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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, write to the Free |
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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include <string> |
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29 |
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30 #include <iomanip> |
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31 #include <iostream> |
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32 |
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33 #include "LSODE.h" |
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34 #include "lo-mappers.h" |
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35 |
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36 #include "defun-dld.h" |
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37 #include "error.h" |
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38 #include "gripes.h" |
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39 #include "oct-obj.h" |
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40 #include "ov-fcn.h" |
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41 #include "ov-cell.h" |
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42 #include "pager.h" |
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43 #include "pr-output.h" |
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44 #include "unwind-prot.h" |
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45 #include "utils.h" |
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46 #include "variables.h" |
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47 |
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48 #include "LSODE-opts.cc" |
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49 |
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50 // Global pointer for user defined function required by lsode. |
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51 static octave_function *lsode_fcn; |
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52 |
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53 // Global pointer for optional user defined jacobian function used by lsode. |
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54 static octave_function *lsode_jac; |
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55 |
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56 // Have we warned about imaginary values returned from user function? |
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57 static bool warned_fcn_imaginary = false; |
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58 static bool warned_jac_imaginary = false; |
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59 |
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60 // Is this a recursive call? |
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61 static int call_depth = 0; |
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62 |
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63 ColumnVector |
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64 lsode_user_function (const ColumnVector& x, double t) |
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65 { |
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66 ColumnVector retval; |
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67 |
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68 octave_value_list args; |
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69 args(1) = t; |
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70 args(0) = x; |
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71 |
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72 if (lsode_fcn) |
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73 { |
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74 octave_value_list tmp = lsode_fcn->do_multi_index_op (1, args); |
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75 |
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76 if (error_state) |
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77 { |
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78 gripe_user_supplied_eval ("lsode"); |
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79 return retval; |
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80 } |
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81 |
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82 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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83 { |
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84 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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85 { |
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86 warning ("lsode: ignoring imaginary part returned from user-supplied function"); |
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87 warned_fcn_imaginary = true; |
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88 } |
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89 |
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90 retval = ColumnVector (tmp(0).vector_value ()); |
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91 |
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92 if (error_state || retval.length () == 0) |
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93 gripe_user_supplied_eval ("lsode"); |
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94 } |
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95 else |
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96 gripe_user_supplied_eval ("lsode"); |
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97 } |
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98 |
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99 return retval; |
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100 } |
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101 |
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102 Matrix |
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103 lsode_user_jacobian (const ColumnVector& x, double t) |
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104 { |
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105 Matrix retval; |
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106 |
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107 octave_value_list args; |
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108 args(1) = t; |
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109 args(0) = x; |
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110 |
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111 if (lsode_jac) |
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112 { |
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113 octave_value_list tmp = lsode_jac->do_multi_index_op (1, args); |
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114 |
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115 if (error_state) |
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116 { |
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117 gripe_user_supplied_eval ("lsode"); |
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118 return retval; |
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119 } |
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120 |
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121 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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122 { |
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123 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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124 { |
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125 warning ("lsode: ignoring imaginary part returned from user-supplied jacobian function"); |
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126 warned_jac_imaginary = true; |
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127 } |
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128 |
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129 retval = tmp(0).matrix_value (); |
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130 |
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131 if (error_state || retval.length () == 0) |
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132 gripe_user_supplied_eval ("lsode"); |
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133 } |
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134 else |
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135 gripe_user_supplied_eval ("lsode"); |
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136 } |
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137 |
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138 return retval; |
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139 } |
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140 |
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141 #define LSODE_ABORT() \ |
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142 do \ |
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143 { \ |
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144 unwind_protect::run_frame ("Flsode"); \ |
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145 return retval; \ |
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146 } \ |
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147 while (0) |
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148 |
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149 #define LSODE_ABORT1(msg) \ |
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150 do \ |
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151 { \ |
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152 ::error ("lsode: " msg); \ |
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153 LSODE_ABORT (); \ |
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154 } \ |
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155 while (0) |
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156 |
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157 #define LSODE_ABORT2(fmt, arg) \ |
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158 do \ |
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159 { \ |
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160 ::error ("lsode: " fmt, arg); \ |
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161 LSODE_ABORT (); \ |
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162 } \ |
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163 while (0) |
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164 |
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165 DEFUN_DLD (lsode, args, nargout, |
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166 "-*- texinfo -*-\n\ |
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167 @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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168 Solve the set of differential equations\n\ |
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169 @tex\n\ |
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170 $$ {dx \\over dt} = f (x, t) $$\n\ |
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171 with\n\ |
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172 $$ x(t_0) = x_0 $$\n\ |
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173 @end tex\n\ |
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174 @ifinfo\n\ |
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175 \n\ |
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176 @example\n\ |
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177 dx\n\ |
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178 -- = f(x, t)\n\ |
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179 dt\n\ |
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180 @end example\n\ |
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181 \n\ |
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182 with\n\ |
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183 \n\ |
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184 @example\n\ |
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185 x(t_0) = x_0\n\ |
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186 @end example\n\ |
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187 \n\ |
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188 @end ifinfo\n\ |
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189 The solution is returned in the matrix @var{x}, with each row\n\ |
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190 corresponding to an element of the vector @var{t}. The first element\n\ |
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191 of @var{t} should be @math{t_0} and should correspond to the initial\n\ |
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192 state of the system @var{x_0}, so that the first row of the output\n\ |
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193 is @var{x_0}.\n\ |
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194 \n\ |
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195 The first argument, @var{fcn}, is a string, or cell array of strings,\n\ |
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196 inline or function handles, that names the function to call to compute\n\ |
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197 the vector of right hand sides for the set of equations. The function\n\ |
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198 must have the form\n\ |
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199 \n\ |
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200 @example\n\ |
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201 @var{xdot} = f (@var{x}, @var{t})\n\ |
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202 @end example\n\ |
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203 \n\ |
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204 @noindent\n\ |
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205 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.\n\ |
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206 \n\ |
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207 If @var{fcn} is a two-element string array, the first element names the\n\ |
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208 function @math{f} described above, and the second element names a function\n\ |
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209 to compute the Jacobian of @math{f}. The Jacobian function must have the\n\ |
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210 form\n\ |
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211 \n\ |
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212 @example\n\ |
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213 @var{jac} = j (@var{x}, @var{t})\n\ |
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214 @end example\n\ |
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215 \n\ |
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216 in which @var{jac} is the matrix of partial derivatives\n\ |
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217 @tex\n\ |
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218 $$ J = {\\partial f_i \\over \\partial x_j} = \\left[\\matrix{\n\ |
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219 {\\partial f_1 \\over \\partial x_1}\n\ |
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220 & {\\partial f_1 \\over \\partial x_2}\n\ |
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221 & \\cdots\n\ |
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222 & {\\partial f_1 \\over \\partial x_N} \\cr\n\ |
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223 {\\partial f_2 \\over \\partial x_1}\n\ |
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224 & {\\partial f_2 \\over \\partial x_2}\n\ |
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225 & \\cdots\n\ |
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226 & {\\partial f_2 \\over \\partial x_N} \\cr\n\ |
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227 \\vdots & \\vdots & \\ddots & \\vdots \\cr\n\ |
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228 {\\partial f_3 \\over \\partial x_1}\n\ |
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229 & {\\partial f_3 \\over \\partial x_2}\n\ |
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230 & \\cdots\n\ |
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231 & {\\partial f_3 \\over \\partial x_N} \\cr}\\right]$$\n\ |
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232 @end tex\n\ |
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233 @ifinfo\n\ |
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234 \n\ |
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235 @example\n\ |
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236 | df_1 df_1 df_1 |\n\ |
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237 | ---- ---- ... ---- |\n\ |
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238 | dx_1 dx_2 dx_N |\n\ |
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239 | |\n\ |
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240 | df_2 df_2 df_2 |\n\ |
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241 | ---- ---- ... ---- |\n\ |
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242 df_i | dx_1 dx_2 dx_N |\n\ |
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243 jac = ---- = | |\n\ |
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244 dx_j | . . . . |\n\ |
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245 | . . . . |\n\ |
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246 | . . . . |\n\ |
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247 | |\n\ |
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248 | df_N df_N df_N |\n\ |
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249 | ---- ---- ... ---- |\n\ |
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250 | dx_1 dx_2 dx_N |\n\ |
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251 @end example\n\ |
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252 \n\ |
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253 @end ifinfo\n\ |
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254 \n\ |
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255 The second and third arguments specify the intial state of the system,\n\ |
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256 @math{x_0}, and the initial value of the independent variable @math{t_0}.\n\ |
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257 \n\ |
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258 The fourth argument is optional, and may be used to specify a set of\n\ |
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259 times that the ODE solver should not integrate past. It is useful for\n\ |
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260 avoiding difficulties with singularities and points where there is a\n\ |
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261 discontinuity in the derivative.\n\ |
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262 \n\ |
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263 After a successful computation, the value of @var{istate} will be 2\n\ |
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264 (consistent with the Fortran version of @sc{Lsode}).\n\ |
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265 \n\ |
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266 If the computation is not successful, @var{istate} will be something\n\ |
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267 other than 2 and @var{msg} will contain additional information.\n\ |
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268 \n\ |
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269 You can use the function @code{lsode_options} to set optional\n\ |
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270 parameters for @code{lsode}.\n\ |
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271 @seealso{daspk, dassl, dasrt}\n\ |
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272 @end deftypefn") |
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273 { |
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274 octave_value_list retval; |
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275 |
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276 warned_fcn_imaginary = false; |
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277 warned_jac_imaginary = false; |
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278 |
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279 unwind_protect::begin_frame ("Flsode"); |
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280 |
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281 unwind_protect_int (call_depth); |
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282 call_depth++; |
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283 |
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284 if (call_depth > 1) |
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285 LSODE_ABORT1 ("invalid recursive call"); |
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286 |
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287 int nargin = args.length (); |
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288 |
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289 if (nargin > 2 && nargin < 5 && nargout < 4) |
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290 { |
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291 std::string fcn_name, fname, jac_name, jname; |
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292 lsode_fcn = 0; |
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293 lsode_jac = 0; |
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294 |
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295 octave_value f_arg = args(0); |
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296 |
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297 if (f_arg.is_cell ()) |
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298 { |
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299 Cell c = f_arg.cell_value (); |
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300 if (c.length() == 1) |
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301 f_arg = c(0); |
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302 else if (c.length() == 2) |
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303 { |
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304 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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305 lsode_fcn = c(0).function_value (); |
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306 else |
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307 { |
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308 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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309 fname = "function y = "; |
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310 fname.append (fcn_name); |
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311 fname.append (" (x, t) y = "); |
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312 lsode_fcn = extract_function |
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313 (c(0), "lsode", fcn_name, fname, "; endfunction"); |
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314 } |
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315 |
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316 if (lsode_fcn) |
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317 { |
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318 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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319 lsode_jac = c(1).function_value (); |
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320 else |
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321 { |
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322 jac_name = unique_symbol_name ("__lsode_jac__"); |
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323 jname = "function jac = "; |
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324 jname.append(jac_name); |
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325 jname.append (" (x, t) jac = "); |
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326 lsode_jac = extract_function |
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327 (c(1), "lsode", jac_name, jname, "; endfunction"); |
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328 |
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329 if (!lsode_jac) |
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330 { |
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331 if (fcn_name.length()) |
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332 clear_function (fcn_name); |
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333 lsode_fcn = 0; |
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334 } |
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335 } |
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336 } |
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337 } |
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338 else |
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339 LSODE_ABORT1 ("incorrect number of elements in cell array"); |
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340 } |
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341 |
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342 if (!lsode_fcn && ! f_arg.is_cell()) |
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343 { |
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344 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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345 lsode_fcn = f_arg.function_value (); |
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346 else |
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347 { |
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348 switch (f_arg.rows ()) |
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349 { |
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350 case 1: |
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351 do |
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352 { |
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353 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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354 fname = "function y = "; |
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355 fname.append (fcn_name); |
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356 fname.append (" (x, t) y = "); |
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357 lsode_fcn = extract_function |
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358 (f_arg, "lsode", fcn_name, fname, "; endfunction"); |
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359 } |
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360 while (0); |
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361 break; |
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362 |
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363 case 2: |
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364 { |
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365 string_vector tmp = f_arg.all_strings (); |
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366 |
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367 if (! error_state) |
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368 { |
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369 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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370 fname = "function y = "; |
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371 fname.append (fcn_name); |
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372 fname.append (" (x, t) y = "); |
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373 lsode_fcn = extract_function |
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374 (tmp(0), "lsode", fcn_name, fname, "; endfunction"); |
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375 |
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376 if (lsode_fcn) |
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377 { |
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378 jac_name = unique_symbol_name ("__lsode_jac__"); |
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379 jname = "function jac = "; |
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380 jname.append(jac_name); |
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381 jname.append (" (x, t) jac = "); |
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382 lsode_jac = extract_function |
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383 (tmp(1), "lsode", jac_name, jname, |
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384 "; endfunction"); |
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385 |
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386 if (!lsode_jac) |
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387 { |
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388 if (fcn_name.length()) |
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389 clear_function (fcn_name); |
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390 lsode_fcn = 0; |
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391 } |
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392 } |
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393 } |
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394 } |
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395 break; |
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396 |
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397 default: |
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398 LSODE_ABORT1 |
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399 ("first arg should be a string or 2-element string array"); |
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400 } |
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401 } |
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402 } |
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403 |
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404 if (error_state || ! lsode_fcn) |
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405 LSODE_ABORT (); |
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406 |
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407 ColumnVector state (args(1).vector_value ()); |
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408 |
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409 if (error_state) |
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410 LSODE_ABORT1 ("expecting state vector as second argument"); |
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411 |
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412 ColumnVector out_times (args(2).vector_value ()); |
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413 |
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414 if (error_state) |
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415 LSODE_ABORT1 ("expecting output time vector as third argument"); |
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416 |
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417 ColumnVector crit_times; |
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418 |
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419 int crit_times_set = 0; |
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420 if (nargin > 3) |
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421 { |
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422 crit_times = ColumnVector (args(3).vector_value ()); |
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423 |
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424 if (error_state) |
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425 LSODE_ABORT1 ("expecting critical time vector as fourth argument"); |
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426 |
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427 crit_times_set = 1; |
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428 } |
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429 |
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3243
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430 double tzero = out_times (0); |
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431 |
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432 ODEFunc func (lsode_user_function); |
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433 if (lsode_jac) |
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434 func.set_jacobian_function (lsode_user_jacobian); |
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435 |
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3243
|
436 LSODE ode (state, tzero, func); |
|
|
437 |
|
4122
|
438 ode.set_options (lsode_opts); |
|
3243
|
439 |
|
3859
|
440 Matrix output; |
|
3243
|
441 if (crit_times_set) |
|
|
442 output = ode.integrate (out_times, crit_times); |
|
|
443 else |
|
|
444 output = ode.integrate (out_times); |
|
|
445 |
|
5729
|
446 if (fcn_name.length()) |
|
|
447 clear_function (fcn_name); |
|
|
448 if (jac_name.length()) |
|
|
449 clear_function (jac_name); |
|
|
450 |
|
3243
|
451 if (! error_state) |
|
|
452 { |
|
3997
|
453 std::string msg = ode.error_message (); |
|
|
454 |
|
|
455 retval(2) = msg; |
|
3959
|
456 retval(1) = static_cast<double> (ode.integration_state ()); |
|
|
457 |
|
|
458 if (ode.integration_ok ()) |
|
3971
|
459 retval(0) = output; |
|
3959
|
460 else |
|
|
461 { |
|
3971
|
462 retval(0) = Matrix (); |
|
3959
|
463 |
|
|
464 if (nargout < 2) |
|
3997
|
465 error ("lsode: %s", msg.c_str ()); |
|
3959
|
466 } |
|
3243
|
467 } |
|
|
468 } |
|
2928
|
469 else |
|
5823
|
470 print_usage (); |
|
2928
|
471 |
|
3243
|
472 unwind_protect::run_frame ("Flsode"); |
|
2928
|
473 |
|
|
474 return retval; |
|
|
475 } |
|
|
476 |
|
|
477 /* |
|
|
478 ;;; Local Variables: *** |
|
|
479 ;;; mode: C++ *** |
|
|
480 ;;; End: *** |
|
|
481 */ |
