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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 3 of the License, or (at your |
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10 option) any 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, see |
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19 <http://www.gnu.org/licenses/>. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include <string> |
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28 |
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29 #include <iomanip> |
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30 #include <iostream> |
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31 |
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32 #include "LSODE.h" |
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33 #include "lo-mappers.h" |
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34 |
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35 #include "defun-dld.h" |
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36 #include "error.h" |
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37 #include "gripes.h" |
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38 #include "oct-obj.h" |
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39 #include "ov-fcn.h" |
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40 #include "ov-cell.h" |
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41 #include "pager.h" |
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42 #include "pr-output.h" |
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43 #include "unwind-prot.h" |
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44 #include "utils.h" |
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45 #include "variables.h" |
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46 |
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47 #include "LSODE-opts.cc" |
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48 |
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49 // Global pointer for user defined function required by lsode. |
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50 static octave_function *lsode_fcn; |
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51 |
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52 // Global pointer for optional user defined jacobian function used by lsode. |
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53 static octave_function *lsode_jac; |
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54 |
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55 // Have we warned about imaginary values returned from user function? |
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56 static bool warned_fcn_imaginary = false; |
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57 static bool warned_jac_imaginary = false; |
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58 |
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59 // Is this a recursive call? |
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60 static int call_depth = 0; |
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61 |
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62 ColumnVector |
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63 lsode_user_function (const ColumnVector& x, double t) |
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64 { |
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65 ColumnVector retval; |
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66 |
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67 octave_value_list args; |
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68 args(1) = t; |
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69 args(0) = x; |
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70 |
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71 if (lsode_fcn) |
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72 { |
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73 octave_value_list tmp = lsode_fcn->do_multi_index_op (1, args); |
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74 |
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75 if (error_state) |
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76 { |
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77 gripe_user_supplied_eval ("lsode"); |
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78 return retval; |
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79 } |
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80 |
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81 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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82 { |
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83 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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84 { |
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85 warning ("lsode: ignoring imaginary part returned from user-supplied function"); |
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86 warned_fcn_imaginary = true; |
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87 } |
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88 |
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89 retval = ColumnVector (tmp(0).vector_value ()); |
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90 |
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91 if (error_state || retval.length () == 0) |
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92 gripe_user_supplied_eval ("lsode"); |
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93 } |
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94 else |
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95 gripe_user_supplied_eval ("lsode"); |
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96 } |
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97 |
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98 return retval; |
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99 } |
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100 |
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101 Matrix |
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102 lsode_user_jacobian (const ColumnVector& x, double t) |
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103 { |
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104 Matrix retval; |
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105 |
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106 octave_value_list args; |
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107 args(1) = t; |
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108 args(0) = x; |
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109 |
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110 if (lsode_jac) |
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111 { |
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112 octave_value_list tmp = lsode_jac->do_multi_index_op (1, args); |
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113 |
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114 if (error_state) |
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115 { |
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116 gripe_user_supplied_eval ("lsode"); |
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117 return retval; |
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118 } |
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119 |
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120 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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121 { |
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122 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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123 { |
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124 warning ("lsode: ignoring imaginary part returned from user-supplied jacobian function"); |
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125 warned_jac_imaginary = true; |
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126 } |
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127 |
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128 retval = tmp(0).matrix_value (); |
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129 |
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130 if (error_state || retval.length () == 0) |
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131 gripe_user_supplied_eval ("lsode"); |
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132 } |
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133 else |
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134 gripe_user_supplied_eval ("lsode"); |
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135 } |
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136 |
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137 return retval; |
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138 } |
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139 |
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140 #define LSODE_ABORT() \ |
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141 do \ |
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142 { \ |
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143 unwind_protect::run_frame ("Flsode"); \ |
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144 return retval; \ |
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145 } \ |
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146 while (0) |
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147 |
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148 #define LSODE_ABORT1(msg) \ |
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149 do \ |
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150 { \ |
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151 ::error ("lsode: " msg); \ |
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152 LSODE_ABORT (); \ |
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153 } \ |
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154 while (0) |
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155 |
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156 #define LSODE_ABORT2(fmt, arg) \ |
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157 do \ |
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158 { \ |
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159 ::error ("lsode: " fmt, arg); \ |
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160 LSODE_ABORT (); \ |
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161 } \ |
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162 while (0) |
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163 |
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164 DEFUN_DLD (lsode, args, nargout, |
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165 "-*- texinfo -*-\n\ |
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166 @deftypefn {Loadable Function} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}, @var{t_crit})\n\ |
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167 Solve the set of differential equations\n\ |
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168 @tex\n\ |
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169 $$ {dx \\over dt} = f (x, t) $$\n\ |
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170 with\n\ |
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171 $$ x(t_0) = x_0 $$\n\ |
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172 @end tex\n\ |
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173 @ifinfo\n\ |
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174 \n\ |
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175 @example\n\ |
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176 dx\n\ |
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177 -- = f(x, t)\n\ |
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178 dt\n\ |
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179 @end example\n\ |
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180 \n\ |
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181 with\n\ |
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182 \n\ |
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183 @example\n\ |
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184 x(t_0) = x_0\n\ |
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185 @end example\n\ |
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186 \n\ |
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187 @end ifinfo\n\ |
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188 The solution is returned in the matrix @var{x}, with each row\n\ |
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189 corresponding to an element of the vector @var{t}. The first element\n\ |
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190 of @var{t} should be @math{t_0} and should correspond to the initial\n\ |
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191 state of the system @var{x_0}, so that the first row of the output\n\ |
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192 is @var{x_0}.\n\ |
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193 \n\ |
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194 The first argument, @var{fcn}, is a string, or cell array of strings,\n\ |
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195 inline or function handles, that names the function to call to compute\n\ |
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196 the vector of right hand sides for the set of equations. The function\n\ |
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197 must have the form\n\ |
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198 \n\ |
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199 @example\n\ |
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200 @var{xdot} = f (@var{x}, @var{t})\n\ |
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201 @end example\n\ |
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202 \n\ |
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203 @noindent\n\ |
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204 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.\n\ |
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205 \n\ |
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206 If @var{fcn} is a two-element string array, the first element names the\n\ |
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207 function @math{f} described above, and the second element names a function\n\ |
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208 to compute the Jacobian of @math{f}. The Jacobian function must have the\n\ |
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209 form\n\ |
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210 \n\ |
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211 @example\n\ |
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212 @var{jac} = j (@var{x}, @var{t})\n\ |
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213 @end example\n\ |
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214 \n\ |
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215 in which @var{jac} is the matrix of partial derivatives\n\ |
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216 @tex\n\ |
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217 $$ J = {\\partial f_i \\over \\partial x_j} = \\left[\\matrix{\n\ |
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218 {\\partial f_1 \\over \\partial x_1}\n\ |
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219 & {\\partial f_1 \\over \\partial x_2}\n\ |
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220 & \\cdots\n\ |
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221 & {\\partial f_1 \\over \\partial x_N} \\cr\n\ |
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222 {\\partial f_2 \\over \\partial x_1}\n\ |
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223 & {\\partial f_2 \\over \\partial x_2}\n\ |
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224 & \\cdots\n\ |
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225 & {\\partial f_2 \\over \\partial x_N} \\cr\n\ |
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226 \\vdots & \\vdots & \\ddots & \\vdots \\cr\n\ |
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227 {\\partial f_3 \\over \\partial x_1}\n\ |
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228 & {\\partial f_3 \\over \\partial x_2}\n\ |
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229 & \\cdots\n\ |
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230 & {\\partial f_3 \\over \\partial x_N} \\cr}\\right]$$\n\ |
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231 @end tex\n\ |
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232 @ifinfo\n\ |
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233 \n\ |
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234 @example\n\ |
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235 | df_1 df_1 df_1 |\n\ |
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236 | ---- ---- ... ---- |\n\ |
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237 | dx_1 dx_2 dx_N |\n\ |
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238 | |\n\ |
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239 | df_2 df_2 df_2 |\n\ |
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240 | ---- ---- ... ---- |\n\ |
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241 df_i | dx_1 dx_2 dx_N |\n\ |
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242 jac = ---- = | |\n\ |
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243 dx_j | . . . . |\n\ |
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244 | . . . . |\n\ |
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245 | . . . . |\n\ |
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246 | |\n\ |
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247 | df_N df_N df_N |\n\ |
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248 | ---- ---- ... ---- |\n\ |
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249 | dx_1 dx_2 dx_N |\n\ |
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250 @end example\n\ |
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251 \n\ |
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252 @end ifinfo\n\ |
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253 \n\ |
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254 The second and third arguments specify the initial state of the system,\n\ |
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255 @math{x_0}, and the initial value of the independent variable @math{t_0}.\n\ |
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256 \n\ |
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257 The fourth argument is optional, and may be used to specify a set of\n\ |
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258 times that the ODE solver should not integrate past. It is useful for\n\ |
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259 avoiding difficulties with singularities and points where there is a\n\ |
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260 discontinuity in the derivative.\n\ |
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261 \n\ |
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262 After a successful computation, the value of @var{istate} will be 2\n\ |
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263 (consistent with the Fortran version of @sc{Lsode}).\n\ |
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264 \n\ |
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265 If the computation is not successful, @var{istate} will be something\n\ |
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266 other than 2 and @var{msg} will contain additional information.\n\ |
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267 \n\ |
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268 You can use the function @code{lsode_options} to set optional\n\ |
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269 parameters for @code{lsode}.\n\ |
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270 @seealso{daspk, dassl, dasrt}\n\ |
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271 @end deftypefn") |
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272 { |
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273 octave_value_list retval; |
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274 |
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275 warned_fcn_imaginary = false; |
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276 warned_jac_imaginary = false; |
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277 |
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278 unwind_protect::begin_frame ("Flsode"); |
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279 |
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280 unwind_protect_int (call_depth); |
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281 call_depth++; |
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282 |
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283 if (call_depth > 1) |
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284 LSODE_ABORT1 ("invalid recursive call"); |
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285 |
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286 int nargin = args.length (); |
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287 |
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288 if (nargin > 2 && nargin < 5 && nargout < 4) |
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289 { |
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290 std::string fcn_name, fname, jac_name, jname; |
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291 lsode_fcn = 0; |
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292 lsode_jac = 0; |
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293 |
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294 octave_value f_arg = args(0); |
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295 |
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296 if (f_arg.is_cell ()) |
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297 { |
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298 Cell c = f_arg.cell_value (); |
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299 if (c.length() == 1) |
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300 f_arg = c(0); |
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301 else if (c.length() == 2) |
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302 { |
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303 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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304 lsode_fcn = c(0).function_value (); |
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305 else |
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306 { |
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307 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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308 fname = "function y = "; |
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309 fname.append (fcn_name); |
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310 fname.append (" (x, t) y = "); |
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311 lsode_fcn = extract_function |
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312 (c(0), "lsode", fcn_name, fname, "; endfunction"); |
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313 } |
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314 |
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315 if (lsode_fcn) |
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316 { |
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317 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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318 lsode_jac = c(1).function_value (); |
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319 else |
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320 { |
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321 jac_name = unique_symbol_name ("__lsode_jac__"); |
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322 jname = "function jac = "; |
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323 jname.append(jac_name); |
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324 jname.append (" (x, t) jac = "); |
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325 lsode_jac = extract_function |
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326 (c(1), "lsode", jac_name, jname, "; endfunction"); |
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327 |
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328 if (!lsode_jac) |
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329 { |
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330 if (fcn_name.length()) |
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331 clear_function (fcn_name); |
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332 lsode_fcn = 0; |
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333 } |
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334 } |
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335 } |
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336 } |
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337 else |
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338 LSODE_ABORT1 ("incorrect number of elements in cell array"); |
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339 } |
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340 |
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341 if (!lsode_fcn && ! f_arg.is_cell()) |
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342 { |
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343 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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344 lsode_fcn = f_arg.function_value (); |
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345 else |
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346 { |
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347 switch (f_arg.rows ()) |
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348 { |
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349 case 1: |
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350 do |
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351 { |
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352 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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353 fname = "function y = "; |
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354 fname.append (fcn_name); |
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355 fname.append (" (x, t) y = "); |
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356 lsode_fcn = extract_function |
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357 (f_arg, "lsode", fcn_name, fname, "; endfunction"); |
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358 } |
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359 while (0); |
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360 break; |
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361 |
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362 case 2: |
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363 { |
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364 string_vector tmp = f_arg.all_strings (); |
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365 |
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366 if (! error_state) |
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367 { |
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368 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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369 fname = "function y = "; |
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370 fname.append (fcn_name); |
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371 fname.append (" (x, t) y = "); |
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372 lsode_fcn = extract_function |
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373 (tmp(0), "lsode", fcn_name, fname, "; endfunction"); |
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374 |
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375 if (lsode_fcn) |
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376 { |
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377 jac_name = unique_symbol_name ("__lsode_jac__"); |
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378 jname = "function jac = "; |
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379 jname.append(jac_name); |
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380 jname.append (" (x, t) jac = "); |
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381 lsode_jac = extract_function |
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382 (tmp(1), "lsode", jac_name, jname, |
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383 "; endfunction"); |
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384 |
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385 if (!lsode_jac) |
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386 { |
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387 if (fcn_name.length()) |
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388 clear_function (fcn_name); |
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389 lsode_fcn = 0; |
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390 } |
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391 } |
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392 } |
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393 } |
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394 break; |
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395 |
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396 default: |
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397 LSODE_ABORT1 |
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398 ("first arg should be a string or 2-element string array"); |
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399 } |
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400 } |
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401 } |
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402 |
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403 if (error_state || ! lsode_fcn) |
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404 LSODE_ABORT (); |
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405 |
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406 ColumnVector state (args(1).vector_value ()); |
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407 |
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408 if (error_state) |
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409 LSODE_ABORT1 ("expecting state vector as second argument"); |
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410 |
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411 ColumnVector out_times (args(2).vector_value ()); |
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412 |
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413 if (error_state) |
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414 LSODE_ABORT1 ("expecting output time vector as third argument"); |
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415 |
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416 ColumnVector crit_times; |
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417 |
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418 int crit_times_set = 0; |
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419 if (nargin > 3) |
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420 { |
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421 crit_times = ColumnVector (args(3).vector_value ()); |
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422 |
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423 if (error_state) |
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424 LSODE_ABORT1 ("expecting critical time vector as fourth argument"); |
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425 |
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426 crit_times_set = 1; |
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427 } |
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428 |
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429 double tzero = out_times (0); |
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430 |
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431 ODEFunc func (lsode_user_function); |
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432 if (lsode_jac) |
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433 func.set_jacobian_function (lsode_user_jacobian); |
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434 |
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3243
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435 LSODE ode (state, tzero, func); |
|
|
436 |
|
4122
|
437 ode.set_options (lsode_opts); |
|
3243
|
438 |
|
3859
|
439 Matrix output; |
|
3243
|
440 if (crit_times_set) |
|
|
441 output = ode.integrate (out_times, crit_times); |
|
|
442 else |
|
|
443 output = ode.integrate (out_times); |
|
|
444 |
|
5729
|
445 if (fcn_name.length()) |
|
|
446 clear_function (fcn_name); |
|
|
447 if (jac_name.length()) |
|
|
448 clear_function (jac_name); |
|
|
449 |
|
3243
|
450 if (! error_state) |
|
|
451 { |
|
3997
|
452 std::string msg = ode.error_message (); |
|
|
453 |
|
|
454 retval(2) = msg; |
|
3959
|
455 retval(1) = static_cast<double> (ode.integration_state ()); |
|
|
456 |
|
|
457 if (ode.integration_ok ()) |
|
3971
|
458 retval(0) = output; |
|
3959
|
459 else |
|
|
460 { |
|
3971
|
461 retval(0) = Matrix (); |
|
3959
|
462 |
|
|
463 if (nargout < 2) |
|
3997
|
464 error ("lsode: %s", msg.c_str ()); |
|
3959
|
465 } |
|
3243
|
466 } |
|
|
467 } |
|
2928
|
468 else |
|
5823
|
469 print_usage (); |
|
2928
|
470 |
|
3243
|
471 unwind_protect::run_frame ("Flsode"); |
|
2928
|
472 |
|
|
473 return retval; |
|
|
474 } |
|
|
475 |
|
|
476 /* |
|
|
477 ;;; Local Variables: *** |
|
|
478 ;;; mode: C++ *** |
|
|
479 ;;; End: *** |
|
|
480 */ |
