Actual source code: ex16opt_ic.c
petsc-3.7.5 2017-01-01
1: static char help[] = "Solves an ODE-constrained optimization problem -- finding the optimal initial conditions for the van der Pol equation.\n\
2: Input parameters include:\n\
3: -mu : stiffness parameter\n\n";
5: /*
6: Concepts: TS^time-dependent nonlinear problems
7: Concepts: TS^van der Pol equation
8: Concepts: Optimization using adjoint sensitivities
9: Processors: 1
10: */
11: /* ------------------------------------------------------------------------
13: Notes:
14: This code demonstrates how to solve an ODE-constrained optimization problem with TAO, TSAdjoint and TS.
15: The objective is to minimize the difference between observation and model prediction by finding optimal values for initial conditions.
16: The gradient is computed with the discrete adjoint of an explicit Runge-Kutta method, see ex16adj.c for details.
17: ------------------------------------------------------------------------- */
18: #include <petsctao.h>
19: #include <petscts.h>
20: #include <petscmat.h>
21: typedef struct _n_User *User;
22: struct _n_User {
23: PetscReal mu;
24: PetscReal next_output;
26: PetscInt steps;
27: PetscReal ftime,x_ob[2];
28: Mat A; /* Jacobian matrix */
29: Vec x,lambda[2]; /* adjoint variables */
30: };
32: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
34: /*
35: * User-defined routines
36: */
39: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
40: {
41: PetscErrorCode ierr;
42: User user = (User)ctx;
43: PetscScalar *f;
44: const PetscScalar *x;
47: VecGetArrayRead(X,&x);
48: VecGetArray(F,&f);
49: f[0] = x[1];
50: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
51: VecRestoreArrayRead(X,&x);
52: VecRestoreArray(F,&f);
53: return(0);
54: }
58: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
59: {
60: PetscErrorCode ierr;
61: User user = (User)ctx;
62: PetscReal mu = user->mu;
63: PetscInt rowcol[] = {0,1};
64: PetscScalar J[2][2];
65: const PetscScalar *x;
68: VecGetArrayRead(X,&x);
69: J[0][0] = 0;
70: J[1][0] = -2.*mu*x[1]*x[0]-1;
71: J[0][1] = 1.0;
72: J[1][1] = mu*(1.0-x[0]*x[0]);
73: MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
74: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
75: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
76: if (A != B) {
77: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
78: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
79: }
80: VecRestoreArrayRead(X,&x);
81: return(0);
82: }
86: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
87: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
88: {
89: PetscErrorCode ierr;
90: const PetscScalar *x;
91: PetscReal tfinal, dt, tprev;
92: User user = (User)ctx;
95: TSGetTimeStep(ts,&dt);
96: TSGetDuration(ts,NULL,&tfinal);
97: TSGetPrevTime(ts,&tprev);
98: VecGetArrayRead(X,&x);
99: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D 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]));
100: PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
101: VecGetArrayRead(X,&x);
102: return(0);
103: }
107: int main(int argc,char **argv)
108: {
109: TS ts; /* nonlinear solver */
110: Vec ic;
111: PetscBool monitor = PETSC_FALSE;
112: PetscScalar *x_ptr;
113: PetscMPIInt size;
114: struct _n_User user;
115: PetscErrorCode ierr;
116: Tao tao;
117: KSP ksp;
118: PC pc;
120: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: Initialize program
122: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: PetscInitialize(&argc,&argv,NULL,help);
125: MPI_Comm_size(PETSC_COMM_WORLD,&size);
126: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
128: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129: Set runtime options
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: user.mu = 1.0;
132: user.next_output = 0.0;
133: user.steps = 0;
134: user.ftime = 0.5;
136: PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
137: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Create necessary matrix and vectors, solve same ODE on every process
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: MatCreate(PETSC_COMM_WORLD,&user.A);
143: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
144: MatSetFromOptions(user.A);
145: MatSetUp(user.A);
146: MatCreateVecs(user.A,&user.x,NULL);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Create timestepping solver context
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151: TSCreate(PETSC_COMM_WORLD,&ts);
152: TSSetType(ts,TSRK);
153: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
154: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
155: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
156: if (monitor) {
157: TSMonitorSet(ts,Monitor,&user,NULL);
158: }
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Set initial conditions
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: VecGetArray(user.x,&x_ptr);
164: x_ptr[0] = 2.0; x_ptr[1] = 0.66666654321;
165: VecRestoreArray(user.x,&x_ptr);
166: TSSetTime(ts,0.0);
167: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)(user.ftime));
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Save trajectory of solution so that TSAdjointSolve() may be used
171: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
172: TSSetSaveTrajectory(ts);
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Set runtime options
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177: TSSetFromOptions(ts);
179: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: Solve nonlinear system
181: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182: TSSolve(ts,user.x);
183: TSGetSolveTime(ts,&(user.ftime));
184: TSGetTimeStepNumber(ts,&user.steps);
185: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);
187: VecGetArray(user.x,&x_ptr);
188: user.x_ob[0] = x_ptr[0];
189: user.x_ob[1] = x_ptr[1];
191: MatCreateVecs(user.A,&user.lambda[0],NULL);
193: /* Create TAO solver and set desired solution method */
194: TaoCreate(PETSC_COMM_WORLD,&tao);
195: TaoSetType(tao,TAOCG);
197: /* Set initial solution guess */
198: MatCreateVecs(user.A,&ic,NULL);
199: VecGetArray(ic,&x_ptr);
200: x_ptr[0] = 2.1;
201: x_ptr[1] = 0.7;
202: VecRestoreArray(ic,&x_ptr);
204: TaoSetInitialVector(tao,ic);
206: /* Set routine for function and gradient evaluation */
207: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
209: /* Check for any TAO command line options */
210: TaoSetFromOptions(tao);
211: TaoGetKSP(tao,&ksp);
212: if (ksp) {
213: KSPGetPC(ksp,&pc);
214: PCSetType(pc,PCNONE);
215: }
217: TaoSetTolerances(tao,1e-10,PETSC_DEFAULT,PETSC_DEFAULT);
219: /* SOLVE THE APPLICATION */
220: TaoSolve(tao);
222: /* Free TAO data structures */
223: TaoDestroy(&tao);
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Free work space. All PETSc objects should be destroyed when they
227: are no longer needed.
228: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
229: MatDestroy(&user.A);
230: VecDestroy(&user.x);
231: VecDestroy(&user.lambda[0]);
232: TSDestroy(&ts);
234: VecDestroy(&ic);
235: PetscFinalize();
236: return(0);
237: }
239: /* ------------------------------------------------------------------ */
242: /*
243: FormFunctionGradient - Evaluates the function and corresponding gradient.
245: Input Parameters:
246: tao - the Tao context
247: X - the input vector
248: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
250: Output Parameters:
251: f - the newly evaluated function
252: G - the newly evaluated gradient
253: */
254: PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
255: {
256: User user = (User)ctx;
257: TS ts;
258: PetscScalar *x_ptr,*y_ptr;
259: PetscErrorCode ierr;
260: PetscScalar *ic_ptr;
262: VecCopy(IC,user->x);
264: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
265: Create timestepping solver context
266: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
267: TSCreate(PETSC_COMM_WORLD,&ts);
268: TSSetType(ts,TSRK);
269: TSSetRHSFunction(ts,NULL,RHSFunction,user);
271: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: Set time
273: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
274: TSSetTime(ts,0.0);
275: TSSetInitialTimeStep(ts,0.0,.001);
276: TSSetDuration(ts,2000,0.5);
277: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
279: TSSetTolerances(ts,1e-7,NULL,1e-7,NULL);
281: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
282: Save trajectory of solution so that TSAdjointSolve() may be used
283: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
284: TSSetSaveTrajectory(ts);
286: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
287: Set runtime options
288: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
289: TSSetFromOptions(ts);
291: TSSolve(ts,user->x);
292: TSGetSolveTime(ts,&user->ftime);
293: TSGetTimeStepNumber(ts,&user->steps);
294: PetscPrintf(PETSC_COMM_WORLD,"mu %.6f, steps %D, ftime %g\n",(double)user->mu,user->steps,(double)user->ftime);
296: VecGetArray(IC,&ic_ptr);
297: VecGetArray(user->x,&x_ptr);
298: *f = (x_ptr[0]-user->x_ob[0])*(x_ptr[0]-user->x_ob[0])+(x_ptr[1]-user->x_ob[1])*(x_ptr[1]-user->x_ob[1]);
299: PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%f; %f], ODE solution y=[%f;%f], Cost function f=%f\n",(double)user->x_ob[0],(double)user->x_ob[1],(double)x_ptr[0],(double)x_ptr[1],(double)(*f));
301: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: Adjoint model starts here
303: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
304: /* Redet initial conditions for the adjoint integration */
305: VecGetArray(user->lambda[0],&y_ptr);
306: y_ptr[0] = 2.*(x_ptr[0]-user->x_ob[0]);
307: y_ptr[1] = 2.*(x_ptr[1]-user->x_ob[1]);
308: VecRestoreArray(user->lambda[0],&y_ptr);
309: TSSetCostGradients(ts,1,user->lambda,NULL);
311: /* Set RHS Jacobian for the adjoint integration */
312: TSSetRHSJacobian(ts,user->A,user->A,RHSJacobian,user);
314: TSAdjointSolve(ts);
316: VecCopy(user->lambda[0],G);
318: TSDestroy(&ts);
319: return(0);
320: }