |
|
|
739 int nc = a.columns (); |
|
|
740 |
|
|
741 ComplexMatrix result (nr, nc); |
|
|
742 |
|
|
743 for (int j = 0; j < nc; j++) |
|
|
744 for (int i = 0; i < nr; i++) |
|
|
745 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
746 |
|
1567
|
747 return result; |
|
1
|
748 } |
|
|
749 |
|
|
750 /* |
|
|
751 ;;; Local Variables: *** |
|
|
752 ;;; mode: C++ *** |
|
|
753 ;;; page-delimiter: "^/\\*" *** |
|
|
754 ;;; End: *** |
|
|
755 */ |
