Actual source code: ex16adj.cxx
1: static char help[] = "Demonstrates automatic Jacobian generation using ADOL-C for an adjoint sensitivity analysis of the van der Pol equation.\n\
2: Input parameters include:\n\
3: -mu : stiffness parameter\n\n";
5: /*
6: REQUIRES configuration of PETSc with option --download-adolc.
8: For documentation on ADOL-C, see
9: $PETSC_ARCH/externalpackages/ADOL-C-2.6.0/ADOL-C/doc/adolc-manual.pdf
10: */
11: /* ------------------------------------------------------------------------
12: See ex16adj for a description of the problem being solved.
13: ------------------------------------------------------------------------- */
15: #include <petscts.h>
16: #include <petscmat.h>
17: #include "adolc-utils/drivers.cxx"
18: #include <adolc/adolc.h>
20: typedef struct _n_User *User;
21: struct _n_User {
22: PetscReal mu;
23: PetscReal next_output;
24: PetscReal tprev;
26: /* Automatic differentiation support */
27: AdolcCtx *adctx;
28: };
30: /*
31: 'Passive' RHS function, used in residual evaluations during the time integration.
32: */
33: static PetscErrorCode RHSFunctionPassive(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
34: {
35: User user = (User)ctx;
36: PetscScalar *f;
37: const PetscScalar *x;
39: PetscFunctionBeginUser;
40: PetscCall(VecGetArrayRead(X, &x));
41: PetscCall(VecGetArray(F, &f));
42: f[0] = x[1];
43: f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
44: PetscCall(VecRestoreArrayRead(X, &x));
45: PetscCall(VecRestoreArray(F, &f));
46: PetscFunctionReturn(PETSC_SUCCESS);
47: }
49: /*
50: Trace RHS to mark on tape 1 the dependence of f upon x. This tape is used in generating the
51: Jacobian transform.
52: */
53: static PetscErrorCode RHSFunctionActive(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
54: {
55: User user = (User)ctx;
56: PetscScalar *f;
57: const PetscScalar *x;
59: adouble f_a[2]; /* 'active' double for dependent variables */
60: adouble x_a[2]; /* 'active' double for independent variables */
62: PetscFunctionBeginUser;
63: PetscCall(VecGetArrayRead(X, &x));
64: PetscCall(VecGetArray(F, &f));
66: /* Start of active section */
67: trace_on(1);
68: x_a[0] <<= x[0];
69: x_a[1] <<= x[1]; /* Mark independence */
70: f_a[0] = x_a[1];
71: f_a[1] = user->mu * (1. - x_a[0] * x_a[0]) * x_a[1] - x_a[0];
72: f_a[0] >>= f[0];
73: f_a[1] >>= f[1]; /* Mark dependence */
74: trace_off();
75: /* End of active section */
77: PetscCall(VecRestoreArrayRead(X, &x));
78: PetscCall(VecRestoreArray(F, &f));
79: PetscFunctionReturn(PETSC_SUCCESS);
80: }
82: /*
83: Trace RHS again to mark on tape 2 the dependence of f upon the parameter mu. This tape is used in
84: generating JacobianP.
85: */
86: static PetscErrorCode RHSFunctionActiveP(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
87: {
88: User user = (User)ctx;
89: PetscScalar *f;
90: const PetscScalar *x;
92: adouble f_a[2]; /* 'active' double for dependent variables */
93: adouble x_a[2], mu_a; /* 'active' double for independent variables */
95: PetscFunctionBeginUser;
96: PetscCall(VecGetArrayRead(X, &x));
97: PetscCall(VecGetArray(F, &f));
99: /* Start of active section */
100: trace_on(3);
101: x_a[0] <<= x[0];
102: x_a[1] <<= x[1];
103: mu_a <<= user->mu; /* Mark independence */
104: f_a[0] = x_a[1];
105: f_a[1] = mu_a * (1. - x_a[0] * x_a[0]) * x_a[1] - x_a[0];
106: f_a[0] >>= f[0];
107: f_a[1] >>= f[1]; /* Mark dependence */
108: trace_off();
109: /* End of active section */
111: PetscCall(VecRestoreArrayRead(X, &x));
112: PetscCall(VecRestoreArray(F, &f));
113: PetscFunctionReturn(PETSC_SUCCESS);
114: }
116: /*
117: Compute the Jacobian w.r.t. x using PETSc-ADOL-C driver for explicit TS.
118: */
119: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat A, Mat B, void *ctx)
120: {
121: User user = (User)ctx;
122: const PetscScalar *x;
124: PetscFunctionBeginUser;
125: PetscCall(VecGetArrayRead(X, &x));
126: PetscCall(PetscAdolcComputeRHSJacobian(1, A, x, user->adctx));
127: PetscCall(VecRestoreArrayRead(X, &x));
128: PetscFunctionReturn(PETSC_SUCCESS);
129: }
131: /*
132: Compute the Jacobian w.r.t. mu using PETSc-ADOL-C driver for explicit TS.
133: */
134: static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx)
135: {
136: User user = (User)ctx;
137: const PetscScalar *x;
139: PetscFunctionBeginUser;
140: PetscCall(VecGetArrayRead(X, &x));
141: PetscCall(PetscAdolcComputeRHSJacobianP(3, A, x, &user->mu, user->adctx));
142: PetscCall(VecRestoreArrayRead(X, &x));
143: PetscFunctionReturn(PETSC_SUCCESS);
144: }
146: /*
147: Monitor timesteps and use interpolation to output at integer multiples of 0.1
148: */
149: static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, void *ctx)
150: {
151: const PetscScalar *x;
152: PetscReal tfinal, dt, tprev;
153: User user = (User)ctx;
155: PetscFunctionBeginUser;
156: PetscCall(TSGetTimeStep(ts, &dt));
157: PetscCall(TSGetMaxTime(ts, &tfinal));
158: PetscCall(TSGetPrevTime(ts, &tprev));
159: PetscCall(VecGetArrayRead(X, &x));
160: 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])));
161: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "t %.6f (tprev = %.6f) \n", (double)t, (double)tprev));
162: PetscCall(VecRestoreArrayRead(X, &x));
163: PetscFunctionReturn(PETSC_SUCCESS);
164: }
166: int main(int argc, char **argv)
167: {
168: TS ts; /* nonlinear solver */
169: Vec x; /* solution, residual vectors */
170: Mat A; /* Jacobian matrix */
171: Mat Jacp; /* JacobianP matrix */
172: PetscInt steps;
173: PetscReal ftime = 0.5;
174: PetscBool monitor = PETSC_FALSE;
175: PetscScalar *x_ptr;
176: PetscMPIInt size;
177: struct _n_User user;
178: AdolcCtx *adctx;
179: Vec lambda[2], mu[2], r;
181: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: Initialize program
183: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
184: PetscFunctionBeginUser;
185: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
186: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
187: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Set runtime options and create AdolcCtx
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: PetscCall(PetscNew(&adctx));
193: user.mu = 1;
194: user.next_output = 0.0;
195: adctx->m = 2;
196: adctx->n = 2;
197: adctx->p = 2;
198: adctx->num_params = 1;
199: user.adctx = adctx;
201: PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &user.mu, NULL));
202: PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));
204: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: Create necessary matrix and vectors, solve same ODE on every process
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
207: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
208: PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
209: PetscCall(MatSetFromOptions(A));
210: PetscCall(MatSetUp(A));
211: PetscCall(MatCreateVecs(A, &x, NULL));
213: PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
214: PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
215: PetscCall(MatSetFromOptions(Jacp));
216: PetscCall(MatSetUp(Jacp));
218: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219: Create timestepping solver context
220: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
222: PetscCall(TSSetType(ts, TSRK));
223: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionPassive, &user));
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Set initial conditions
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: PetscCall(VecGetArray(x, &x_ptr));
229: x_ptr[0] = 2;
230: x_ptr[1] = 0.66666654321;
231: PetscCall(VecRestoreArray(x, &x_ptr));
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Trace just once on each tape and put zeros on Jacobian diagonal
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: PetscCall(VecDuplicate(x, &r));
237: PetscCall(RHSFunctionActive(ts, 0., x, r, &user));
238: PetscCall(RHSFunctionActiveP(ts, 0., x, r, &user));
239: PetscCall(VecSet(r, 0));
240: PetscCall(MatDiagonalSet(A, r, INSERT_VALUES));
241: PetscCall(VecDestroy(&r));
243: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244: Set RHS Jacobian for the adjoint integration
245: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
246: PetscCall(TSSetRHSJacobian(ts, A, A, RHSJacobian, &user));
247: PetscCall(TSSetMaxTime(ts, ftime));
248: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
249: if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));
250: PetscCall(TSSetTimeStep(ts, .001));
252: /*
253: Have the TS save its trajectory so that TSAdjointSolve() may be used
254: */
255: PetscCall(TSSetSaveTrajectory(ts));
257: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
258: Set runtime options
259: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
260: PetscCall(TSSetFromOptions(ts));
262: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
263: Solve nonlinear system
264: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
265: PetscCall(TSSolve(ts, x));
266: PetscCall(TSGetSolveTime(ts, &ftime));
267: PetscCall(TSGetStepNumber(ts, &steps));
268: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.mu, steps, (double)ftime));
269: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));
271: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: Start the Adjoint model
273: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
274: PetscCall(MatCreateVecs(A, &lambda[0], NULL));
275: PetscCall(MatCreateVecs(A, &lambda[1], NULL));
276: /* Reset initial conditions for the adjoint integration */
277: PetscCall(VecGetArray(lambda[0], &x_ptr));
278: x_ptr[0] = 1.0;
279: x_ptr[1] = 0.0;
280: PetscCall(VecRestoreArray(lambda[0], &x_ptr));
281: PetscCall(VecGetArray(lambda[1], &x_ptr));
282: x_ptr[0] = 0.0;
283: x_ptr[1] = 1.0;
284: PetscCall(VecRestoreArray(lambda[1], &x_ptr));
286: PetscCall(MatCreateVecs(Jacp, &mu[0], NULL));
287: PetscCall(MatCreateVecs(Jacp, &mu[1], NULL));
288: PetscCall(VecGetArray(mu[0], &x_ptr));
289: x_ptr[0] = 0.0;
290: PetscCall(VecRestoreArray(mu[0], &x_ptr));
291: PetscCall(VecGetArray(mu[1], &x_ptr));
292: x_ptr[0] = 0.0;
293: PetscCall(VecRestoreArray(mu[1], &x_ptr));
294: PetscCall(TSSetCostGradients(ts, 2, lambda, mu));
296: /* Set RHS JacobianP */
297: PetscCall(TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &user));
299: PetscCall(TSAdjointSolve(ts));
301: PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD));
302: PetscCall(VecView(lambda[1], PETSC_VIEWER_STDOUT_WORLD));
303: PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD));
304: PetscCall(VecView(mu[1], PETSC_VIEWER_STDOUT_WORLD));
306: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: Free work space. All PETSc objects should be destroyed when they
308: are no longer needed.
309: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
310: PetscCall(MatDestroy(&A));
311: PetscCall(MatDestroy(&Jacp));
312: PetscCall(VecDestroy(&x));
313: PetscCall(VecDestroy(&lambda[0]));
314: PetscCall(VecDestroy(&lambda[1]));
315: PetscCall(VecDestroy(&mu[0]));
316: PetscCall(VecDestroy(&mu[1]));
317: PetscCall(TSDestroy(&ts));
318: PetscCall(PetscFree(adctx));
319: PetscCall(PetscFinalize());
320: return 0;
321: }
323: /*TEST
325: build:
326: requires: double !complex adolc
328: test:
329: suffix: 1
330: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor
331: output_file: output/ex16adj_1.out
333: test:
334: suffix: 2
335: args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -mu 5
336: output_file: output/ex16adj_2.out
338: test:
339: suffix: 3
340: args: -ts_max_steps 10 -monitor
341: output_file: output/ex16adj_3.out
343: test:
344: suffix: 4
345: args: -ts_max_steps 10 -monitor -mu 5
346: output_file: output/ex16adj_4.out
348: TEST*/