1 static char help[] = "An example of hybrid system using TS event.\n";
2
3 /*
4 The dynamics is described by the ODE
5 u_t = A_i u
6
7 where A_1 = [ 1 -100
8 10 1 ],
9 A_2 = [ 1 10
10 -100 1 ].
11 The index i changes from 1 to 2 when u[1]=2.75u[0] and from 2 to 1 when u[1]=0.36u[0].
12 Initially u=[0 1]^T and i=1.
13
14 Reference:
15 I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000
16 */
17
18 #include <petscts.h>
19
20 typedef struct {
21 PetscReal lambda1;
22 PetscReal lambda2;
23 PetscInt mode; /* mode flag*/
24 } AppCtx;
25
26 PetscErrorCode FWDRun(TS, Vec, void *);
27
EventFunction(TS ts,PetscReal t,Vec U,PetscReal * fvalue,PetscCtx ctx)28 PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, PetscCtx ctx)
29 {
30 AppCtx *actx = (AppCtx *)ctx;
31 const PetscScalar *u;
32
33 PetscFunctionBegin;
34 PetscCall(VecGetArrayRead(U, &u));
35 if (actx->mode == 1) {
36 fvalue[0] = PetscRealPart(u[1] - actx->lambda1 * u[0]);
37 } else if (actx->mode == 2) {
38 fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]);
39 }
40 PetscCall(VecRestoreArrayRead(U, &u));
41 PetscFunctionReturn(PETSC_SUCCESS);
42 }
43
ShiftGradients(TS ts,Vec U,AppCtx * actx)44 PetscErrorCode ShiftGradients(TS ts, Vec U, AppCtx *actx)
45 {
46 Vec *lambda, *mu;
47 PetscScalar *x, *y;
48 const PetscScalar *u;
49 PetscScalar tmp[2], A1[2][2], A2[2], denorm1, denorm2;
50 PetscInt numcost;
51
52 PetscFunctionBegin;
53 PetscCall(TSGetCostGradients(ts, &numcost, &lambda, &mu));
54 PetscCall(VecGetArrayRead(U, &u));
55
56 if (actx->mode == 2) {
57 denorm1 = -actx->lambda1 * (u[0] - 100. * u[1]) + 1. * (10. * u[0] + u[1]);
58 denorm2 = -actx->lambda1 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]);
59 A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm1 + 1.;
60 A1[0][1] = -110. * u[0] * (-actx->lambda1) / denorm1;
61 A1[1][0] = 110. * u[1] * 1. / denorm1;
62 A1[1][1] = -110. * u[0] * 1. / denorm1 + 1.;
63
64 A2[0] = 110. * u[1] * (-u[0]) / denorm2;
65 A2[1] = -110. * u[0] * (-u[0]) / denorm2;
66 } else {
67 denorm2 = -actx->lambda2 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]);
68 A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm2 + 1;
69 A1[0][1] = -110. * u[0] * (-actx->lambda1) / denorm2;
70 A1[1][0] = 110. * u[1] * 1. / denorm2;
71 A1[1][1] = -110. * u[0] * 1. / denorm2 + 1.;
72
73 A2[0] = 0;
74 A2[1] = 0;
75 }
76
77 PetscCall(VecRestoreArrayRead(U, &u));
78
79 PetscCall(VecGetArray(lambda[0], &x));
80 PetscCall(VecGetArray(mu[0], &y));
81 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1];
82 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1];
83 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1];
84 x[0] = tmp[0];
85 x[1] = tmp[1];
86 PetscCall(VecRestoreArray(mu[0], &y));
87 PetscCall(VecRestoreArray(lambda[0], &x));
88
89 PetscCall(VecGetArray(lambda[1], &x));
90 PetscCall(VecGetArray(mu[1], &y));
91 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1];
92 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1];
93 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1];
94 x[0] = tmp[0];
95 x[1] = tmp[1];
96 PetscCall(VecRestoreArray(mu[1], &y));
97 PetscCall(VecRestoreArray(lambda[1], &x));
98 PetscFunctionReturn(PETSC_SUCCESS);
99 }
100
PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,PetscCtx ctx)101 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, PetscCtx ctx)
102 {
103 AppCtx *actx = (AppCtx *)ctx;
104
105 PetscFunctionBegin;
106 if (!forwardsolve) PetscCall(ShiftGradients(ts, U, actx));
107 if (actx->mode == 1) {
108 actx->mode = 2;
109 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 1 to 2 at t = %f \n", (double)t));
110 } else if (actx->mode == 2) {
111 actx->mode = 1;
112 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 2 to 1 at t = %f \n", (double)t));
113 }
114 PetscFunctionReturn(PETSC_SUCCESS);
115 }
116
117 /*
118 Defines the ODE passed to the ODE solver
119 */
IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,PetscCtx ctx)120 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx)
121 {
122 AppCtx *actx = (AppCtx *)ctx;
123 PetscScalar *f;
124 const PetscScalar *u, *udot;
125
126 PetscFunctionBegin;
127 /* The next three lines allow us to access the entries of the vectors directly */
128 PetscCall(VecGetArrayRead(U, &u));
129 PetscCall(VecGetArrayRead(Udot, &udot));
130 PetscCall(VecGetArray(F, &f));
131
132 if (actx->mode == 1) {
133 f[0] = udot[0] - u[0] + 100 * u[1];
134 f[1] = udot[1] - 10 * u[0] - u[1];
135 } else if (actx->mode == 2) {
136 f[0] = udot[0] - u[0] - 10 * u[1];
137 f[1] = udot[1] + 100 * u[0] - u[1];
138 }
139
140 PetscCall(VecRestoreArrayRead(U, &u));
141 PetscCall(VecRestoreArrayRead(Udot, &udot));
142 PetscCall(VecRestoreArray(F, &f));
143 PetscFunctionReturn(PETSC_SUCCESS);
144 }
145
146 /*
147 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
148 */
IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,PetscCtx ctx)149 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, PetscCtx ctx)
150 {
151 AppCtx *actx = (AppCtx *)ctx;
152 PetscInt rowcol[] = {0, 1};
153 PetscScalar J[2][2];
154 const PetscScalar *u, *udot;
155
156 PetscFunctionBegin;
157 PetscCall(VecGetArrayRead(U, &u));
158 PetscCall(VecGetArrayRead(Udot, &udot));
159
160 if (actx->mode == 1) {
161 J[0][0] = a - 1;
162 J[0][1] = 100;
163 J[1][0] = -10;
164 J[1][1] = a - 1;
165 } else if (actx->mode == 2) {
166 J[0][0] = a - 1;
167 J[0][1] = -10;
168 J[1][0] = 100;
169 J[1][1] = a - 1;
170 }
171 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
172
173 PetscCall(VecRestoreArrayRead(U, &u));
174 PetscCall(VecRestoreArrayRead(Udot, &udot));
175
176 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
177 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
178 if (A != B) {
179 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
180 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
181 }
182 PetscFunctionReturn(PETSC_SUCCESS);
183 }
184
main(int argc,char ** argv)185 int main(int argc, char **argv)
186 {
187 TS ts; /* ODE integrator */
188 Vec U; /* solution will be stored here */
189 Mat A; /* Jacobian matrix */
190 Mat Ap; /* dfdp */
191 PetscMPIInt size;
192 PetscInt n = 2;
193 PetscScalar *u;
194 AppCtx app;
195 PetscInt direction[1];
196 PetscBool terminate[1];
197 PetscReal delta;
198 PetscScalar tmp[2], sensi[2];
199
200 delta = 1e-8;
201
202 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203 Initialize program
204 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205 PetscFunctionBeginUser;
206 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
207 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
208 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
209 app.mode = 1;
210 app.lambda1 = 2.75;
211 app.lambda2 = 0.36;
212 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1 options", "");
213 {
214 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL));
215 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL));
216 }
217 PetscOptionsEnd();
218
219 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220 Create necessary matrix and vectors
221 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
222 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
223 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
224 PetscCall(MatSetType(A, MATDENSE));
225 PetscCall(MatSetFromOptions(A));
226 PetscCall(MatSetUp(A));
227
228 PetscCall(MatCreateVecs(A, &U, NULL));
229
230 PetscCall(MatCreate(PETSC_COMM_WORLD, &Ap));
231 PetscCall(MatSetSizes(Ap, n, 1, PETSC_DETERMINE, PETSC_DETERMINE));
232 PetscCall(MatSetType(Ap, MATDENSE));
233 PetscCall(MatSetFromOptions(Ap));
234 PetscCall(MatSetUp(Ap));
235 PetscCall(MatZeroEntries(Ap)); /* initialize to zeros */
236
237 PetscCall(VecGetArray(U, &u));
238 u[0] = 0;
239 u[1] = 1;
240 PetscCall(VecRestoreArray(U, &u));
241 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
242 Create timestepping solver context
243 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
244 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
245 PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
246 PetscCall(TSSetType(ts, TSCN));
247 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app));
248 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app));
249
250 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
251 Set initial conditions
252 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
253 PetscCall(TSSetSolution(ts, U));
254
255 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
256 Set solver options
257 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
258 PetscCall(TSSetMaxTime(ts, 0.125));
259 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
260 PetscCall(TSSetTimeStep(ts, 1. / 256.));
261 PetscCall(TSSetFromOptions(ts));
262
263 /* Set directions and terminate flags for the two events */
264 direction[0] = 0;
265 terminate[0] = PETSC_FALSE;
266 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app));
267
268 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269 Run timestepping solver
270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271 PetscCall(TSSolve(ts, U));
272
273 PetscCall(VecGetArray(U, &u));
274 tmp[0] = u[0];
275 tmp[1] = u[1];
276
277 u[0] = 0 + delta;
278 u[1] = 1;
279 PetscCall(VecRestoreArray(U, &u));
280
281 PetscCall(FWDRun(ts, U, (void *)&app));
282
283 PetscCall(VecGetArray(U, &u));
284 sensi[0] = (u[0] - tmp[0]) / delta;
285 sensi[1] = (u[1] - tmp[1]) / delta;
286 PetscCall(PetscPrintf(PETSC_COMM_SELF, "d x1(tf) /d x1(t0) = %f d x2(tf) / d x1(t0) = %f \n", (double)sensi[0], (double)sensi[1]));
287 u[0] = 0;
288 u[1] = 1 + delta;
289 PetscCall(VecRestoreArray(U, &u));
290
291 PetscCall(FWDRun(ts, U, (void *)&app));
292
293 PetscCall(VecGetArray(U, &u));
294 sensi[0] = (u[0] - tmp[0]) / delta;
295 sensi[1] = (u[1] - tmp[1]) / delta;
296 PetscCall(PetscPrintf(PETSC_COMM_SELF, "d x1(tf) /d x2(t0) = %f d x2(tf) / d x2(t0) = %f \n", (double)sensi[0], (double)sensi[1]));
297 u[0] = 0;
298 u[1] = 1;
299 app.lambda1 = app.lambda1 + delta;
300 PetscCall(VecRestoreArray(U, &u));
301
302 PetscCall(FWDRun(ts, U, (void *)&app));
303
304 PetscCall(VecGetArray(U, &u));
305 sensi[0] = (u[0] - tmp[0]) / delta;
306 sensi[1] = (u[1] - tmp[1]) / delta;
307 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Final gradients: d x1(tf) /d p = %f d x2(tf) / d p = %f \n", (double)sensi[0], (double)sensi[1]));
308 PetscCall(VecRestoreArray(U, &u));
309
310 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
311 Free work space. All PETSc objects should be destroyed when they are no longer needed.
312 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
313 PetscCall(MatDestroy(&A));
314 PetscCall(VecDestroy(&U));
315 PetscCall(TSDestroy(&ts));
316
317 PetscCall(MatDestroy(&Ap));
318 PetscCall(PetscFinalize());
319 return 0;
320 }
321
FWDRun(TS ts,Vec U0,PetscCtx ctx0)322 PetscErrorCode FWDRun(TS ts, Vec U0, PetscCtx ctx0)
323 {
324 Vec U; /* solution will be stored here */
325 AppCtx *ctx = (AppCtx *)ctx0;
326
327 PetscFunctionBeginUser;
328 PetscCall(TSGetSolution(ts, &U));
329 PetscCall(VecCopy(U0, U));
330
331 ctx->mode = 1;
332 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
333 Run timestepping solver
334 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
335 PetscCall(TSSetTime(ts, 0.0));
336
337 PetscCall(TSSolve(ts, U));
338 PetscFunctionReturn(PETSC_SUCCESS);
339 }
340
341 /*TEST
342
343 build:
344 requires: !defined(PETSC_USE_CXXCOMPLEX)
345
346 test:
347 args: -ts_event_tol 1e-9
348 timeoutfactor: 18
349 requires: !single
350
351 TEST*/
352