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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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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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1352
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30 #include "CColVector.h" |
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453
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31 #include "CDiagMatrix.h" |
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1352
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32 #include "CMatrix.h" |
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453
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33 #include "EIG.h" |
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1352
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34 #include "dDiagMatrix.h" |
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35 #include "dMatrix.h" |
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3585
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36 #include "mx-cm-cdm.h" |
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1651
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37 #include "oct-cmplx.h" |
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4153
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38 #include "quit.h" |
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1352
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39 |
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40 #include "error.h" |
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4055
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41 #include "oct-obj.h" |
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1567
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42 #include "utils.h" |
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1352
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43 #include "xpow.h" |
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1
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44 |
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1567
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45 static inline int |
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46 xisint (double x) |
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47 { |
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48 return (D_NINT (x) == x |
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49 && ((x >= 0 && x < INT_MAX) |
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50 || (x <= 0 && x > INT_MIN))); |
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51 } |
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52 |
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767
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53 // Safer pow functions. |
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54 // |
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55 // op2 \ op1: s m cs cm |
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56 // +-- +---+---+----+----+ |
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57 // scalar | | 1 | 5 | 7 | 11 | |
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58 // +---+---+----+----+ |
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2365
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59 // matrix | 2 | * | 8 | * | |
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767
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60 // +---+---+----+----+ |
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61 // complex_scalar | 3 | 6 | 9 | 12 | |
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62 // +---+---+----+----+ |
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2365
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63 // complex_matrix | 4 | * | 10 | * | |
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767
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64 // +---+---+----+----+ |
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1
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65 |
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767
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66 // -*- 1 -*- |
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2086
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67 octave_value |
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1
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68 xpow (double a, double b) |
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69 { |
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2800
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70 if (a < 0.0 && static_cast<int> (b) != b) |
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1
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71 { |
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72 Complex atmp (a); |
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1567
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73 return pow (atmp, b); |
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1
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74 } |
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75 else |
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1567
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76 return pow (a, b); |
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1
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77 } |
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78 |
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767
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79 // -*- 2 -*- |
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2086
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80 octave_value |
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164
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81 xpow (double a, const Matrix& b) |
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1
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82 { |
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2086
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83 octave_value retval; |
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1
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84 |
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85 int nr = b.rows (); |
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2365
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86 int nc = b.cols (); |
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1
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87 |
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88 if (nr == 0 || nc == 0 || nr != nc) |
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89 error ("for x^A, A must be square"); |
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90 else |
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91 { |
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92 EIG b_eig (b); |
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93 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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94 ComplexMatrix Q (b_eig.eigenvectors ()); |
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95 |
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96 for (int i = 0; i < nr; i++) |
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97 { |
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2305
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98 Complex elt = lambda (i); |
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1
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99 if (imag (elt) == 0.0) |
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2305
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100 lambda (i) = pow (a, real (elt)); |
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1
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101 else |
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2305
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102 lambda (i) = pow (a, elt); |
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1
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103 } |
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104 ComplexDiagMatrix D (lambda); |
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105 |
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106 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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107 } |
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108 |
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109 return retval; |
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110 } |
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111 |
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767
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112 // -*- 3 -*- |
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2086
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113 octave_value |
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164
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114 xpow (double a, const Complex& b) |
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1
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115 { |
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116 Complex result; |
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117 Complex atmp (a); |
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118 result = pow (atmp, b); |
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119 return result; |
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1
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120 } |
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121 |
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767
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122 // -*- 4 -*- |
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2086
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123 octave_value |
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164
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124 xpow (double a, const ComplexMatrix& b) |
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1
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125 { |
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2086
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126 octave_value retval; |
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1
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127 |
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128 int nr = b.rows (); |
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2365
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129 int nc = b.cols (); |
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1
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130 |
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131 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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132 error ("for x^A, A must be square"); |
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1
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133 else |
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134 { |
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135 EIG b_eig (b); |
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136 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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137 ComplexMatrix Q (b_eig.eigenvectors ()); |
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138 |
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139 for (int i = 0; i < nr; i++) |
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140 { |
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2305
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141 Complex elt = lambda (i); |
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1
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142 if (imag (elt) == 0.0) |
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2305
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143 lambda (i) = pow (a, real (elt)); |
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1
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144 else |
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2305
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145 lambda (i) = pow (a, elt); |
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1
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146 } |
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147 ComplexDiagMatrix D (lambda); |
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148 |
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149 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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150 } |
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151 |
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152 return retval; |
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153 } |
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154 |
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767
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155 // -*- 5 -*- |
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2086
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156 octave_value |
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164
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157 xpow (const Matrix& a, double b) |
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1
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158 { |
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2086
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159 octave_value retval; |
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1
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160 |
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161 int nr = a.rows (); |
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2365
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162 int nc = a.cols (); |
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1
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163 |
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164 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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165 error ("for A^b, A must be square"); |
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1567
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166 else |
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1
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167 { |
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2800
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168 if (static_cast<int> (b) == b) |
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1
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169 { |
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2804
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170 int btmp = static_cast<int> (b); |
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171 if (btmp == 0) |
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172 { |
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173 retval = DiagMatrix (nr, nr, 1.0); |
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174 } |
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175 else |
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176 { |
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177 // Too much copying? |
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178 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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179 // large... |
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180 |
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181 Matrix atmp; |
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182 if (btmp < 0) |
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183 { |
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184 btmp = -btmp; |
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185 |
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186 int info; |
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187 double rcond = 0.0; |
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188 |
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189 atmp = a.inverse (info, rcond, 1); |
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190 |
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191 if (info == -1) |
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192 warning ("inverse: matrix singular to machine\ |
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193 precision, rcond = %g", rcond); |
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1567
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194 } |
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195 else |
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196 atmp = a; |
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197 |
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198 Matrix result (atmp); |
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199 |
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200 btmp--; |
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201 |
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202 while (btmp > 0) |
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203 { |
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204 if (btmp & 1) |
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205 result = result * atmp; |
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206 |
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207 btmp >>= 1; |
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208 |
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209 if (btmp > 0) |
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210 atmp = atmp * atmp; |
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211 } |
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212 |
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213 retval = result; |
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214 } |
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1
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215 } |
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216 else |
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217 { |
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218 EIG a_eig (a); |
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219 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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220 ComplexMatrix Q (a_eig.eigenvectors ()); |
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221 |
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222 for (int i = 0; i < nr; i++) |
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223 lambda (i) = pow (lambda (i), b); |
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224 |
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225 ComplexDiagMatrix D (lambda); |
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226 |
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227 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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228 } |
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229 } |
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230 |
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231 return retval; |
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232 } |
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1
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233 |
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1567
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234 // -*- 6 -*- |
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2086
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235 octave_value |
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1567
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236 xpow (const Matrix& a, const Complex& b) |
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237 { |
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2086
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238 octave_value retval; |
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1
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239 |
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1567
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240 int nr = a.rows (); |
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2365
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241 int nc = a.cols (); |
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1567
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242 |
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243 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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244 error ("for A^b, A must be square"); |
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1
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245 else |
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246 { |
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247 EIG a_eig (a); |
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248 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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249 ComplexMatrix Q (a_eig.eigenvectors ()); |
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250 |
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251 for (int i = 0; i < nr; i++) |
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2305
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252 lambda (i) = pow (lambda (i), b); |
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1
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253 |
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254 ComplexDiagMatrix D (lambda); |
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255 |
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256 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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257 } |
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258 |
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259 return retval; |
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260 } |
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261 |
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767
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262 // -*- 7 -*- |
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2086
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263 octave_value |
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164
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264 xpow (const Complex& a, double b) |
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1
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265 { |
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266 Complex result; |
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1567
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267 |
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268 if (xisint (b)) |
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2800
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269 result = pow (a, static_cast<int> (b)); |
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270 else |
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271 result = pow (a, b); |
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272 |
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273 return result; |
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1
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274 } |
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275 |
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767
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276 // -*- 8 -*- |
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2086
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277 octave_value |
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164
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278 xpow (const Complex& a, const Matrix& b) |
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1
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279 { |
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2086
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280 octave_value retval; |
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1
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281 |
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282 int nr = b.rows (); |
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2365
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283 int nc = b.cols (); |
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1
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284 |
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285 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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286 error ("for x^A, A must be square"); |
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1
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287 else |
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288 { |
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289 EIG b_eig (b); |
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290 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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291 ComplexMatrix Q (b_eig.eigenvectors ()); |
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292 |
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293 for (int i = 0; i < nr; i++) |
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294 { |
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2305
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295 Complex elt = lambda (i); |
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1
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296 if (imag (elt) == 0.0) |
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2305
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297 lambda (i) = pow (a, real (elt)); |
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1
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298 else |
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2305
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299 lambda (i) = pow (a, elt); |
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1
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300 } |
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301 ComplexDiagMatrix D (lambda); |
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302 |
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1567
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303 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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304 } |
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305 |
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306 return retval; |
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307 } |
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308 |
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767
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309 // -*- 9 -*- |
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2086
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310 octave_value |
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164
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311 xpow (const Complex& a, const Complex& b) |
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1
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312 { |
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313 Complex result; |
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314 result = pow (a, b); |
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1567
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315 return result; |
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1
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316 } |
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317 |
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767
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318 // -*- 10 -*- |
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2086
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319 octave_value |
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164
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320 xpow (const Complex& a, const ComplexMatrix& b) |
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1
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321 { |
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2086
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322 octave_value retval; |
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1
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323 |
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324 int nr = b.rows (); |
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2365
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325 int nc = b.cols (); |
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1
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326 |
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327 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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328 error ("for x^A, A must be square"); |
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1
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329 else |
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330 { |
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331 EIG b_eig (b); |
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332 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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333 ComplexMatrix Q (b_eig.eigenvectors ()); |
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334 |
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335 for (int i = 0; i < nr; i++) |
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336 { |
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2305
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337 Complex elt = lambda (i); |
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1
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338 if (imag (elt) == 0.0) |
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2305
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339 lambda (i) = pow (a, real (elt)); |
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1
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340 else |
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2305
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341 lambda (i) = pow (a, elt); |
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1
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342 } |
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343 ComplexDiagMatrix D (lambda); |
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344 |
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1567
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345 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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346 } |
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347 |
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348 return retval; |
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349 } |
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350 |
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767
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351 // -*- 11 -*- |
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2086
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352 octave_value |
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164
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353 xpow (const ComplexMatrix& a, double b) |
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1
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354 { |
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2086
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355 octave_value retval; |
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1
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356 |
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357 int nr = a.rows (); |
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2365
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358 int nc = a.cols (); |
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1
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359 |
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360 if (nr == 0 || nc == 0 || nr != nc) |
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2365
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361 error ("for A^b, A must be square"); |
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1567
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362 else |
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1
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363 { |
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2800
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364 if (static_cast<int> (b) == b) |
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1
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365 { |
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2804
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366 int btmp = static_cast<int> (b); |
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1567
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367 if (btmp == 0) |
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368 { |
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369 retval = DiagMatrix (nr, nr, 1.0); |
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370 } |
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371 else |
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372 { |
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373 // Too much copying? |
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374 // XXX FIXME XXX -- we shouldn't do this if the exponent is |
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375 // large... |
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376 |
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377 ComplexMatrix atmp; |
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378 if (btmp < 0) |
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379 { |
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380 btmp = -btmp; |
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1655
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381 |
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382 int info; |
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383 double rcond = 0.0; |
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384 |
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1656
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385 atmp = a.inverse (info, rcond, 1); |
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1655
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386 |
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387 if (info == -1) |
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388 warning ("inverse: matrix singular to machine\ |
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389 precision, rcond = %g", rcond); |
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1567
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390 } |
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391 else |
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392 atmp = a; |
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393 |
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394 ComplexMatrix result (atmp); |
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3178
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395 |
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396 btmp--; |
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397 |
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398 while (btmp > 0) |
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399 { |
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400 if (btmp & 1) |
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401 result = result * atmp; |
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402 |
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403 btmp >>= 1; |
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404 |
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405 if (btmp > 0) |
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406 atmp = atmp * atmp; |
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407 } |
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1567
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408 |
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409 retval = result; |
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410 } |
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1
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411 } |
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412 else |
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413 { |
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1567
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414 EIG a_eig (a); |
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415 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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416 ComplexMatrix Q (a_eig.eigenvectors ()); |
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417 |
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418 for (int i = 0; i < nr; i++) |
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2305
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419 lambda (i) = pow (lambda (i), b); |
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1567
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420 |
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421 ComplexDiagMatrix D (lambda); |
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422 |
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423 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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424 } |
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425 } |
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1358
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426 |
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1567
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427 return retval; |
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428 } |
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1
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429 |
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1567
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430 // -*- 12 -*- |
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2086
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431 octave_value |
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1567
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432 xpow (const ComplexMatrix& a, const Complex& b) |
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433 { |
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2086
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434 octave_value retval; |
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1
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435 |
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1567
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436 int nr = a.rows (); |
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2365
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437 int nc = a.cols (); |
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1567
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438 |
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439 if (nr == 0 || nc == 0 || nr != nc) |
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2365
|
440 error ("for A^b, A must be square"); |
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1
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441 else |
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442 { |
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443 EIG a_eig (a); |
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444 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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445 ComplexMatrix Q (a_eig.eigenvectors ()); |
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446 |
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447 for (int i = 0; i < nr; i++) |
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2305
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448 lambda (i) = pow (lambda (i), b); |
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1
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449 |
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450 ComplexDiagMatrix D (lambda); |
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451 |
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1567
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452 retval = ComplexMatrix (Q * D * Q.inverse ()); |
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1
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453 } |
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454 |
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455 return retval; |
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456 } |
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457 |
|
767
|
458 // Safer pow functions that work elementwise for matrices. |
|
|
459 // |
|
|
460 // op2 \ op1: s m cs cm |
|
|
461 // +-- +---+---+----+----+ |
|
|
462 // scalar | | * | 3 | * | 9 | |
|
|
463 // +---+---+----+----+ |
|
|
464 // matrix | 1 | 4 | 7 | 10 | |
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465 // +---+---+----+----+ |
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|
466 // complex_scalar | * | 5 | * | 11 | |
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467 // +---+---+----+----+ |
|
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468 // complex_matrix | 2 | 6 | 8 | 12 | |
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469 // +---+---+----+----+ |
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470 // |
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471 // * -> not needed. |
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1
|
472 |
|
3162
|
473 // XXX FIXME XXX -- these functions need to be fixed so that things |
|
|
474 // like |
|
|
475 // |
|
|
476 // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b |
|
|
477 // |
|
|
478 // and |
|
|
479 // |
|
|
480 // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end |
|
|
481 // |
|
|
482 // produce identical results. Also, it would be nice if -1^0.5 |
|
|
483 // produced a pure imaginary result instead of a complex number with a |
|
|
484 // small real part. But perhaps that's really a problem with the math |
|
|
485 // library... |
|
|
486 |
|
767
|
487 // -*- 1 -*- |
|
2086
|
488 octave_value |
|
164
|
489 elem_xpow (double a, const Matrix& b) |
|
1
|
490 { |
|
2086
|
491 octave_value retval; |
|
1
|
492 |
|
|
493 int nr = b.rows (); |
|
2365
|
494 int nc = b.cols (); |
|
1
|
495 |
|
3162
|
496 double d1, d2; |
|
1358
|
497 |
|
3162
|
498 if (a < 0.0 && ! b.all_integers (d1, d2)) |
|
1
|
499 { |
|
|
500 Complex atmp (a); |
|
|
501 ComplexMatrix result (nr, nc); |
|
|
502 for (int j = 0; j < nc; j++) |
|
|
503 for (int i = 0; i < nr; i++) |
|
4153
|
504 { |
|
|
505 OCTAVE_QUIT; |
|
|
506 result (i, j) = pow (atmp, b (i, j)); |
|
|
507 } |
|
1
|
508 |
|
1567
|
509 retval = result; |
|
1
|
510 } |
|
|
511 else |
|
|
512 { |
|
|
513 Matrix result (nr, nc); |
|
|
514 for (int j = 0; j < nc; j++) |
|
|
515 for (int i = 0; i < nr; i++) |
|
4153
|
516 { |
|
|
517 OCTAVE_QUIT; |
|
|
518 result (i, j) = pow (a, b (i, j)); |
|
|
519 } |
|
1
|
520 |
|
1567
|
521 retval = result; |
|
1
|
522 } |
|
|
523 |
|
|
524 return retval; |
|
|
525 } |
|
|
526 |
|
767
|
527 // -*- 2 -*- |
|
2086
|
528 octave_value |
|
164
|
529 elem_xpow (double a, const ComplexMatrix& b) |
|
1
|
530 { |
|
|
531 int nr = b.rows (); |
|
2365
|
532 int nc = b.cols (); |
|
1
|
533 |
|
|
534 ComplexMatrix result (nr, nc); |
|
3125
|
535 Complex atmp (a); |
|
1
|
536 for (int j = 0; j < nc; j++) |
|
|
537 for (int i = 0; i < nr; i++) |
|
4153
|
538 { |
|
|
539 OCTAVE_QUIT; |
|
|
540 result (i, j) = pow (atmp, b (i, j)); |
|
|
541 } |
|
1
|
542 |
|
1567
|
543 return result; |
|
1
|
544 } |
|
|
545 |
|
767
|
546 // -*- 3 -*- |
|
2086
|
547 octave_value |
|
164
|
548 elem_xpow (const Matrix& a, double b) |
|
1
|
549 { |
|
2086
|
550 octave_value retval; |
|
1
|
551 |
|
|
552 int nr = a.rows (); |
|
2365
|
553 int nc = a.cols (); |
|
1
|
554 |
|
2800
|
555 if (static_cast<int> (b) != b && a.any_element_is_negative ()) |
|
1
|
556 { |
|
|
557 ComplexMatrix result (nr, nc); |
|
|
558 for (int j = 0; j < nc; j++) |
|
|
559 for (int i = 0; i < nr; i++) |
|
|
560 { |
|
4153
|
561 OCTAVE_QUIT; |
|
2305
|
562 Complex atmp (a (i, j)); |
|
|
563 result (i, j) = pow (atmp, b); |
|
1
|
564 } |
|
|
565 |
|
1567
|
566 retval = result; |
|
1
|
567 } |
|
|
568 else |
|
|
569 { |
|
|
570 Matrix result (nr, nc); |
|
|
571 for (int j = 0; j < nc; j++) |
|
|
572 for (int i = 0; i < nr; i++) |
|
4153
|
573 { |
|
|
574 OCTAVE_QUIT; |
|
|
575 result (i, j) = pow (a (i, j), b); |
|
|
576 } |
|
1
|
577 |
|
1567
|
578 retval = result; |
|
1
|
579 } |
|
|
580 |
|
|
581 return retval; |
|
|
582 } |
|
|
583 |
|
767
|
584 // -*- 4 -*- |
|
2086
|
585 octave_value |
|
164
|
586 elem_xpow (const Matrix& a, const Matrix& b) |
|
1
|
587 { |
|
2086
|
588 octave_value retval; |
|
1567
|
589 |
|
1
|
590 int nr = a.rows (); |
|
2365
|
591 int nc = a.cols (); |
|
|
592 |
|
|
593 int b_nr = b.rows (); |
|
|
594 int b_nc = b.cols (); |
|
1
|
595 |
|
2365
|
596 if (nr != b_nr || nc != b_nc) |
|
|
597 { |
|
|
598 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
599 return octave_value (); |
|
|
600 } |
|
1
|
601 |
|
|
602 int convert_to_complex = 0; |
|
|
603 for (int j = 0; j < nc; j++) |
|
1321
|
604 for (int i = 0; i < nr; i++) |
|
1
|
605 { |
|
4153
|
606 OCTAVE_QUIT; |
|
2305
|
607 double atmp = a (i, j); |
|
|
608 double btmp = b (i, j); |
|
2800
|
609 if (atmp < 0.0 && static_cast<int> (btmp) != btmp) |
|
1
|
610 { |
|
|
611 convert_to_complex = 1; |
|
|
612 goto done; |
|
|
613 } |
|
|
614 } |
|
|
615 |
|
2365
|
616 done: |
|
1
|
617 |
|
|
618 if (convert_to_complex) |
|
|
619 { |
|
|
620 ComplexMatrix complex_result (nr, nc); |
|
|
621 |
|
1321
|
622 for (int j = 0; j < nc; j++) |
|
|
623 for (int i = 0; i < nr; i++) |
|
1
|
624 { |
|
4153
|
625 OCTAVE_QUIT; |
|
2305
|
626 Complex atmp (a (i, j)); |
|
|
627 Complex btmp (b (i, j)); |
|
|
628 complex_result (i, j) = pow (atmp, btmp); |
|
1
|
629 } |
|
1567
|
630 |
|
|
631 retval = complex_result; |
|
1
|
632 } |
|
|
633 else |
|
|
634 { |
|
|
635 Matrix result (nr, nc); |
|
|
636 |
|
1321
|
637 for (int j = 0; j < nc; j++) |
|
|
638 for (int i = 0; i < nr; i++) |
|
4153
|
639 { |
|
|
640 OCTAVE_QUIT; |
|
|
641 result (i, j) = pow (a (i, j), b (i, j)); |
|
|
642 } |
|
1
|
643 |
|
1567
|
644 retval = result; |
|
1
|
645 } |
|
1567
|
646 |
|
|
647 return retval; |
|
1
|
648 } |
|
|
649 |
|
767
|
650 // -*- 5 -*- |
|
2086
|
651 octave_value |
|
164
|
652 elem_xpow (const Matrix& a, const Complex& b) |
|
1
|
653 { |
|
|
654 int nr = a.rows (); |
|
2365
|
655 int nc = a.cols (); |
|
1
|
656 |
|
|
657 ComplexMatrix result (nr, nc); |
|
|
658 for (int j = 0; j < nc; j++) |
|
|
659 for (int i = 0; i < nr; i++) |
|
4153
|
660 { |
|
|
661 OCTAVE_QUIT; |
|
|
662 result (i, j) = pow (Complex (a (i, j)), b); |
|
|
663 } |
|
1
|
664 |
|
1567
|
665 return result; |
|
1
|
666 } |
|
|
667 |
|
767
|
668 // -*- 6 -*- |
|
2086
|
669 octave_value |
|
164
|
670 elem_xpow (const Matrix& a, const ComplexMatrix& b) |
|
1
|
671 { |
|
|
672 int nr = a.rows (); |
|
2365
|
673 int nc = a.cols (); |
|
|
674 |
|
|
675 int b_nr = b.rows (); |
|
|
676 int b_nc = b.cols (); |
|
1
|
677 |
|
2365
|
678 if (nr != b_nr || nc != b_nc) |
|
|
679 { |
|
|
680 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
681 return octave_value (); |
|
|
682 } |
|
1
|
683 |
|
|
684 ComplexMatrix result (nr, nc); |
|
|
685 for (int j = 0; j < nc; j++) |
|
|
686 for (int i = 0; i < nr; i++) |
|
4153
|
687 { |
|
|
688 OCTAVE_QUIT; |
|
|
689 result (i, j) = pow (Complex (a (i, j)), b (i, j)); |
|
|
690 } |
|
1
|
691 |
|
1567
|
692 return result; |
|
1
|
693 } |
|
|
694 |
|
767
|
695 // -*- 7 -*- |
|
2086
|
696 octave_value |
|
164
|
697 elem_xpow (const Complex& a, const Matrix& b) |
|
1
|
698 { |
|
|
699 int nr = b.rows (); |
|
2365
|
700 int nc = b.cols (); |
|
1
|
701 |
|
|
702 ComplexMatrix result (nr, nc); |
|
|
703 for (int j = 0; j < nc; j++) |
|
|
704 for (int i = 0; i < nr; i++) |
|
1567
|
705 { |
|
4153
|
706 OCTAVE_QUIT; |
|
2305
|
707 double btmp = b (i, j); |
|
1567
|
708 if (xisint (btmp)) |
|
2800
|
709 result (i, j) = pow (a, static_cast<int> (btmp)); |
|
1567
|
710 else |
|
2305
|
711 result (i, j) = pow (a, btmp); |
|
1567
|
712 } |
|
1
|
713 |
|
1567
|
714 return result; |
|
1
|
715 } |
|
|
716 |
|
767
|
717 // -*- 8 -*- |
|
2086
|
718 octave_value |
|
164
|
719 elem_xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
720 { |
|
|
721 int nr = b.rows (); |
|
2365
|
722 int nc = b.cols (); |
|
1
|
723 |
|
|
724 ComplexMatrix result (nr, nc); |
|
|
725 for (int j = 0; j < nc; j++) |
|
|
726 for (int i = 0; i < nr; i++) |
|
4153
|
727 { |
|
|
728 OCTAVE_QUIT; |
|
|
729 result (i, j) = pow (a, b (i, j)); |
|
|
730 } |
|
1
|
731 |
|
1567
|
732 return result; |
|
1
|
733 } |
|
|
734 |
|
767
|
735 // -*- 9 -*- |
|
2086
|
736 octave_value |
|
164
|
737 elem_xpow (const ComplexMatrix& a, double b) |
|
1
|
738 { |
|
|
739 int nr = a.rows (); |
|
2365
|
740 int nc = a.cols (); |
|
1
|
741 |
|
|
742 ComplexMatrix result (nr, nc); |
|
|
743 |
|
1567
|
744 if (xisint (b)) |
|
|
745 { |
|
|
746 for (int j = 0; j < nc; j++) |
|
|
747 for (int i = 0; i < nr; i++) |
|
4153
|
748 { |
|
|
749 OCTAVE_QUIT; |
|
|
750 result (i, j) = pow (a (i, j), static_cast<int> (b)); |
|
|
751 } |
|
1567
|
752 } |
|
|
753 else |
|
|
754 { |
|
|
755 for (int j = 0; j < nc; j++) |
|
|
756 for (int i = 0; i < nr; i++) |
|
4153
|
757 { |
|
|
758 OCTAVE_QUIT; |
|
|
759 result (i, j) = pow (a (i, j), b); |
|
|
760 } |
|
1567
|
761 } |
|
|
762 |
|
|
763 return result; |
|
1
|
764 } |
|
|
765 |
|
767
|
766 // -*- 10 -*- |
|
2086
|
767 octave_value |
|
164
|
768 elem_xpow (const ComplexMatrix& a, const Matrix& b) |
|
1
|
769 { |
|
|
770 int nr = a.rows (); |
|
2365
|
771 int nc = a.cols (); |
|
|
772 |
|
|
773 int b_nr = b.rows (); |
|
|
774 int b_nc = b.cols (); |
|
1
|
775 |
|
2365
|
776 if (nr != b_nr || nc != b_nc) |
|
|
777 { |
|
|
778 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
779 return octave_value (); |
|
|
780 } |
|
1
|
781 |
|
|
782 ComplexMatrix result (nr, nc); |
|
|
783 for (int j = 0; j < nc; j++) |
|
|
784 for (int i = 0; i < nr; i++) |
|
1567
|
785 { |
|
4153
|
786 OCTAVE_QUIT; |
|
2305
|
787 double btmp = b (i, j); |
|
1567
|
788 if (xisint (btmp)) |
|
2800
|
789 result (i, j) = pow (a (i, j), static_cast<int> (btmp)); |
|
1567
|
790 else |
|
2305
|
791 result (i, j) = pow (a (i, j), btmp); |
|
1567
|
792 } |
|
1
|
793 |
|
1567
|
794 return result; |
|
1
|
795 } |
|
|
796 |
|
767
|
797 // -*- 11 -*- |
|
2086
|
798 octave_value |
|
164
|
799 elem_xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
800 { |
|
|
801 int nr = a.rows (); |
|
2365
|
802 int nc = a.cols (); |
|
1
|
803 |
|
|
804 ComplexMatrix result (nr, nc); |
|
|
805 for (int j = 0; j < nc; j++) |
|
|
806 for (int i = 0; i < nr; i++) |
|
4153
|
807 { |
|
|
808 OCTAVE_QUIT; |
|
|
809 result (i, j) = pow (a (i, j), b); |
|
|
810 } |
|
1
|
811 |
|
1567
|
812 return result; |
|
1
|
813 } |
|
|
814 |
|
767
|
815 // -*- 12 -*- |
|
2086
|
816 octave_value |
|
164
|
817 elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b) |
|
1
|
818 { |
|
|
819 int nr = a.rows (); |
|
2365
|
820 int nc = a.cols (); |
|
|
821 |
|
|
822 int b_nr = b.rows (); |
|
|
823 int b_nc = b.cols (); |
|
|
824 |
|
|
825 if (nr != b_nr || nc != b_nc) |
|
|
826 { |
|
|
827 gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc); |
|
|
828 return octave_value (); |
|
|
829 } |
|
1
|
830 |
|
|
831 ComplexMatrix result (nr, nc); |
|
|
832 for (int j = 0; j < nc; j++) |
|
|
833 for (int i = 0; i < nr; i++) |
|
4153
|
834 { |
|
|
835 OCTAVE_QUIT; |
|
|
836 result (i, j) = pow (a (i, j), b (i, j)); |
|
|
837 } |
|
1
|
838 |
|
1567
|
839 return result; |
|
1
|
840 } |
|
|
841 |
|
4543
|
842 // Safer pow functions that work elementwise for N-d arrays. |
|
|
843 // |
|
|
844 // op2 \ op1: s nd cs cnd |
|
|
845 // +-- +---+---+----+----+ |
|
|
846 // scalar | | * | 3 | * | 9 | |
|
|
847 // +---+---+----+----+ |
|
|
848 // N_d | 1 | 4 | 7 | 10 | |
|
|
849 // +---+---+----+----+ |
|
|
850 // complex_scalar | * | 5 | * | 11 | |
|
|
851 // +---+---+----+----+ |
|
|
852 // complex_N_d | 2 | 6 | 8 | 12 | |
|
|
853 // +---+---+----+----+ |
|
|
854 // |
|
|
855 // * -> not needed. |
|
|
856 |
|
|
857 // XXX FIXME XXX -- these functions need to be fixed so that things |
|
|
858 // like |
|
|
859 // |
|
|
860 // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b |
|
|
861 // |
|
|
862 // and |
|
|
863 // |
|
|
864 // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end |
|
|
865 // |
|
|
866 // produce identical results. Also, it would be nice if -1^0.5 |
|
|
867 // produced a pure imaginary result instead of a complex number with a |
|
|
868 // small real part. But perhaps that's really a problem with the math |
|
|
869 // library... |
|
|
870 |
|
|
871 // -*- 1 -*- |
|
|
872 octave_value |
|
|
873 elem_xpow (double a, const NDArray& b) |
|
|
874 { |
|
|
875 octave_value retval; |
|
|
876 |
|
|
877 double d1, d2; |
|
|
878 |
|
|
879 if (a < 0.0 && ! b.all_integers (d1, d2)) |
|
|
880 { |
|
|
881 Complex atmp (a); |
|
|
882 ComplexNDArray result (b.dims ()); |
|
|
883 for (int i = 0; i < b.length (); i++) |
|
|
884 { |
|
|
885 OCTAVE_QUIT; |
|
|
886 result(i) = pow (atmp, b(i)); |
|
|
887 } |
|
|
888 |
|
|
889 retval = result; |
|
|
890 } |
|
|
891 else |
|
|
892 { |
|
|
893 NDArray result (b.dims ()); |
|
|
894 for (int i = 0; i < b.length (); i++) |
|
|
895 { |
|
|
896 OCTAVE_QUIT; |
|
|
897 result (i) = pow (a, b(i)); |
|
|
898 } |
|
|
899 |
|
|
900 retval = result; |
|
|
901 } |
|
|
902 |
|
|
903 return retval; |
|
|
904 } |
|
|
905 |
|
|
906 // -*- 2 -*- |
|
|
907 octave_value |
|
|
908 elem_xpow (double a, const ComplexNDArray& b) |
|
|
909 { |
|
|
910 ComplexNDArray result (b.dims ()); |
|
|
911 Complex atmp (a); |
|
|
912 for (int i = 0; i < b.length (); i++) |
|
|
913 { |
|
|
914 OCTAVE_QUIT; |
|
|
915 result(i) = pow (atmp, b(i)); |
|
|
916 } |
|
|
917 |
|
|
918 return result; |
|
|
919 } |
|
|
920 |
|
|
921 // -*- 3 -*- |
|
|
922 octave_value |
|
|
923 elem_xpow (const NDArray& a, double b) |
|
|
924 { |
|
|
925 octave_value retval; |
|
|
926 |
|
|
927 if (static_cast<int> (b) != b && a.any_element_is_negative ()) |
|
|
928 { |
|
|
929 ComplexNDArray result (a.dims ()); |
|
|
930 |
|
|
931 for (int i = 0; i < a.length (); i++) |
|
|
932 { |
|
|
933 OCTAVE_QUIT; |
|
|
934 Complex atmp (a(i)); |
|
|
935 result(i) = pow (atmp, b); |
|
|
936 } |
|
|
937 |
|
|
938 retval = result; |
|
|
939 } |
|
|
940 else |
|
|
941 { |
|
|
942 NDArray result (a.dims ()); |
|
|
943 |
|
|
944 for (int i = 0; i < a.length (); i++) |
|
|
945 { |
|
|
946 OCTAVE_QUIT; |
|
|
947 result(i) = pow (a(i), b); |
|
|
948 } |
|
|
949 |
|
|
950 retval = result; |
|
|
951 } |
|
|
952 |
|
|
953 return retval; |
|
|
954 } |
|
|
955 |
|
|
956 // -*- 4 -*- |
|
|
957 octave_value |
|
|
958 elem_xpow (const NDArray& a, const NDArray& b) |
|
|
959 { |
|
|
960 octave_value retval; |
|
|
961 |
|
|
962 dim_vector a_dims = a.dims (); |
|
|
963 dim_vector b_dims = b.dims (); |
|
|
964 |
|
|
965 if (a_dims != b_dims) |
|
|
966 { |
|
|
967 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
968 return octave_value (); |
|
|
969 } |
|
|
970 |
|
|
971 int len = a.length (); |
|
|
972 |
|
|
973 bool convert_to_complex = false; |
|
|
974 |
|
|
975 for (int i = 0; i < len; i++) |
|
|
976 { |
|
|
977 OCTAVE_QUIT; |
|
|
978 double atmp = a(i); |
|
|
979 double btmp = b(i); |
|
|
980 if (atmp < 0.0 && static_cast<int> (btmp) != btmp) |
|
|
981 { |
|
|
982 convert_to_complex = true; |
|
|
983 goto done; |
|
|
984 } |
|
|
985 } |
|
|
986 |
|
|
987 done: |
|
|
988 |
|
|
989 if (convert_to_complex) |
|
|
990 { |
|
|
991 ComplexNDArray complex_result (a_dims); |
|
|
992 |
|
|
993 for (int i = 0; i < len; i++) |
|
|
994 { |
|
|
995 OCTAVE_QUIT; |
|
|
996 Complex atmp (a(i)); |
|
|
997 Complex btmp (b(i)); |
|
|
998 complex_result(i) = pow (atmp, btmp); |
|
|
999 } |
|
|
1000 |
|
|
1001 retval = complex_result; |
|
|
1002 } |
|
|
1003 else |
|
|
1004 { |
|
|
1005 NDArray result (a_dims); |
|
|
1006 |
|
|
1007 for (int i = 0; i < len; i++) |
|
|
1008 { |
|
|
1009 OCTAVE_QUIT; |
|
|
1010 result(i) = pow (a(i), b(i)); |
|
|
1011 } |
|
|
1012 |
|
|
1013 retval = result; |
|
|
1014 } |
|
|
1015 |
|
|
1016 return retval; |
|
|
1017 } |
|
|
1018 |
|
|
1019 // -*- 5 -*- |
|
|
1020 octave_value |
|
|
1021 elem_xpow (const NDArray& a, const Complex& b) |
|
|
1022 { |
|
|
1023 ComplexNDArray result (a.dims ()); |
|
|
1024 |
|
|
1025 for (int i = 0; i < a.length (); i++) |
|
|
1026 { |
|
|
1027 OCTAVE_QUIT; |
|
|
1028 result(i) = pow (Complex (a(i)), b); |
|
|
1029 } |
|
|
1030 |
|
|
1031 return result; |
|
|
1032 } |
|
|
1033 |
|
|
1034 // -*- 6 -*- |
|
|
1035 octave_value |
|
|
1036 elem_xpow (const NDArray& a, const ComplexNDArray& b) |
|
|
1037 { |
|
|
1038 dim_vector a_dims = a.dims (); |
|
|
1039 dim_vector b_dims = b.dims (); |
|
|
1040 |
|
|
1041 if (a_dims != b_dims) |
|
|
1042 { |
|
|
1043 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1044 return octave_value (); |
|
|
1045 } |
|
|
1046 |
|
|
1047 ComplexNDArray result (a_dims); |
|
|
1048 for (int i = 0; i < a.length (); i++) |
|
|
1049 { |
|
|
1050 OCTAVE_QUIT; |
|
|
1051 result(i) = pow (Complex (a(i)), b(i)); |
|
|
1052 } |
|
|
1053 |
|
|
1054 return result; |
|
|
1055 } |
|
|
1056 |
|
|
1057 // -*- 7 -*- |
|
|
1058 octave_value |
|
|
1059 elem_xpow (const Complex& a, const NDArray& b) |
|
|
1060 { |
|
|
1061 ComplexNDArray result (b.dims ()); |
|
|
1062 for (int i = 0; i < b.length (); i++) |
|
|
1063 { |
|
|
1064 OCTAVE_QUIT; |
|
|
1065 double btmp = b(i); |
|
|
1066 if (xisint (btmp)) |
|
|
1067 result(i) = pow (a, static_cast<int> (btmp)); |
|
|
1068 else |
|
|
1069 result(i) = pow (a, btmp); |
|
|
1070 } |
|
|
1071 |
|
|
1072 return result; |
|
|
1073 } |
|
|
1074 |
|
|
1075 // -*- 8 -*- |
|
|
1076 octave_value |
|
|
1077 elem_xpow (const Complex& a, const ComplexNDArray& b) |
|
|
1078 { |
|
|
1079 ComplexNDArray result (b.dims ()); |
|
|
1080 for (int i = 0; i < b.length (); i++) |
|
|
1081 { |
|
|
1082 OCTAVE_QUIT; |
|
|
1083 result(i) = pow (a, b(i)); |
|
|
1084 } |
|
|
1085 |
|
|
1086 return result; |
|
|
1087 } |
|
|
1088 |
|
|
1089 // -*- 9 -*- |
|
|
1090 octave_value |
|
|
1091 elem_xpow (const ComplexNDArray& a, double b) |
|
|
1092 { |
|
|
1093 ComplexNDArray result (a.dims ()); |
|
|
1094 |
|
|
1095 if (xisint (b)) |
|
|
1096 { |
|
|
1097 for (int i = 0; i < a.length (); i++) |
|
|
1098 { |
|
|
1099 OCTAVE_QUIT; |
|
|
1100 result(i) = pow (a(i), static_cast<int> (b)); |
|
|
1101 } |
|
|
1102 } |
|
|
1103 else |
|
|
1104 { |
|
|
1105 for (int i = 0; i < a.length (); i++) |
|
|
1106 { |
|
|
1107 OCTAVE_QUIT; |
|
|
1108 result(i) = pow (a(i), b); |
|
|
1109 } |
|
|
1110 } |
|
|
1111 |
|
|
1112 return result; |
|
|
1113 } |
|
|
1114 |
|
|
1115 // -*- 10 -*- |
|
|
1116 octave_value |
|
|
1117 elem_xpow (const ComplexNDArray& a, const NDArray& b) |
|
|
1118 { |
|
|
1119 dim_vector a_dims = a.dims (); |
|
|
1120 dim_vector b_dims = b.dims (); |
|
|
1121 |
|
|
1122 if (a_dims != b_dims) |
|
|
1123 { |
|
|
1124 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1125 return octave_value (); |
|
|
1126 } |
|
|
1127 |
|
|
1128 ComplexNDArray result (a_dims); |
|
|
1129 for (int i = 0; i < a.length (); i++) |
|
|
1130 { |
|
|
1131 OCTAVE_QUIT; |
|
|
1132 double btmp = b(i); |
|
|
1133 if (xisint (btmp)) |
|
|
1134 result(i) = pow (a(i), static_cast<int> (btmp)); |
|
|
1135 else |
|
|
1136 result(i) = pow (a(i), btmp); |
|
|
1137 } |
|
|
1138 |
|
|
1139 return result; |
|
|
1140 } |
|
|
1141 |
|
|
1142 // -*- 11 -*- |
|
|
1143 octave_value |
|
|
1144 elem_xpow (const ComplexNDArray& a, const Complex& b) |
|
|
1145 { |
|
|
1146 ComplexNDArray result (a.dims ()); |
|
|
1147 for (int i = 0; i < a.length (); i++) |
|
|
1148 { |
|
|
1149 OCTAVE_QUIT; |
|
|
1150 result(i) = pow (a(i), b); |
|
|
1151 } |
|
|
1152 |
|
|
1153 return result; |
|
|
1154 } |
|
|
1155 |
|
|
1156 // -*- 12 -*- |
|
|
1157 octave_value |
|
|
1158 elem_xpow (const ComplexNDArray& a, const ComplexNDArray& b) |
|
|
1159 { |
|
|
1160 dim_vector a_dims = a.dims (); |
|
|
1161 dim_vector b_dims = b.dims (); |
|
|
1162 |
|
|
1163 if (a_dims != b_dims) |
|
|
1164 { |
|
|
1165 gripe_nonconformant ("operator .^", a_dims, b_dims); |
|
|
1166 return octave_value (); |
|
|
1167 } |
|
|
1168 |
|
|
1169 ComplexNDArray result (a_dims); |
|
|
1170 for (int i = 0; i < a.length (); i++) |
|
|
1171 { |
|
|
1172 OCTAVE_QUIT; |
|
|
1173 result(i) = pow (a(i), b(i)); |
|
|
1174 } |
|
|
1175 |
|
|
1176 return result; |
|
|
1177 } |
|
|
1178 |
|
1
|
1179 /* |
|
|
1180 ;;; Local Variables: *** |
|
|
1181 ;;; mode: C++ *** |
|
|
1182 ;;; End: *** |
|
|
1183 */ |
