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;
65: VecGetArrayRead(X, &x);
66: VecGetArray(F, &f);
67: f[0] = x[1];
68: f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
69: VecRestoreArrayRead(X, &x);
70: VecRestoreArray(F, &f);
71: return 0;
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;
83: 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: MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES);
89: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
91: if (A != B) {
92: MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
93: MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
94: }
95: VecRestoreArrayRead(X, &x);
96: return 0;
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;
106: VecGetArrayRead(X, &x);
107: J[0][0] = 0;
108: J[1][0] = (1. - x[0] * x[0]) * x[1];
109: VecRestoreArrayRead(X, &x);
110: MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES);
112: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
113: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
114: return 0;
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;
125: TSGetTimeStep(ts, &dt);
126: TSGetMaxTime(ts, &tfinal);
127: TSGetPrevTime(ts, &tprev);
128: VecGetArrayRead(X, &x);
129: 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: PetscPrintf(PETSC_COMM_WORLD, "t %.6f (tprev = %.6f) \n", (double)t, (double)tprev);
131: VecRestoreArrayRead(X, &x);
132: return 0;
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: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: PetscInitialize(&argc, &argv, NULL, help);
154: MPI_Comm_size(PETSC_COMM_WORLD, &size);
157: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: Set runtime options
159: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: user.mu = 1;
161: user.next_output = 0.0;
163: PetscOptionsGetReal(NULL, NULL, "-mu", &user.mu, NULL);
164: PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Create necessary matrix and vectors, solve same ODE on every process
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: MatCreate(PETSC_COMM_WORLD, &A);
170: MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2);
171: MatSetFromOptions(A);
172: MatSetUp(A);
173: MatCreateVecs(A, &x, NULL);
175: MatCreate(PETSC_COMM_WORLD, &Jacp);
176: MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 3);
177: MatSetFromOptions(Jacp);
178: MatSetUp(Jacp);
180: MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 3, NULL, &sp);
181: MatZeroEntries(sp);
182: MatShift(sp, 1.0);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Create timestepping solver context
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: TSCreate(PETSC_COMM_WORLD, &ts);
188: TSSetType(ts, TSRK);
189: TSSetRHSFunction(ts, NULL, RHSFunction, &user);
190: /* Set RHS Jacobian for the adjoint integration */
191: TSSetRHSJacobian(ts, A, A, RHSJacobian, &user);
192: TSSetMaxTime(ts, ftime);
193: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
194: if (monitor) TSMonitorSet(ts, Monitor, &user, NULL);
195: TSForwardSetSensitivities(ts, 3, sp);
196: TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &user);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Set initial conditions
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: VecGetArray(x, &x_ptr);
203: x_ptr[0] = 2;
204: x_ptr[1] = 0.66666654321;
205: VecRestoreArray(x, &x_ptr);
206: TSSetTimeStep(ts, .001);
208: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: Set runtime options
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: TSSetFromOptions(ts);
213: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: Solve nonlinear system
215: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
216: TSSolve(ts, x);
217: TSGetSolveTime(ts, &ftime);
218: TSGetStepNumber(ts, &steps);
219: PetscPrintf(PETSC_COMM_WORLD, "mu %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.mu, steps, (double)ftime);
220: VecView(x, PETSC_VIEWER_STDOUT_WORLD);
222: PetscPrintf(PETSC_COMM_WORLD, "\n forward sensitivity: d[y(tf) z(tf)]/d[y0 z0 mu]\n");
223: 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: MatDestroy(&A);
230: MatDestroy(&Jacp);
231: VecDestroy(&x);
232: MatDestroy(&sp);
233: TSDestroy(&ts);
234: PetscFinalize();
235: return 0;
236: }
238: /*TEST
240: test:
241: args: -monitor 0 -ts_adapt_type none
243: TEST*/