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 PetscScalar lambda1;
22 PetscScalar lambda2;
23 PetscInt mode; /* mode flag*/
24 } AppCtx;
25
EventFunction(TS ts,PetscReal t,Vec U,PetscReal * fvalue,PetscCtx ctx)26 PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, PetscCtx ctx)
27 {
28 AppCtx *actx = (AppCtx *)ctx;
29 const PetscScalar *u;
30
31 PetscFunctionBegin;
32 PetscCall(VecGetArrayRead(U, &u));
33 if (actx->mode == 1) {
34 fvalue[0] = PetscRealPart(u[1] - actx->lambda1 * u[0]);
35 } else if (actx->mode == 2) {
36 fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]);
37 }
38 PetscCall(VecRestoreArrayRead(U, &u));
39 PetscFunctionReturn(PETSC_SUCCESS);
40 }
41
PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,PetscCtx ctx)42 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, PetscCtx ctx)
43 {
44 AppCtx *actx = (AppCtx *)ctx;
45
46 PetscFunctionBegin;
47 if (actx->mode == 1) {
48 actx->mode = 2;
49 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 1 to 2 at t = %f \n", (double)t));
50 } else if (actx->mode == 2) {
51 actx->mode = 1;
52 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 2 to 1 at t = %f \n", (double)t));
53 }
54 PetscFunctionReturn(PETSC_SUCCESS);
55 }
56
57 /*
58 Defines the ODE passed to the ODE solver
59 */
IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,PetscCtx ctx)60 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx)
61 {
62 AppCtx *actx = (AppCtx *)ctx;
63 PetscScalar *f;
64 const PetscScalar *u, *udot;
65
66 PetscFunctionBegin;
67 /* The next three lines allow us to access the entries of the vectors directly */
68 PetscCall(VecGetArrayRead(U, &u));
69 PetscCall(VecGetArrayRead(Udot, &udot));
70 PetscCall(VecGetArray(F, &f));
71
72 if (actx->mode == 1) {
73 f[0] = udot[0] - u[0] + 100 * u[1];
74 f[1] = udot[1] - 10 * u[0] - u[1];
75 } else if (actx->mode == 2) {
76 f[0] = udot[0] - u[0] - 10 * u[1];
77 f[1] = udot[1] + 100 * u[0] - u[1];
78 }
79
80 PetscCall(VecRestoreArrayRead(U, &u));
81 PetscCall(VecRestoreArrayRead(Udot, &udot));
82 PetscCall(VecRestoreArray(F, &f));
83 PetscFunctionReturn(PETSC_SUCCESS);
84 }
85
86 /*
87 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
88 */
IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,PetscCtx ctx)89 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, PetscCtx ctx)
90 {
91 AppCtx *actx = (AppCtx *)ctx;
92 PetscInt rowcol[] = {0, 1};
93 PetscScalar J[2][2];
94 const PetscScalar *u, *udot;
95
96 PetscFunctionBegin;
97 PetscCall(VecGetArrayRead(U, &u));
98 PetscCall(VecGetArrayRead(Udot, &udot));
99
100 if (actx->mode == 1) {
101 J[0][0] = a - 1;
102 J[0][1] = 100;
103 J[1][0] = -10;
104 J[1][1] = a - 1;
105 } else if (actx->mode == 2) {
106 J[0][0] = a - 1;
107 J[0][1] = -10;
108 J[1][0] = 100;
109 J[1][1] = a - 1;
110 }
111 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
112
113 PetscCall(VecRestoreArrayRead(U, &u));
114 PetscCall(VecRestoreArrayRead(Udot, &udot));
115
116 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
117 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
118 if (A != B) {
119 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
120 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
121 }
122 PetscFunctionReturn(PETSC_SUCCESS);
123 }
124
main(int argc,char ** argv)125 int main(int argc, char **argv)
126 {
127 TS ts; /* ODE integrator */
128 Vec U; /* solution will be stored here */
129 Mat A; /* Jacobian matrix */
130 PetscMPIInt size;
131 PetscInt n = 2;
132 PetscScalar *u;
133 AppCtx app;
134 PetscInt direction[1];
135 PetscBool terminate[1];
136
137 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138 Initialize program
139 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140 PetscFunctionBeginUser;
141 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
142 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
143 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
144 app.mode = 1;
145 app.lambda1 = 2.75;
146 app.lambda2 = 0.36;
147 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1 options", "");
148 {
149 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL));
150 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL));
151 }
152 PetscOptionsEnd();
153
154 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155 Create necessary matrix and vectors
156 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
158 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
159 PetscCall(MatSetType(A, MATDENSE));
160 PetscCall(MatSetFromOptions(A));
161 PetscCall(MatSetUp(A));
162
163 PetscCall(MatCreateVecs(A, &U, NULL));
164
165 PetscCall(VecGetArray(U, &u));
166 u[0] = 0;
167 u[1] = 1;
168 PetscCall(VecRestoreArray(U, &u));
169 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170 Create timestepping solver context
171 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
172 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
173 PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
174 PetscCall(TSSetType(ts, TSCN));
175 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app));
176 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app));
177
178 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179 Set initial conditions
180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181 PetscCall(TSSetSolution(ts, U));
182
183 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184 Set solver options
185 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
186 PetscCall(TSSetMaxTime(ts, 0.125));
187 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
188 PetscCall(TSSetTimeStep(ts, 1. / 256.));
189 PetscCall(TSSetFromOptions(ts));
190
191 /* Set directions and terminate flags for the two events */
192 direction[0] = 0;
193 terminate[0] = PETSC_FALSE;
194 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app));
195
196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197 Run timestepping solver
198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
199 PetscCall(TSSolve(ts, U));
200
201 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202 Free work space. All PETSc objects should be destroyed when they are no longer needed.
203 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204 PetscCall(MatDestroy(&A));
205 PetscCall(VecDestroy(&U));
206 PetscCall(TSDestroy(&ts));
207
208 PetscCall(PetscFinalize());
209 return 0;
210 }
211
212 /*TEST
213
214 build:
215 requires: !complex
216 test:
217 args: -ts_monitor
218
219 test:
220 suffix: 2
221 args: -ts_monitor_lg_solution -1
222 requires: x
223
224 TEST*/
225