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1 /* |
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2 |
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2847
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3 Copyright (C) 1996, 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, write to the Free |
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1315
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19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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240
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23 #ifdef HAVE_CONFIG_H |
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1192
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24 #include <config.h> |
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1
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25 #endif |
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26 |
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1343
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27 #include <cassert> |
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1580
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28 #include <climits> |
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1343
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29 |
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4669
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30 #include "Array-util.h" |
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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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1352
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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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1352
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35 #include "dDiagMatrix.h" |
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36 #include "dMatrix.h" |
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3585
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37 #include "mx-cm-cdm.h" |
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1651
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38 #include "oct-cmplx.h" |
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4153
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39 #include "quit.h" |
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1352
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40 |
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41 #include "error.h" |
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4055
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42 #include "oct-obj.h" |
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1567
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43 #include "utils.h" |
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1352
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44 #include "xpow.h" |
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1
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45 |
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1567
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46 static inline int |
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47 xisint (double x) |
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48 { |
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49 return (D_NINT (x) == x |
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50 && ((x >= 0 && x < INT_MAX) |
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51 || (x <= 0 && x > INT_MIN))); |
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52 } |
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53 |
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767
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54 // Safer pow functions. |
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55 // |
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56 // op2 \ op1: s m cs cm |
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57 // +-- +---+---+----+----+ |
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58 // scalar | | 1 | 5 | 7 | 11 | |
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59 // +---+---+----+----+ |
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2365
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60 // matrix | 2 | * | 8 | * | |
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767
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61 // +---+---+----+----+ |
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62 // complex_scalar | 3 | 6 | 9 | 12 | |
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63 // +---+---+----+----+ |
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2365
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64 // complex_matrix | 4 | * | 10 | * | |
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767
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65 // +---+---+----+----+ |
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1
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66 |
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767
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67 // -*- 1 -*- |
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2086
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68 octave_value |
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1
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69 xpow (double a, double b) |
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70 { |
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2800
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71 if (a < 0.0 && static_cast<int> (b) != b) |
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1
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72 { |
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5260
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73 Complex atmp (a); |
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4682
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74 |
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5260
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75 return std::pow (atmp, b); |
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1
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76 } |
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77 else |
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5260
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78 return std::pow (a, b); |
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1
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79 } |
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80 |
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767
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81 // -*- 2 -*- |
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2086
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82 octave_value |
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164
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83 xpow (double a, const Matrix& b) |
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1
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84 { |
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2086
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85 octave_value retval; |
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1
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86 |
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87 int nr = b.rows (); |
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2365
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88 int nc = b.cols (); |
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1
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89 |
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90 if (nr == 0 || nc == 0 || nr != nc) |
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91 error ("for x^A, A must be square"); |
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92 else |
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93 { |
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94 EIG b_eig (b); |
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95 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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96 ComplexMatrix Q (b_eig.eigenvectors ()); |
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97 |
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98 for (int i = 0; i < nr; i++) |
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99 { |
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2305
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100 Complex elt = lambda (i); |
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5260
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101 if (std::imag (elt) == 0.0) |
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102 lambda (i) = std::pow (a, std::real (elt)); |
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1
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103 else |
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5260
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104 lambda (i) = std::pow (a, elt); |
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1
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105 } |
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106 ComplexDiagMatrix D (lambda); |
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107 |
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1567
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108 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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109 } |
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110 |
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111 return retval; |
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112 } |
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113 |
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767
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114 // -*- 3 -*- |
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2086
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115 octave_value |
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164
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116 xpow (double a, const Complex& b) |
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1
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117 { |
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118 Complex result; |
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119 Complex atmp (a); |
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5260
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120 result = std::pow (atmp, b); |
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121 return result; |
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1
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122 } |
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123 |
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767
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124 // -*- 4 -*- |
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2086
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125 octave_value |
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164
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126 xpow (double a, const ComplexMatrix& b) |
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1
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127 { |
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2086
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128 octave_value retval; |
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1
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129 |
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130 int nr = b.rows (); |
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2365
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131 int nc = b.cols (); |
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1
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132 |
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133 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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134 error ("for x^A, A must be square"); |
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1
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135 else |
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136 { |
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137 EIG b_eig (b); |
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138 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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139 ComplexMatrix Q (b_eig.eigenvectors ()); |
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140 |
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141 for (int i = 0; i < nr; i++) |
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142 { |
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2305
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143 Complex elt = lambda (i); |
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5260
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144 if (std::imag (elt) == 0.0) |
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145 lambda (i) = std::pow (a, std::real (elt)); |
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1
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146 else |
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5260
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147 lambda (i) = std::pow (a, elt); |
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1
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148 } |
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149 ComplexDiagMatrix D (lambda); |
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150 |
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1567
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151 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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152 } |
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153 |
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154 return retval; |
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155 } |
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156 |
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767
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157 // -*- 5 -*- |
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2086
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158 octave_value |
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164
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159 xpow (const Matrix& a, double b) |
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1
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160 { |
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2086
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161 octave_value retval; |
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1
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162 |
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163 int nr = a.rows (); |
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2365
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164 int nc = a.cols (); |
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1
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165 |
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166 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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167 error ("for A^b, A must be square"); |
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1567
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168 else |
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1
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169 { |
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2800
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170 if (static_cast<int> (b) == b) |
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1
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171 { |
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2804
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172 int btmp = static_cast<int> (b); |
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1567
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173 if (btmp == 0) |
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174 { |
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175 retval = DiagMatrix (nr, nr, 1.0); |
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176 } |
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177 else |
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178 { |
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179 // Too much copying? |
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180 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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181 // large... |
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182 |
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183 Matrix atmp; |
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184 if (btmp < 0) |
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185 { |
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186 btmp = -btmp; |
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187 |
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188 int info; |
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189 double rcond = 0.0; |
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190 |
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1656
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191 atmp = a.inverse (info, rcond, 1); |
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1655
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192 |
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193 if (info == -1) |
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194 warning ("inverse: matrix singular to machine\ |
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195 precision, rcond = %g", rcond); |
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1567
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196 } |
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197 else |
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198 atmp = a; |
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199 |
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200 Matrix result (atmp); |
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3178
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201 |
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202 btmp--; |
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203 |
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204 while (btmp > 0) |
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205 { |
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206 if (btmp & 1) |
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207 result = result * atmp; |
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208 |
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209 btmp >>= 1; |
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210 |
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211 if (btmp > 0) |
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212 atmp = atmp * atmp; |
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213 } |
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214 |
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215 retval = result; |
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216 } |
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1
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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 (i) = std::pow (lambda (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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1567
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233 return retval; |
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234 } |
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1
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235 |
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1567
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236 // -*- 6 -*- |
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2086
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237 octave_value |
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1567
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238 xpow (const Matrix& a, const Complex& b) |
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239 { |
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2086
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240 octave_value retval; |
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1
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241 |
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1567
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242 int nr = a.rows (); |
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2365
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243 int nc = a.cols (); |
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1567
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244 |
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245 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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246 error ("for A^b, A must be square"); |
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1
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247 else |
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248 { |
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249 EIG a_eig (a); |
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250 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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251 ComplexMatrix Q (a_eig.eigenvectors ()); |
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252 |
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253 for (int i = 0; i < nr; i++) |
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5260
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254 lambda (i) = std::pow (lambda (i), b); |
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1
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255 |
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256 ComplexDiagMatrix D (lambda); |
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257 |
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1567
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258 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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259 } |
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260 |
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261 return retval; |
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262 } |
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263 |
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767
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264 // -*- 7 -*- |
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2086
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265 octave_value |
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164
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266 xpow (const Complex& a, double b) |
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1
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267 { |
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268 Complex result; |
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1567
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269 |
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270 if (xisint (b)) |
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5260
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271 result = std::pow (a, static_cast<int> (b)); |
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1567
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272 else |
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5260
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273 result = std::pow (a, b); |
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1567
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274 |
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275 return result; |
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1
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276 } |
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277 |
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767
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278 // -*- 8 -*- |
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2086
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279 octave_value |
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164
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280 xpow (const Complex& a, const Matrix& b) |
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1
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281 { |
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2086
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282 octave_value retval; |
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1
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283 |
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284 int nr = b.rows (); |
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2365
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285 int nc = b.cols (); |
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1
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286 |
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287 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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288 error ("for x^A, A must be square"); |
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1
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289 else |
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290 { |
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291 EIG b_eig (b); |
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292 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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293 ComplexMatrix Q (b_eig.eigenvectors ()); |
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294 |
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295 for (int i = 0; i < nr; i++) |
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296 { |
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2305
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297 Complex elt = lambda (i); |
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5260
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298 if (std::imag (elt) == 0.0) |
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299 lambda (i) = std::pow (a, std::real (elt)); |
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1
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300 else |
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5260
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301 lambda (i) = std::pow (a, elt); |
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1
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302 } |
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303 ComplexDiagMatrix D (lambda); |
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304 |
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1567
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305 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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306 } |
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307 |
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308 return retval; |
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309 } |
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310 |
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767
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311 // -*- 9 -*- |
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2086
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312 octave_value |
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164
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313 xpow (const Complex& a, const Complex& b) |
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1
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314 { |
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315 Complex result; |
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5260
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316 result = std::pow (a, b); |
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1567
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317 return result; |
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1
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318 } |
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319 |
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767
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320 // -*- 10 -*- |
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2086
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321 octave_value |
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164
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322 xpow (const Complex& a, const ComplexMatrix& b) |
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1
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323 { |
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2086
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324 octave_value retval; |
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1
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325 |
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326 int nr = b.rows (); |
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2365
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327 int nc = b.cols (); |
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1
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328 |
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329 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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330 error ("for x^A, A must be square"); |
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1
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331 else |
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332 { |
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333 EIG b_eig (b); |
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334 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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335 ComplexMatrix Q (b_eig.eigenvectors ()); |
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336 |
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337 for (int i = 0; i < nr; i++) |
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338 { |
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2305
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339 Complex elt = lambda (i); |
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5260
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340 if (std::imag (elt) == 0.0) |
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341 lambda (i) = std::pow (a, std::real (elt)); |
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1
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342 else |
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5260
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343 lambda (i) = std::pow (a, elt); |
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1
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344 } |
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345 ComplexDiagMatrix D (lambda); |
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346 |
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1567
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347 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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348 } |
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349 |
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350 return retval; |
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351 } |
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352 |
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767
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353 // -*- 11 -*- |
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2086
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354 octave_value |
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164
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355 xpow (const ComplexMatrix& a, double b) |
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1
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356 { |
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2086
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357 octave_value retval; |
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1
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358 |
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359 int nr = a.rows (); |
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2365
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360 int nc = a.cols (); |
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1
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361 |
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362 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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363 error ("for A^b, A must be square"); |
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1567
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364 else |
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1
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365 { |
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2800
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366 if (static_cast<int> (b) == b) |
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1
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367 { |
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2804
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368 int btmp = static_cast<int> (b); |
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1567
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369 if (btmp == 0) |
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370 { |
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371 retval = DiagMatrix (nr, nr, 1.0); |
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372 } |
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373 else |
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374 { |
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375 // Too much copying? |
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376 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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377 // large... |
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378 |
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379 ComplexMatrix atmp; |
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380 if (btmp < 0) |
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381 { |
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382 btmp = -btmp; |
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1655
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383 |
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384 int info; |
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385 double rcond = 0.0; |
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386 |
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1656
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387 atmp = a.inverse (info, rcond, 1); |
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1655
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388 |
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389 if (info == -1) |
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390 warning ("inverse: matrix singular to machine\ |
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391 precision, rcond = %g", rcond); |
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1567
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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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3178
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397 |
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398 btmp--; |
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399 |
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400 while (btmp > 0) |
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401 { |
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402 if (btmp & 1) |
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403 result = result * atmp; |
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404 |
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405 btmp >>= 1; |
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406 |
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407 if (btmp > 0) |
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408 atmp = atmp * atmp; |
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409 } |
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1567
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410 |
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411 retval = result; |
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412 } |
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1
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413 } |
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414 else |
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415 { |
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1567
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416 EIG a_eig (a); |
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417 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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418 ComplexMatrix Q (a_eig.eigenvectors ()); |
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419 |
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420 for (int i = 0; i < nr; i++) |
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5260
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421 lambda (i) = std::pow (lambda (i), b); |
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1567
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422 |
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423 ComplexDiagMatrix D (lambda); |
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424 |
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425 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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426 } |
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427 } |
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1358
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428 |
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1567
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429 return retval; |
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430 } |
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1
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431 |
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1567
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432 // -*- 12 -*- |
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2086
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433 octave_value |
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1567
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434 xpow (const ComplexMatrix& a, const Complex& b) |
|
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435 { |
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2086
|
436 octave_value retval; |
|
1
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437 |
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1567
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438 int nr = a.rows (); |
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2365
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439 int nc = a.cols (); |
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1567
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440 |
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441 if (nr == 0 || nc == 0 || nr != nc) |
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2365
|
442 error ("for A^b, A must be square"); |
|
1
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443 else |
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444 { |
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445 EIG a_eig (a); |
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446 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
|
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447 ComplexMatrix Q (a_eig.eigenvectors ()); |
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448 |
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449 for (int i = 0; i < nr; i++) |
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5260
|
450 lambda (i) = std::pow (lambda (i), b); |
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1
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451 |
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452 ComplexDiagMatrix D (lambda); |
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453 |
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1567
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454 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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455 } |
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456 |
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457 return retval; |
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458 } |
|
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459 |
|
767
|
460 // Safer pow functions that work elementwise for matrices. |
|
|
461 // |
|
|
462 // op2 \ op1: s m cs cm |
|
|
463 // +-- +---+---+----+----+ |
|
|
464 // scalar | | * | 3 | * | 9 | |
|
|
465 // +---+---+----+----+ |
|
|
466 // matrix | 1 | 4 | 7 | 10 | |
|
|
467 // +---+---+----+----+ |
|
|
468 // complex_scalar | * | 5 | * | 11 | |
|
|
469 // +---+---+----+----+ |
|
|
470 // complex_matrix | 2 | 6 | 8 | 12 | |
|
|
471 // +---+---+----+----+ |
|
|
472 // |
|
|
473 // * -> not needed. |
|
1
|
474 |
|
3162
|
475 // XXX FIXME XXX -- these functions need to be fixed so that things |
|
|
476 // like |
|
|
477 // |
|
|
478 // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b |
|
|
479 // |
|
|
480 // and |
|
|
481 // |
|
|
482 // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end |
|
|
483 // |
|
|
484 // produce identical results. Also, it would be nice if -1^0.5 |
|
|
485 // produced a pure imaginary result instead of a complex number with a |
|
|
486 // small real part. But perhaps that's really a problem with the math |
|
|
487 // library... |
|
|
488 |
|
767
|
489 // -*- 1 -*- |
|
2086
|
490 octave_value |
|
164
|
491 elem_xpow (double a, const Matrix& b) |
|
1
|
492 { |
|
2086
|
493 octave_value retval; |
|
1
|
494 |
|
|
495 int nr = b.rows (); |
|
2365
|
496 int nc = b.cols (); |
|
1
|
497 |
|
3162
|
498 double d1, d2; |
|
1358
|
499 |
|
3162
|
500 if (a < 0.0 && ! b.all_integers (d1, d2)) |
|
1
|
501 { |
|
|
502 Complex atmp (a); |
|
|
503 ComplexMatrix result (nr, nc); |
|
|
504 for (int j = 0; j < nc; j++) |
|
|
505 for (int i = 0; i < nr; i++) |
|
4153
|
506 { |
|
|
507 OCTAVE_QUIT; |
|
5260
|
508 result (i, j) = std::pow (atmp, b (i, j)); |
|
4153
|
509 } |
|
1
|
510 |
|
1567
|
511 retval = result; |
|
1
|
512 } |
|
|
513 else |
|
|
514 { |
|
|
515 Matrix result (nr, nc); |
|
|
516 for (int j = 0; j < nc; j++) |
|
|
517 for (int i = 0; i < nr; i++) |
|
4153
|
518 { |
|
|
519 OCTAVE_QUIT; |
|
5260
|
520 result (i, j) = std::pow (a, b (i, j)); |
|
4153
|
521 } |
|
1
|
522 |
|
1567
|
523 retval = result; |
|
1
|
524 } |
|
|
525 |
|
|
526 return retval; |
|
|
527 } |
|
|
528 |
|
767
|
529 // -*- 2 -*- |
|
2086
|
530 octave_value |
|
164
|
531 elem_xpow (double a, const ComplexMatrix& b) |
|
1
|
532 { |
|
|
533 int nr = b.rows (); |
|
2365
|
534 int nc = b.cols (); |
|
1
|
535 |
|
|
536 ComplexMatrix result (nr, nc); |
|
3125
|
537 Complex atmp (a); |
|
1
|
538 for (int j = 0; j < nc; j++) |
|
|
539 for (int i = 0; i < nr; i++) |
|
4153
|
540 { |
|
|
541 OCTAVE_QUIT; |
|
5260
|
542 result (i, j) = std::pow (atmp, b (i, j)); |
|
4153
|
543 } |
|
1
|
544 |
|
1567
|
545 return result; |
|
1
|
546 } |
|
|
547 |
|
767
|
548 // -*- 3 -*- |
|
2086
|
549 octave_value |
|
164
|
550 elem_xpow (const Matrix& a, double b) |
|
1
|
551 { |
|
2086
|
552 octave_value retval; |
|
1
|
553 |
|
|
554 int nr = a.rows (); |
|
2365
|
555 int nc = a.cols (); |
|
1
|
556 |
|
2800
|
557 if (static_cast<int> (b) != b && a.any_element_is_negative ()) |
|
1
|
558 { |
|
|
559 ComplexMatrix result (nr, nc); |
|
|
560 for (int j = 0; j < nc; j++) |
|
|
561 for (int i = 0; i < nr; i++) |
|
|
562 { |
|
4153
|
563 OCTAVE_QUIT; |
|
4790
|
564 |
|
5260
|
565 Complex atmp (a (i, j)); |
|
4790
|
566 |
|
5260
|
567 result (i, j) = std::pow (atmp, b); |
|
1
|
568 } |
|
|
569 |
|
1567
|
570 retval = result; |
|
1
|
571 } |
|
|
572 else |
|
|
573 { |
|
|
574 Matrix result (nr, nc); |
|
|
575 for (int j = 0; j < nc; j++) |
|
|
576 for (int i = 0; i < nr; i++) |
|
4153
|
577 { |
|
|
578 OCTAVE_QUIT; |
|
5260
|
579 result (i, j) = std::pow (a (i, j), b); |
|
4153
|
580 } |
|
1
|
581 |
|
1567
|
582 retval = result; |
|
1
|
583 } |
|
|
584 |
|
|
585 return retval; |
|
|
586 } |
|
|
587 |
|
767
|
588 // -*- 4 -*- |
|
2086
|
589 octave_value |
|
164
|
590 elem_xpow (const Matrix& a, const Matrix& b) |
|
1
|
591 { |
|
2086
|
592 octave_value retval; |
|
1567
|
593 |
|
1
|
594 int nr = a.rows (); |
|
2365
|
595 int nc = a.cols (); |
|
|
596 |
|
|
597 int b_nr = b.rows (); |
|
|
598 int b_nc = b.cols (); |
|
1
|
599 |
|
2365
|
600 if (nr != b_nr || nc != b_nc) |
|
|
601 { |
|
|
602 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
603 return octave_value (); |
|
|
604 } |
|
1
|
605 |
|
|
606 int convert_to_complex = 0; |
|
|
607 for (int j = 0; j < nc; j++) |
|
1321
|
608 for (int i = 0; i < nr; i++) |
|
1
|
609 { |
|
4153
|
610 OCTAVE_QUIT; |
|
2305
|
611 double atmp = a (i, j); |
|
|
612 double btmp = b (i, j); |
|
2800
|
613 if (atmp < 0.0 && static_cast<int> (btmp) != btmp) |
|
1
|
614 { |
|
|
615 convert_to_complex = 1; |
|
|
616 goto done; |
|
|
617 } |
|
|
618 } |
|
|
619 |
|
2365
|
620 done: |
|
1
|
621 |
|
|
622 if (convert_to_complex) |
|
|
623 { |
|
|
624 ComplexMatrix complex_result (nr, nc); |
|
|
625 |
|
1321
|
626 for (int j = 0; j < nc; j++) |
|
|
627 for (int i = 0; i < nr; i++) |
|
1
|
628 { |
|
4153
|
629 OCTAVE_QUIT; |
|
2305
|
630 Complex atmp (a (i, j)); |
|
|
631 Complex btmp (b (i, j)); |
|
5260
|
632 complex_result (i, j) = std::pow (atmp, btmp); |
|
1
|
633 } |
|
1567
|
634 |
|
|
635 retval = complex_result; |
|
1
|
636 } |
|
|
637 else |
|
|
638 { |
|
|
639 Matrix result (nr, nc); |
|
|
640 |
|
1321
|
641 for (int j = 0; j < nc; j++) |
|
|
642 for (int i = 0; i < nr; i++) |
|
4153
|
643 { |
|
|
644 OCTAVE_QUIT; |
|
5260
|
645 result (i, j) = std::pow (a (i, j), b (i, j)); |
|
4153
|
646 } |
|
1
|
647 |
|
1567
|
648 retval = result; |
|
1
|
649 } |
|
1567
|
650 |
|
|
651 return retval; |
|
1
|
652 } |
|
|
653 |
|
767
|
654 // -*- 5 -*- |
|
2086
|
655 octave_value |
|
164
|
656 elem_xpow (const Matrix& a, const Complex& b) |
|
1
|
657 { |
|
|
658 int nr = a.rows (); |
|
2365
|
659 int nc = a.cols (); |
|
1
|
660 |
|
|
661 ComplexMatrix result (nr, nc); |
|
|
662 for (int j = 0; j < nc; j++) |
|
|
663 for (int i = 0; i < nr; i++) |
|
4153
|
664 { |
|
|
665 OCTAVE_QUIT; |
|
5260
|
666 result (i, j) = std::pow (Complex (a (i, j)), b); |
|
4153
|
667 } |
|
1
|
668 |
|
1567
|
669 return result; |
|
1
|
670 } |
|
|
671 |
|
767
|
672 // -*- 6 -*- |
|
2086
|
673 octave_value |
|
164
|
674 elem_xpow (const Matrix& a, const ComplexMatrix& b) |
|
1
|
675 { |
|
|
676 int nr = a.rows (); |
|
2365
|
677 int nc = a.cols (); |
|
|
678 |
|
|
679 int b_nr = b.rows (); |
|
|
680 int b_nc = b.cols (); |
|
1
|
681 |
|
2365
|
682 if (nr != b_nr || nc != b_nc) |
|
|
683 { |
|
|
684 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
685 return octave_value (); |
|
|
686 } |
|
1
|
687 |
|
|
688 ComplexMatrix result (nr, nc); |
|
|
689 for (int j = 0; j < nc; j++) |
|
|
690 for (int i = 0; i < nr; i++) |
|
4153
|
691 { |
|
|
692 OCTAVE_QUIT; |
|
5260
|
693 result (i, j) = std::pow (Complex (a (i, j)), b (i, j)); |
|
4153
|
694 } |
|
1
|
695 |
|
1567
|
696 return result; |
|
1
|
697 } |
|
|
698 |
|
767
|
699 // -*- 7 -*- |
|
2086
|
700 octave_value |
|
164
|
701 elem_xpow (const Complex& a, const Matrix& b) |
|
1
|
702 { |
|
|
703 int nr = b.rows (); |
|
2365
|
704 int nc = b.cols (); |
|
1
|
705 |
|
|
706 ComplexMatrix result (nr, nc); |
|
|
707 for (int j = 0; j < nc; j++) |
|
|
708 for (int i = 0; i < nr; i++) |
|
1567
|
709 { |
|
4153
|
710 OCTAVE_QUIT; |
|
2305
|
711 double btmp = b (i, j); |
|
1567
|
712 if (xisint (btmp)) |
|
5260
|
713 result (i, j) = std::pow (a, static_cast<int> (btmp)); |
|
1567
|
714 else |
|
5260
|
715 result (i, j) = std::pow (a, btmp); |
|
1567
|
716 } |
|
1
|
717 |
|
1567
|
718 return result; |
|
1
|
719 } |
|
|
720 |
|
767
|
721 // -*- 8 -*- |
|
2086
|
722 octave_value |
|
164
|
723 elem_xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
724 { |
|
|
725 int nr = b.rows (); |
|
2365
|
726 int nc = b.cols (); |
|
1
|
727 |
|
|
728 ComplexMatrix result (nr, nc); |
|
|
729 for (int j = 0; j < nc; j++) |
|
|
730 for (int i = 0; i < nr; i++) |
|
4153
|
731 { |
|
|
732 OCTAVE_QUIT; |
|
5260
|
733 result (i, j) = std::pow (a, b (i, j)); |
|
4153
|
734 } |
|
1
|
735 |
|
1567
|
736 return result; |
|
1
|
737 } |
|
|
738 |
|
767
|
739 // -*- 9 -*- |
|
2086
|
740 octave_value |
|
164
|
741 elem_xpow (const ComplexMatrix& a, double b) |
|
1
|
742 { |
|
|
743 int nr = a.rows (); |
|
2365
|
744 int nc = a.cols (); |
|
1
|
745 |
|
|
746 ComplexMatrix result (nr, nc); |
|
|
747 |
|
1567
|
748 if (xisint (b)) |
|
|
749 { |
|
|
750 for (int j = 0; j < nc; j++) |
|
|
751 for (int i = 0; i < nr; i++) |
|
4153
|
752 { |
|
|
753 OCTAVE_QUIT; |
|
5260
|
754 result (i, j) = std::pow (a (i, j), static_cast<int> (b)); |
|
4153
|
755 } |
|
1567
|
756 } |
|
|
757 else |
|
|
758 { |
|
|
759 for (int j = 0; j < nc; j++) |
|
|
760 for (int i = 0; i < nr; i++) |
|
4153
|
761 { |
|
|
762 OCTAVE_QUIT; |
|
5260
|
763 result (i, j) = std::pow (a (i, j), b); |
|
4153
|
764 } |
|
1567
|
765 } |
|
|
766 |
|
|
767 return result; |
|
1
|
768 } |
|
|
769 |
|
767
|
770 // -*- 10 -*- |
|
2086
|
771 octave_value |
|
164
|
772 elem_xpow (const ComplexMatrix& a, const Matrix& b) |
|
1
|
773 { |
|
|
774 int nr = a.rows (); |
|
2365
|
775 int nc = a.cols (); |
|
|
776 |
|
|
777 int b_nr = b.rows (); |
|
|
778 int b_nc = b.cols (); |
|
1
|
779 |
|
2365
|
780 if (nr != b_nr || nc != b_nc) |
|
|
781 { |
|
|
782 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
783 return octave_value (); |
|
|
784 } |
|
1
|
785 |
|
|
786 ComplexMatrix result (nr, nc); |
|
|
787 for (int j = 0; j < nc; j++) |
|
|
788 for (int i = 0; i < nr; i++) |
|
1567
|
789 { |
|
4153
|
790 OCTAVE_QUIT; |
|
2305
|
791 double btmp = b (i, j); |
|
1567
|
792 if (xisint (btmp)) |
|
5260
|
793 result (i, j) = std::pow (a (i, j), static_cast<int> (btmp)); |
|
1567
|
794 else |
|
5260
|
795 result (i, j) = std::pow (a (i, j), btmp); |
|
1567
|
796 } |
|
1
|
797 |
|
1567
|
798 return result; |
|
1
|
799 } |
|
|
800 |
|
767
|
801 // -*- 11 -*- |
|
2086
|
802 octave_value |
|
164
|
803 elem_xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
804 { |
|
|
805 int nr = a.rows (); |
|
2365
|
806 int nc = a.cols (); |
|
1
|
807 |
|
|
808 ComplexMatrix result (nr, nc); |
|
|
809 for (int j = 0; j < nc; j++) |
|
|
810 for (int i = 0; i < nr; i++) |
|
4153
|
811 { |
|
|
812 OCTAVE_QUIT; |
|
5260
|
813 result (i, j) = std::pow (a (i, j), b); |
|
4153
|
814 } |
|
1
|
815 |
|
1567
|
816 return result; |
|
1
|
817 } |
|
|
818 |
|
767
|
819 // -*- 12 -*- |
|
2086
|
820 octave_value |
|
164
|
821 elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b) |
|
1
|
822 { |
|
|
823 int nr = a.rows (); |
|
2365
|
824 int nc = a.cols (); |
|
|
825 |
|
|
826 int b_nr = b.rows (); |
|
|
827 int b_nc = b.cols (); |
|
|
828 |
|
|
829 if (nr != b_nr || nc != b_nc) |
|
|
830 { |
|
|
831 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
832 return octave_value (); |
|
|
833 } |
|
1
|
834 |
|
|
835 ComplexMatrix result (nr, nc); |
|
|
836 for (int j = 0; j < nc; j++) |
|
|
837 for (int i = 0; i < nr; i++) |
|
4153
|
838 { |
|
|
839 OCTAVE_QUIT; |
|
5260
|
840 result (i, j) = std::pow (a (i, j), b (i, j)); |
|
4153
|
841 } |
|
1
|
842 |
|
1567
|
843 return result; |
|
1
|
844 } |
|
|
845 |
|
4543
|
846 // Safer pow functions that work elementwise for N-d arrays. |
|
|
847 // |
|
|
848 // op2 \ op1: s nd cs cnd |
|
|
849 // +-- +---+---+----+----+ |
|
|
850 // scalar | | * | 3 | * | 9 | |
|
|
851 // +---+---+----+----+ |
|
|
852 // N_d | 1 | 4 | 7 | 10 | |
|
|
853 // +---+---+----+----+ |
|
|
854 // complex_scalar | * | 5 | * | 11 | |
|
|
855 // +---+---+----+----+ |
|
|
856 // complex_N_d | 2 | 6 | 8 | 12 | |
|
|
857 // +---+---+----+----+ |
|
|
858 // |
|
|
859 // * -> not needed. |
|
|
860 |
|
|
861 // XXX FIXME XXX -- these functions need to be fixed so that things |
|
|
862 // like |
|
|
863 // |
|
|
864 // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b |
|
|
865 // |
|
|
866 // and |
|
|
867 // |
|
|
868 // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end |
|
|
869 // |
|
|
870 // produce identical results. Also, it would be nice if -1^0.5 |
|
|
871 // produced a pure imaginary result instead of a complex number with a |
|
|
872 // small real part. But perhaps that's really a problem with the math |
|
|
873 // library... |
|
|
874 |
|
|
875 // -*- 1 -*- |
|
|
876 octave_value |
|
|
877 elem_xpow (double a, const NDArray& b) |
|
|
878 { |
|
|
879 octave_value retval; |
|
|
880 |
|
|
881 double d1, d2; |
|
|
882 |
|
|
883 if (a < 0.0 && ! b.all_integers (d1, d2)) |
|
|
884 { |
|
|
885 Complex atmp (a); |
|
|
886 ComplexNDArray result (b.dims ()); |
|
|
887 for (int i = 0; i < b.length (); i++) |
|
|
888 { |
|
|
889 OCTAVE_QUIT; |
|
5260
|
890 result(i) = std::pow (atmp, b(i)); |
|
4543
|
891 } |
|
|
892 |
|
|
893 retval = result; |
|
|
894 } |
|
|
895 else |
|
|
896 { |
|
|
897 NDArray result (b.dims ()); |
|
|
898 for (int i = 0; i < b.length (); i++) |
|
|
899 { |
|
|
900 OCTAVE_QUIT; |
|
5260
|
901 result (i) = std::pow (a, b(i)); |
|
4543
|
902 } |
|
|
903 |
|
|
904 retval = result; |
|
|
905 } |
|
|
906 |
|
|
907 return retval; |
|
|
908 } |
|
|
909 |
|
|
910 // -*- 2 -*- |
|
|
911 octave_value |
|
|
912 elem_xpow (double a, const ComplexNDArray& b) |
|
|
913 { |
|
|
914 ComplexNDArray result (b.dims ()); |
|
|
915 Complex atmp (a); |
|
|
916 for (int i = 0; i < b.length (); i++) |
|
|
917 { |
|
|
918 OCTAVE_QUIT; |
|
5260
|
919 result(i) = std::pow (atmp, b(i)); |
|
4543
|
920 } |
|
|
921 |
|
|
922 return result; |
|
|
923 } |
|
|
924 |
|
|
925 // -*- 3 -*- |
|
|
926 octave_value |
|
|
927 elem_xpow (const NDArray& a, double b) |
|
|
928 { |
|
|
929 octave_value retval; |
|
|
930 |
|
|
931 if (static_cast<int> (b) != b && a.any_element_is_negative ()) |
|
|
932 { |
|
|
933 ComplexNDArray result (a.dims ()); |
|
|
934 |
|
|
935 for (int i = 0; i < a.length (); i++) |
|
|
936 { |
|
|
937 OCTAVE_QUIT; |
|
4790
|
938 |
|
5260
|
939 Complex atmp (a (i)); |
|
4790
|
940 |
|
5260
|
941 result(i) = std::pow (atmp, b); |
|
4543
|
942 } |
|
|
943 |
|
|
944 retval = result; |
|
|
945 } |
|
|
946 else |
|
|
947 { |
|
|
948 NDArray result (a.dims ()); |
|
|
949 |
|
|
950 for (int i = 0; i < a.length (); i++) |
|
|
951 { |
|
|
952 OCTAVE_QUIT; |
|
5260
|
953 result(i) = std::pow (a(i), b); |
|
4543
|
954 } |
|
|
955 |
|
|
956 retval = result; |
|
|
957 } |
|
|
958 |
|
|
959 return retval; |
|
|
960 } |
|
|
961 |
|
|
962 // -*- 4 -*- |
|
|
963 octave_value |
|
|
964 elem_xpow (const NDArray& a, const NDArray& b) |
|
|
965 { |
|
|
966 octave_value retval; |
|
|
967 |
|
|
968 dim_vector a_dims = a.dims (); |
|
|
969 dim_vector b_dims = b.dims (); |
|
|
970 |
|
|
971 if (a_dims != b_dims) |
|
|
972 { |
|
|
973 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
974 return octave_value (); |
|
|
975 } |
|
|
976 |
|
|
977 int len = a.length (); |
|
|
978 |
|
|
979 bool convert_to_complex = false; |
|
|
980 |
|
|
981 for (int i = 0; i < len; i++) |
|
|
982 { |
|
|
983 OCTAVE_QUIT; |
|
|
984 double atmp = a(i); |
|
|
985 double btmp = b(i); |
|
|
986 if (atmp < 0.0 && static_cast<int> (btmp) != btmp) |
|
|
987 { |
|
|
988 convert_to_complex = true; |
|
|
989 goto done; |
|
|
990 } |
|
|
991 } |
|
|
992 |
|
|
993 done: |
|
|
994 |
|
|
995 if (convert_to_complex) |
|
|
996 { |
|
|
997 ComplexNDArray complex_result (a_dims); |
|
|
998 |
|
|
999 for (int i = 0; i < len; i++) |
|
|
1000 { |
|
|
1001 OCTAVE_QUIT; |
|
|
1002 Complex atmp (a(i)); |
|
|
1003 Complex btmp (b(i)); |
|
5260
|
1004 complex_result(i) = std::pow (atmp, btmp); |
|
4543
|
1005 } |
|
|
1006 |
|
|
1007 retval = complex_result; |
|
|
1008 } |
|
|
1009 else |
|
|
1010 { |
|
|
1011 NDArray result (a_dims); |
|
|
1012 |
|
|
1013 for (int i = 0; i < len; i++) |
|
|
1014 { |
|
|
1015 OCTAVE_QUIT; |
|
5260
|
1016 result(i) = std::pow (a(i), b(i)); |
|
4543
|
1017 } |
|
|
1018 |
|
|
1019 retval = result; |
|
|
1020 } |
|
|
1021 |
|
|
1022 return retval; |
|
|
1023 } |
|
|
1024 |
|
|
1025 // -*- 5 -*- |
|
|
1026 octave_value |
|
|
1027 elem_xpow (const NDArray& a, const Complex& b) |
|
|
1028 { |
|
|
1029 ComplexNDArray result (a.dims ()); |
|
|
1030 |
|
|
1031 for (int i = 0; i < a.length (); i++) |
|
|
1032 { |
|
|
1033 OCTAVE_QUIT; |
|
5260
|
1034 result(i) = std::pow (Complex (a(i)), b); |
|
4543
|
1035 } |
|
|
1036 |
|
|
1037 return result; |
|
|
1038 } |
|
|
1039 |
|
|
1040 // -*- 6 -*- |
|
|
1041 octave_value |
|
|
1042 elem_xpow (const NDArray& a, const ComplexNDArray& b) |
|
|
1043 { |
|
|
1044 dim_vector a_dims = a.dims (); |
|
|
1045 dim_vector b_dims = b.dims (); |
|
|
1046 |
|
|
1047 if (a_dims != b_dims) |
|
|
1048 { |
|
|
1049 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1050 return octave_value (); |
|
|
1051 } |
|
|
1052 |
|
|
1053 ComplexNDArray result (a_dims); |
|
|
1054 for (int i = 0; i < a.length (); i++) |
|
|
1055 { |
|
|
1056 OCTAVE_QUIT; |
|
5260
|
1057 result(i) = std::pow (Complex (a(i)), b(i)); |
|
4543
|
1058 } |
|
|
1059 |
|
|
1060 return result; |
|
|
1061 } |
|
|
1062 |
|
|
1063 // -*- 7 -*- |
|
|
1064 octave_value |
|
|
1065 elem_xpow (const Complex& a, const NDArray& b) |
|
|
1066 { |
|
|
1067 ComplexNDArray result (b.dims ()); |
|
|
1068 for (int i = 0; i < b.length (); i++) |
|
|
1069 { |
|
|
1070 OCTAVE_QUIT; |
|
|
1071 double btmp = b(i); |
|
|
1072 if (xisint (btmp)) |
|
5260
|
1073 result(i) = std::pow (a, static_cast<int> (btmp)); |
|
4543
|
1074 else |
|
5260
|
1075 result(i) = std::pow (a, btmp); |
|
4543
|
1076 } |
|
|
1077 |
|
|
1078 return result; |
|
|
1079 } |
|
|
1080 |
|
|
1081 // -*- 8 -*- |
|
|
1082 octave_value |
|
|
1083 elem_xpow (const Complex& a, const ComplexNDArray& b) |
|
|
1084 { |
|
|
1085 ComplexNDArray result (b.dims ()); |
|
|
1086 for (int i = 0; i < b.length (); i++) |
|
|
1087 { |
|
|
1088 OCTAVE_QUIT; |
|
5260
|
1089 result(i) = std::pow (a, b(i)); |
|
4543
|
1090 } |
|
|
1091 |
|
|
1092 return result; |
|
|
1093 } |
|
|
1094 |
|
|
1095 // -*- 9 -*- |
|
|
1096 octave_value |
|
|
1097 elem_xpow (const ComplexNDArray& a, double b) |
|
|
1098 { |
|
|
1099 ComplexNDArray result (a.dims ()); |
|
|
1100 |
|
|
1101 if (xisint (b)) |
|
|
1102 { |
|
|
1103 for (int i = 0; i < a.length (); i++) |
|
|
1104 { |
|
|
1105 OCTAVE_QUIT; |
|
5260
|
1106 result(i) = std::pow (a(i), static_cast<int> (b)); |
|
4543
|
1107 } |
|
|
1108 } |
|
|
1109 else |
|
|
1110 { |
|
|
1111 for (int i = 0; i < a.length (); i++) |
|
|
1112 { |
|
|
1113 OCTAVE_QUIT; |
|
5260
|
1114 result(i) = std::pow (a(i), b); |
|
4543
|
1115 } |
|
|
1116 } |
|
|
1117 |
|
|
1118 return result; |
|
|
1119 } |
|
|
1120 |
|
|
1121 // -*- 10 -*- |
|
|
1122 octave_value |
|
|
1123 elem_xpow (const ComplexNDArray& a, const NDArray& b) |
|
|
1124 { |
|
|
1125 dim_vector a_dims = a.dims (); |
|
|
1126 dim_vector b_dims = b.dims (); |
|
|
1127 |
|
|
1128 if (a_dims != b_dims) |
|
|
1129 { |
|
|
1130 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1131 return octave_value (); |
|
|
1132 } |
|
|
1133 |
|
|
1134 ComplexNDArray result (a_dims); |
|
|
1135 for (int i = 0; i < a.length (); i++) |
|
|
1136 { |
|
|
1137 OCTAVE_QUIT; |
|
|
1138 double btmp = b(i); |
|
|
1139 if (xisint (btmp)) |
|
5260
|
1140 result(i) = std::pow (a(i), static_cast<int> (btmp)); |
|
4543
|
1141 else |
|
5260
|
1142 result(i) = std::pow (a(i), btmp); |
|
4543
|
1143 } |
|
|
1144 |
|
|
1145 return result; |
|
|
1146 } |
|
|
1147 |
|
|
1148 // -*- 11 -*- |
|
|
1149 octave_value |
|
|
1150 elem_xpow (const ComplexNDArray& a, const Complex& b) |
|
|
1151 { |
|
|
1152 ComplexNDArray result (a.dims ()); |
|
|
1153 for (int i = 0; i < a.length (); i++) |
|
|
1154 { |
|
|
1155 OCTAVE_QUIT; |
|
5260
|
1156 result(i) = std::pow (a(i), b); |
|
4543
|
1157 } |
|
|
1158 |
|
|
1159 return result; |
|
|
1160 } |
|
|
1161 |
|
|
1162 // -*- 12 -*- |
|
|
1163 octave_value |
|
|
1164 elem_xpow (const ComplexNDArray& a, const ComplexNDArray& b) |
|
|
1165 { |
|
|
1166 dim_vector a_dims = a.dims (); |
|
|
1167 dim_vector b_dims = b.dims (); |
|
|
1168 |
|
|
1169 if (a_dims != b_dims) |
|
|
1170 { |
|
|
1171 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1172 return octave_value (); |
|
|
1173 } |
|
|
1174 |
|
|
1175 ComplexNDArray result (a_dims); |
|
|
1176 for (int i = 0; i < a.length (); i++) |
|
|
1177 { |
|
|
1178 OCTAVE_QUIT; |
|
5260
|
1179 result(i) = std::pow (a(i), b(i)); |
|
4543
|
1180 } |
|
|
1181 |
|
|
1182 return result; |
|
|
1183 } |
|
|
1184 |
|
1
|
1185 /* |
|
|
1186 ;;; Local Variables: *** |
|
|
1187 ;;; mode: C++ *** |
|
|
1188 ;;; End: *** |
|
|
1189 */ |
