Mercurial > octave
annotate libinterp/corefcn/dassl.cc @ 20940:48b2ad5ee801
maint: Rename oct-obj.[cc|h] to ovl.[cc|h] for clarity.
* libinterp/corefcn/oct-obj.h: Replaced. Contains a #warning issued if used in
compilation and includes "ovl.h" instead. Original file renamed to
libinterp/octave-value/ovl.h
* libinterp/corefcn/oct-obj.cc: Renamed to libinterp/octave-value/ovl.cc.
* oct-obj.cc (ovl ()): Added new function to return empty octave_value_list.
* libinterp/corefcn/module.mk: Remove oct-obj.cc from build system.
* libinterp/octave-value/module.mk: Add ovl.h and ovl.cc to build system.
* mk-opts.pl, annotation-dialog.h, Cell.cc, __contourc__.cc, __dsearchn__.cc,
__lin_interpn__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc,
betainc.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, dlmread.cc, eig.cc,
error.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
graphics.cc, gripes.cc, help.cc, hess.cc, hex2num.cc, hook-fcn.h, input.cc,
input.h, inv.cc, kron.cc, load-save.cc, lookup.cc, ls-hdf5.cc, ls-mat-ascii.cc,
ls-mat4.cc, ls-mat5.cc, ls-oct-binary.cc, ls-oct-text.cc, lsode.cc, lu.cc,
luinc.cc, max.cc, mex.cc, oct-hist.cc, oct-lvalue.cc, oct-lvalue.h, oct-map.h,
oct-stream.cc, oct.h, ordschur.cc, pager.cc, pinv.cc, pr-output.cc, quad.cc,
quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sparse-xpow.cc,
strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symtab.h, syscalls.cc, sysdep.cc,
time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc,
variables.cc, xpow.cc, __delaunayn__.cc, __glpk__.cc, __voronoi__.cc,
audiodevinfo.cc, audioread.cc, chol.cc, convhulln.cc, dmperm.cc, qr.cc,
symbfact.cc, mkbuiltins, ov-base-diag.h, ov-base-int.cc, ov-base-mat.cc,
ov-base-mat.h, ov-base-scalar.cc, ov-base-sparse.cc, ov-base-sparse.h,
ov-base.cc, ov-bool-mat.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc, ov-colon.cc,
ov-complex.cc, ov-cs-list.h, ov-cx-mat.cc, ov-dld-fcn.cc, ov-fcn.cc, ov-fcn.h,
ov-float.cc, ov-flt-complex.cc, ov-flt-cx-mat.cc, ov-flt-re-mat.cc,
ov-int16.cc, ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.h, ov-mex-fcn.cc,
ov-perm.h, ov-range.cc, ov-re-mat.cc, ov-scalar.cc, ov-str-mat.cc,
ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc, ov-usr-fcn.cc,
ov-usr-fcn.h, ov.cc, octave.cc, op-b-b.cc, op-b-bm.cc, op-b-sbm.cc, op-bm-b.cc,
op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc, op-chm.cc, op-class.cc,
op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc, op-cm-scm.cc, op-cm-sm.cc,
op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc, op-cs-scm.cc, op-cs-sm.cc,
op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc, op-double-conv.cc, op-fcdm-fcdm.cc,
op-fcdm-fdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc,
op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc,
op-fdm-fdm.cc, op-float-conv.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc,
op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc,
op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc,
op-int-conv.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc,
op-m-sm.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-range.cc, op-s-cm.cc,
op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc,
op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc,
op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc,
op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc,
op-struct.cc, op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc,
parse.h, pt-arg-list.cc, pt-assign.cc, pt-binop.cc, pt-cbinop.cc, pt-cell.cc,
pt-colon.cc, pt-const.cc, pt-eval.h, pt-fcn-handle.cc, pt-funcall.h, pt-id.cc,
pt-idx.cc, pt-jump.cc, pt-mat.cc, pt-select.cc, pt-unop.cc, token.cc,
Array-sym.cc: replace '#include "oct-obj.h"' with '#include "ovl.h"'.
author | Rik <rik@octave.org> |
---|---|
date | Fri, 18 Dec 2015 16:04:56 -0800 |
parents | 6f0bd96f93c0 |
children | 9db35d2042be |
rev | line source |
---|---|
2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2015 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" | |
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37 #include "ovl.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 | |
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66 assert (x.numel () == xdot.numel ()); |
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 { | |
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76 octave_value_list tmp; |
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77 |
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78 try |
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79 { |
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80 tmp = dassl_fcn->do_multi_index_op (1, args); |
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81 } |
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82 catch (octave_execution_exception& e) |
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83 { |
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84 gripe_user_supplied_eval (e, "dassl"); |
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85 } |
2928 | 86 |
3849 | 87 int tlen = tmp.length (); |
88 if (tlen > 0 && tmp(0).is_defined ()) | |
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89 { |
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90 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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91 { |
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92 warning ("dassl: ignoring imaginary part returned from user-supplied function"); |
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93 warned_fcn_imaginary = true; |
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94 } |
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96 retval = tmp(0).vector_value (); |
2928 | 97 |
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98 if (tlen > 1) |
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99 ires = tmp(1).int_value (); |
3849 | 100 |
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101 if (retval.numel () == 0) |
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102 gripe_user_supplied_eval ("dassl"); |
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103 } |
2928 | 104 else |
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105 gripe_user_supplied_eval ("dassl"); |
2928 | 106 } |
107 | |
108 return retval; | |
109 } | |
110 | |
3991 | 111 Matrix |
112 dassl_user_jacobian (const ColumnVector& x, const ColumnVector& xdot, | |
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113 double t, double cj) |
3991 | 114 { |
115 Matrix retval; | |
116 | |
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117 assert (x.numel () == xdot.numel ()); |
3991 | 118 |
119 octave_value_list args; | |
120 | |
121 args(3) = cj; | |
122 args(2) = t; | |
4628 | 123 args(1) = xdot; |
124 args(0) = x; | |
3991 | 125 |
126 if (dassl_jac) | |
127 { | |
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128 octave_value_list tmp; |
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129 |
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130 try |
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131 { |
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132 tmp = dassl_jac->do_multi_index_op (1, args); |
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133 } |
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134 catch (octave_execution_exception& e) |
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135 { |
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136 gripe_user_supplied_eval (e, "dassl"); |
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137 } |
3991 | 138 |
139 int tlen = tmp.length (); | |
140 if (tlen > 0 && tmp(0).is_defined ()) | |
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141 { |
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142 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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143 { |
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144 warning ("dassl: ignoring imaginary part returned from user-supplied jacobian function"); |
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145 warned_jac_imaginary = true; |
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146 } |
4140 | 147 |
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148 retval = tmp(0).matrix_value (); |
3991 | 149 |
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150 if (retval.numel () == 0) |
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151 gripe_user_supplied_eval ("dassl"); |
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152 } |
3991 | 153 else |
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154 gripe_user_supplied_eval ("dassl"); |
3991 | 155 } |
156 | |
157 return retval; | |
158 } | |
159 | |
3323 | 160 #define DASSL_ABORT() \ |
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161 return retval |
3323 | 162 |
163 #define DASSL_ABORT1(msg) \ | |
164 do \ | |
165 { \ | |
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166 error ("dassl: " msg); \ |
3323 | 167 DASSL_ABORT (); \ |
168 } \ | |
169 while (0) | |
170 | |
171 #define DASSL_ABORT2(fmt, arg) \ | |
172 do \ | |
173 { \ | |
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174 error ("dassl: " fmt, arg); \ |
3323 | 175 DASSL_ABORT (); \ |
176 } \ | |
177 while (0) | |
178 | |
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179 DEFUN (dassl, args, nargout, |
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180 "-*- texinfo -*-\n\ |
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181 @deftypefn {} {[@var{x}, @var{xdot}, @var{istate}, @var{msg}] =} dassl (@var{fcn}, @var{x_0}, @var{xdot_0}, @var{t}, @var{t_crit})\n\ |
4115 | 182 Solve the set of differential-algebraic equations\n\ |
183 @tex\n\ | |
4852 | 184 $$ 0 = f (x, \\dot{x}, t) $$\n\ |
4115 | 185 with\n\ |
186 $$ x(t_0) = x_0, \\dot{x}(t_0) = \\dot{x}_0 $$\n\ | |
187 @end tex\n\ | |
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188 @ifnottex\n\ |
4115 | 189 \n\ |
190 @example\n\ | |
4698 | 191 0 = f (x, xdot, t)\n\ |
4115 | 192 @end example\n\ |
193 \n\ | |
4912 | 194 @noindent\n\ |
4115 | 195 with\n\ |
196 \n\ | |
197 @example\n\ | |
198 x(t_0) = x_0, xdot(t_0) = xdot_0\n\ | |
199 @end example\n\ | |
200 \n\ | |
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201 @end ifnottex\n\ |
4115 | 202 The solution is returned in the matrices @var{x} and @var{xdot},\n\ |
203 with each row in the result matrices corresponding to one of the\n\ | |
3373 | 204 elements in the vector @var{t}. The first element of @var{t}\n\ |
4115 | 205 should be @math{t_0} and correspond to the initial state of the\n\ |
206 system @var{x_0} and its derivative @var{xdot_0}, so that the first\n\ | |
207 row of the output @var{x} is @var{x_0} and the first row\n\ | |
208 of the output @var{xdot} is @var{xdot_0}.\n\ | |
3373 | 209 \n\ |
8787 | 210 The first argument, @var{fcn}, is a string, inline, or function handle\n\ |
211 that names the function @math{f} to call to compute the vector of\n\ | |
212 residuals for the set of equations. It must have the form\n\ | |
3373 | 213 \n\ |
214 @example\n\ | |
215 @var{res} = f (@var{x}, @var{xdot}, @var{t})\n\ | |
216 @end example\n\ | |
2928 | 217 \n\ |
3373 | 218 @noindent\n\ |
4115 | 219 in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a\n\ |
3373 | 220 scalar.\n\ |
221 \n\ | |
8787 | 222 If @var{fcn} is a two-element string array or a two-element cell array\n\ |
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223 of strings, inline functions, or function handles, the first element names\n\ |
8787 | 224 the function @math{f} described above, and the second element names a\n\ |
225 function to compute the modified Jacobian\n\ | |
4115 | 226 \n\ |
227 @tex\n\ | |
228 $$\n\ | |
229 J = {\\partial f \\over \\partial x}\n\ | |
230 + c {\\partial f \\over \\partial \\dot{x}}\n\ | |
231 $$\n\ | |
232 @end tex\n\ | |
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233 @ifnottex\n\ |
10840 | 234 \n\ |
4888 | 235 @example\n\ |
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236 @group\n\ |
4115 | 237 df df\n\ |
238 jac = -- + c ------\n\ | |
239 dx d xdot\n\ | |
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240 @end group\n\ |
4115 | 241 @end example\n\ |
10840 | 242 \n\ |
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243 @end ifnottex\n\ |
4115 | 244 \n\ |
245 The modified Jacobian function must have the form\n\ | |
246 \n\ | |
247 @example\n\ | |
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248 @group\n\ |
4115 | 249 \n\ |
250 @var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c})\n\ | |
251 \n\ | |
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252 @end group\n\ |
4115 | 253 @end example\n\ |
254 \n\ | |
3373 | 255 The second and third arguments to @code{dassl} specify the initial\n\ |
256 condition of the states and their derivatives, and the fourth argument\n\ | |
4115 | 257 specifies a vector of output times at which the solution is desired,\n\ |
3373 | 258 including the time corresponding to the initial condition.\n\ |
2928 | 259 \n\ |
3373 | 260 The set of initial states and derivatives are not strictly required to\n\ |
10840 | 261 be consistent. In practice, however, @sc{dassl} is not very good at\n\ |
3373 | 262 determining a consistent set for you, so it is best if you ensure that\n\ |
263 the initial values result in the function evaluating to zero.\n\ | |
2928 | 264 \n\ |
3373 | 265 The fifth argument is optional, and may be used to specify a set of\n\ |
266 times that the DAE solver should not integrate past. It is useful for\n\ | |
267 avoiding difficulties with singularities and points where there is a\n\ | |
268 discontinuity in the derivative.\n\ | |
3964 | 269 \n\ |
4115 | 270 After a successful computation, the value of @var{istate} will be\n\ |
10840 | 271 greater than zero (consistent with the Fortran version of @sc{dassl}).\n\ |
4115 | 272 \n\ |
273 If the computation is not successful, the value of @var{istate} will be\n\ | |
274 less than zero and @var{msg} will contain additional information.\n\ | |
275 \n\ | |
3964 | 276 You can use the function @code{dassl_options} to set optional\n\ |
277 parameters for @code{dassl}.\n\ | |
5694 | 278 @seealso{daspk, dasrt, lsode}\n\ |
5642 | 279 @end deftypefn") |
2928 | 280 { |
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281 int nargin = args.length (); |
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282 |
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283 if (nargin < 4 || nargin > 5) |
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284 print_usage (); |
2928 | 285 |
4140 | 286 warned_fcn_imaginary = false; |
287 warned_jac_imaginary = false; | |
288 | |
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289 octave_value_list retval (4); |
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290 |
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291 unwind_protect frame; |
2928 | 292 |
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293 frame.protect_var (call_depth); |
3243 | 294 call_depth++; |
2928 | 295 |
3243 | 296 if (call_depth > 1) |
3323 | 297 DASSL_ABORT1 ("invalid recursive call"); |
2928 | 298 |
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299 std::string fcn_name, fname, jac_name, jname; |
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300 dassl_fcn = 0; |
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301 dassl_jac = 0; |
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302 |
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303 octave_value f_arg = args(0); |
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304 |
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305 if (f_arg.is_cell ()) |
2928 | 306 { |
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307 Cell c = f_arg.cell_value (); |
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308 if (c.numel () == 1) |
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309 f_arg = c(0); |
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310 else if (c.numel () == 2) |
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311 { |
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312 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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313 dassl_fcn = c(0).function_value (); |
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314 else |
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315 { |
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316 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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317 fname = "function y = "; |
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318 fname.append (fcn_name); |
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319 fname.append (" (x, xdot, t) y = "); |
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320 dassl_fcn = extract_function (c(0), "dassl", fcn_name, fname, |
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321 "; endfunction"); |
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322 } |
3991 | 323 |
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324 if (dassl_fcn) |
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325 { |
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326 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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327 dassl_jac = c(1).function_value (); |
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328 else |
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329 { |
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330 jac_name = unique_symbol_name ("__dassl_jac__"); |
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331 jname = "function jac = "; |
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332 jname.append (jac_name); |
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333 jname.append (" (x, xdot, t, cj) jac = "); |
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334 dassl_jac = extract_function (c(1), "dassl", jac_name, |
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335 jname, "; endfunction"); |
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336 |
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337 if (! dassl_jac) |
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338 { |
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339 if (fcn_name.length ()) |
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340 clear_function (fcn_name); |
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341 dassl_fcn = 0; |
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342 } |
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343 } |
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344 } |
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345 } |
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346 else |
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347 DASSL_ABORT1 ("incorrect number of elements in cell array"); |
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348 } |
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349 |
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350 if (! dassl_fcn && ! f_arg.is_cell ()) |
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351 { |
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352 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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353 dassl_fcn = f_arg.function_value (); |
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354 else |
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355 { |
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356 switch (f_arg.rows ()) |
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357 { |
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358 case 1: |
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359 do |
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360 { |
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361 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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362 fname = "function y = "; |
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363 fname.append (fcn_name); |
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364 fname.append (" (x, xdot, t) y = "); |
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365 dassl_fcn = extract_function (f_arg, "dassl", fcn_name, |
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366 fname, "; endfunction"); |
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367 } |
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368 while (0); |
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369 break; |
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370 |
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371 case 2: |
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372 { |
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373 string_vector tmp = f_arg.all_strings (); |
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375 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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376 fname = "function y = "; |
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377 fname.append (fcn_name); |
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378 fname.append (" (x, xdot, t) y = "); |
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379 dassl_fcn = extract_function (tmp(0), "dassl", fcn_name, |
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380 fname, "; endfunction"); |
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382 if (dassl_fcn) |
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383 { |
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384 jac_name = unique_symbol_name ("__dassl_jac__"); |
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385 jname = "function jac = "; |
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386 jname.append (jac_name); |
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387 jname.append (" (x, xdot, t, cj) jac = "); |
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388 dassl_jac = extract_function (tmp(1), "dassl", |
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389 jac_name, jname, |
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390 "; endfunction"); |
5729 | 391 |
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392 if (! dassl_jac) |
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393 { |
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394 if (fcn_name.length ()) |
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395 clear_function (fcn_name); |
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396 dassl_fcn = 0; |
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397 } |
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398 } |
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399 } |
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400 } |
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401 } |
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402 } |
3243 | 403 |
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404 if (! dassl_fcn) |
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405 DASSL_ABORT (); |
3243 | 406 |
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407 ColumnVector state = args(1).xvector_value ("dassl: initial state X_0 must be a vector"); |
2928 | 408 |
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409 ColumnVector deriv = args(2).xvector_value ("dassl: initial derivatives XDOT_0 must be a vector"); |
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410 |
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411 ColumnVector out_times = args(3).xvector_value ("dassl: output time variable T must be a vector"); |
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413 ColumnVector crit_times; |
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414 int crit_times_set = 0; |
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415 if (nargin > 4) |
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416 { |
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417 crit_times = args(4).xvector_value ("dassl: list of critical times T_CRIT must be a vector"); |
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419 crit_times_set = 1; |
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420 } |
3991 | 421 |
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422 if (state.numel () != deriv.numel ()) |
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423 DASSL_ABORT1 ("X and XDOT_0 must have the same size"); |
3991 | 424 |
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425 double tzero = out_times (0); |
2928 | 426 |
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427 DAEFunc func (dassl_user_function); |
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428 if (dassl_jac) |
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429 func.set_jacobian_function (dassl_user_jacobian); |
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431 DASSL dae (state, deriv, tzero, func); |
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433 dae.set_options (dassl_opts); |
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435 Matrix output; |
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436 Matrix deriv_output; |
3997 | 437 |
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438 if (crit_times_set) |
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439 output = dae.integrate (out_times, deriv_output, crit_times); |
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440 else |
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441 output = dae.integrate (out_times, deriv_output); |
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442 |
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443 if (fcn_name.length ()) |
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444 clear_function (fcn_name); |
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445 if (jac_name.length ()) |
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446 clear_function (jac_name); |
3997 | 447 |
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448 std::string msg = dae.error_message (); |
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449 |
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450 if (dae.integration_ok ()) |
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451 { |
20892 | 452 retval(0) = output; |
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453 retval(1) = deriv_output; |
2928 | 454 } |
3243 | 455 else |
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456 { |
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457 if (nargout < 3) |
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458 error ("dassl: %s", msg.c_str ()); |
20892 | 459 |
460 retval(0) = Matrix (); | |
461 retval(1) = Matrix (); | |
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462 } |
3243 | 463 |
20892 | 464 retval(2) = static_cast<double> (dae.integration_state ()); |
465 retval(3) = msg; | |
466 | |
2928 | 467 return retval; |
468 } | |
469 | |
470 /* | |
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471 ## dassl-1.m |
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472 ## |
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473 ## Test dassl() function |
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474 ## |
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475 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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476 ## Comalco Research and Technology |
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477 ## 20 May 1998 |
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478 ## |
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479 ## Problem |
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480 ## |
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481 ## y1' = -y2, y1(0) = 1 |
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482 ## y2' = y1, y2(0) = 0 |
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483 ## |
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484 ## Solution |
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485 ## |
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486 ## y1(t) = cos(t) |
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487 ## y2(t) = sin(t) |
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488 ## |
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489 %!function res = __f (x, xdot, t) |
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490 %! res = [xdot(1)+x(2); xdot(2)-x(1)]; |
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491 %!endfunction |
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492 |
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493 %!test |
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494 %! |
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495 %! x0 = [1; 0]; |
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496 %! xdot0 = [0; 1]; |
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497 %! t = (0:1:10)'; |
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498 %! |
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499 %! tol = 100 * dassl_options ("relative tolerance"); |
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500 %! |
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501 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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502 %! |
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503 %! y = [cos(t), sin(t)]; |
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504 %! |
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505 %! assert (x, y, tol); |
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506 |
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507 ## dassl-2.m |
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508 ## |
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509 ## Test dassl() function |
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510 ## |
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511 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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512 ## Comalco Research and Technology |
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513 ## 20 May 1998 |
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514 ## |
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515 ## Based on SLATEC quick check for DASSL by Linda Petzold |
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516 ## |
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517 ## Problem |
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518 ## |
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519 ## x1' + 10*x1 = 0, x1(0) = 1 |
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520 ## x1 + x2 = 1, x2(0) = 0 |
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521 ## |
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522 ## |
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523 ## Solution |
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524 ## |
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525 ## x1(t) = exp(-10*t) |
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526 ## x2(t) = 1 - x(1) |
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527 ## |
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528 %!function res = __f (x, xdot, t) |
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529 %! res = [xdot(1)+10*x(1); x(1)+x(2)-1]; |
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530 %!endfunction |
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531 |
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532 %!test |
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533 %! |
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534 %! x0 = [1; 0]; |
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535 %! xdot0 = [-10; 10]; |
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536 %! t = (0:0.2:1)'; |
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537 %! |
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538 %! tol = 500 * dassl_options ("relative tolerance"); |
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539 %! |
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540 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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541 %! |
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542 %! y = [exp(-10*t), 1-exp(-10*t)]; |
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543 %! |
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544 %! assert (x, y, tol); |
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545 |
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546 %!test |
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547 %! old_tol = dassl_options ("absolute tolerance"); |
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548 %! dassl_options ("absolute tolerance", eps); |
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549 %! assert (dassl_options ("absolute tolerance") == eps); |
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550 %! ## Restore old value of tolerance |
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551 %! dassl_options ("absolute tolerance", old_tol); |
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552 |
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553 %!error dassl_options ("foo", 1, 2) |
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554 */ |