Actual source code: ex16opt_p.c

petsc-3.7.7 2017-09-25
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  1: static char help[] = "Solves an ODE-constrained optimization problem -- finding the optimal stiffness parameter 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 an optimal value for parameter \mu.
 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;
 25:   PetscInt  steps;
 26:   PetscReal ftime,x_ob[2];
 27:   Mat       A;             /* Jacobian matrix */
 28:   Mat       Jacp;          /* JacobianP matrix */
 29:   Vec       x,lambda[2],mup[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: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx)
 87: {
 88:   PetscErrorCode    ierr;
 89:   PetscInt          row[] = {0,1},col[]={0};
 90:   PetscScalar       J[2][1];
 91:   const PetscScalar *x;

 94:   VecGetArrayRead(X,&x);
 95:   J[0][0] = 0;
 96:   J[1][0] = (1.-x[0]*x[0])*x[1];
 97:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
 98:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 99:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
100:   VecRestoreArrayRead(X,&x);
101:   return(0);
102: }

106: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
107: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
108: {
109:   PetscErrorCode    ierr;
110:   const PetscScalar *x;
111:   PetscReal         tfinal, dt, tprev;
112:   User              user = (User)ctx;

115:   TSGetTimeStep(ts,&dt);
116:   TSGetDuration(ts,NULL,&tfinal);
117:   TSGetPrevTime(ts,&tprev);
118:   VecGetArrayRead(X,&x);
119:   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]));
120:   PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev);
121:   VecRestoreArrayRead(X,&x);
122:   return(0);
123: }

127: int main(int argc,char **argv)
128: {
129:   TS                 ts;          /* nonlinear solver */
130:   Vec                p;
131:   PetscBool          monitor = PETSC_FALSE;
132:   PetscScalar        *x_ptr;
133:   PetscMPIInt        size;
134:   struct _n_User     user;
135:   PetscErrorCode     ierr;
136:   Tao                tao;
137:   Vec                lowerb,upperb;
138:   KSP                ksp;
139:   PC                 pc;

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:      Initialize program
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144:   PetscInitialize(&argc,&argv,NULL,help);

146:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
147:   if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:     Set runtime options
151:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152:   user.mu          = 1.0;
153:   user.next_output = 0.0;
154:   user.steps       = 0;
155:   user.ftime       = 0.5;

157:   PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
158:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161:     Create necessary matrix and vectors, solve same ODE on every process
162:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163:   MatCreate(PETSC_COMM_WORLD,&user.A);
164:   MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
165:   MatSetFromOptions(user.A);
166:   MatSetUp(user.A);
167:   MatCreateVecs(user.A,&user.x,NULL);

169:   MatCreate(PETSC_COMM_WORLD,&user.Jacp);
170:   MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
171:   MatSetFromOptions(user.Jacp);
172:   MatSetUp(user.Jacp);

174:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175:      Create timestepping solver context
176:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177:   TSCreate(PETSC_COMM_WORLD,&ts);
178:   TSSetType(ts,TSRK);
179:   TSSetRHSFunction(ts,NULL,RHSFunction,&user);
180:   TSSetDuration(ts,PETSC_DEFAULT,user.ftime);
181:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
182:   if (monitor) {
183:     TSMonitorSet(ts,Monitor,&user,NULL);
184:   }

186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187:      Set initial conditions
188:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189:   VecGetArray(user.x,&x_ptr);
190:   x_ptr[0] = 2.0;   x_ptr[1] = 0.66666654321;
191:   VecRestoreArray(user.x,&x_ptr);
192:   TSSetTime(ts,0.0);
193:   PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)(user.ftime));

195:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196:     Save trajectory of solution so that TSAdjointSolve() may be used
197:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198:   TSSetSaveTrajectory(ts);

200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201:      Set runtime options
202:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203:   TSSetFromOptions(ts);

205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
206:      Solve nonlinear system
207:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
208:   TSSolve(ts,user.x);
209:   TSGetSolveTime(ts,&(user.ftime));
210:   TSGetTimeStepNumber(ts,&user.steps);
211:   PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);

213:   VecGetArray(user.x,&x_ptr);
214:   user.x_ob[0] = x_ptr[0];
215:   user.x_ob[1] = x_ptr[1];

217:   MatCreateVecs(user.A,&user.lambda[0],NULL);
218:   MatCreateVecs(user.A,&user.lambda[1],NULL);
219:   MatCreateVecs(user.Jacp,&user.mup[0],NULL);
220:   MatCreateVecs(user.Jacp,&user.mup[1],NULL);

222:   /* Create TAO solver and set desired solution method */
223:   TaoCreate(PETSC_COMM_WORLD,&tao);
224:   TaoSetType(tao,TAOCG);

226:   /* Set initial solution guess */
227:   MatCreateVecs(user.Jacp,&p,NULL);
228:   VecGetArray(p,&x_ptr);
229:   x_ptr[0]   = 6.0;
230:   VecRestoreArray(p,&x_ptr);

232:   TaoSetInitialVector(tao,p);

234:   /* Set routine for function and gradient evaluation */
235:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);

237:   VecDuplicate(p,&lowerb);
238:   VecDuplicate(p,&upperb);
239:   VecGetArray(lowerb,&x_ptr);
240:   x_ptr[0] = 0.0;
241:   VecRestoreArray(lowerb,&x_ptr);
242:   VecGetArray(upperb,&x_ptr);
243:   x_ptr[0] = 100.0;
244:   VecRestoreArray(upperb,&x_ptr);

246:   TaoSetVariableBounds(tao,lowerb,upperb);

248:   /* Check for any TAO command line options */
249:   TaoSetFromOptions(tao);
250:   TaoGetKSP(tao,&ksp);
251:   if (ksp) {
252:     KSPGetPC(ksp,&pc);
253:     PCSetType(pc,PCNONE);
254:   }

256:   TaoSetTolerances(tao,1e-13,PETSC_DEFAULT,PETSC_DEFAULT);

258:   /* SOLVE THE APPLICATION */
259:   TaoSolve(tao);

261:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
262:   /* Free TAO data structures */
263:   TaoDestroy(&tao);

265:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
266:      Free work space.  All PETSc objects should be destroyed when they
267:      are no longer needed.
268:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
269:   MatDestroy(&user.A);
270:   MatDestroy(&user.Jacp);
271:   VecDestroy(&user.x);
272:   VecDestroy(&user.lambda[0]);
273:   VecDestroy(&user.lambda[1]);
274:   VecDestroy(&user.mup[0]);
275:   VecDestroy(&user.mup[1]);
276:   TSDestroy(&ts);

278:   VecDestroy(&lowerb);
279:   VecDestroy(&upperb);
280:   VecDestroy(&p);
281:   PetscFinalize();
282:   return(0);
283: }

285: /* ------------------------------------------------------------------ */
288: /*
289:    FormFunctionGradient - Evaluates the function and corresponding gradient.

291:    Input Parameters:
292:    tao - the Tao context
293:    X   - the input vector
294:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

296:    Output Parameters:
297:    f   - the newly evaluated function
298:    G   - the newly evaluated gradient
299: */
300: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
301: {
302:   User              user = (User)ctx;
303:   TS                ts;
304:   PetscScalar       *x_ptr,*y_ptr;
305:   PetscErrorCode    ierr;

307:   VecGetArray(P,&x_ptr);
308:   user->mu = x_ptr[0];

310:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
311:      Create timestepping solver context
312:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
313:   TSCreate(PETSC_COMM_WORLD,&ts);
314:   TSSetType(ts,TSRK);
315:   TSSetRHSFunction(ts,NULL,RHSFunction,user);

317:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318:      Set initial conditions
319:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
320:   VecGetArray(user->x,&x_ptr);
321:   x_ptr[0] = 2;   x_ptr[1] = 0.66666654321;
322:   VecRestoreArray(user->x,&x_ptr);
323:   TSSetTime(ts,0.0);
324:   TSSetDuration(ts,PETSC_DEFAULT,0.5);
325:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);

327:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
328:     Save trajectory of solution so that TSAdjointSolve() may be used
329:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
330:   TSSetSaveTrajectory(ts);

332:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
333:      Set runtime options
334:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
335:   TSSetFromOptions(ts);

337:   TSSolve(ts,user->x);
338:   TSGetSolveTime(ts,&user->ftime);
339:   TSGetTimeStepNumber(ts,&user->steps);
340:   PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user->mu,user->steps,(double)user->ftime);

342:   VecGetArray(user->x,&x_ptr);
343:   *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]);
344:   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));

346:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
347:      Adjoint model starts here
348:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
349:   /*   Redet initial conditions for the adjoint integration */
350:   VecGetArray(user->lambda[0],&y_ptr);
351:   y_ptr[0] = 2.*(x_ptr[0]-user->x_ob[0]);
352:   y_ptr[1] = 2.*(x_ptr[1]-user->x_ob[1]);
353:   VecRestoreArray(user->lambda[0],&y_ptr);
354:   VecGetArray(user->lambda[1],&x_ptr);
355:   x_ptr[0] = 0.0;   x_ptr[1] = 1.0;
356:   VecRestoreArray(user->lambda[1],&x_ptr);

358:   VecGetArray(user->mup[0],&x_ptr);
359:   x_ptr[0] = 0.0;
360:   VecRestoreArray(user->mup[0],&x_ptr);
361:   VecGetArray(user->mup[1],&x_ptr);
362:   x_ptr[0] = 0.0;
363:   VecRestoreArray(user->mup[1],&x_ptr);
364:   TSSetCostGradients(ts,1,user->lambda,user->mup);

366:   TSSetRHSJacobian(ts,user->A,user->A,RHSJacobian,user);
367:   TSAdjointSetRHSJacobian(ts,user->Jacp,RHSJacobianP,user);

369:   TSAdjointSolve(ts);

371:   VecCopy(user->mup[0],G);

373:   TSDestroy(&ts);
374:   return(0);
375: }