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