Actual source code: ex1.c

  1: #include <petsctao.h>
  2: #include <petscts.h>

  4: typedef struct _n_aircraft *Aircraft;
  5: struct _n_aircraft {
  6:   TS        ts,quadts;
  7:   Vec       V,W;    /* control variables V and W */
  8:   PetscInt  nsteps; /* number of time steps */
  9:   PetscReal ftime;
 10:   Mat       A,H;
 11:   Mat       Jacp,DRDU,DRDP;
 12:   Vec       U,Lambda[1],Mup[1],Lambda2[1],Mup2[1],Dir;
 13:   Vec       rhshp1[1],rhshp2[1],rhshp3[1],rhshp4[1],inthp1[1],inthp2[1],inthp3[1],inthp4[1];
 14:   PetscReal lv,lw;
 15:   PetscBool mf,eh;
 16: };

 18: PetscErrorCode FormObjFunctionGradient(Tao,Vec,PetscReal *,Vec,void *);
 19: PetscErrorCode FormObjHessian(Tao,Vec,Mat,Mat,void *);
 20: PetscErrorCode ComputeObjHessianWithSOA(Vec,PetscScalar[],Aircraft);
 21: PetscErrorCode MatrixFreeObjHessian(Tao,Vec,Mat,Mat,void *);
 22: PetscErrorCode MyMatMult(Mat,Vec,Vec);

 24: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
 25: {
 26:   Aircraft          actx = (Aircraft)ctx;
 27:   const PetscScalar *u,*v,*w;
 28:   PetscScalar       *f;
 29:   PetscInt          step;
 30:   PetscErrorCode    ierr;

 33:   TSGetStepNumber(ts,&step);
 34:   VecGetArrayRead(U,&u);
 35:   VecGetArrayRead(actx->V,&v);
 36:   VecGetArrayRead(actx->W,&w);
 37:   VecGetArray(F,&f);
 38:   f[0] = v[step]*PetscCosReal(w[step]);
 39:   f[1] = v[step]*PetscSinReal(w[step]);
 40:   VecRestoreArrayRead(U,&u);
 41:   VecRestoreArrayRead(actx->V,&v);
 42:   VecRestoreArrayRead(actx->W,&w);
 43:   VecRestoreArray(F,&f);
 44:   return(0);
 45: }

 47: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec U,Mat A,void *ctx)
 48: {
 49:   Aircraft          actx = (Aircraft)ctx;
 50:   const PetscScalar *u,*v,*w;
 51:   PetscInt          step,rows[2] = {0,1},rowcol[2];
 52:   PetscScalar       Jp[2][2];
 53:   PetscErrorCode    ierr;

 56:   MatZeroEntries(A);
 57:   TSGetStepNumber(ts,&step);
 58:   VecGetArrayRead(U,&u);
 59:   VecGetArrayRead(actx->V,&v);
 60:   VecGetArrayRead(actx->W,&w);

 62:   Jp[0][0] = PetscCosReal(w[step]);
 63:   Jp[0][1] = -v[step]*PetscSinReal(w[step]);
 64:   Jp[1][0] = PetscSinReal(w[step]);
 65:   Jp[1][1] = v[step]*PetscCosReal(w[step]);

 67:   VecRestoreArrayRead(U,&u);
 68:   VecRestoreArrayRead(actx->V,&v);
 69:   VecRestoreArrayRead(actx->W,&w);

 71:   rowcol[0] = 2*step;
 72:   rowcol[1] = 2*step+1;
 73:   MatSetValues(A,2,rows,2,rowcol,&Jp[0][0],INSERT_VALUES);

 75:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 76:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 77:   return(0);
 78: }

 80: static PetscErrorCode RHSHessianProductUU(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
 81: {
 83:   return(0);
 84: }

 86: static PetscErrorCode RHSHessianProductUP(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
 87: {
 89:   return(0);
 90: }

 92: static PetscErrorCode RHSHessianProductPU(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
 93: {
 95:   return(0);
 96: }

 98: static PetscErrorCode RHSHessianProductPP(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
 99: {
100:   Aircraft          actx = (Aircraft)ctx;
101:   const PetscScalar *v,*w,*vl,*vr,*u;
102:   PetscScalar       *vhv;
103:   PetscScalar       dJpdP[2][2][2]={{{0}}};
104:   PetscInt          step,i,j,k;
105:   PetscErrorCode    ierr;

108:   TSGetStepNumber(ts,&step);
109:   VecGetArrayRead(U,&u);
110:   VecGetArrayRead(actx->V,&v);
111:   VecGetArrayRead(actx->W,&w);
112:   VecGetArrayRead(Vl[0],&vl);
113:   VecGetArrayRead(Vr,&vr);
114:   VecSet(VHV[0],0.0);
115:   VecGetArray(VHV[0],&vhv);

117:   dJpdP[0][0][1] = -PetscSinReal(w[step]);
118:   dJpdP[0][1][0] = -PetscSinReal(w[step]);
119:   dJpdP[0][1][1] = -v[step]*PetscCosReal(w[step]);
120:   dJpdP[1][0][1] = PetscCosReal(w[step]);
121:   dJpdP[1][1][0] = PetscCosReal(w[step]);
122:   dJpdP[1][1][1] = -v[step]*PetscSinReal(w[step]);

124:   for (j=0; j<2; j++) {
125:     vhv[2*step+j] = 0;
126:     for (k=0; k<2; k++)
127:       for (i=0; i<2; i++)
128:         vhv[2*step+j] += vl[i]*dJpdP[i][j][k]*vr[2*step+k];
129:   }
130:   VecRestoreArrayRead(U,&u);
131:   VecRestoreArrayRead(Vl[0],&vl);
132:   VecRestoreArrayRead(Vr,&vr);
133:   VecRestoreArray(VHV[0],&vhv);
134:   return(0);
135: }

137: /* Vl in NULL,updates to VHV must be added */
138: static PetscErrorCode IntegrandHessianProductUU(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
139: {
140:   Aircraft          actx = (Aircraft)ctx;
141:   const PetscScalar *v,*w,*vr,*u;
142:   PetscScalar       *vhv;
143:   PetscScalar       dRudU[2][2]={{0}};
144:   PetscInt          step,j,k;
145:   PetscErrorCode    ierr;

148:   TSGetStepNumber(ts,&step);
149:   VecGetArrayRead(U,&u);
150:   VecGetArrayRead(actx->V,&v);
151:   VecGetArrayRead(actx->W,&w);
152:   VecGetArrayRead(Vr,&vr);
153:   VecGetArray(VHV[0],&vhv);

155:   dRudU[0][0] = 2.0;
156:   dRudU[1][1] = 2.0;

158:   for (j=0; j<2; j++) {
159:     vhv[j] = 0;
160:     for (k=0; k<2; k++)
161:         vhv[j] += dRudU[j][k]*vr[k];
162:   }
163:   VecRestoreArrayRead(U,&u);
164:   VecRestoreArrayRead(Vr,&vr);
165:   VecRestoreArray(VHV[0],&vhv);
166:   return(0);
167: }

169: static PetscErrorCode IntegrandHessianProductUP(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
170: {
172:   return(0);
173: }

175: static PetscErrorCode IntegrandHessianProductPU(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
176: {
178:   return(0);
179: }

181: static PetscErrorCode IntegrandHessianProductPP(TS ts,PetscReal t,Vec U,Vec *Vl,Vec Vr,Vec *VHV,void *ctx)
182: {
184:   return(0);
185: }

187: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,void *ctx)
188: {
189:   Aircraft          actx = (Aircraft)ctx;
190:   PetscScalar       *r;
191:   PetscReal         dx,dy;
192:   const PetscScalar *u;
193:   PetscErrorCode    ierr;

196:   VecGetArrayRead(U,&u);
197:   VecGetArray(R,&r);
198:   dx   = u[0] - actx->lv*t*PetscCosReal(actx->lw);
199:   dy   = u[1] - actx->lv*t*PetscSinReal(actx->lw);
200:   r[0] = dx*dx+dy*dy;
201:   VecRestoreArray(R,&r);
202:   VecRestoreArrayRead(U,&u);
203:   return(0);
204: }

206: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,void *ctx)
207: {
208:   Aircraft          actx = (Aircraft)ctx;
209:   PetscScalar       drdu[2][1];
210:   const PetscScalar *u;
211:   PetscReal         dx,dy;
212:   PetscInt          row[] = {0,1},col[] = {0};
213:   PetscErrorCode    ierr;

216:   VecGetArrayRead(U,&u);
217:   dx      = u[0] - actx->lv*t*PetscCosReal(actx->lw);
218:   dy      = u[1] - actx->lv*t*PetscSinReal(actx->lw);
219:   drdu[0][0] = 2.*dx;
220:   drdu[1][0] = 2.*dy;
221:   MatSetValues(DRDU,2,row,1,col,&drdu[0][0],INSERT_VALUES);
222:   VecRestoreArrayRead(U,&u);
223:   MatAssemblyBegin(DRDU,MAT_FINAL_ASSEMBLY);
224:   MatAssemblyEnd(DRDU,MAT_FINAL_ASSEMBLY);
225:   return(0);
226: }

228: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,void *ctx)
229: {

233:   MatZeroEntries(DRDP);
234:   MatAssemblyBegin(DRDP,MAT_FINAL_ASSEMBLY);
235:   MatAssemblyEnd(DRDP,MAT_FINAL_ASSEMBLY);
236:   return(0);
237: }

239: int main(int argc,char **argv)
240: {
241:   Vec                P,PL,PU;
242:   struct _n_aircraft aircraft;
243:   PetscMPIInt        size;
244:   Tao                tao;
245:   KSP                ksp;
246:   PC                 pc;
247:   PetscScalar        *u,*p;
248:   PetscInt           i;
249:   PetscErrorCode     ierr;

251:   /* Initialize program */
252:   PetscInitialize(&argc,&argv,NULL,NULL);if (ierr) return ierr;
253:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
254:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

256:   /* Parameter settings */
257:   aircraft.ftime = 1.;   /* time interval in hour */
258:   aircraft.nsteps = 10; /* number of steps */
259:   aircraft.lv = 2.0; /* leader speed in kmph */
260:   aircraft.lw = PETSC_PI/4.; /* leader heading angle */

262:   PetscOptionsGetReal(NULL,NULL,"-ftime",&aircraft.ftime,NULL);
263:   PetscOptionsGetInt(NULL,NULL,"-nsteps",&aircraft.nsteps,NULL);
264:   PetscOptionsHasName(NULL,NULL,"-matrixfree",&aircraft.mf);
265:   PetscOptionsHasName(NULL,NULL,"-exacthessian",&aircraft.eh);

267:   /* Create TAO solver and set desired solution method */
268:   TaoCreate(PETSC_COMM_WORLD,&tao);
269:   TaoSetType(tao,TAOBQNLS);

271:   /* Create necessary matrix and vectors, solve same ODE on every process */
272:   MatCreate(PETSC_COMM_WORLD,&aircraft.A);
273:   MatSetSizes(aircraft.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
274:   MatSetFromOptions(aircraft.A);
275:   MatSetUp(aircraft.A);
276:   MatAssemblyBegin(aircraft.A,MAT_FINAL_ASSEMBLY);
277:   MatAssemblyEnd(aircraft.A,MAT_FINAL_ASSEMBLY);
278:   MatShift(aircraft.A,1);
279:   MatShift(aircraft.A,-1);

281:   MatCreate(PETSC_COMM_WORLD,&aircraft.Jacp);
282:   MatSetSizes(aircraft.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,2*aircraft.nsteps);
283:   MatSetFromOptions(aircraft.Jacp);
284:   MatSetUp(aircraft.Jacp);
285:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2*aircraft.nsteps,1,NULL,&aircraft.DRDP);
286:   MatSetUp(aircraft.DRDP);
287:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,&aircraft.DRDU);
288:   MatSetUp(aircraft.DRDU);

290:   /* Create timestepping solver context */
291:   TSCreate(PETSC_COMM_WORLD,&aircraft.ts);
292:   TSSetType(aircraft.ts,TSRK);
293:   TSSetRHSFunction(aircraft.ts,NULL,RHSFunction,&aircraft);
294:   TSSetRHSJacobian(aircraft.ts,aircraft.A,aircraft.A,TSComputeRHSJacobianConstant,&aircraft);
295:   TSSetRHSJacobianP(aircraft.ts,aircraft.Jacp,RHSJacobianP,&aircraft);
296:   TSSetExactFinalTime(aircraft.ts,TS_EXACTFINALTIME_MATCHSTEP);
297:   TSSetEquationType(aircraft.ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */

299:   /* Set initial conditions */
300:   MatCreateVecs(aircraft.A,&aircraft.U,NULL);
301:   TSSetSolution(aircraft.ts,aircraft.U);
302:   VecGetArray(aircraft.U,&u);
303:   u[0] = 1.5;
304:   u[1] = 0;
305:   VecRestoreArray(aircraft.U,&u);
306:   VecCreate(PETSC_COMM_WORLD,&aircraft.V);
307:   VecSetSizes(aircraft.V,PETSC_DECIDE,aircraft.nsteps);
308:   VecSetUp(aircraft.V);
309:   VecDuplicate(aircraft.V,&aircraft.W);
310:   VecSet(aircraft.V,1.);
311:   VecSet(aircraft.W,PETSC_PI/4.);

313:   /* Save trajectory of solution so that TSAdjointSolve() may be used */
314:   TSSetSaveTrajectory(aircraft.ts);

316:   /* Set sensitivity context */
317:   TSCreateQuadratureTS(aircraft.ts,PETSC_FALSE,&aircraft.quadts);
318:   TSSetRHSFunction(aircraft.quadts,NULL,(TSRHSFunction)CostIntegrand,&aircraft);
319:   TSSetRHSJacobian(aircraft.quadts,aircraft.DRDU,aircraft.DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&aircraft);
320:   TSSetRHSJacobianP(aircraft.quadts,aircraft.DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,&aircraft);
321:   MatCreateVecs(aircraft.A,&aircraft.Lambda[0],NULL);
322:   MatCreateVecs(aircraft.Jacp,&aircraft.Mup[0],NULL);
323:   if (aircraft.eh) {
324:     MatCreateVecs(aircraft.A,&aircraft.rhshp1[0],NULL);
325:     MatCreateVecs(aircraft.A,&aircraft.rhshp2[0],NULL);
326:     MatCreateVecs(aircraft.Jacp,&aircraft.rhshp3[0],NULL);
327:     MatCreateVecs(aircraft.Jacp,&aircraft.rhshp4[0],NULL);
328:     MatCreateVecs(aircraft.DRDU,&aircraft.inthp1[0],NULL);
329:     MatCreateVecs(aircraft.DRDU,&aircraft.inthp2[0],NULL);
330:     MatCreateVecs(aircraft.DRDP,&aircraft.inthp3[0],NULL);
331:     MatCreateVecs(aircraft.DRDP,&aircraft.inthp4[0],NULL);
332:     MatCreateVecs(aircraft.Jacp,&aircraft.Dir,NULL);
333:     TSSetRHSHessianProduct(aircraft.ts,aircraft.rhshp1,RHSHessianProductUU,aircraft.rhshp2,RHSHessianProductUP,aircraft.rhshp3,RHSHessianProductPU,aircraft.rhshp4,RHSHessianProductPP,&aircraft);
334:     TSSetRHSHessianProduct(aircraft.quadts,aircraft.inthp1,IntegrandHessianProductUU,aircraft.inthp2,IntegrandHessianProductUP,aircraft.inthp3,IntegrandHessianProductPU,aircraft.inthp4,IntegrandHessianProductPP,&aircraft);
335:     MatCreateVecs(aircraft.A,&aircraft.Lambda2[0],NULL);
336:     MatCreateVecs(aircraft.Jacp,&aircraft.Mup2[0],NULL);
337:   }
338:   TSSetFromOptions(aircraft.ts);
339:   TSSetMaxTime(aircraft.ts,aircraft.ftime);
340:   TSSetTimeStep(aircraft.ts,aircraft.ftime/aircraft.nsteps);

342:   /* Set initial solution guess */
343:   MatCreateVecs(aircraft.Jacp,&P,NULL);
344:   VecGetArray(P,&p);
345:   for (i=0; i<aircraft.nsteps; i++) {
346:     p[2*i] = 2.0;
347:     p[2*i+1] = PETSC_PI/2.0;
348:   }
349:   VecRestoreArray(P,&p);
350:   VecDuplicate(P,&PU);
351:   VecDuplicate(P,&PL);
352:   VecGetArray(PU,&p);
353:   for (i=0; i<aircraft.nsteps; i++) {
354:     p[2*i] = 2.0;
355:     p[2*i+1] = PETSC_PI;
356:   }
357:   VecRestoreArray(PU,&p);
358:   VecGetArray(PL,&p);
359:   for (i=0; i<aircraft.nsteps; i++) {
360:     p[2*i] = 0.0;
361:     p[2*i+1] = -PETSC_PI;
362:   }
363:   VecRestoreArray(PL,&p);

365:   TaoSetInitialVector(tao,P);
366:   TaoSetVariableBounds(tao,PL,PU);
367:   /* Set routine for function and gradient evaluation */
368:   TaoSetObjectiveAndGradientRoutine(tao,FormObjFunctionGradient,(void *)&aircraft);

370:   if (aircraft.eh) {
371:     if (aircraft.mf) {
372:       MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2*aircraft.nsteps,2*aircraft.nsteps,(void*)&aircraft,&aircraft.H);
373:       MatShellSetOperation(aircraft.H,MATOP_MULT,(void(*)(void))MyMatMult);
374:       MatSetOption(aircraft.H,MAT_SYMMETRIC,PETSC_TRUE);
375:       TaoSetHessianRoutine(tao,aircraft.H,aircraft.H,MatrixFreeObjHessian,(void*)&aircraft);
376:     } else {
377:       MatCreateDense(MPI_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,2*aircraft.nsteps,2*aircraft.nsteps,NULL,&(aircraft.H));
378:       MatSetOption(aircraft.H,MAT_SYMMETRIC,PETSC_TRUE);
379:       TaoSetHessianRoutine(tao,aircraft.H,aircraft.H,FormObjHessian,(void *)&aircraft);
380:     }
381:   }

383:   /* Check for any TAO command line options */
384:   TaoGetKSP(tao,&ksp);
385:   if (ksp) {
386:     KSPGetPC(ksp,&pc);
387:     PCSetType(pc,PCNONE);
388:   }
389:   TaoSetFromOptions(tao);

391:   TaoSolve(tao);
392:   VecView(P,PETSC_VIEWER_STDOUT_WORLD);

394:   /* Free TAO data structures */
395:   TaoDestroy(&tao);

397:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
398:      Free work space.  All PETSc objects should be destroyed when they
399:      are no longer needed.
400:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
401:   TSDestroy(&aircraft.ts);
402:   MatDestroy(&aircraft.A);
403:   VecDestroy(&aircraft.U);
404:   VecDestroy(&aircraft.V);
405:   VecDestroy(&aircraft.W);
406:   VecDestroy(&P);
407:   VecDestroy(&PU);
408:   VecDestroy(&PL);
409:   MatDestroy(&aircraft.Jacp);
410:   MatDestroy(&aircraft.DRDU);
411:   MatDestroy(&aircraft.DRDP);
412:   VecDestroy(&aircraft.Lambda[0]);
413:   VecDestroy(&aircraft.Mup[0]);
414:   VecDestroy(&P);
415:   if (aircraft.eh) {
416:     VecDestroy(&aircraft.Lambda2[0]);
417:     VecDestroy(&aircraft.Mup2[0]);
418:     VecDestroy(&aircraft.Dir);
419:     VecDestroy(&aircraft.rhshp1[0]);
420:     VecDestroy(&aircraft.rhshp2[0]);
421:     VecDestroy(&aircraft.rhshp3[0]);
422:     VecDestroy(&aircraft.rhshp4[0]);
423:     VecDestroy(&aircraft.inthp1[0]);
424:     VecDestroy(&aircraft.inthp2[0]);
425:     VecDestroy(&aircraft.inthp3[0]);
426:     VecDestroy(&aircraft.inthp4[0]);
427:     MatDestroy(&aircraft.H);
428:   }
429:   PetscFinalize();
430:   return ierr;
431: }

433: /*
434:    FormObjFunctionGradient - Evaluates the function and corresponding gradient.

436:    Input Parameters:
437:    tao - the Tao context
438:    P   - the input vector
439:    ctx - optional aircraft-defined context, as set by TaoSetObjectiveAndGradientRoutine()

441:    Output Parameters:
442:    f   - the newly evaluated function
443:    G   - the newly evaluated gradient
444: */
445: PetscErrorCode FormObjFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx)
446: {
447:   Aircraft          actx = (Aircraft)ctx;
448:   TS                ts = actx->ts;
449:   Vec               Q;
450:   const PetscScalar *p,*q;
451:   PetscScalar       *u,*v,*w;
452:   PetscInt          i;
453:   PetscErrorCode    ierr;

456:   VecGetArrayRead(P,&p);
457:   VecGetArray(actx->V,&v);
458:   VecGetArray(actx->W,&w);
459:   for (i=0; i<actx->nsteps; i++) {
460:     v[i] = p[2*i];
461:     w[i] = p[2*i+1];
462:   }
463:   VecRestoreArrayRead(P,&p);
464:   VecRestoreArray(actx->V,&v);
465:   VecRestoreArray(actx->W,&w);

467:   TSSetTime(ts,0.0);
468:   TSSetStepNumber(ts,0);
469:   TSSetFromOptions(ts);
470:   TSSetTimeStep(ts,actx->ftime/actx->nsteps);

472:   /* reinitialize system state */
473:   VecGetArray(actx->U,&u);
474:   u[0] = 2.0;
475:   u[1] = 0;
476:   VecRestoreArray(actx->U,&u);

478:   /* reinitialize the integral value */
479:   TSGetCostIntegral(ts,&Q);
480:   VecSet(Q,0.0);

482:   TSSolve(ts,actx->U);

484:   /* Reset initial conditions for the adjoint integration */
485:   VecSet(actx->Lambda[0],0.0);
486:   VecSet(actx->Mup[0],0.0);
487:   TSSetCostGradients(ts,1,actx->Lambda,actx->Mup);

489:   TSAdjointSolve(ts);
490:   VecCopy(actx->Mup[0],G);
491:   TSGetCostIntegral(ts,&Q);
492:   VecGetArrayRead(Q,&q);
493:   *f   = q[0];
494:   VecRestoreArrayRead(Q,&q);
495:   return(0);
496: }

498: PetscErrorCode FormObjHessian(Tao tao,Vec P,Mat H,Mat Hpre,void *ctx)
499: {
500:   Aircraft          actx = (Aircraft)ctx;
501:   const PetscScalar *p;
502:   PetscScalar       *harr,*v,*w,one = 1.0;
503:   PetscInt          ind[1];
504:   PetscInt          *cols,i;
505:   Vec               Dir;
506:   PetscErrorCode    ierr;

509:   /* set up control parameters */
510:   VecGetArrayRead(P,&p);
511:   VecGetArray(actx->V,&v);
512:   VecGetArray(actx->W,&w);
513:   for (i=0; i<actx->nsteps; i++) {
514:     v[i] = p[2*i];
515:     w[i] = p[2*i+1];
516:   }
517:   VecRestoreArrayRead(P,&p);
518:   VecRestoreArray(actx->V,&v);
519:   VecRestoreArray(actx->W,&w);

521:   PetscMalloc1(2*actx->nsteps,&harr);
522:   PetscMalloc1(2*actx->nsteps,&cols);
523:   for (i=0; i<2*actx->nsteps; i++) cols[i] = i;
524:   VecDuplicate(P,&Dir);
525:   for (i=0; i<2*actx->nsteps; i++) {
526:     ind[0] = i;
527:     VecSet(Dir,0.0);
528:     VecSetValues(Dir,1,ind,&one,INSERT_VALUES);
529:     VecAssemblyBegin(Dir);
530:     VecAssemblyEnd(Dir);
531:     ComputeObjHessianWithSOA(Dir,harr,actx);
532:     MatSetValues(H,1,ind,2*actx->nsteps,cols,harr,INSERT_VALUES);
533:     MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
534:     MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
535:     if (H != Hpre) {
536:       MatAssemblyBegin(Hpre,MAT_FINAL_ASSEMBLY);
537:       MatAssemblyEnd(Hpre,MAT_FINAL_ASSEMBLY);
538:     }
539:   }
540:   PetscFree(cols);
541:   PetscFree(harr);
542:   VecDestroy(&Dir);
543:   return(0);
544: }

546: PetscErrorCode MatrixFreeObjHessian(Tao tao, Vec P, Mat H, Mat Hpre, void *ctx)
547: {
548:   Aircraft          actx = (Aircraft)ctx;
549:   PetscScalar       *v,*w;
550:   const PetscScalar *p;
551:   PetscInt          i;
552:   PetscErrorCode    ierr;

555:   VecGetArrayRead(P,&p);
556:   VecGetArray(actx->V,&v);
557:   VecGetArray(actx->W,&w);
558:   for (i=0; i<actx->nsteps; i++) {
559:     v[i] = p[2*i];
560:     w[i] = p[2*i+1];
561:   }
562:   VecRestoreArrayRead(P,&p);
563:   VecRestoreArray(actx->V,&v);
564:   VecRestoreArray(actx->W,&w);
565:   return(0);
566: }

568: PetscErrorCode MyMatMult(Mat H_shell, Vec X, Vec Y)
569: {
570:   PetscScalar    *y;
571:   void           *ptr;

575:   MatShellGetContext(H_shell,&ptr);
576:   VecGetArray(Y,&y);
577:   ComputeObjHessianWithSOA(X,y,(Aircraft)ptr);
578:   VecRestoreArray(Y,&y);
579:   return(0);
580: }

582: PetscErrorCode ComputeObjHessianWithSOA(Vec Dir,PetscScalar arr[],Aircraft actx)
583: {
584:   TS                ts = actx->ts;
585:   const PetscScalar *z_ptr;
586:   PetscScalar       *u;
587:   Vec               Q;
588:   PetscInt          i;
589:   PetscErrorCode    ierr;

592:   /* Reset TSAdjoint so that AdjointSetUp will be called again */
593:   TSAdjointReset(ts);

595:   TSSetTime(ts,0.0);
596:   TSSetStepNumber(ts,0);
597:   TSSetFromOptions(ts);
598:   TSSetTimeStep(ts,actx->ftime/actx->nsteps);
599:   TSSetCostHessianProducts(actx->ts,1,actx->Lambda2,actx->Mup2,Dir);

601:   /* reinitialize system state */
602:   VecGetArray(actx->U,&u);
603:   u[0] = 2.0;
604:   u[1] = 0;
605:   VecRestoreArray(actx->U,&u);

607:   /* reinitialize the integral value */
608:   TSGetCostIntegral(ts,&Q);
609:   VecSet(Q,0.0);

611:   /* initialize tlm variable */
612:   MatZeroEntries(actx->Jacp);
613:   MatAssemblyBegin(actx->Jacp,MAT_FINAL_ASSEMBLY);
614:   MatAssemblyEnd(actx->Jacp,MAT_FINAL_ASSEMBLY);
615:   TSAdjointSetForward(ts,actx->Jacp);

617:   TSSolve(ts,actx->U);

619:   /* Set terminal conditions for first- and second-order adjonts */
620:   VecSet(actx->Lambda[0],0.0);
621:   VecSet(actx->Mup[0],0.0);
622:   VecSet(actx->Lambda2[0],0.0);
623:   VecSet(actx->Mup2[0],0.0);
624:   TSSetCostGradients(ts,1,actx->Lambda,actx->Mup);

626:   TSGetCostIntegral(ts,&Q);

628:   /* Reset initial conditions for the adjoint integration */
629:   TSAdjointSolve(ts);

631:   /* initial condition does not depend on p, so that lambda is not needed to assemble G */
632:   VecGetArrayRead(actx->Mup2[0],&z_ptr);
633:   for (i=0; i<2*actx->nsteps; i++) arr[i] = z_ptr[i];
634:   VecRestoreArrayRead(actx->Mup2[0],&z_ptr);

636:   /* Disable second-order adjoint mode */
637:   TSAdjointReset(ts);
638:   TSAdjointResetForward(ts);
639:   return(0);
640: }

642: /*TEST
643:     build:
644:       requires: !complex !single

646:     test:
647:       args:  -ts_adapt_type none -ts_type rk -ts_rk_type 3 -viewer_binary_skip_info -tao_monitor -tao_gatol 1e-7

649:     test:
650:       suffix: 2
651:       args:  -ts_adapt_type none -ts_type rk -ts_rk_type 3 -viewer_binary_skip_info -tao_monitor -tao_view -tao_type bntr -tao_bnk_pc_type none -exacthessian

653:     test:
654:       suffix: 3
655:       args:  -ts_adapt_type none -ts_type rk -ts_rk_type 3 -viewer_binary_skip_info -tao_monitor -tao_view -tao_type bntr -tao_bnk_pc_type none -exacthessian -matrixfree
656: TEST*/