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