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1
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1 // xpow.cc -*- C++ -*- |
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2 /* |
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3 |
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4 Copyright (C) 1992, 1993 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, 675 Mass Ave, Cambridge, MA 02139, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef __GNUG__ |
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25 #pragma implementation |
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26 #endif |
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27 |
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28 #include <assert.h> |
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29 #include "error.h" |
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30 #include "xpow.h" |
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31 |
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32 // This function also appears in tree-const.cc. Maybe it should be a |
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33 // member function of the Matrix class. |
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34 |
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35 static int |
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36 any_element_is_negative (const Matrix& a) |
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37 { |
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38 int nr = a.rows (); |
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39 int nc = a.columns (); |
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40 for (int j = 0; j < nc; j++) |
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41 for (int i = 0; i < nr; i++) |
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42 if (a.elem (i, j) < 0.0) |
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43 return 1; |
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44 return 0; |
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45 } |
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46 |
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47 /* |
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48 * Safer pow functions. |
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49 * |
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50 * op2 \ op1: s m cs cm |
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51 * +-- +---+---+----+----+ |
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52 * scalar | | 1 | 5 | 7 | 11 | |
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53 * +---+---+----+----+ |
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54 * matrix | 2 | E | 8 | E | |
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55 * +---+---+----+----+ |
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56 * complex_scalar | 3 | 6 | 9 | 12 | |
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57 * +---+---+----+----+ |
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58 * complex_matrix | 4 | E | 10 | E | |
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59 * +---+---+----+----+ |
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60 * |
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61 * E -> error, trapped in arith-ops.cc. |
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62 */ |
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63 |
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64 tree_constant |
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65 xpow (double a, double b) |
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66 { |
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67 if (a < 0.0 && (int) b != b) |
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68 { |
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69 Complex atmp (a); |
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70 return tree_constant (pow (atmp, b)); |
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71 } |
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72 else |
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73 return tree_constant (pow (a, b)); |
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74 } |
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75 |
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76 tree_constant |
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77 xpow (double a, Matrix& b) |
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78 { |
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79 tree_constant retval; |
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80 |
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81 int nr = b.rows (); |
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82 int nc = b.columns (); |
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83 |
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84 if (nr == 0 || nc == 0 || nr != nc) |
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85 error ("for x^A, A must be square"); |
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86 else |
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87 { |
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88 EIG b_eig (b); |
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89 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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90 ComplexMatrix Q (b_eig.eigenvectors ()); |
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91 |
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92 for (int i = 0; i < nr; i++) |
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93 { |
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94 Complex elt = lambda.elem (i); |
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95 if (imag (elt) == 0.0) |
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96 lambda.elem (i) = pow (a, real (elt)); |
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97 else |
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98 lambda.elem (i) = pow (a, elt); |
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99 } |
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100 ComplexDiagMatrix D (lambda); |
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101 |
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102 ComplexMatrix result = Q * D * Q.inverse (); |
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103 retval = tree_constant (result); |
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104 } |
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105 |
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106 return retval; |
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107 } |
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108 |
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109 tree_constant |
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110 xpow (double a, Complex& b) |
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111 { |
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112 Complex result; |
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113 Complex atmp (a); |
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114 result = pow (atmp, b); |
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115 return tree_constant (result); |
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116 } |
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117 |
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118 tree_constant |
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119 xpow (double a, ComplexMatrix& b) |
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120 { |
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121 tree_constant retval; |
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122 |
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123 int nr = b.rows (); |
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124 int nc = b.columns (); |
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125 |
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126 if (nr == 0 || nc == 0 || nr != nc) |
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127 error ("for x^A, A must be square"); |
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128 else |
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129 { |
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130 EIG b_eig (b); |
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131 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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132 ComplexMatrix Q (b_eig.eigenvectors ()); |
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133 |
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134 for (int i = 0; i < nr; i++) |
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135 { |
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136 Complex elt = lambda.elem (i); |
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137 if (imag (elt) == 0.0) |
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138 lambda.elem (i) = pow (a, real (elt)); |
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139 else |
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140 lambda.elem (i) = pow (a, elt); |
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141 } |
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142 ComplexDiagMatrix D (lambda); |
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143 |
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144 ComplexMatrix result = Q * D * Q.inverse (); |
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145 retval = tree_constant (result); |
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146 } |
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147 |
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148 return retval; |
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149 } |
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150 |
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151 tree_constant |
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152 xpow (Matrix& a, double b) |
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153 { |
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154 tree_constant retval; |
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155 |
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156 int nr = a.rows (); |
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157 int nc = a.columns (); |
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158 |
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159 if (nr == 0 || nc == 0 || nr != nc) |
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160 { |
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161 error ("for A^b, A must be square"); |
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162 return retval; |
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163 } |
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164 |
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165 if ((int) b == b) |
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166 { |
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167 int btmp = (int) b; |
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168 if (btmp == 0) |
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169 { |
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170 DiagMatrix result (nr, nr, 1.0); |
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171 retval = tree_constant (result); |
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172 } |
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173 else |
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174 { |
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175 // Too much copying? |
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176 // XXX FIXME XXX -- we shouldn\'t do this if the exponent is large... |
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177 Matrix atmp; |
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178 if (btmp < 0) |
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179 { |
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180 btmp = -btmp; |
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181 atmp = a.inverse (); |
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182 } |
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183 else |
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184 atmp = a; |
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185 |
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186 Matrix result (atmp); |
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187 for (int i = 1; i < btmp; i++) |
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188 result = result * atmp; |
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189 |
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190 retval = tree_constant (result); |
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191 } |
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192 } |
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193 else |
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194 { |
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195 EIG a_eig (a); |
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196 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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197 ComplexMatrix Q (a_eig.eigenvectors ()); |
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198 |
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199 for (int i = 0; i < nr; i++) |
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200 lambda.elem (i) = pow (lambda.elem (i), b); |
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201 |
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202 ComplexDiagMatrix D (lambda); |
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203 |
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204 ComplexMatrix result = Q * D * Q.inverse (); |
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205 retval = tree_constant (result); |
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206 } |
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207 |
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208 return retval; |
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209 } |
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210 |
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211 tree_constant |
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212 xpow (Matrix& a, Complex& b) |
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213 { |
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214 int nr = a.rows (); |
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215 int nc = a.columns (); |
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216 |
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217 if (nr == 0 || nc == 0 || nr != nc) |
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218 { |
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219 error ("for A^b, A must be square"); |
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220 return tree_constant (); |
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221 } |
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222 |
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223 EIG a_eig (a); |
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224 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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225 ComplexMatrix Q (a_eig.eigenvectors ()); |
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226 |
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227 for (int i = 0; i < nr; i++) |
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228 lambda.elem (i) = pow (lambda.elem (i), b); |
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229 |
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230 ComplexDiagMatrix D (lambda); |
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231 |
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232 ComplexMatrix result = Q * D * Q.inverse (); |
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233 |
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234 return tree_constant (result); |
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235 } |
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236 |
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237 tree_constant |
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238 xpow (Complex& a, double b) |
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239 { |
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240 Complex result; |
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241 result = pow (a, b); |
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242 return tree_constant (result); |
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243 } |
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244 |
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245 tree_constant |
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246 xpow (Complex& a, Matrix& b) |
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247 { |
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248 tree_constant retval; |
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249 |
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250 int nr = b.rows (); |
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251 int nc = b.columns (); |
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252 |
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253 if (nr == 0 || nc == 0 || nr != nc) |
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254 { |
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255 error ("for x^A, A must be square"); |
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256 } |
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257 else |
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258 { |
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259 EIG b_eig (b); |
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260 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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261 ComplexMatrix Q (b_eig.eigenvectors ()); |
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262 |
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263 for (int i = 0; i < nr; i++) |
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264 { |
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265 Complex elt = lambda.elem (i); |
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266 if (imag (elt) == 0.0) |
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267 lambda.elem (i) = pow (a, real (elt)); |
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268 else |
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269 lambda.elem (i) = pow (a, elt); |
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270 } |
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271 ComplexDiagMatrix D (lambda); |
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272 |
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273 ComplexMatrix result = Q * D * Q.inverse (); |
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274 retval = tree_constant (result); |
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275 } |
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276 |
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277 return retval; |
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278 } |
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279 |
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280 tree_constant |
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281 xpow (Complex& a, Complex& b) |
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282 { |
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283 Complex result; |
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284 result = pow (a, b); |
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285 return tree_constant (result); |
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286 } |
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287 |
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288 tree_constant |
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289 xpow (Complex& a, ComplexMatrix& b) |
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290 { |
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291 tree_constant retval; |
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292 |
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293 int nr = b.rows (); |
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294 int nc = b.columns (); |
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295 |
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296 if (nr == 0 || nc == 0 || nr != nc) |
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297 error ("for x^A, A must be square"); |
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298 else |
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299 { |
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300 EIG b_eig (b); |
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301 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
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302 ComplexMatrix Q (b_eig.eigenvectors ()); |
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303 |
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304 for (int i = 0; i < nr; i++) |
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305 { |
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306 Complex elt = lambda.elem (i); |
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307 if (imag (elt) == 0.0) |
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308 lambda.elem (i) = pow (a, real (elt)); |
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309 else |
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310 lambda.elem (i) = pow (a, elt); |
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311 } |
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312 ComplexDiagMatrix D (lambda); |
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313 |
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314 ComplexMatrix result = Q * D * Q.inverse (); |
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315 retval = tree_constant (result); |
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316 } |
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317 |
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318 return retval; |
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319 } |
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320 |
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321 tree_constant |
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322 xpow (ComplexMatrix& a, double b) |
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323 { |
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324 tree_constant retval; |
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325 |
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326 int nr = a.rows (); |
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327 int nc = a.columns (); |
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328 |
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329 if (nr == 0 || nc == 0 || nr != nc) |
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330 { |
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331 error ("for A^b, A must be square"); |
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332 return retval; |
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333 } |
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334 |
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335 if ((int) b == b) |
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336 { |
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337 int btmp = (int) b; |
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338 if (btmp == 0) |
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339 { |
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340 DiagMatrix result (nr, nr, 1.0); |
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341 retval = tree_constant (result); |
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342 } |
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343 else |
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344 { |
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345 // Too much copying? |
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346 // XXX FIXME XXX -- we shouldn\'t do this if the exponent is large... |
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347 ComplexMatrix atmp; |
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348 if (btmp < 0) |
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349 { |
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350 btmp = -btmp; |
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351 atmp = a.inverse (); |
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352 } |
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353 else |
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354 atmp = a; |
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355 |
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356 ComplexMatrix result (atmp); |
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357 for (int i = 1; i < btmp; i++) |
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358 result = result * atmp; |
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359 |
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360 retval = tree_constant (result); |
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361 } |
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362 } |
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363 else |
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364 { |
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365 EIG a_eig (a); |
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366 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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367 ComplexMatrix Q (a_eig.eigenvectors ()); |
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368 |
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369 for (int i = 0; i < nr; i++) |
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370 lambda.elem (i) = pow (lambda.elem (i), b); |
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371 |
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372 ComplexDiagMatrix D (lambda); |
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373 |
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374 ComplexMatrix result = Q * D * Q.inverse (); |
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375 retval = tree_constant (result); |
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376 } |
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377 |
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378 return retval; |
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379 } |
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380 |
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381 tree_constant |
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382 xpow (ComplexMatrix& a, Complex& b) |
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383 { |
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384 int nr = a.rows (); |
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385 int nc = a.columns (); |
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386 |
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387 if (nr == 0 || nc == 0 || nr != nc) |
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388 { |
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389 error ("for A^b, A must be square"); |
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390 return tree_constant (); |
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391 } |
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392 |
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393 EIG a_eig (a); |
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394 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
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395 ComplexMatrix Q (a_eig.eigenvectors ()); |
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396 |
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397 for (int i = 0; i < nr; i++) |
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398 lambda.elem (i) = pow (lambda.elem (i), b); |
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399 |
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400 ComplexDiagMatrix D (lambda); |
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401 |
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402 ComplexMatrix result = Q * D * Q.inverse (); |
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403 |
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404 return tree_constant (result); |
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405 } |
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406 |
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407 /* |
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408 * Safer pow functions that work elementwise for matrices. |
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409 * |
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410 * op2 \ op1: s m cs cm |
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411 * +-- +---+---+----+----+ |
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412 * scalar | | * | 3 | * | 9 | |
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413 * +---+---+----+----+ |
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414 * matrix | 1 | 4 | 7 | 10 | |
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415 * +---+---+----+----+ |
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416 * complex_scalar | * | 5 | * | 11 | |
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417 * +---+---+----+----+ |
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418 * complex_matrix | 2 | 6 | 8 | 12 | |
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419 * +---+---+----+----+ |
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420 * |
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421 * * -> not needed. |
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422 */ |
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423 |
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424 tree_constant |
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425 elem_xpow (double a, Matrix& b) |
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426 { |
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427 tree_constant retval; |
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428 |
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429 int nr = b.rows (); |
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430 int nc = b.columns (); |
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431 |
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432 // For now, assume the worst. |
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433 if (a < 0.0) |
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434 { |
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435 Complex atmp (a); |
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436 ComplexMatrix result (nr, nc); |
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437 for (int j = 0; j < nc; j++) |
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438 for (int i = 0; i < nr; i++) |
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439 result.elem (i, j) = pow (atmp, b.elem (i, j)); |
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440 |
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441 retval = tree_constant (result); |
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442 } |
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443 else |
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444 { |
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445 Matrix result (nr, nc); |
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446 for (int j = 0; j < nc; j++) |
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447 for (int i = 0; i < nr; i++) |
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448 result.elem (i, j) = pow (a, b.elem (i, j)); |
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449 |
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450 retval = tree_constant (result); |
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451 } |
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452 |
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453 return retval; |
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454 } |
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455 |
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456 tree_constant |
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457 elem_xpow (double a, ComplexMatrix& b) |
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458 { |
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459 int nr = b.rows (); |
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460 int nc = b.columns (); |
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461 |
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462 ComplexMatrix result (nr, nc); |
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463 for (int j = 0; j < nc; j++) |
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464 for (int i = 0; i < nr; i++) |
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465 result.elem (i, j) = pow (a, b.elem (i, j)); |
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466 |
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467 return tree_constant (result); |
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468 } |
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469 |
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470 tree_constant |
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471 elem_xpow (Matrix& a, double b) |
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472 { |
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473 tree_constant retval; |
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474 |
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475 int nr = a.rows (); |
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476 int nc = a.columns (); |
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477 |
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478 if ((int) b != b && any_element_is_negative (a)) |
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479 { |
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480 ComplexMatrix result (nr, nc); |
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481 for (int j = 0; j < nc; j++) |
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482 for (int i = 0; i < nr; i++) |
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483 { |
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484 Complex atmp (a.elem (i, j)); |
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485 result.elem (i, j) = pow (atmp, b); |
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486 } |
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487 |
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488 retval = tree_constant (result); |
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489 } |
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490 else |
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491 { |
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492 Matrix result (nr, nc); |
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493 for (int j = 0; j < nc; j++) |
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494 for (int i = 0; i < nr; i++) |
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495 result.elem (i, j) = pow (a.elem (i, j), b); |
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496 |
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497 retval = tree_constant (result); |
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498 } |
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499 |
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500 return retval; |
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501 } |
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502 |
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503 tree_constant |
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504 elem_xpow (Matrix& a, Matrix& b) |
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505 { |
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506 int nr = a.rows (); |
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507 int nc = a.columns (); |
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508 |
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509 assert (nr == b.rows () && nc == b.columns ()); |
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510 |
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511 int convert_to_complex = 0; |
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|
512 int i; |
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513 for (int j = 0; j < nc; j++) |
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514 for (i = 0; i < nr; i++) |
|
|
515 { |
|
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516 double atmp = a.elem (i, j); |
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517 double btmp = b.elem (i, j); |
|
|
518 if (atmp < 0.0 && (int) btmp != btmp) |
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519 { |
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|
520 convert_to_complex = 1; |
|
|
521 goto done; |
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|
522 } |
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523 } |
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524 |
|
|
525 done: |
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|
526 |
|
|
527 if (convert_to_complex) |
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528 { |
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|
529 ComplexMatrix complex_result (nr, nc); |
|
|
530 |
|
|
531 for (j = 0; j < nc; j++) |
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|
532 for (i = 0; i < nr; i++) |
|
|
533 { |
|
|
534 Complex atmp (a.elem (i, j)); |
|
|
535 Complex btmp (b.elem (i, j)); |
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|
536 complex_result.elem (i, j) = pow (atmp, btmp); |
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537 } |
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538 return tree_constant (complex_result); |
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|
539 } |
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540 else |
|
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541 { |
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|
542 Matrix result (nr, nc); |
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|
543 |
|
|
544 for (j = 0; j < nc; j++) |
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545 for (i = 0; i < nr; i++) |
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546 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
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547 |
|
|
548 return tree_constant (result); |
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|
549 } |
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|
550 } |
|
|
551 |
|
|
552 tree_constant |
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|
553 elem_xpow (Matrix& a, Complex& b) |
|
|
554 { |
|
|
555 int nr = a.rows (); |
|
|
556 int nc = a.columns (); |
|
|
557 |
|
|
558 ComplexMatrix result (nr, nc); |
|
|
559 for (int j = 0; j < nc; j++) |
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|
560 for (int i = 0; i < nr; i++) |
|
|
561 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
562 |
|
|
563 return tree_constant (result); |
|
|
564 } |
|
|
565 |
|
|
566 tree_constant |
|
|
567 elem_xpow (Matrix& a, ComplexMatrix& b) |
|
|
568 { |
|
|
569 int nr = a.rows (); |
|
|
570 int nc = a.columns (); |
|
|
571 |
|
|
572 assert (nr == b.rows () && nc == b.columns ()); |
|
|
573 |
|
|
574 ComplexMatrix result (nr, nc); |
|
|
575 for (int j = 0; j < nc; j++) |
|
|
576 for (int i = 0; i < nr; i++) |
|
|
577 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
578 |
|
|
579 return tree_constant (result); |
|
|
580 } |
|
|
581 |
|
|
582 tree_constant |
|
|
583 elem_xpow (Complex& a, Matrix& b) |
|
|
584 { |
|
|
585 int nr = b.rows (); |
|
|
586 int nc = b.columns (); |
|
|
587 |
|
|
588 ComplexMatrix result (nr, nc); |
|
|
589 for (int j = 0; j < nc; j++) |
|
|
590 for (int i = 0; i < nr; i++) |
|
|
591 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
592 |
|
|
593 return tree_constant (result); |
|
|
594 } |
|
|
595 |
|
|
596 tree_constant |
|
|
597 elem_xpow (Complex& a, ComplexMatrix& b) |
|
|
598 { |
|
|
599 int nr = b.rows (); |
|
|
600 int nc = b.columns (); |
|
|
601 |
|
|
602 ComplexMatrix result (nr, nc); |
|
|
603 for (int j = 0; j < nc; j++) |
|
|
604 for (int i = 0; i < nr; i++) |
|
|
605 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
606 |
|
|
607 return tree_constant (result); |
|
|
608 } |
|
|
609 |
|
|
610 tree_constant |
|
|
611 elem_xpow (ComplexMatrix& a, double b) |
|
|
612 { |
|
|
613 int nr = a.rows (); |
|
|
614 int nc = a.columns (); |
|
|
615 |
|
|
616 ComplexMatrix result (nr, nc); |
|
|
617 for (int j = 0; j < nc; j++) |
|
|
618 for (int i = 0; i < nr; i++) |
|
|
619 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
620 |
|
|
621 return tree_constant (result); |
|
|
622 } |
|
|
623 |
|
|
624 tree_constant |
|
|
625 elem_xpow (ComplexMatrix& a, Matrix& b) |
|
|
626 { |
|
|
627 int nr = a.rows (); |
|
|
628 int nc = a.columns (); |
|
|
629 |
|
|
630 assert (nr == b.rows () && nc == b.columns ()); |
|
|
631 |
|
|
632 ComplexMatrix result (nr, nc); |
|
|
633 for (int j = 0; j < nc; j++) |
|
|
634 for (int i = 0; i < nr; i++) |
|
|
635 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
636 |
|
|
637 return tree_constant (result); |
|
|
638 } |
|
|
639 |
|
|
640 tree_constant |
|
|
641 elem_xpow (ComplexMatrix& a, Complex& b) |
|
|
642 { |
|
|
643 int nr = a.rows (); |
|
|
644 int nc = a.columns (); |
|
|
645 |
|
|
646 ComplexMatrix result (nr, nc); |
|
|
647 for (int j = 0; j < nc; j++) |
|
|
648 for (int i = 0; i < nr; i++) |
|
|
649 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
650 |
|
|
651 return tree_constant (result); |
|
|
652 } |
|
|
653 |
|
|
654 tree_constant |
|
|
655 elem_xpow (ComplexMatrix& a, ComplexMatrix& b) |
|
|
656 { |
|
|
657 int nr = a.rows (); |
|
|
658 int nc = a.columns (); |
|
|
659 |
|
|
660 ComplexMatrix result (nr, nc); |
|
|
661 |
|
|
662 for (int j = 0; j < nc; j++) |
|
|
663 for (int i = 0; i < nr; i++) |
|
|
664 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
665 |
|
|
666 return tree_constant (result); |
|
|
667 } |
|
|
668 |
|
|
669 /* |
|
|
670 ;;; Local Variables: *** |
|
|
671 ;;; mode: C++ *** |
|
|
672 ;;; page-delimiter: "^/\\*" *** |
|
|
673 ;;; End: *** |
|
|
674 */ |
