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DLD-FUNCTIONS/expm.cc (expm): Avoid GCC warning
author John W. Eaton <jwe@octave.org>
date Wed, 09 Jul 2008 12:26:37 -0400
parents 87865ed7405f
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2
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3 Copyright (C) 1996, 1997, 1999, 2000, 2002, 2005, 2006, 2007
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4 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 3 of the License, or (at your
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11 option) any 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, see
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20 <http://www.gnu.org/licenses/>.
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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 bool isfloat = arg.is_single_type ();
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138 int arg_is_empty = empty_arg ("expm", nr, nc);
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139
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140 if (arg_is_empty < 0)
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141 return retval;
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142
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143 if (arg_is_empty > 0)
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144 return isfloat ? octave_value (FloatMatrix ()) : octave_value (Matrix ());
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145
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146 if (nr != nc)
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147 {
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148 gripe_square_matrix_required ("expm");
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149 return retval;
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150 }
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151
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152 if (isfloat)
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153 {
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154 if (arg.is_real_type ())
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155 {
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156 FloatMatrix m = arg.float_matrix_value ();
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157
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158 if (error_state)
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159 return retval;
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160 else
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161 retval = m.expm ();
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162 }
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163 else if (arg.is_complex_type ())
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164 {
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165 FloatComplexMatrix m = arg.float_complex_matrix_value ();
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166
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167 if (error_state)
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168 return retval;
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169 else
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170 retval = m.expm ();
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171 }
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172 }
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173 else
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174 {
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175 if (arg.is_real_type ())
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176 {
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177 Matrix m = arg.matrix_value ();
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178
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179 if (error_state)
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180 return retval;
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181 else
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182 retval = m.expm ();
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183 }
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184 else if (arg.is_complex_type ())
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185 {
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186 ComplexMatrix m = arg.complex_matrix_value ();
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187
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188 if (error_state)
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189 return retval;
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190 else
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191 retval = m.expm ();
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192 }
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193 else
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194 {
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195 gripe_wrong_type_arg ("expm", arg);
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196 }
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197 }
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198
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199 return retval;
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200 }
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201
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202 /*
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203
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204 %!assert(expm ([-49, 24; -64, 31]), [-0.735758758144742, 0.551819099658089;
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205 %! -1.471517599088239, 1.103638240715556], 128*eps);
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206
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207 %!assert(expm ([1, 1; 0, 1]), [2.718281828459045, 2.718281828459045;
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208 %! 0.000000000000000, 2.718281828459045],4 * eps);
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209
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210 %!test
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211 %! arg = diag ([6, 6, 6], 1);
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212 %! result = [1, 6, 18, 36;
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213 %! 0, 1, 6, 18;
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214 %! 0, 0, 1, 6;
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215 %! 0, 0, 0, 1];
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216 %! assert(expm (arg), result);
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217
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218 %!assert(expm (single([-49, 24; -64, 31])), single([-0.735758758144742, ...
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219 %! 0.551819099658089; -1.471517599088239, 1.103638240715556]), ...
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220 %! 512*eps('single'));
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221
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222 %!assert(expm (single([1, 1; 0, 1])), single([2.718281828459045, ...
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223 %! 2.718281828459045; 0.000000000000000, 2.718281828459045]), ...
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224 %! 4 * eps('single'));
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225
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226 %!test
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227 %! arg = single(diag ([6, 6, 6], 1));
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228 %! result = single([1, 6, 18, 36;
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229 %! 0, 1, 6, 18;
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230 %! 0, 0, 1, 6;
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231 %! 0, 0, 0, 1]);
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232 %! assert(expm (arg), result);
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233
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234 %!error <Invalid call to expm.*> expm();
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235 %!error <Invalid call to expm.*> expm(1,2);
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236
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237 */
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238
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239 /*
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240 ;;; Local Variables: ***
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241 ;;; mode: C++ ***
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242 ;;; End: ***
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243 */