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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 #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 "pager.h" |
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41 #include "pr-output.h" |
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42 #include "unwind-prot.h" |
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43 #include "utils.h" |
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44 #include "variables.h" |
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45 |
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46 #include "LSODE-opts.cc" |
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47 |
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48 // Global pointer for user defined function required by lsode. |
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49 static octave_function *lsode_fcn; |
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50 |
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51 // Global pointer for optional user defined jacobian function used by lsode. |
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52 static octave_function *lsode_jac; |
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53 |
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54 // Is this a recursive call? |
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55 static int call_depth = 0; |
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56 |
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57 ColumnVector |
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58 lsode_user_function (const ColumnVector& x, double t) |
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59 { |
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60 ColumnVector retval; |
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61 |
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62 int nstates = x.capacity (); |
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63 |
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64 octave_value_list args; |
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65 args(1) = t; |
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66 |
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67 Matrix m (nstates, 1); |
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68 for (int i = 0; i < nstates; i++) |
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69 m (i, 0) = x (i); |
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70 octave_value state (m); |
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71 args(0) = state; |
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72 |
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73 if (lsode_fcn) |
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74 { |
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75 octave_value_list tmp = lsode_fcn->do_multi_index_op (1, args); |
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76 |
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77 if (error_state) |
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78 { |
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79 gripe_user_supplied_eval ("lsode"); |
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80 return retval; |
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81 } |
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82 |
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83 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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84 { |
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85 retval = ColumnVector (tmp(0).vector_value ()); |
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86 |
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87 if (error_state || retval.length () == 0) |
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88 gripe_user_supplied_eval ("lsode"); |
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89 } |
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90 else |
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91 gripe_user_supplied_eval ("lsode"); |
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92 } |
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93 |
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94 return retval; |
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95 } |
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96 |
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97 Matrix |
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98 lsode_user_jacobian (const ColumnVector& x, double t) |
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99 { |
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100 Matrix retval; |
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101 |
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102 int nstates = x.capacity (); |
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103 |
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104 octave_value_list args; |
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105 args(1) = t; |
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106 |
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107 Matrix m (nstates, 1); |
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108 for (int i = 0; i < nstates; i++) |
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109 m (i, 0) = x (i); |
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110 octave_value state (m); |
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111 args(0) = state; |
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112 |
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113 if (lsode_jac) |
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114 { |
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115 octave_value_list tmp = lsode_jac->do_multi_index_op (1, args); |
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116 |
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117 if (error_state) |
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118 { |
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119 gripe_user_supplied_eval ("lsode"); |
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120 return retval; |
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121 } |
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122 |
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123 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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124 { |
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125 retval = tmp(0).matrix_value (); |
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126 |
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127 if (error_state || retval.length () == 0) |
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128 gripe_user_supplied_eval ("lsode"); |
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129 } |
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130 else |
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131 gripe_user_supplied_eval ("lsode"); |
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132 } |
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133 |
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134 return retval; |
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135 } |
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136 |
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137 #define LSODE_ABORT() \ |
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138 do \ |
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139 { \ |
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140 unwind_protect::run_frame ("Flsode"); \ |
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141 return retval; \ |
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142 } \ |
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143 while (0) |
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144 |
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145 #define LSODE_ABORT1(msg) \ |
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146 do \ |
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147 { \ |
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148 ::error ("lsode: " msg); \ |
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149 LSODE_ABORT (); \ |
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150 } \ |
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151 while (0) |
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152 |
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153 #define LSODE_ABORT2(fmt, arg) \ |
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154 do \ |
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155 { \ |
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156 ::error ("lsode: " fmt, arg); \ |
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157 LSODE_ABORT (); \ |
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158 } \ |
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159 while (0) |
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160 |
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161 DEFUN_DLD (lsode, args, nargout, |
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162 "-*- texinfo -*-\n\ |
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163 @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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164 Solve the set of differential equations\n\ |
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165 @tex\n\ |
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166 $$ {dx \\over dt} = f (x, t) $$\n\ |
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167 with\n\ |
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168 $$ x(t_0) = x_0 $$\n\ |
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169 @end tex\n\ |
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170 @ifinfo\n\ |
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171 \n\ |
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172 @example\n\ |
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173 dx\n\ |
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174 -- = f(x, t)\n\ |
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175 dt |
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176 @end example\n\ |
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177 \n\ |
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178 with\n\ |
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179 \n\ |
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180 @example\n\ |
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181 x(t_0) = x_0\n\ |
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182 @end example\n\ |
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183 \n\ |
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184 @end ifinfo\n\ |
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185 The solution is returned in the matrix @var{x}, with each row\n\ |
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186 corresponding to an element of the vector @var{t}. The first element\n\ |
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187 of @var{t} should be @math{t_0} and should correspond to the initial\n\ |
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188 state of the system @var{x_0}, so that the first row of the output\n\ |
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189 is @var{x_0}.\n\ |
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190 \n\ |
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191 The first argument, @var{fcn}, is a string that names the function to\n\ |
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192 call to compute the vector of right hand sides for the set of equations.\n\ |
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193 The function must have the form\n\ |
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194 \n\ |
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195 @example\n\ |
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196 @var{xdot} = f (@var{x}, @var{t})\n\ |
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197 @end example\n\ |
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198 \n\ |
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199 @noindent\n\ |
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200 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.\n\ |
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201 \n\ |
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202 If @var{fcn} is a two-element string array, the first element names the\n\ |
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203 function @math{f} described above, and the second element names a function\n\ |
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204 to compute the Jacobian of @math{f}. The Jacobian function must have the\n\ |
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205 form\n\ |
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206 \n\ |
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207 @example\n\ |
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208 @var{jac} = j (@var{x}, @var{t})\n\ |
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209 @end example\n\ |
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210 \n\ |
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211 in which @var{jac} is the matrix of partial derivatives\n\ |
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212 @tex\n\ |
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213 $$ J = {\\partial f_i \\over \\partial x_j} = \\left[\\matrix{\n\ |
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214 {\\partial f_1 \\over \\partial x_1}\n\ |
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215 & {\\partial f_1 \\over \\partial x_2}\n\ |
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216 & \\cdots\n\ |
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217 & {\\partial f_1 \\over \\partial x_N} \\cr\n\ |
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218 {\\partial f_2 \\over \\partial x_1}\n\ |
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219 & {\\partial f_2 \\over \\partial x_2}\n\ |
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220 & \\cdots\n\ |
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221 & {\\partial f_2 \\over \\partial x_N} \\cr\n\ |
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222 \\vdots & \\vdots & \\ddots & \\vdots \\cr\n\ |
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223 {\\partial f_3 \\over \\partial x_1}\n\ |
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224 & {\\partial f_3 \\over \\partial x_2}\n\ |
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225 & \\cdots\n\ |
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226 & {\\partial f_3 \\over \\partial x_N} \\cr}\\right]$$\n\ |
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227 @end tex\n\ |
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228 @ifinfo\n\ |
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229 \n\ |
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230 @example\n\ |
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231 | df_1 df_1 df_1 |\n\ |
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232 | ---- ---- ... ---- |\n\ |
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233 | dx_1 dx_2 dx_N |\n\ |
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234 | |\n\ |
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235 | df_2 df_2 df_2 |\n\ |
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236 | ---- ---- ... ---- |\n\ |
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237 df_i | dx_1 dx_2 dx_N |\n\ |
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238 jac = ---- = | |\n\ |
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239 dx_j | . . . . |\n\ |
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240 | . . . . |\n\ |
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241 | . . . . |\n\ |
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242 | |\n\ |
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243 | df_N df_N df_N |\n\ |
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244 | ---- ---- ... ---- |\n\ |
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245 | dx_1 dx_2 dx_N |\n\ |
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246 @end example\n\ |
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247 \n\ |
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248 @end ifinfo\n\ |
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249 \n\ |
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250 The second and third arguments specify the intial state of the system,\n\ |
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251 @math{x_0}, and the initial value of the independent variable @math{t_0}.\n\ |
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252 \n\ |
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253 The fourth argument is optional, and may be used to specify a set of\n\ |
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254 times that the ODE solver should not integrate past. It is useful for\n\ |
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255 avoiding difficulties with singularities and points where there is a\n\ |
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256 discontinuity in the derivative.\n\ |
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257 \n\ |
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258 After a successful computation, the value of @var{istate} will be 2\n\ |
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259 (consistent with the Fortran version of @sc{Lsode}).\n\ |
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260 \n\ |
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261 If the computation is not successful, @var{istate} will be something\n\ |
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262 other than 2 and @var{msg} will contain additional information.\n\ |
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263 \n\ |
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264 You can use the function @code{lsode_options} to set optional\n\ |
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265 parameters for @code{lsode}.\n\ |
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266 @end deftypefn\n\ |
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267 @seealso{daspk, dassl, dasrt, odessa}") |
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268 { |
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269 octave_value_list retval; |
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270 |
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271 unwind_protect::begin_frame ("Flsode"); |
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272 |
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273 unwind_protect_int (call_depth); |
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274 call_depth++; |
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275 |
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276 if (call_depth > 1) |
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277 LSODE_ABORT1 ("invalid recursive call"); |
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278 |
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279 int nargin = args.length (); |
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280 |
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281 if (nargin > 2 && nargin < 5 && nargout < 4) |
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282 { |
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283 lsode_fcn = 0; |
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284 lsode_jac = 0; |
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285 |
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286 octave_value f_arg = args(0); |
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287 |
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288 switch (f_arg.rows ()) |
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289 { |
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290 case 1: |
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291 lsode_fcn = extract_function |
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292 (f_arg, "lsode", "__lsode_fcn__", |
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293 "function xdot = __lsode_fcn__ (x, t) xdot = ", |
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294 "; endfunction"); |
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295 break; |
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296 |
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297 case 2: |
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298 { |
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299 string_vector tmp = f_arg.all_strings (); |
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300 |
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301 if (! error_state) |
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302 { |
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303 lsode_fcn = extract_function |
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304 (tmp(0), "lsode", "__lsode_fcn__", |
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305 "function xdot = __lsode_fcn__ (x, t) xdot = ", |
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306 "; endfunction"); |
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307 |
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308 if (lsode_fcn) |
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309 { |
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310 lsode_jac = extract_function |
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311 (tmp(1), "lsode", "__lsode_jac__", |
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312 "function jac = __lsode_jac__ (x, t) jac = ", |
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313 "; endfunction"); |
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314 |
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315 if (! lsode_jac) |
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316 lsode_fcn = 0; |
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317 } |
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318 } |
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319 } |
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320 break; |
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321 |
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322 default: |
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323 LSODE_ABORT1 |
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324 ("first arg should be a string or 2-element string array"); |
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325 } |
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326 |
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327 if (error_state || ! lsode_fcn) |
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328 LSODE_ABORT (); |
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329 |
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330 ColumnVector state (args(1).vector_value ()); |
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331 |
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332 if (error_state) |
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333 LSODE_ABORT1 ("expecting state vector as second argument"); |
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334 |
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335 ColumnVector out_times (args(2).vector_value ()); |
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336 |
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337 if (error_state) |
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338 LSODE_ABORT1 ("expecting output time vector as third argument"); |
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339 |
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340 ColumnVector crit_times; |
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341 |
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342 int crit_times_set = 0; |
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343 if (nargin > 3) |
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344 { |
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345 crit_times = ColumnVector (args(3).vector_value ()); |
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346 |
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347 if (error_state) |
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348 LSODE_ABORT1 ("expecting critical time vector as fourth argument"); |
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349 |
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350 crit_times_set = 1; |
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351 } |
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352 |
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353 double tzero = out_times (0); |
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354 |
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355 ODEFunc func (lsode_user_function); |
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356 if (lsode_jac) |
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357 func.set_jacobian_function (lsode_user_jacobian); |
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358 |
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359 LSODE ode (state, tzero, func); |
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360 |
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361 ode.copy (lsode_opts); |
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362 |
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363 Matrix output; |
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364 if (crit_times_set) |
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365 output = ode.integrate (out_times, crit_times); |
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366 else |
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367 output = ode.integrate (out_times); |
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368 |
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369 if (! error_state) |
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370 { |
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371 std::string msg = ode.error_message (); |
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372 |
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373 retval(2) = msg; |
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374 retval(1) = static_cast<double> (ode.integration_state ()); |
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375 |
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376 if (ode.integration_ok ()) |
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377 retval(0) = output; |
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378 else |
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379 { |
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380 retval(0) = Matrix (); |
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381 |
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382 if (nargout < 2) |
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383 error ("lsode: %s", msg.c_str ()); |
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384 } |
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385 } |
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386 } |
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387 else |
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388 print_usage ("lsode"); |
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389 |
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390 unwind_protect::run_frame ("Flsode"); |
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391 |
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392 return retval; |
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393 } |
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394 |
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395 /* |
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396 ;;; Local Variables: *** |
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397 ;;; mode: C++ *** |
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398 ;;; End: *** |
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399 */ |
