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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, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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23 // Author: A. S. Hodel <scotte@eng.auburn.edu> |
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24 |
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25 #ifdef HAVE_CONFIG_H |
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26 #include <config.h> |
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27 #endif |
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28 |
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29 #include "defun-dld.h" |
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30 #include "error.h" |
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31 #include "gripes.h" |
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32 #include "oct-obj.h" |
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33 #include "utils.h" |
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34 |
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35 DEFUN_DLD (expm, args, , |
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36 "-*- texinfo -*-\n\ |
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37 @deftypefn {Loadable Function} {} expm (@var{a})\n\ |
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38 Return the exponential of a matrix, defined as the infinite Taylor\n\ |
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39 series\n\ |
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40 @iftex\n\ |
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41 @tex\n\ |
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42 $$\n\ |
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43 \\exp (A) = I + A + {A^2 \\over 2!} + {A^3 \\over 3!} + \\cdots\n\ |
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44 $$\n\ |
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45 @end tex\n\ |
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46 @end iftex\n\ |
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47 @ifinfo\n\ |
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48 \n\ |
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49 @example\n\ |
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50 expm(a) = I + a + a^2/2! + a^3/3! + ...\n\ |
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51 @end example\n\ |
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52 \n\ |
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53 @end ifinfo\n\ |
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54 The Taylor series is @emph{not} the way to compute the matrix\n\ |
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55 exponential; see Moler and Van Loan, @cite{Nineteen Dubious Ways to\n\ |
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56 Compute the Exponential of a Matrix}, SIAM Review, 1978. This routine\n\ |
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57 uses Ward's diagonal\n\ |
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58 @iftex\n\ |
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59 @tex\n\ |
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60 Pad\\'e\n\ |
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61 @end tex\n\ |
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62 @end iftex\n\ |
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63 @ifinfo\n\ |
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64 Pade'\n\ |
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65 @end ifinfo\n\ |
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66 approximation method with three step preconditioning (SIAM Journal on\n\ |
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67 Numerical Analysis, 1977). Diagonal\n\ |
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68 @iftex\n\ |
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69 @tex\n\ |
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70 Pad\\'e\n\ |
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71 @end tex\n\ |
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72 @end iftex\n\ |
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73 @ifinfo\n\ |
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74 Pade'\n\ |
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75 @end ifinfo\n\ |
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76 approximations are rational polynomials of matrices\n\ |
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77 @iftex\n\ |
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78 @tex\n\ |
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79 $D_q(a)^{-1}N_q(a)$\n\ |
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80 @end tex\n\ |
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81 @end iftex\n\ |
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82 @ifinfo\n\ |
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83 \n\ |
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84 @example\n\ |
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85 -1\n\ |
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86 D (a) N (a)\n\ |
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87 @end example\n\ |
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88 \n\ |
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89 @end ifinfo\n\ |
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90 whose Taylor series matches the first\n\ |
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91 @iftex\n\ |
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92 @tex\n\ |
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93 $2 q + 1 $\n\ |
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94 @end tex\n\ |
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95 @end iftex\n\ |
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96 @ifinfo\n\ |
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97 @code{2q+1}\n\ |
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98 @end ifinfo\n\ |
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99 terms of the Taylor series above; direct evaluation of the Taylor series\n\ |
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100 (with the same preconditioning steps) may be desirable in lieu of the\n\ |
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101 @iftex\n\ |
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102 @tex\n\ |
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103 Pad\\'e\n\ |
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104 @end tex\n\ |
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105 @end iftex\n\ |
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106 @ifinfo\n\ |
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107 Pade'\n\ |
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108 @end ifinfo\n\ |
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109 approximation when\n\ |
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110 @iftex\n\ |
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111 @tex\n\ |
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112 $D_q(a)$\n\ |
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113 @end tex\n\ |
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114 @end iftex\n\ |
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115 @ifinfo\n\ |
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116 @code{Dq(a)}\n\ |
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117 @end ifinfo\n\ |
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118 is ill-conditioned.\n\ |
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119 @end deftypefn") |
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120 { |
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121 octave_value retval; |
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122 |
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123 int nargin = args.length (); |
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124 |
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125 if (nargin != 1) |
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126 { |
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127 print_usage ("expm"); |
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128 return retval; |
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129 } |
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130 |
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131 octave_value arg = args(0); |
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132 |
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133 int nr = arg.rows (); |
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134 int nc = arg.columns (); |
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135 |
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136 int arg_is_empty = empty_arg ("expm", nr, nc); |
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137 |
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138 if (arg_is_empty < 0) |
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139 return retval; |
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140 if (arg_is_empty > 0) |
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141 return octave_value (Matrix ()); |
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142 |
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143 if (nr != nc) |
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144 { |
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145 gripe_square_matrix_required ("expm"); |
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146 return retval; |
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147 } |
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148 |
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149 if (arg.is_real_type ()) |
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150 { |
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151 Matrix m = arg.matrix_value (); |
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152 |
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153 if (error_state) |
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154 return retval; |
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155 else |
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156 retval = m.expm (); |
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157 } |
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158 else if (arg.is_complex_type ()) |
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159 { |
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160 ComplexMatrix m = arg.complex_matrix_value (); |
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161 |
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162 if (error_state) |
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163 return retval; |
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164 else |
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165 retval = m.expm (); |
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166 } |
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167 else |
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168 { |
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169 gripe_wrong_type_arg ("expm", arg); |
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170 } |
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171 |
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172 return retval; |
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173 } |
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174 |
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175 /* |
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176 ;;; Local Variables: *** |
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177 ;;; mode: C++ *** |
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178 ;;; End: *** |
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179 */ |
