Actual source code: ex16fwd.c
1: static char help[] = "Performs adjoint sensitivity analysis for the van der Pol equation.\n\
2: Input parameters include:\n\
3: -mu : stiffness parameter\n\n";
5: /* ------------------------------------------------------------------------
7: This program solves the van der Pol equation
8: y'' - \mu (1-y^2)*y' + y = 0 (1)
9: on the domain 0 <= x <= 1, with the boundary conditions
10: y(0) = 2, y'(0) = 0,
11: and computes the sensitivities of the final solution w.r.t. initial conditions and parameter \mu with an explicit Runge-Kutta method and its discrete tangent linear model.
13: Notes:
14: This code demonstrates the TSForward interface to a system of ordinary differential equations (ODEs) in the form of u_t = f(u,t).
16: (1) can be turned into a system of first order ODEs
17: [ y' ] = [ z ]
18: [ z' ] [ \mu (1 - y^2) z - y ]
20: which then we can write as a vector equation
22: [ u_1' ] = [ u_2 ] (2)
23: [ u_2' ] [ \mu (1 - u_1^2) u_2 - u_1 ]
25: which is now in the form of u_t = F(u,t).
27: The user provides the right-hand-side function
29: [ f(u,t) ] = [ u_2 ]
30: [ \mu (1 - u_1^2) u_2 - u_1 ]
32: the Jacobian function
34: df [ 0 ; 1 ]
35: -- = [ ]
36: du [ -2 \mu u_1*u_2 - 1; \mu (1 - u_1^2) ]
38: and the JacobainP (the Jacobian w.r.t. parameter) function
40: df [ 0; 0; 0 ]
41: --- = [ ]
42: d\mu [ 0; 0; (1 - u_1^2) u_2 ]
44: ------------------------------------------------------------------------- */
46: #include <petscts.h>
47: #include <petscmat.h>
48: typedef struct _n_User *User;
49: struct _n_User {
50: PetscReal mu;
51: PetscReal next_output;
52: PetscReal tprev;
53: };
55: /*
56: User-defined routines
57: */
58: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
59: {
60: User user = (User)ctx;
61: PetscScalar *f;
62: const PetscScalar *x;
64: PetscFunctionBeginUser;
65: PetscCall(VecGetArrayRead(X, &x));
66: PetscCall(VecGetArray(F, &f));
67: f[0] = x[1];
68: f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
69: PetscCall(VecRestoreArrayRead(X, &x));
70: PetscCall(VecRestoreArray(F, &f));
71: PetscFunctionReturn(PETSC_SUCCESS);
72: }
74: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat A, Mat B, void *ctx)
75: {
76: User user = (User)ctx;
77: PetscReal mu = user->mu;
78: PetscInt rowcol[] = {0, 1};
79: PetscScalar J[2][2];
80: const PetscScalar *x;
82: PetscFunctionBeginUser;
83: PetscCall(VecGetArrayRead(X, &x));
84: J[0][0] = 0;
85: J[1][0] = -2. * mu * x[1] * x[0] - 1.;
86: J[0][1] = 1.0;
87: J[1][1] = mu * (1.0 - x[0] * x[0]);
88: PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
89: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
90: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
91: if (A != B) {
92: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
93: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
94: }
95: PetscCall(VecRestoreArrayRead(X, &x));
96: PetscFunctionReturn(PETSC_SUCCESS);
97: }
99: static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx)
100: {
101: PetscInt row[] = {0, 1}, col[] = {2};
102: PetscScalar J[2][1];
103: const PetscScalar *x;
105: PetscFunctionBeginUser;
106: PetscCall(VecGetArrayRead(X, &x));
107: J[0][0] = 0;
108: J[1][0] = (1. - x[0] * x[0]) * x[1];
109: PetscCall(VecRestoreArrayRead(X, &x));
110: PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES));
112: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
113: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
114: PetscFunctionReturn(PETSC_SUCCESS);
115: }
117: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
118: static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, void *ctx)
119: {
120: const PetscScalar *x;
121: PetscReal tfinal, dt, tprev;
122: User user = (User)ctx;
124: PetscFunctionBeginUser;
125: PetscCall(TSGetTimeStep(ts, &dt));
126: PetscCall(TSGetMaxTime(ts, &tfinal));
127: PetscCall(TSGetPrevTime(ts, &tprev));
128: PetscCall(VecGetArrayRead(X, &x));
129: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(x[0]), (double)PetscRealPart(x[1])));
130: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "t %.6f (tprev = %.6f) \n", (double)t, (double)tprev));
131: PetscCall(VecRestoreArrayRead(X, &x));
132: PetscFunctionReturn(PETSC_SUCCESS);
133: }
135: int main(int argc, char **argv)
136: {
137: TS ts; /* nonlinear solver */
138: Vec x; /* solution, residual vectors */
139: Mat A; /* Jacobian matrix */
140: Mat Jacp; /* JacobianP matrix */
141: PetscInt steps;
142: PetscReal ftime = 0.5;
143: PetscBool monitor = PETSC_FALSE;
144: PetscScalar *x_ptr;
145: PetscMPIInt size;
146: struct _n_User user;
147: Mat sp;
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Initialize program
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: PetscFunctionBeginUser;
153: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
154: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
155: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
157: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: Set runtime options
159: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: user.mu = 1;
161: user.next_output = 0.0;
163: PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &user.mu, NULL));
164: PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Create necessary matrix and vectors, solve same ODE on every process
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
170: PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
171: PetscCall(MatSetFromOptions(A));
172: PetscCall(MatSetUp(A));
173: PetscCall(MatCreateVecs(A, &x, NULL));
175: PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
176: PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 3));
177: PetscCall(MatSetFromOptions(Jacp));
178: PetscCall(MatSetUp(Jacp));
180: PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 3, NULL, &sp));
181: PetscCall(MatZeroEntries(sp));
182: PetscCall(MatShift(sp, 1.0));
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Create timestepping solver context
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
188: PetscCall(TSSetType(ts, TSRK));
189: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
190: /* Set RHS Jacobian for the adjoint integration */
191: PetscCall(TSSetRHSJacobian(ts, A, A, RHSJacobian, &user));
192: PetscCall(TSSetMaxTime(ts, ftime));
193: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
194: if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));
195: PetscCall(TSForwardSetSensitivities(ts, 3, sp));
196: PetscCall(TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &user));
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Set initial conditions
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: PetscCall(VecGetArray(x, &x_ptr));
203: x_ptr[0] = 2;
204: x_ptr[1] = 0.66666654321;
205: PetscCall(VecRestoreArray(x, &x_ptr));
206: PetscCall(TSSetTimeStep(ts, .001));
208: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: Set runtime options
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: PetscCall(TSSetFromOptions(ts));
213: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: Solve nonlinear system
215: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
216: PetscCall(TSSolve(ts, x));
217: PetscCall(TSGetSolveTime(ts, &ftime));
218: PetscCall(TSGetStepNumber(ts, &steps));
219: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.mu, steps, (double)ftime));
220: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));
222: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n forward sensitivity: d[y(tf) z(tf)]/d[y0 z0 mu]\n"));
223: PetscCall(MatView(sp, PETSC_VIEWER_STDOUT_WORLD));
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Free work space. All PETSc objects should be destroyed when they
227: are no longer needed.
228: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
229: PetscCall(MatDestroy(&A));
230: PetscCall(MatDestroy(&Jacp));
231: PetscCall(VecDestroy(&x));
232: PetscCall(MatDestroy(&sp));
233: PetscCall(TSDestroy(&ts));
234: PetscCall(PetscFinalize());
235: return 0;
236: }
238: /*TEST
240: test:
241: args: -monitor 0 -ts_adapt_type none
243: TEST*/