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1 /* |
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2 |
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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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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 // Author: A. S. Hodel <scotte@eng.auburn.edu> |
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25 |
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26 #ifdef HAVE_CONFIG_H |
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27 #include <config.h> |
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28 #endif |
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29 |
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30 #include "defun-dld.h" |
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31 #include "error.h" |
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32 #include "gripes.h" |
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33 #include "oct-obj.h" |
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34 #include "utils.h" |
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35 |
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36 DEFUN_DLD (expm, args, , |
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37 "-*- texinfo -*-\n\ |
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38 @deftypefn {Loadable Function} {} expm (@var{a})\n\ |
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39 Return the exponential of a matrix, defined as the infinite Taylor\n\ |
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40 series\n\ |
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41 @iftex\n\ |
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42 @tex\n\ |
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43 $$\n\ |
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44 \\exp (A) = I + A + {A^2 \\over 2!} + {A^3 \\over 3!} + \\cdots\n\ |
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45 $$\n\ |
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46 @end tex\n\ |
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47 @end iftex\n\ |
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48 @ifinfo\n\ |
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49 \n\ |
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50 @example\n\ |
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51 expm(a) = I + a + a^2/2! + a^3/3! + ...\n\ |
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52 @end example\n\ |
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53 \n\ |
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54 @end ifinfo\n\ |
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55 The Taylor series is @emph{not} the way to compute the matrix\n\ |
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56 exponential; see Moler and Van Loan, @cite{Nineteen Dubious Ways to\n\ |
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57 Compute the Exponential of a Matrix}, SIAM Review, 1978. This routine\n\ |
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58 uses Ward's diagonal\n\ |
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59 @iftex\n\ |
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60 @tex\n\ |
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61 Pad\\'e\n\ |
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62 @end tex\n\ |
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63 @end iftex\n\ |
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64 @ifinfo\n\ |
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65 Pade'\n\ |
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66 @end ifinfo\n\ |
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67 approximation method with three step preconditioning (SIAM Journal on\n\ |
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68 Numerical Analysis, 1977). Diagonal\n\ |
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69 @iftex\n\ |
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70 @tex\n\ |
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71 Pad\\'e\n\ |
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72 @end tex\n\ |
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73 @end iftex\n\ |
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74 @ifinfo\n\ |
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75 Pade'\n\ |
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76 @end ifinfo\n\ |
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77 approximations are rational polynomials of matrices\n\ |
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78 @iftex\n\ |
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79 @tex\n\ |
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80 $D_q(a)^{-1}N_q(a)$\n\ |
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81 @end tex\n\ |
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82 @end iftex\n\ |
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83 @ifinfo\n\ |
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84 \n\ |
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85 @example\n\ |
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86 -1\n\ |
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87 D (a) N (a)\n\ |
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88 @end example\n\ |
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89 \n\ |
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90 @end ifinfo\n\ |
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91 whose Taylor series matches the first\n\ |
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92 @iftex\n\ |
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93 @tex\n\ |
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94 $2 q + 1 $\n\ |
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95 @end tex\n\ |
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96 @end iftex\n\ |
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97 @ifinfo\n\ |
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98 @code{2q+1}\n\ |
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99 @end ifinfo\n\ |
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100 terms of the Taylor series above; direct evaluation of the Taylor series\n\ |
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101 (with the same preconditioning steps) may be desirable in lieu of the\n\ |
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102 @iftex\n\ |
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103 @tex\n\ |
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104 Pad\\'e\n\ |
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105 @end tex\n\ |
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106 @end iftex\n\ |
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107 @ifinfo\n\ |
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108 Pade'\n\ |
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109 @end ifinfo\n\ |
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110 approximation when\n\ |
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111 @iftex\n\ |
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112 @tex\n\ |
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113 $D_q(a)$\n\ |
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114 @end tex\n\ |
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115 @end iftex\n\ |
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116 @ifinfo\n\ |
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117 @code{Dq(a)}\n\ |
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118 @end ifinfo\n\ |
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119 is ill-conditioned.\n\ |
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120 @end deftypefn") |
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121 { |
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122 octave_value retval; |
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123 |
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124 int nargin = args.length (); |
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125 |
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126 if (nargin != 1) |
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127 { |
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128 print_usage (); |
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129 return retval; |
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130 } |
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131 |
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132 octave_value arg = args(0); |
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133 |
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134 octave_idx_type nr = arg.rows (); |
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135 octave_idx_type nc = arg.columns (); |
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136 |
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137 int arg_is_empty = empty_arg ("expm", nr, nc); |
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138 |
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139 if (arg_is_empty < 0) |
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140 return retval; |
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141 if (arg_is_empty > 0) |
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142 return octave_value (Matrix ()); |
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143 |
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144 if (nr != nc) |
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145 { |
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146 gripe_square_matrix_required ("expm"); |
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147 return retval; |
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148 } |
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149 |
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150 if (arg.is_real_type ()) |
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151 { |
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152 Matrix m = arg.matrix_value (); |
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153 |
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154 if (error_state) |
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155 return retval; |
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156 else |
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157 retval = m.expm (); |
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158 } |
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159 else if (arg.is_complex_type ()) |
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160 { |
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161 ComplexMatrix m = arg.complex_matrix_value (); |
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162 |
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163 if (error_state) |
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164 return retval; |
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165 else |
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166 retval = m.expm (); |
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167 } |
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168 else |
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169 { |
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170 gripe_wrong_type_arg ("expm", arg); |
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171 } |
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172 |
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173 return retval; |
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174 } |
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175 |
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176 /* |
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177 ;;; Local Variables: *** |
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178 ;;; mode: C++ *** |
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179 ;;; End: *** |
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180 */ |
