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annotate libinterp/corefcn/dassl.cc @ 19840:c5270263d466 gui-release
close gui-release branch
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 30 Jan 2015 17:41:50 -0500 |
parents | 175b392e91fe |
children | 4197fc428c7d |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2013 John W. Eaton |
2928 | 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 | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 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 | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 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 "DASSL.h" | |
33 | |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
36 #include "gripes.h" | |
37 #include "oct-obj.h" | |
2968 | 38 #include "ov-fcn.h" |
5729 | 39 #include "ov-cell.h" |
2928 | 40 #include "pager.h" |
3243 | 41 #include "unwind-prot.h" |
2928 | 42 #include "utils.h" |
43 #include "variables.h" | |
44 | |
3998 | 45 #include "DASSL-opts.cc" |
46 | |
2928 | 47 // Global pointer for user defined function required by dassl. |
2968 | 48 static octave_function *dassl_fcn; |
2928 | 49 |
3991 | 50 // Global pointer for optional user defined jacobian function. |
51 static octave_function *dassl_jac; | |
52 | |
4140 | 53 // Have we warned about imaginary values returned from user function? |
54 static bool warned_fcn_imaginary = false; | |
55 static bool warned_jac_imaginary = false; | |
56 | |
3243 | 57 // Is this a recursive call? |
58 static int call_depth = 0; | |
59 | |
2928 | 60 ColumnVector |
3849 | 61 dassl_user_function (const ColumnVector& x, const ColumnVector& xdot, |
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62 double t, octave_idx_type& ires) |
2928 | 63 { |
64 ColumnVector retval; | |
65 | |
4628 | 66 assert (x.capacity () == xdot.capacity ()); |
2928 | 67 |
68 octave_value_list args; | |
4628 | 69 |
2928 | 70 args(2) = t; |
4628 | 71 args(1) = xdot; |
72 args(0) = x; | |
2928 | 73 |
74 if (dassl_fcn) | |
75 { | |
3544 | 76 octave_value_list tmp = dassl_fcn->do_multi_index_op (1, args); |
2928 | 77 |
78 if (error_state) | |
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79 { |
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80 gripe_user_supplied_eval ("dassl"); |
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81 return retval; |
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82 } |
2928 | 83 |
3849 | 84 int tlen = tmp.length (); |
85 if (tlen > 0 && tmp(0).is_defined ()) | |
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86 { |
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87 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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88 { |
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89 warning ("dassl: ignoring imaginary part returned from user-supplied function"); |
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90 warned_fcn_imaginary = true; |
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91 } |
4140 | 92 |
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93 retval = ColumnVector (tmp(0).vector_value ()); |
2928 | 94 |
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95 if (tlen > 1) |
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96 ires = tmp(1).int_value (); |
3849 | 97 |
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98 if (error_state || retval.length () == 0) |
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99 gripe_user_supplied_eval ("dassl"); |
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100 } |
2928 | 101 else |
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102 gripe_user_supplied_eval ("dassl"); |
2928 | 103 } |
104 | |
105 return retval; | |
106 } | |
107 | |
3991 | 108 Matrix |
109 dassl_user_jacobian (const ColumnVector& x, const ColumnVector& xdot, | |
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110 double t, double cj) |
3991 | 111 { |
112 Matrix retval; | |
113 | |
4628 | 114 assert (x.capacity () == xdot.capacity ()); |
3991 | 115 |
116 octave_value_list args; | |
117 | |
118 args(3) = cj; | |
119 args(2) = t; | |
4628 | 120 args(1) = xdot; |
121 args(0) = x; | |
3991 | 122 |
123 if (dassl_jac) | |
124 { | |
125 octave_value_list tmp = dassl_jac->do_multi_index_op (1, args); | |
126 | |
127 if (error_state) | |
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128 { |
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129 gripe_user_supplied_eval ("dassl"); |
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130 return retval; |
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131 } |
3991 | 132 |
133 int tlen = tmp.length (); | |
134 if (tlen > 0 && tmp(0).is_defined ()) | |
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135 { |
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136 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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137 { |
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138 warning ("dassl: ignoring imaginary part returned from user-supplied jacobian function"); |
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139 warned_jac_imaginary = true; |
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140 } |
4140 | 141 |
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142 retval = tmp(0).matrix_value (); |
3991 | 143 |
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144 if (error_state || retval.length () == 0) |
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145 gripe_user_supplied_eval ("dassl"); |
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146 } |
3991 | 147 else |
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148 gripe_user_supplied_eval ("dassl"); |
3991 | 149 } |
150 | |
151 return retval; | |
152 } | |
153 | |
3323 | 154 #define DASSL_ABORT() \ |
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155 return retval |
3323 | 156 |
157 #define DASSL_ABORT1(msg) \ | |
158 do \ | |
159 { \ | |
3747 | 160 ::error ("dassl: " msg); \ |
3323 | 161 DASSL_ABORT (); \ |
162 } \ | |
163 while (0) | |
164 | |
165 #define DASSL_ABORT2(fmt, arg) \ | |
166 do \ | |
167 { \ | |
3747 | 168 ::error ("dassl: " fmt, arg); \ |
3323 | 169 DASSL_ABORT (); \ |
170 } \ | |
171 while (0) | |
172 | |
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173 DEFUN (dassl, args, nargout, |
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174 "-*- texinfo -*-\n\ |
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175 @deftypefn {Built-in Function} {[@var{x}, @var{xdot}, @var{istate}, @var{msg}] =} dassl (@var{fcn}, @var{x_0}, @var{xdot_0}, @var{t}, @var{t_crit})\n\ |
4115 | 176 Solve the set of differential-algebraic equations\n\ |
177 @tex\n\ | |
4852 | 178 $$ 0 = f (x, \\dot{x}, t) $$\n\ |
4115 | 179 with\n\ |
180 $$ x(t_0) = x_0, \\dot{x}(t_0) = \\dot{x}_0 $$\n\ | |
181 @end tex\n\ | |
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182 @ifnottex\n\ |
4115 | 183 \n\ |
184 @example\n\ | |
4698 | 185 0 = f (x, xdot, t)\n\ |
4115 | 186 @end example\n\ |
187 \n\ | |
4912 | 188 @noindent\n\ |
4115 | 189 with\n\ |
190 \n\ | |
191 @example\n\ | |
192 x(t_0) = x_0, xdot(t_0) = xdot_0\n\ | |
193 @end example\n\ | |
194 \n\ | |
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195 @end ifnottex\n\ |
4115 | 196 The solution is returned in the matrices @var{x} and @var{xdot},\n\ |
197 with each row in the result matrices corresponding to one of the\n\ | |
3373 | 198 elements in the vector @var{t}. The first element of @var{t}\n\ |
4115 | 199 should be @math{t_0} and correspond to the initial state of the\n\ |
200 system @var{x_0} and its derivative @var{xdot_0}, so that the first\n\ | |
201 row of the output @var{x} is @var{x_0} and the first row\n\ | |
202 of the output @var{xdot} is @var{xdot_0}.\n\ | |
3373 | 203 \n\ |
8787 | 204 The first argument, @var{fcn}, is a string, inline, or function handle\n\ |
205 that names the function @math{f} to call to compute the vector of\n\ | |
206 residuals for the set of equations. It must have the form\n\ | |
3373 | 207 \n\ |
208 @example\n\ | |
209 @var{res} = f (@var{x}, @var{xdot}, @var{t})\n\ | |
210 @end example\n\ | |
2928 | 211 \n\ |
3373 | 212 @noindent\n\ |
4115 | 213 in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a\n\ |
3373 | 214 scalar.\n\ |
215 \n\ | |
8787 | 216 If @var{fcn} is a two-element string array or a two-element cell array\n\ |
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217 of strings, inline functions, or function handles, the first element names\n\ |
8787 | 218 the function @math{f} described above, and the second element names a\n\ |
219 function to compute the modified Jacobian\n\ | |
4115 | 220 \n\ |
221 @tex\n\ | |
222 $$\n\ | |
223 J = {\\partial f \\over \\partial x}\n\ | |
224 + c {\\partial f \\over \\partial \\dot{x}}\n\ | |
225 $$\n\ | |
226 @end tex\n\ | |
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227 @ifnottex\n\ |
10840 | 228 \n\ |
4888 | 229 @example\n\ |
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230 @group\n\ |
4115 | 231 df df\n\ |
232 jac = -- + c ------\n\ | |
233 dx d xdot\n\ | |
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234 @end group\n\ |
4115 | 235 @end example\n\ |
10840 | 236 \n\ |
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237 @end ifnottex\n\ |
4115 | 238 \n\ |
239 The modified Jacobian function must have the form\n\ | |
240 \n\ | |
241 @example\n\ | |
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242 @group\n\ |
4115 | 243 \n\ |
244 @var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c})\n\ | |
245 \n\ | |
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246 @end group\n\ |
4115 | 247 @end example\n\ |
248 \n\ | |
3373 | 249 The second and third arguments to @code{dassl} specify the initial\n\ |
250 condition of the states and their derivatives, and the fourth argument\n\ | |
4115 | 251 specifies a vector of output times at which the solution is desired,\n\ |
3373 | 252 including the time corresponding to the initial condition.\n\ |
2928 | 253 \n\ |
3373 | 254 The set of initial states and derivatives are not strictly required to\n\ |
10840 | 255 be consistent. In practice, however, @sc{dassl} is not very good at\n\ |
3373 | 256 determining a consistent set for you, so it is best if you ensure that\n\ |
257 the initial values result in the function evaluating to zero.\n\ | |
2928 | 258 \n\ |
3373 | 259 The fifth argument is optional, and may be used to specify a set of\n\ |
260 times that the DAE solver should not integrate past. It is useful for\n\ | |
261 avoiding difficulties with singularities and points where there is a\n\ | |
262 discontinuity in the derivative.\n\ | |
3964 | 263 \n\ |
4115 | 264 After a successful computation, the value of @var{istate} will be\n\ |
10840 | 265 greater than zero (consistent with the Fortran version of @sc{dassl}).\n\ |
4115 | 266 \n\ |
267 If the computation is not successful, the value of @var{istate} will be\n\ | |
268 less than zero and @var{msg} will contain additional information.\n\ | |
269 \n\ | |
3964 | 270 You can use the function @code{dassl_options} to set optional\n\ |
271 parameters for @code{dassl}.\n\ | |
5694 | 272 @seealso{daspk, dasrt, lsode}\n\ |
5642 | 273 @end deftypefn") |
2928 | 274 { |
275 octave_value_list retval; | |
276 | |
4140 | 277 warned_fcn_imaginary = false; |
278 warned_jac_imaginary = false; | |
279 | |
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280 unwind_protect frame; |
2928 | 281 |
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282 frame.protect_var (call_depth); |
3243 | 283 call_depth++; |
2928 | 284 |
3243 | 285 if (call_depth > 1) |
3323 | 286 DASSL_ABORT1 ("invalid recursive call"); |
2928 | 287 |
3243 | 288 int nargin = args.length (); |
289 | |
3991 | 290 if (nargin > 3 && nargin < 6 && nargout < 5) |
2928 | 291 { |
5729 | 292 std::string fcn_name, fname, jac_name, jname; |
3991 | 293 dassl_fcn = 0; |
294 dassl_jac = 0; | |
295 | |
296 octave_value f_arg = args(0); | |
297 | |
5729 | 298 if (f_arg.is_cell ()) |
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299 { |
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300 Cell c = f_arg.cell_value (); |
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301 if (c.length () == 1) |
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302 f_arg = c(0); |
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303 else if (c.length () == 2) |
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304 { |
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305 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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306 dassl_fcn = c(0).function_value (); |
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307 else |
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308 { |
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309 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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310 fname = "function y = "; |
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311 fname.append (fcn_name); |
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312 fname.append (" (x, xdot, t) y = "); |
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313 dassl_fcn = extract_function (c(0), "dassl", fcn_name, fname, |
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314 "; endfunction"); |
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315 } |
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316 |
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317 if (dassl_fcn) |
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318 { |
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319 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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320 dassl_jac = c(1).function_value (); |
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321 else |
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322 { |
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323 jac_name = unique_symbol_name ("__dassl_jac__"); |
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324 jname = "function jac = "; |
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325 jname.append (jac_name); |
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326 jname.append (" (x, xdot, t, cj) jac = "); |
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327 dassl_jac = extract_function (c(1), "dassl", jac_name, |
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328 jname, "; endfunction"); |
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330 if (!dassl_jac) |
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331 { |
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332 if (fcn_name.length ()) |
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333 clear_function (fcn_name); |
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334 dassl_fcn = 0; |
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335 } |
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336 } |
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337 } |
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338 } |
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339 else |
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340 DASSL_ABORT1 ("incorrect number of elements in cell array"); |
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341 } |
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343 if (!dassl_fcn && ! f_arg.is_cell ()) |
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344 { |
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345 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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346 dassl_fcn = f_arg.function_value (); |
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347 else |
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348 { |
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349 switch (f_arg.rows ()) |
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350 { |
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351 case 1: |
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352 do |
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353 { |
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354 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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355 fname = "function y = "; |
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356 fname.append (fcn_name); |
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357 fname.append (" (x, xdot, t) y = "); |
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358 dassl_fcn = extract_function (f_arg, "dassl", fcn_name, |
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359 fname, "; endfunction"); |
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360 } |
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361 while (0); |
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362 break; |
3991 | 363 |
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364 case 2: |
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365 { |
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366 string_vector tmp = f_arg.all_strings (); |
5729 | 367 |
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368 if (! error_state) |
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369 { |
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370 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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371 fname = "function y = "; |
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372 fname.append (fcn_name); |
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373 fname.append (" (x, xdot, t) y = "); |
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374 dassl_fcn = extract_function (tmp(0), "dassl", fcn_name, |
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375 fname, "; endfunction"); |
3991 | 376 |
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377 if (dassl_fcn) |
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378 { |
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379 jac_name = unique_symbol_name ("__dassl_jac__"); |
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380 jname = "function jac = "; |
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381 jname.append (jac_name); |
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382 jname.append (" (x, xdot, t, cj) jac = "); |
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383 dassl_jac = extract_function (tmp(1), "dassl", |
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384 jac_name, jname, |
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385 "; endfunction"); |
5729 | 386 |
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387 if (!dassl_jac) |
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388 { |
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389 if (fcn_name.length ()) |
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390 clear_function (fcn_name); |
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391 dassl_fcn = 0; |
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392 } |
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393 } |
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394 } |
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395 } |
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396 } |
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397 } |
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398 } |
3991 | 399 |
400 if (error_state || ! dassl_fcn) | |
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401 DASSL_ABORT (); |
3243 | 402 |
3419 | 403 ColumnVector state = ColumnVector (args(1).vector_value ()); |
2928 | 404 |
405 if (error_state) | |
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406 DASSL_ABORT1 ("expecting state vector as second argument"); |
3243 | 407 |
3419 | 408 ColumnVector deriv (args(2).vector_value ()); |
3243 | 409 |
410 if (error_state) | |
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411 DASSL_ABORT1 ("expecting derivative vector as third argument"); |
3243 | 412 |
3419 | 413 ColumnVector out_times (args(3).vector_value ()); |
3243 | 414 |
415 if (error_state) | |
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416 DASSL_ABORT1 ("expecting output time vector as fourth argument"); |
2928 | 417 |
3243 | 418 ColumnVector crit_times; |
419 int crit_times_set = 0; | |
420 if (nargin > 4) | |
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421 { |
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422 crit_times = ColumnVector (args(4).vector_value ()); |
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424 if (error_state) |
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425 DASSL_ABORT1 ("expecting critical time vector as fifth argument"); |
2928 | 426 |
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427 crit_times_set = 1; |
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428 } |
2928 | 429 |
3243 | 430 if (state.capacity () != deriv.capacity ()) |
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431 DASSL_ABORT1 ("x and xdot must have the same size"); |
3243 | 432 |
433 double tzero = out_times (0); | |
2928 | 434 |
3243 | 435 DAEFunc func (dassl_user_function); |
3991 | 436 if (dassl_jac) |
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437 func.set_jacobian_function (dassl_user_jacobian); |
3991 | 438 |
3243 | 439 DASSL dae (state, deriv, tzero, func); |
3991 | 440 |
4122 | 441 dae.set_options (dassl_opts); |
2928 | 442 |
3243 | 443 Matrix output; |
444 Matrix deriv_output; | |
445 | |
446 if (crit_times_set) | |
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447 output = dae.integrate (out_times, deriv_output, crit_times); |
3243 | 448 else |
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449 output = dae.integrate (out_times, deriv_output); |
2928 | 450 |
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451 if (fcn_name.length ()) |
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452 clear_function (fcn_name); |
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453 if (jac_name.length ()) |
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454 clear_function (jac_name); |
5729 | 455 |
3243 | 456 if (! error_state) |
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457 { |
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458 std::string msg = dae.error_message (); |
3997 | 459 |
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460 retval(3) = msg; |
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461 retval(2) = static_cast<double> (dae.integration_state ()); |
3997 | 462 |
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463 if (dae.integration_ok ()) |
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464 { |
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465 retval(1) = deriv_output; |
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466 retval(0) = output; |
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467 } |
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468 else |
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469 { |
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470 retval(1) = Matrix (); |
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471 retval(0) = Matrix (); |
3997 | 472 |
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473 if (nargout < 3) |
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474 error ("dassl: %s", msg.c_str ()); |
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475 } |
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476 } |
2928 | 477 } |
3243 | 478 else |
5823 | 479 print_usage (); |
3243 | 480 |
2928 | 481 return retval; |
482 } | |
483 | |
484 /* | |
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485 ## dassl-1.m |
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486 ## |
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487 ## Test dassl() function |
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488 ## |
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489 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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490 ## Comalco Research and Technology |
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491 ## 20 May 1998 |
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492 ## |
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493 ## Problem |
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494 ## |
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495 ## y1' = -y2, y1(0) = 1 |
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496 ## y2' = y1, y2(0) = 0 |
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497 ## |
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498 ## Solution |
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499 ## |
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500 ## y1(t) = cos(t) |
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501 ## y2(t) = sin(t) |
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502 ## |
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503 %!function res = __f (x, xdot, t) |
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504 %! res = [xdot(1)+x(2); xdot(2)-x(1)]; |
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505 %!endfunction |
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506 |
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507 %!test |
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508 %! |
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509 %! x0 = [1; 0]; |
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510 %! xdot0 = [0; 1]; |
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511 %! t = (0:1:10)'; |
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512 %! |
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513 %! tol = 100 * dassl_options ("relative tolerance"); |
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514 %! |
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515 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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516 %! |
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517 %! y = [cos(t), sin(t)]; |
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518 %! |
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519 %! assert (x, y, tol); |
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520 |
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521 ## dassl-2.m |
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522 ## |
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523 ## Test dassl() function |
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524 ## |
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525 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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526 ## Comalco Research and Technology |
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527 ## 20 May 1998 |
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528 ## |
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529 ## Based on SLATEC quick check for DASSL by Linda Petzold |
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530 ## |
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531 ## Problem |
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532 ## |
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533 ## x1' + 10*x1 = 0, x1(0) = 1 |
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534 ## x1 + x2 = 1, x2(0) = 0 |
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535 ## |
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536 ## |
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537 ## Solution |
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538 ## |
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539 ## x1(t) = exp(-10*t) |
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540 ## x2(t) = 1 - x(1) |
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541 ## |
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542 %!function res = __f (x, xdot, t) |
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543 %! res = [xdot(1)+10*x(1); x(1)+x(2)-1]; |
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544 %!endfunction |
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545 |
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546 %!test |
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547 %! |
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548 %! x0 = [1; 0]; |
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549 %! xdot0 = [-10; 10]; |
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550 %! t = (0:0.2:1)'; |
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551 %! |
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552 %! tol = 500 * dassl_options ("relative tolerance"); |
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553 %! |
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554 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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555 %! |
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556 %! y = [exp(-10*t), 1-exp(-10*t)]; |
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557 %! |
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558 %! assert (x, y, tol); |
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559 |
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560 %!test |
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561 %! old_tol = dassl_options ("absolute tolerance"); |
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562 %! dassl_options ("absolute tolerance", eps); |
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563 %! assert (dassl_options ("absolute tolerance") == eps); |
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564 %! ## Restore old value of tolerance |
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565 %! dassl_options ("absolute tolerance", old_tol); |
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566 |
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567 %!error dassl_options ("foo", 1, 2) |
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568 */ |