|
2928
|
1 /* |
|
|
2 |
|
|
3 Copyright (C) 1996, 1997 John W. Eaton |
|
|
4 |
|
|
5 This file is part of Octave. |
|
|
6 |
|
|
7 Octave is free software; you can redistribute it and/or modify it |
|
|
8 under the terms of the GNU General Public License as published by the |
|
|
9 Free Software Foundation; either version 2, or (at your option) any |
|
|
10 later version. |
|
|
11 |
|
|
12 Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
15 for more details. |
|
|
16 |
|
|
17 You should have received a copy of the GNU General Public License |
|
|
18 along with Octave; see the file COPYING. If not, write to the Free |
|
|
19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
|
20 |
|
|
21 */ |
|
|
22 |
|
|
23 #ifdef HAVE_CONFIG_H |
|
|
24 #include <config.h> |
|
|
25 #endif |
|
|
26 |
|
|
27 #include <string> |
|
|
28 |
|
3567
|
29 #include <iomanip> |
|
3523
|
30 #include <iostream> |
|
2928
|
31 |
|
|
32 #include "LSODE.h" |
|
|
33 #include "lo-mappers.h" |
|
|
34 |
|
|
35 #include "defun-dld.h" |
|
|
36 #include "error.h" |
|
|
37 #include "gripes.h" |
|
|
38 #include "oct-obj.h" |
|
2968
|
39 #include "ov-fcn.h" |
|
2928
|
40 #include "pager.h" |
|
3952
|
41 #include "pr-output.h" |
|
3243
|
42 #include "unwind-prot.h" |
|
2928
|
43 #include "utils.h" |
|
|
44 #include "variables.h" |
|
|
45 |
|
3998
|
46 #include "LSODE-opts.cc" |
|
|
47 |
|
2928
|
48 // Global pointer for user defined function required by lsode. |
|
2968
|
49 static octave_function *lsode_fcn; |
|
2928
|
50 |
|
|
51 // Global pointer for optional user defined jacobian function used by lsode. |
|
2968
|
52 static octave_function *lsode_jac; |
|
2928
|
53 |
|
4140
|
54 // Have we warned about imaginary values returned from user function? |
|
|
55 static bool warned_fcn_imaginary = false; |
|
|
56 static bool warned_jac_imaginary = false; |
|
|
57 |
|
3243
|
58 // Is this a recursive call? |
|
|
59 static int call_depth = 0; |
|
|
60 |
|
2928
|
61 ColumnVector |
|
|
62 lsode_user_function (const ColumnVector& x, double t) |
|
|
63 { |
|
|
64 ColumnVector retval; |
|
|
65 |
|
|
66 octave_value_list args; |
|
|
67 args(1) = t; |
|
4628
|
68 args(0) = x; |
|
2928
|
69 |
|
|
70 if (lsode_fcn) |
|
|
71 { |
|
3544
|
72 octave_value_list tmp = lsode_fcn->do_multi_index_op (1, args); |
|
2928
|
73 |
|
|
74 if (error_state) |
|
|
75 { |
|
|
76 gripe_user_supplied_eval ("lsode"); |
|
|
77 return retval; |
|
|
78 } |
|
|
79 |
|
|
80 if (tmp.length () > 0 && tmp(0).is_defined ()) |
|
|
81 { |
|
4140
|
82 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
|
|
83 { |
|
|
84 warning ("lsode: ignoring imaginary part returned from user-supplied function"); |
|
|
85 warned_fcn_imaginary = true; |
|
|
86 } |
|
|
87 |
|
3419
|
88 retval = ColumnVector (tmp(0).vector_value ()); |
|
2928
|
89 |
|
|
90 if (error_state || retval.length () == 0) |
|
|
91 gripe_user_supplied_eval ("lsode"); |
|
|
92 } |
|
|
93 else |
|
|
94 gripe_user_supplied_eval ("lsode"); |
|
|
95 } |
|
|
96 |
|
|
97 return retval; |
|
|
98 } |
|
|
99 |
|
|
100 Matrix |
|
|
101 lsode_user_jacobian (const ColumnVector& x, double t) |
|
|
102 { |
|
|
103 Matrix retval; |
|
|
104 |
|
|
105 octave_value_list args; |
|
|
106 args(1) = t; |
|
4628
|
107 args(0) = x; |
|
2928
|
108 |
|
|
109 if (lsode_jac) |
|
|
110 { |
|
3544
|
111 octave_value_list tmp = lsode_jac->do_multi_index_op (1, args); |
|
2928
|
112 |
|
|
113 if (error_state) |
|
|
114 { |
|
|
115 gripe_user_supplied_eval ("lsode"); |
|
|
116 return retval; |
|
|
117 } |
|
|
118 |
|
|
119 if (tmp.length () > 0 && tmp(0).is_defined ()) |
|
|
120 { |
|
4140
|
121 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
|
|
122 { |
|
|
123 warning ("lsode: ignoring imaginary part returned from user-supplied jacobian function"); |
|
|
124 warned_jac_imaginary = true; |
|
|
125 } |
|
|
126 |
|
2928
|
127 retval = tmp(0).matrix_value (); |
|
|
128 |
|
|
129 if (error_state || retval.length () == 0) |
|
|
130 gripe_user_supplied_eval ("lsode"); |
|
|
131 } |
|
|
132 else |
|
|
133 gripe_user_supplied_eval ("lsode"); |
|
|
134 } |
|
|
135 |
|
|
136 return retval; |
|
|
137 } |
|
|
138 |
|
3323
|
139 #define LSODE_ABORT() \ |
|
|
140 do \ |
|
|
141 { \ |
|
|
142 unwind_protect::run_frame ("Flsode"); \ |
|
|
143 return retval; \ |
|
|
144 } \ |
|
|
145 while (0) |
|
|
146 |
|
|
147 #define LSODE_ABORT1(msg) \ |
|
|
148 do \ |
|
|
149 { \ |
|
3747
|
150 ::error ("lsode: " msg); \ |
|
3323
|
151 LSODE_ABORT (); \ |
|
|
152 } \ |
|
|
153 while (0) |
|
|
154 |
|
|
155 #define LSODE_ABORT2(fmt, arg) \ |
|
|
156 do \ |
|
|
157 { \ |
|
3747
|
158 ::error ("lsode: " fmt, arg); \ |
|
3323
|
159 LSODE_ABORT (); \ |
|
|
160 } \ |
|
|
161 while (0) |
|
|
162 |
|
2928
|
163 DEFUN_DLD (lsode, args, nargout, |
|
3373
|
164 "-*- texinfo -*-\n\ |
|
4115
|
165 @deftypefn {Loadable Function} {[@var{x}, @var{istate}, @var{msg}]} lsode (@var{fcn}, @var{x_0}, @var{t}, @var{t_crit})\n\ |
|
|
166 Solve the set of differential equations\n\ |
|
|
167 @tex\n\ |
|
|
168 $$ {dx \\over dt} = f (x, t) $$\n\ |
|
|
169 with\n\ |
|
|
170 $$ x(t_0) = x_0 $$\n\ |
|
|
171 @end tex\n\ |
|
|
172 @ifinfo\n\ |
|
|
173 \n\ |
|
|
174 @example\n\ |
|
|
175 dx\n\ |
|
|
176 -- = f(x, t)\n\ |
|
4117
|
177 dt\n\ |
|
4115
|
178 @end example\n\ |
|
|
179 \n\ |
|
|
180 with\n\ |
|
|
181 \n\ |
|
|
182 @example\n\ |
|
|
183 x(t_0) = x_0\n\ |
|
|
184 @end example\n\ |
|
|
185 \n\ |
|
|
186 @end ifinfo\n\ |
|
|
187 The solution is returned in the matrix @var{x}, with each row\n\ |
|
|
188 corresponding to an element of the vector @var{t}. The first element\n\ |
|
|
189 of @var{t} should be @math{t_0} and should correspond to the initial\n\ |
|
|
190 state of the system @var{x_0}, so that the first row of the output\n\ |
|
|
191 is @var{x_0}.\n\ |
|
3373
|
192 \n\ |
|
|
193 The first argument, @var{fcn}, is a string that names the function to\n\ |
|
|
194 call to compute the vector of right hand sides for the set of equations.\n\ |
|
4115
|
195 The function must have the form\n\ |
|
2928
|
196 \n\ |
|
3373
|
197 @example\n\ |
|
|
198 @var{xdot} = f (@var{x}, @var{t})\n\ |
|
|
199 @end example\n\ |
|
2928
|
200 \n\ |
|
3373
|
201 @noindent\n\ |
|
4115
|
202 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.\n\ |
|
|
203 \n\ |
|
|
204 If @var{fcn} is a two-element string array, the first element names the\n\ |
|
|
205 function @math{f} described above, and the second element names a function\n\ |
|
|
206 to compute the Jacobian of @math{f}. The Jacobian function must have the\n\ |
|
|
207 form\n\ |
|
|
208 \n\ |
|
|
209 @example\n\ |
|
|
210 @var{jac} = j (@var{x}, @var{t})\n\ |
|
|
211 @end example\n\ |
|
|
212 \n\ |
|
|
213 in which @var{jac} is the matrix of partial derivatives\n\ |
|
|
214 @tex\n\ |
|
|
215 $$ J = {\\partial f_i \\over \\partial x_j} = \\left[\\matrix{\n\ |
|
|
216 {\\partial f_1 \\over \\partial x_1}\n\ |
|
|
217 & {\\partial f_1 \\over \\partial x_2}\n\ |
|
|
218 & \\cdots\n\ |
|
|
219 & {\\partial f_1 \\over \\partial x_N} \\cr\n\ |
|
|
220 {\\partial f_2 \\over \\partial x_1}\n\ |
|
|
221 & {\\partial f_2 \\over \\partial x_2}\n\ |
|
|
222 & \\cdots\n\ |
|
|
223 & {\\partial f_2 \\over \\partial x_N} \\cr\n\ |
|
|
224 \\vdots & \\vdots & \\ddots & \\vdots \\cr\n\ |
|
|
225 {\\partial f_3 \\over \\partial x_1}\n\ |
|
|
226 & {\\partial f_3 \\over \\partial x_2}\n\ |
|
|
227 & \\cdots\n\ |
|
|
228 & {\\partial f_3 \\over \\partial x_N} \\cr}\\right]$$\n\ |
|
|
229 @end tex\n\ |
|
|
230 @ifinfo\n\ |
|
|
231 \n\ |
|
|
232 @example\n\ |
|
|
233 | df_1 df_1 df_1 |\n\ |
|
|
234 | ---- ---- ... ---- |\n\ |
|
|
235 | dx_1 dx_2 dx_N |\n\ |
|
|
236 | |\n\ |
|
|
237 | df_2 df_2 df_2 |\n\ |
|
|
238 | ---- ---- ... ---- |\n\ |
|
|
239 df_i | dx_1 dx_2 dx_N |\n\ |
|
|
240 jac = ---- = | |\n\ |
|
|
241 dx_j | . . . . |\n\ |
|
|
242 | . . . . |\n\ |
|
|
243 | . . . . |\n\ |
|
|
244 | |\n\ |
|
|
245 | df_N df_N df_N |\n\ |
|
|
246 | ---- ---- ... ---- |\n\ |
|
|
247 | dx_1 dx_2 dx_N |\n\ |
|
|
248 @end example\n\ |
|
|
249 \n\ |
|
|
250 @end ifinfo\n\ |
|
|
251 \n\ |
|
|
252 The second and third arguments specify the intial state of the system,\n\ |
|
|
253 @math{x_0}, and the initial value of the independent variable @math{t_0}.\n\ |
|
2928
|
254 \n\ |
|
3373
|
255 The fourth argument is optional, and may be used to specify a set of\n\ |
|
|
256 times that the ODE solver should not integrate past. It is useful for\n\ |
|
|
257 avoiding difficulties with singularities and points where there is a\n\ |
|
|
258 discontinuity in the derivative.\n\ |
|
3964
|
259 \n\ |
|
4115
|
260 After a successful computation, the value of @var{istate} will be 2\n\ |
|
|
261 (consistent with the Fortran version of @sc{Lsode}).\n\ |
|
|
262 \n\ |
|
|
263 If the computation is not successful, @var{istate} will be something\n\ |
|
|
264 other than 2 and @var{msg} will contain additional information.\n\ |
|
|
265 \n\ |
|
3964
|
266 You can use the function @code{lsode_options} to set optional\n\ |
|
|
267 parameters for @code{lsode}.\n\ |
|
4115
|
268 @end deftypefn\n\ |
|
|
269 @seealso{daspk, dassl, dasrt, odessa}") |
|
2928
|
270 { |
|
|
271 octave_value_list retval; |
|
|
272 |
|
4140
|
273 warned_fcn_imaginary = false; |
|
|
274 warned_jac_imaginary = false; |
|
|
275 |
|
3243
|
276 unwind_protect::begin_frame ("Flsode"); |
|
2928
|
277 |
|
3243
|
278 unwind_protect_int (call_depth); |
|
|
279 call_depth++; |
|
|
280 |
|
|
281 if (call_depth > 1) |
|
3323
|
282 LSODE_ABORT1 ("invalid recursive call"); |
|
2928
|
283 |
|
3243
|
284 int nargin = args.length (); |
|
2928
|
285 |
|
3959
|
286 if (nargin > 2 && nargin < 5 && nargout < 4) |
|
2928
|
287 { |
|
3991
|
288 lsode_fcn = 0; |
|
|
289 lsode_jac = 0; |
|
|
290 |
|
3243
|
291 octave_value f_arg = args(0); |
|
2928
|
292 |
|
3243
|
293 switch (f_arg.rows ()) |
|
|
294 { |
|
|
295 case 1: |
|
|
296 lsode_fcn = extract_function |
|
3991
|
297 (f_arg, "lsode", "__lsode_fcn__", |
|
3243
|
298 "function xdot = __lsode_fcn__ (x, t) xdot = ", |
|
|
299 "; endfunction"); |
|
|
300 break; |
|
2928
|
301 |
|
3243
|
302 case 2: |
|
2928
|
303 { |
|
3991
|
304 string_vector tmp = f_arg.all_strings (); |
|
2928
|
305 |
|
3243
|
306 if (! error_state) |
|
2928
|
307 { |
|
3243
|
308 lsode_fcn = extract_function |
|
|
309 (tmp(0), "lsode", "__lsode_fcn__", |
|
|
310 "function xdot = __lsode_fcn__ (x, t) xdot = ", |
|
2928
|
311 "; endfunction"); |
|
|
312 |
|
3243
|
313 if (lsode_fcn) |
|
|
314 { |
|
|
315 lsode_jac = extract_function |
|
|
316 (tmp(1), "lsode", "__lsode_jac__", |
|
|
317 "function jac = __lsode_jac__ (x, t) jac = ", |
|
|
318 "; endfunction"); |
|
|
319 |
|
|
320 if (! lsode_jac) |
|
|
321 lsode_fcn = 0; |
|
|
322 } |
|
2928
|
323 } |
|
|
324 } |
|
3243
|
325 break; |
|
2928
|
326 |
|
3243
|
327 default: |
|
3323
|
328 LSODE_ABORT1 |
|
|
329 ("first arg should be a string or 2-element string array"); |
|
3243
|
330 } |
|
2928
|
331 |
|
3243
|
332 if (error_state || ! lsode_fcn) |
|
3323
|
333 LSODE_ABORT (); |
|
2928
|
334 |
|
3419
|
335 ColumnVector state (args(1).vector_value ()); |
|
2928
|
336 |
|
|
337 if (error_state) |
|
3323
|
338 LSODE_ABORT1 ("expecting state vector as second argument"); |
|
3243
|
339 |
|
3419
|
340 ColumnVector out_times (args(2).vector_value ()); |
|
3243
|
341 |
|
|
342 if (error_state) |
|
3323
|
343 LSODE_ABORT1 ("expecting output time vector as third argument"); |
|
2928
|
344 |
|
3243
|
345 ColumnVector crit_times; |
|
2928
|
346 |
|
3243
|
347 int crit_times_set = 0; |
|
|
348 if (nargin > 3) |
|
|
349 { |
|
3419
|
350 crit_times = ColumnVector (args(3).vector_value ()); |
|
2928
|
351 |
|
3243
|
352 if (error_state) |
|
3323
|
353 LSODE_ABORT1 ("expecting critical time vector as fourth argument"); |
|
2928
|
354 |
|
3243
|
355 crit_times_set = 1; |
|
|
356 } |
|
2928
|
357 |
|
3243
|
358 double tzero = out_times (0); |
|
|
359 |
|
|
360 ODEFunc func (lsode_user_function); |
|
|
361 if (lsode_jac) |
|
|
362 func.set_jacobian_function (lsode_user_jacobian); |
|
2928
|
363 |
|
3243
|
364 LSODE ode (state, tzero, func); |
|
|
365 |
|
4122
|
366 ode.set_options (lsode_opts); |
|
3243
|
367 |
|
3859
|
368 Matrix output; |
|
3243
|
369 if (crit_times_set) |
|
|
370 output = ode.integrate (out_times, crit_times); |
|
|
371 else |
|
|
372 output = ode.integrate (out_times); |
|
|
373 |
|
|
374 if (! error_state) |
|
|
375 { |
|
3997
|
376 std::string msg = ode.error_message (); |
|
|
377 |
|
|
378 retval(2) = msg; |
|
3959
|
379 retval(1) = static_cast<double> (ode.integration_state ()); |
|
|
380 |
|
|
381 if (ode.integration_ok ()) |
|
3971
|
382 retval(0) = output; |
|
3959
|
383 else |
|
|
384 { |
|
3971
|
385 retval(0) = Matrix (); |
|
3959
|
386 |
|
|
387 if (nargout < 2) |
|
3997
|
388 error ("lsode: %s", msg.c_str ()); |
|
3959
|
389 } |
|
3243
|
390 } |
|
|
391 } |
|
2928
|
392 else |
|
3243
|
393 print_usage ("lsode"); |
|
2928
|
394 |
|
3243
|
395 unwind_protect::run_frame ("Flsode"); |
|
2928
|
396 |
|
|
397 return retval; |
|
|
398 } |
|
|
399 |
|
|
400 /* |
|
|
401 ;;; Local Variables: *** |
|
|
402 ;;; mode: C++ *** |
|
|
403 ;;; End: *** |
|
|
404 */ |
