Actual source code: ex16opt_p.c
petsc-3.6.4 2016-04-12
2: static char help[] = "Solves the van der Pol equation.\n\
3: Input parameters include:\n\
4: -mu : stiffness parameter\n\n";
6: /*
7: Concepts: TS^time-dependent nonlinear problems
8: Concepts: TS^van der Pol equation
9: Concepts: Optimization using adjoint sensitivity analysis
10: Processors: 1
11: */
12: /* ------------------------------------------------------------------------
14: This program solves the van der Pol equation
15: y'' - \mu (1-y^2)*y' + y = 0 (1)
16: on the domain 0 <= x <= 1, with the boundary conditions
17: y(0) = 2, y'(0) = 0,
18: This is a nonlinear equation.
20: Notes:
21: This code demonstrates the TS solver interface to two variants of
22: linear problems, u_t = f(u,t), namely turning (1) into a system of
23: first order differential equations,
25: [ y' ] = [ z ]
26: [ z' ] [ \mu (1 - y^2) z - y ]
28: which then we can write as a vector equation
30: [ u_1' ] = [ u_2 ] (2)
31: [ u_2' ] [ \mu (1 - u_1^2) u_2 - u_1 ]
33: which is now in the desired form of u_t = f(u,t).
34: ------------------------------------------------------------------------- */
35: #include <petsctao.h>
36: #include <petscts.h>
37: #include <petscmat.h>
38: typedef struct _n_User *User;
39: struct _n_User {
40: PetscReal mu;
41: PetscReal next_output;
42: PetscInt steps;
43: PetscReal ftime,x_ob[2];
44: Mat A; /* Jacobian matrix */
45: Mat Jacp; /* JacobianP matrix */
46: Vec x,lambda[2],mup[2]; /* adjoint variables */
47: };
49: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
51: /*
52: * User-defined routines
53: */
56: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
57: {
58: PetscErrorCode ierr;
59: User user = (User)ctx;
60: PetscScalar *f;
61: const PetscScalar *x;
64: VecGetArrayRead(X,&x);
65: VecGetArray(F,&f);
66: f[0] = x[1];
67: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
68: VecRestoreArrayRead(X,&x);
69: VecRestoreArray(F,&f);
70: return(0);
71: }
75: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
76: {
77: PetscErrorCode ierr;
78: User user = (User)ctx;
79: PetscReal mu = user->mu;
80: PetscInt rowcol[] = {0,1};
81: PetscScalar J[2][2];
82: const PetscScalar *x;
85: VecGetArrayRead(X,&x);
86: J[0][0] = 0;
87: J[1][0] = -2.*mu*x[1]*x[0]-1.;
88: J[0][1] = 1.0;
89: J[1][1] = mu*(1.0-x[0]*x[0]);
90: MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
91: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
93: if (A != B) {
94: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
95: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
96: }
97: VecRestoreArrayRead(X,&x);
98: return(0);
99: }
103: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
104: {
105: PetscErrorCode ierr;
106: PetscInt row[] = {0,1},col[]={0};
107: PetscScalar J[2][1];
108: const PetscScalar *x;
111: VecGetArrayRead(X,&x);
112: J[0][0] = 0;
113: J[1][0] = (1.-x[0]*x[0])*x[1];
114: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
115: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
116: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
117: VecRestoreArrayRead(X,&x);
118: return(0);
119: }
123: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
124: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
125: {
126: PetscErrorCode ierr;
127: const PetscScalar *x;
128: PetscReal tfinal, dt, tprev;
129: User user = (User)ctx;
132: TSGetTimeStep(ts,&dt);
133: TSGetDuration(ts,NULL,&tfinal);
134: TSGetPrevTime(ts,&tprev);
135: VecGetArrayRead(X,&x);
136: 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]));
137: PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
138: VecRestoreArrayRead(X,&x);
139: return(0);
140: }
144: int main(int argc,char **argv)
145: {
146: TS ts; /* nonlinear solver */
147: Vec p;
148: PetscBool monitor = PETSC_FALSE;
149: PetscScalar *x_ptr;
150: PetscMPIInt size;
151: struct _n_User user;
152: PetscErrorCode ierr;
153: Tao tao;
154: TaoConvergedReason reason;
155: Vec lowerb,upperb;
156: KSP ksp;
157: PC pc;
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Initialize program
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162: PetscInitialize(&argc,&argv,NULL,help);
164: MPI_Comm_size(PETSC_COMM_WORLD,&size);
165: if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
167: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: Set runtime options
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: user.mu = 1.0;
171: user.next_output = 0.0;
172: user.steps = 0;
173: user.ftime = 0.5;
175: PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);
176: PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
178: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Create necessary matrix and vectors, solve same ODE on every process
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: MatCreate(PETSC_COMM_WORLD,&user.A);
182: MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
183: MatSetFromOptions(user.A);
184: MatSetUp(user.A);
185: MatCreateVecs(user.A,&user.x,NULL);
187: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
188: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
189: MatSetFromOptions(user.Jacp);
190: MatSetUp(user.Jacp);
191:
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Create timestepping solver context
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: TSCreate(PETSC_COMM_WORLD,&ts);
196: TSSetType(ts,TSRK);
197: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
198: TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
199: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
200: if (monitor) {
201: TSMonitorSet(ts,Monitor,&user,NULL);
202: }
204: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: Set initial conditions
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
207: VecGetArray(user.x,&x_ptr);
208: x_ptr[0] = 2.0; x_ptr[1] = 0.66666654321;
209: VecRestoreArray(user.x,&x_ptr);
210: TSSetTime(ts,0.0);
211: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)(user.ftime));
213: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: Save trajectory of solution so that TSAdjointSolve() may be used
215: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
216: TSSetSaveTrajectory(ts);
217:
218: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219: Set runtime options
220: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221: TSSetFromOptions(ts);
223: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
224: Solve nonlinear system
225: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226: TSSolve(ts,user.x);
227: TSGetSolveTime(ts,&(user.ftime));
228: TSGetTimeStepNumber(ts,&user.steps);
229: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);
231: VecGetArray(user.x,&x_ptr);
232: user.x_ob[0] = x_ptr[0];
233: user.x_ob[1] = x_ptr[1];
235: MatCreateVecs(user.A,&user.lambda[0],NULL);
236: MatCreateVecs(user.A,&user.lambda[1],NULL);
237: MatCreateVecs(user.Jacp,&user.mup[0],NULL);
238: MatCreateVecs(user.Jacp,&user.mup[1],NULL);
240: /* Create TAO solver and set desired solution method */
241: TaoCreate(PETSC_COMM_WORLD,&tao);
242: TaoSetType(tao,TAOCG);
244: /* Set initial solution guess */
245: MatCreateVecs(user.Jacp,&p,NULL);
246: VecGetArray(p,&x_ptr);
247: x_ptr[0] = 6.0;
248: VecRestoreArray(p,&x_ptr);
250: TaoSetInitialVector(tao,p);
252: /* Set routine for function and gradient evaluation */
253: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);
254:
255: VecDuplicate(p,&lowerb);
256: VecDuplicate(p,&upperb);
257: VecGetArray(lowerb,&x_ptr);
258: x_ptr[0] = 0.0;
259: VecRestoreArray(lowerb,&x_ptr);
260: VecGetArray(upperb,&x_ptr);
261: x_ptr[0] = 100.0;
262: VecRestoreArray(upperb,&x_ptr);
264: TaoSetVariableBounds(tao,lowerb,upperb);
265:
266: /* Check for any TAO command line options */
267: TaoSetFromOptions(tao);
268: TaoGetKSP(tao,&ksp);
269: if (ksp) {
270: KSPGetPC(ksp,&pc);
271: PCSetType(pc,PCNONE);
272: }
273:
274: TaoSetTolerances(tao,1e-13,1e-13,1e-13,PETSC_DEFAULT,PETSC_DEFAULT);
276: /* SOLVE THE APPLICATION */
277: TaoSolve(tao);
279: /* Get information on termination */
280: TaoGetConvergedReason(tao,&reason);
281: if (reason <= 0){
282: ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
283: }
285: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
286: /* Free TAO data structures */
287: TaoDestroy(&tao);
289: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
290: Free work space. All PETSc objects should be destroyed when they
291: are no longer needed.
292: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
293: MatDestroy(&user.A);
294: MatDestroy(&user.Jacp);
295: VecDestroy(&user.x);
296: VecDestroy(&user.lambda[0]);
297: VecDestroy(&user.lambda[1]);
298: VecDestroy(&user.mup[0]);
299: VecDestroy(&user.mup[1]);
300: TSDestroy(&ts);
302: VecDestroy(&lowerb);
303: VecDestroy(&upperb);
304: VecDestroy(&p);
305: PetscFinalize();
306: return(0);
307: }
309: /* ------------------------------------------------------------------ */
312: /*
313: FormFunctionGradient - Evaluates the function and corresponding gradient.
315: Input Parameters:
316: tao - the Tao context
317: X - the input vector
318: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
320: Output Parameters:
321: f - the newly evaluated function
322: G - the newly evaluated gradient
323: */
324: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
325: {
326: User user = (User)ctx;
327: TS ts;
328: PetscScalar *x_ptr,*y_ptr;
329: PetscErrorCode ierr;
331: VecGetArray(P,&x_ptr);
332: user->mu = x_ptr[0];
334: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
335: Create timestepping solver context
336: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
337: TSCreate(PETSC_COMM_WORLD,&ts);
338: TSSetType(ts,TSRK);
339: TSSetRHSFunction(ts,NULL,RHSFunction,user);
340: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
342: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
343: Set initial conditions
344: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
345: VecGetArray(user->x,&x_ptr);
346: x_ptr[0] = 2; x_ptr[1] = 0.66666654321;
347: VecRestoreArray(user->x,&x_ptr);
348: TSSetTime(ts,0.0);
349: TSSetDuration(ts,PETSC_DEFAULT,0.5);
351: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
352: Save trajectory of solution so that TSAdjointSolve() may be used
353: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
354: TSSetSaveTrajectory(ts);
356: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
357: Set runtime options
358: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
359: TSSetFromOptions(ts);
361: TSSolve(ts,user->x);
362: TSGetSolveTime(ts,&user->ftime);
363: TSGetTimeStepNumber(ts,&user->steps);
364: PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user->mu,user->steps,(double)user->ftime);
366: VecGetArray(user->x,&x_ptr);
367: *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]);
368: PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%f; %f], ODE solution y=%f, Cost function f=%f\n",(double)user->x_ob[0],(double)user->x_ob[1],(double)x_ptr[0],(double)(*f));
370: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
371: Adjoint model starts here
372: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
373: /* Redet initial conditions for the adjoint integration */
374: VecGetArray(user->lambda[0],&y_ptr);
375: y_ptr[0] = 2.*(x_ptr[0]-user->x_ob[0]);
376: y_ptr[1] = 2.*(x_ptr[1]-user->x_ob[1]);
377: VecRestoreArray(user->lambda[0],&y_ptr);
378: VecGetArray(user->lambda[1],&x_ptr);
379: x_ptr[0] = 0.0; x_ptr[1] = 1.0;
380: VecRestoreArray(user->lambda[1],&x_ptr);
382: VecGetArray(user->mup[0],&x_ptr);
383: x_ptr[0] = 0.0;
384: VecRestoreArray(user->mup[0],&x_ptr);
385: VecGetArray(user->mup[1],&x_ptr);
386: x_ptr[0] = 0.0;
387: VecRestoreArray(user->mup[1],&x_ptr);
388: TSSetCostGradients(ts,1,user->lambda,user->mup);
390: TSSetRHSJacobian(ts,user->A,user->A,RHSJacobian,user);
391: TSAdjointSetRHSJacobian(ts,user->Jacp,RHSJacobianP,user);
393: TSAdjointSolve(ts);
395: VecCopy(user->mup[0],G);
397: TSDestroy(&ts);
398: return(0);
399: }