1 | /* ode-initval/rk2simp.c |
2 | * |
3 | * Copyright (C) 2004 Tuomo Keskitalo |
4 | * |
5 | * This program is free software; you can redistribute it and/or modify |
6 | * it under the terms of the GNU General Public License as published by |
7 | * the Free Software Foundation; either version 3 of the License, or (at |
8 | * your option) any later version. |
9 | * |
10 | * This program is distributed in the hope that it will be useful, but |
11 | * WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | * General Public License for more details. |
14 | * |
15 | * You should have received a copy of the GNU General Public License |
16 | * along with this program; if not, write to the Free Software |
17 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
18 | */ |
19 | |
20 | /* Runge-Kutta 2, Gaussian implicit. Also known as implicit midpoint rule. |
21 | |
22 | Non-linear equations solved by linearization, LU-decomposition |
23 | and matrix inversion. For reference, see eg. |
24 | |
25 | Ascher, U.M., Petzold, L.R., Computer methods for ordinary |
26 | differential and differential-algebraic equations, SIAM, |
27 | Philadelphia, 1998. |
28 | */ |
29 | |
30 | #include <config.h> |
31 | #include <stdlib.h> |
32 | #include <string.h> |
33 | #include <gsl/gsl_math.h> |
34 | #include <gsl/gsl_errno.h> |
35 | #include <gsl/gsl_odeiv.h> |
36 | #include <gsl/gsl_linalg.h> |
37 | |
38 | #include "odeiv_util.h" |
39 | |
40 | typedef struct |
41 | { |
42 | double *Y1; |
43 | double *y0; |
44 | double *y0_orig; |
45 | double *ytmp; |
46 | double *dfdy; /* Jacobian */ |
47 | double *dfdt; /* time derivatives, not used */ |
48 | double *y_onestep; |
49 | gsl_permutation *p; |
50 | } |
51 | rk2simp_state_t; |
52 | |
53 | static void * |
54 | rk2simp_alloc (size_t dim) |
| 1Start Analysis. |
55 | { |
56 | rk2simp_state_t *state = |
57 | (rk2simp_state_t *) malloc (sizeof (rk2simp_state_t)); |
| 2Call a function.    malloc(sizeof(rk2simp_state_t)) |
58 | |
59 | if (state == 0) |
| 3Take the false branch.    state == 0 |
60 | { |
61 | GSL_ERROR_NULL ("failed to allocate space for rk2simp_state", |
62 | GSL_ENOMEM); |
63 | } |
64 | |
65 | state->Y1 = (double *) malloc (dim * sizeof (double)); |
| 4Call a function.    malloc(dim * sizeof(double)) |
66 | |
67 | if (state->Y1 == 0) |
| 5Take the false branch.    state->Y1 == 0 |
68 | { |
69 | free (state); |
70 | GSL_ERROR_NULL ("failed to allocate space for Y1", GSL_ENOMEM); |
71 | } |
72 | |
73 | state->y0 = (double *) malloc (dim * sizeof (double)); |
| 6Call a function.    malloc(dim * sizeof(double)) |
74 | |
75 | if (state->y0 == 0) |
| 7Take the false branch.    state->y0 == 0 |
76 | { |
77 | free (state->Y1); |
78 | free (state); |
79 | GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM); |
80 | } |
81 | |
82 | state->y0_orig = (double *) malloc (dim * sizeof (double)); |
| 8Call a function.    malloc(dim * sizeof(double)) |
83 | |
84 | if (state->y0_orig == 0) |
| 9Take the false branch.    state->y0_orig == 0 |
85 | { |
86 | free (state->Y1); |
87 | free (state->y0); |
88 | free (state); |
89 | GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM); |
90 | } |
91 | |
92 | state->ytmp = (double *) malloc (dim * sizeof (double)); |
| 10Call a function.    malloc(dim * sizeof(double)) |
93 | |
94 | if (state->ytmp == 0) |
| 11Take the false branch.    state->ytmp == 0 |
95 | { |
96 | free (state->Y1); |
97 | free (state->y0); |
98 | free (state->y0_orig); |
99 | free (state); |
100 | GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM); |
101 | } |
102 | |
103 | state->dfdy = (double *) malloc (dim * dim * sizeof (double)); |
| 12Call a function.    malloc(dim * dim * sizeof(double)) |
104 | |
105 | if (state->dfdy == 0) |
| 13Take the false branch.    state->dfdy == 0 |
106 | { |
107 | free (state->Y1); |
108 | free (state->y0); |
109 | free (state->y0_orig); |
110 | free (state->ytmp); |
111 | free (state); |
112 | GSL_ERROR_NULL ("failed to allocate space for dfdy", GSL_ENOMEM); |
113 | } |
114 | |
115 | state->dfdt = (double *) malloc (dim * sizeof (double)); |
| 14Call a function.    malloc(dim * sizeof(double)) |
116 | |
117 | if (state->dfdt == 0) |
| 15Take the false branch.    state->dfdt == 0 |
118 | { |
119 | free (state->Y1); |
120 | free (state->y0); |
121 | free (state->y0_orig); |
122 | free (state->ytmp); |
123 | free (state->dfdy); |
124 | free (state); |
125 | GSL_ERROR_NULL ("failed to allocate space for dfdt", GSL_ENOMEM); |
126 | } |
127 | |
128 | state->y_onestep = (double *) malloc (dim * sizeof (double)); |
| 16Call a function.    malloc(dim * sizeof(double)) |
| 31Memory allocated in heap space is not freed.    malloc(dim * sizeof(double)) |
129 | |
130 | if (state->y_onestep == 0) |
| 17Take the false branch.    state->y_onestep == 0 |
131 | { |
132 | free (state->Y1); |
133 | free (state->y0); |
134 | free (state->y0_orig); |
135 | free (state->ytmp); |
136 | free (state->dfdy); |
137 | free (state->dfdt); |
138 | free (state); |
139 | GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM); |
140 | } |
141 | |
142 | state->p = gsl_permutation_alloc (dim); |
| 18Call a function.    gsl_permutation_alloc(dim) |
143 | |
144 | if (state->p == 0) |
| 19Take the true branch.    state->p == 0 |
145 | { |
146 | free (state->Y1); |
| 20Call a function.    free(state->Y1) |
147 | free (state->y0); |
| 21Call a function.    free(state->y0) |
148 | free (state->y0_orig); |
| 22Call a function.    free(state->y0_orig) |
149 | free (state->ytmp); |
| 23Call a function.    free(state->ytmp) |
150 | free (state->dfdy); |
| 24Call a function.    free(state->dfdy) |
151 | free (state->dfdt); |
| 25Call a function.    free(state->dfdt) |
152 | free (state); |
| 26Call a function.    free(state) |
153 | GSL_ERROR_NULL ("failed to allocate space for p", GSL_ENOMEM); |
| 27Call a function.    gsl_error("failed to allocate space for p", "/home/xingming/workplace/experiment/fp/gsl-2.1/ode-initval/rk2simp.c", 153, GSL_ENOMEM) |
154 | } |
155 | |
156 | return state; |
157 | } |
158 | |
159 | |
160 | static int |
161 | rk2simp_step (double *y, rk2simp_state_t * state, |
162 | const double h, const double t, |
163 | const size_t dim, const gsl_odeiv_system * sys) |
164 | { |
165 | /* Makes a Runge-Kutta 2nd order semi-implicit advance with step size h. |
166 | y0 is initial values of variables y. |
167 | |
168 | The linearized semi-implicit equations to calculate are: |
169 | |
170 | Y1 = y0 + h/2 * (1 - h/2 * df/dy)^(-1) * f(t + h/2, y0) |
171 | |
172 | y = y0 + h * f(t + h/2, Y1) |
173 | */ |
174 | |
175 | const double *y0 = state->y0; |
176 | double *Y1 = state->Y1; |
177 | double *ytmp = state->ytmp; |
178 | |
179 | size_t i; |
180 | int s, ps; |
181 | |
182 | gsl_matrix_view J = gsl_matrix_view_array (state->dfdy, dim, dim); |
183 | |
184 | /* First solve Y1. |
185 | Calculate the inverse matrix (1 - h/2 * df/dy)^-1 |
186 | */ |
187 | |
188 | /* Create matrix to J */ |
189 | |
190 | s = GSL_ODEIV_JA_EVAL (sys, t, y0, state->dfdy, state->dfdt); |
191 | |
192 | if (s != GSL_SUCCESS) |
193 | { |
194 | return s; |
195 | } |
196 | |
197 | gsl_matrix_scale (&J.matrix, -h / 2.0); |
198 | gsl_matrix_add_diagonal(&J.matrix, 1.0); |
199 | |
200 | /* Invert it by LU-decomposition to invmat */ |
201 | |
202 | s += gsl_linalg_LU_decomp (&J.matrix, state->p, &ps); |
203 | |
204 | if (s != GSL_SUCCESS) |
205 | { |
206 | return GSL_EFAILED; |
207 | } |
208 | |
209 | /* Evaluate f(t + h/2, y0) */ |
210 | |
211 | s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, y0, ytmp); |
212 | |
213 | if (s != GSL_SUCCESS) |
214 | { |
215 | return s; |
216 | } |
217 | |
218 | /* Calculate Y1 = y0 + h/2 * ((1-h/2 * df/dy)^-1) ytmp */ |
219 | |
220 | { |
221 | gsl_vector_const_view y0_view = gsl_vector_const_view_array(y0, dim); |
222 | gsl_vector_view ytmp_view = gsl_vector_view_array(ytmp, dim); |
223 | gsl_vector_view Y1_view = gsl_vector_view_array(Y1, dim); |
224 | |
225 | s = gsl_linalg_LU_solve (&J.matrix, state->p, |
226 | &ytmp_view.vector, &Y1_view.vector); |
227 | |
228 | gsl_vector_scale (&Y1_view.vector, 0.5 * h); |
229 | gsl_vector_add (&Y1_view.vector, &y0_view.vector); |
230 | } |
231 | |
232 | /* And finally evaluation of f(t + h/2, Y1) and calculation of y */ |
233 | |
234 | s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, Y1, ytmp); |
235 | |
236 | if (s != GSL_SUCCESS) |
237 | { |
238 | return s; |
239 | } |
240 | |
241 | for (i = 0; i < dim; i++) |
242 | { |
243 | y[i] = y0[i] + h * ytmp[i]; |
244 | } |
245 | |
246 | return s; |
247 | } |
248 | |
249 | static int |
250 | rk2simp_apply (void *vstate, size_t dim, double t, double h, |
251 | double y[], double yerr[], const double dydt_in[], |
252 | double dydt_out[], const gsl_odeiv_system * sys) |
253 | { |
254 | rk2simp_state_t *state = (rk2simp_state_t *) vstate; |
255 | |
256 | size_t i; |
257 | |
258 | double *y0 = state->y0; |
259 | double *y0_orig = state->y0_orig; |
260 | double *y_onestep = state->y_onestep; |
261 | |
262 | /* Error estimation is done by step doubling procedure */ |
263 | |
264 | DBL_MEMCPY (y0, y, dim); |
265 | |
266 | /* Save initial values in case of failure */ |
267 | DBL_MEMCPY (y0_orig, y, dim); |
268 | |
269 | /* First traverse h with one step (save to y_onestep) */ |
270 | DBL_MEMCPY (y_onestep, y, dim); |
271 | |
272 | { |
273 | int s = rk2simp_step (y_onestep, state, h, t, dim, sys); |
274 | |
275 | if (s != GSL_SUCCESS) |
276 | { |
277 | return s; |
278 | } |
279 | } |
280 | |
281 | /* Then with two steps with half step length (save to y) */ |
282 | |
283 | { |
284 | int s = rk2simp_step (y, state, h / 2.0, t, dim, sys); |
285 | |
286 | if (s != GSL_SUCCESS) |
287 | { |
288 | /* Restore original y vector */ |
289 | DBL_MEMCPY (y, y0_orig, dim); |
290 | return s; |
291 | } |
292 | } |
293 | |
294 | DBL_MEMCPY (y0, y, dim); |
295 | |
296 | { |
297 | int s = rk2simp_step (y, state, h / 2.0, t + h / 2.0, dim, sys); |
298 | |
299 | if (s != GSL_SUCCESS) |
300 | { |
301 | /* Restore original y vector */ |
302 | DBL_MEMCPY (y, y0_orig, dim); |
303 | return s; |
304 | } |
305 | } |
306 | |
307 | /* Derivatives at output */ |
308 | |
309 | if (dydt_out != NULL) |
310 | { |
311 | int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out); |
312 | |
313 | if (s != GSL_SUCCESS) |
314 | { |
315 | /* Restore original y vector */ |
316 | DBL_MEMCPY (y, y0_orig, dim); |
317 | return s; |
318 | } |
319 | } |
320 | |
321 | /* Error estimation */ |
322 | |
323 | for (i = 0; i < dim; i++) |
324 | { |
325 | yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 3.0; |
326 | } |
327 | |
328 | return GSL_SUCCESS; |
329 | } |
330 | |
331 | |
332 | static int |
333 | rk2simp_reset (void *vstate, size_t dim) |
334 | { |
335 | rk2simp_state_t *state = (rk2simp_state_t *) vstate; |
336 | |
337 | DBL_ZERO_MEMSET (state->Y1, dim); |
338 | DBL_ZERO_MEMSET (state->y0, dim); |
339 | DBL_ZERO_MEMSET (state->y0_orig, dim); |
340 | DBL_ZERO_MEMSET (state->ytmp, dim); |
341 | DBL_ZERO_MEMSET (state->dfdt, dim * dim); |
342 | DBL_ZERO_MEMSET (state->dfdt, dim); |
343 | DBL_ZERO_MEMSET (state->y_onestep, dim); |
344 | |
345 | return GSL_SUCCESS; |
346 | } |
347 | |
348 | static unsigned int |
349 | rk2simp_order (void *vstate) |
350 | { |
351 | rk2simp_state_t *state = (rk2simp_state_t *) vstate; |
352 | state = 0; /* prevent warnings about unused parameters */ |
353 | return 2; |
354 | } |
355 | |
356 | static void |
357 | rk2simp_free (void *vstate) |
358 | { |
359 | rk2simp_state_t *state = (rk2simp_state_t *) vstate; |
360 | free (state->Y1); |
361 | free (state->y0); |
362 | free (state->y0_orig); |
363 | free (state->ytmp); |
364 | free (state->dfdy); |
365 | free (state->dfdt); |
366 | free (state->y_onestep); |
367 | gsl_permutation_free (state->p); |
368 | free (state); |
369 | } |
370 | |
371 | static const gsl_odeiv_step_type rk2simp_type = { |
372 | "rk2simp", /* name */ |
373 | 0, /* can use dydt_in? */ |
374 | 1, /* gives exact dydt_out? */ |
375 | &rk2simp_alloc, |
376 | &rk2simp_apply, |
377 | &rk2simp_reset, |
378 | &rk2simp_order, |
379 | &rk2simp_free |
380 | }; |
381 | |
382 | const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp = &rk2simp_type; |
383 | |