Actual source code: elliptic.c

petsc-master 2020-02-15
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  1: #include <petsc/private/taoimpl.h>

  3: /*T
  4:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
  5:    Routines: TaoCreate();
  6:    Routines: TaoSetType();
  7:    Routines: TaoSetInitialVector();
  8:    Routines: TaoSetObjectiveRoutine();
  9:    Routines: TaoSetGradientRoutine();
 10:    Routines: TaoSetConstraintsRoutine();
 11:    Routines: TaoSetJacobianStateRoutine();
 12:    Routines: TaoSetJacobianDesignRoutine();
 13:    Routines: TaoSetStateDesignIS();
 14:    Routines: TaoSetFromOptions();
 15:    Routines: TaoSolve();
 16:    Routines: TaoDestroy();
 17:    Processors: n
 18: T*/



 22: typedef struct {
 23:   PetscInt n; /* Number of total variables */
 24:   PetscInt m; /* Number of constraints */
 25:   PetscInt nstate;
 26:   PetscInt ndesign;
 27:   PetscInt mx; /* grid points in each direction */
 28:   PetscInt ns; /* Number of data samples (1<=ns<=8)
 29:                   Currently only ns=1 is supported */
 30:   PetscInt ndata; /* Number of data points per sample */
 31:   IS       s_is;
 32:   IS       d_is;

 34:   VecScatter state_scatter;
 35:   VecScatter design_scatter;
 36:   VecScatter *yi_scatter, *di_scatter;
 37:   Vec        suby,subq,subd;
 38:   Mat        Js,Jd,JsPrec,JsInv,JsBlock;

 40:   PetscReal alpha; /* Regularization parameter */
 41:   PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
 42:   PetscReal noise; /* Amount of noise to add to data */
 43:   PetscReal *ones;
 44:   Mat       Q;
 45:   Mat       MQ;
 46:   Mat       L;

 48:   Mat Grad;
 49:   Mat Av,Avwork;
 50:   Mat Div, Divwork;
 51:   Mat DSG;
 52:   Mat Diag,Ones;


 55:   Vec q;
 56:   Vec ur; /* reference */

 58:   Vec d;
 59:   Vec dwork;

 61:   Vec x; /* super vec of y,u */

 63:   Vec y; /* state variables */
 64:   Vec ywork;

 66:   Vec ytrue;

 68:   Vec u; /* design variables */
 69:   Vec uwork;

 71:   Vec utrue;

 73:   Vec js_diag;

 75:   Vec c; /* constraint vector */
 76:   Vec cwork;

 78:   Vec lwork;
 79:   Vec S;
 80:   Vec Swork,Twork,Sdiag,Ywork;
 81:   Vec Av_u;

 83:   KSP solver;
 84:   PC  prec;

 86:   PetscReal tola,tolb,tolc,told;
 87:   PetscInt  ksp_its;
 88:   PetscInt  ksp_its_initial;
 89:   PetscLogStage stages[10];
 90:   PetscBool use_ptap;
 91:   PetscBool use_lrc;
 92: } AppCtx;

 94: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
 95: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
 96: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
 97: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
 98: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat,void*);
 99: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
100: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
101: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
102: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
103: PetscErrorCode EllipticInitialize(AppCtx*);
104: PetscErrorCode EllipticDestroy(AppCtx*);
105: PetscErrorCode EllipticMonitor(Tao, void*);

107: PetscErrorCode StateBlockMatMult(Mat,Vec,Vec);
108: PetscErrorCode StateMatMult(Mat,Vec,Vec);

110: PetscErrorCode StateInvMatMult(Mat,Vec,Vec);
111: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
112: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);

114: PetscErrorCode QMatMult(Mat,Vec,Vec);
115: PetscErrorCode QMatMultTranspose(Mat,Vec,Vec);

117: static  char help[]="";

119: int main(int argc, char **argv)
120: {
121:   PetscErrorCode     ierr;
122:   Vec                x0;
123:   Tao                tao;
124:   AppCtx             user;
125:   PetscInt           ntests = 1;
126:   PetscInt           i;

128:   PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
129:   user.mx = 8;
130:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,NULL,NULL);
131:   PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
132:   user.ns = 6;
133:   PetscOptionsInt("-ns","Number of data samples (1<=ns<=8)","",user.ns,&user.ns,NULL);
134:   user.ndata = 64;
135:   PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
136:   user.alpha = 0.1;
137:   PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
138:   user.beta = 0.00001;
139:   PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
140:   user.noise = 0.01;
141:   PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);

143:   user.use_ptap = PETSC_FALSE;
144:   PetscOptionsBool("-use_ptap","Use ptap matrix for DSG","",user.use_ptap,&user.use_ptap,NULL);
145:   user.use_lrc = PETSC_FALSE;
146:   PetscOptionsBool("-use_lrc","Use lrc matrix for Js","",user.use_lrc,&user.use_lrc,NULL);
147:   user.m = user.ns*user.mx*user.mx*user.mx; /* number of constraints */
148:   user.nstate =  user.m;
149:   user.ndesign = user.mx*user.mx*user.mx;
150:   user.n = user.nstate + user.ndesign; /* number of variables */

152:   /* Create TAO solver and set desired solution method */
153:   TaoCreate(PETSC_COMM_WORLD,&tao);
154:   TaoSetType(tao,TAOLCL);

156:   /* Set up initial vectors and matrices */
157:   EllipticInitialize(&user);

159:   Gather(user.x,user.y,user.state_scatter,user.u,user.design_scatter);
160:   VecDuplicate(user.x,&x0);
161:   VecCopy(user.x,x0);

163:   /* Set solution vector with an initial guess */
164:   TaoSetInitialVector(tao,user.x);
165:   TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
166:   TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
167:   TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);

169:   TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, (void *)&user);
170:   TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);

172:   TaoSetStateDesignIS(tao,user.s_is,user.d_is);
173:   TaoSetFromOptions(tao);

175:   /* SOLVE THE APPLICATION */
176:   PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
177:   PetscOptionsEnd();
178:   PetscLogStageRegister("Trials",&user.stages[1]);
179:   PetscLogStagePush(user.stages[1]);
180:   for (i=0; i<ntests; i++){
181:     TaoSolve(tao);
182:     PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its);
183:     VecCopy(x0,user.x);
184:   }
185:   PetscLogStagePop();
186:   PetscBarrier((PetscObject)user.x);
187:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
188:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);

190:   TaoDestroy(&tao);
191:   VecDestroy(&x0);
192:   EllipticDestroy(&user);
193:   PetscFinalize();
194:   return ierr;
195: }
196: /* ------------------------------------------------------------------- */
197: /*
198:    dwork = Qy - d
199:    lwork = L*(u-ur)
200:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
201: */
202: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
203: {
205:   PetscReal      d1=0,d2=0;
206:   AppCtx         *user = (AppCtx*)ptr;

209:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
210:   MatMult(user->MQ,user->y,user->dwork);
211:   VecAXPY(user->dwork,-1.0,user->d);
212:   VecDot(user->dwork,user->dwork,&d1);
213:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
214:   MatMult(user->L,user->uwork,user->lwork);
215:   VecDot(user->lwork,user->lwork,&d2);
216:   *f = 0.5 * (d1 + user->alpha*d2);
217:   return(0);
218: }

220: /* ------------------------------------------------------------------- */
221: /*
222:     state: g_s = Q' *(Qy - d)
223:     design: g_d = alpha*L'*L*(u-ur)
224: */
225: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
226: {
228:   AppCtx         *user = (AppCtx*)ptr;

231:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
232:   MatMult(user->MQ,user->y,user->dwork);
233:   VecAXPY(user->dwork,-1.0,user->d);
234:   MatMultTranspose(user->MQ,user->dwork,user->ywork);
235:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
236:   MatMult(user->L,user->uwork,user->lwork);
237:   MatMultTranspose(user->L,user->lwork,user->uwork);
238:   VecScale(user->uwork, user->alpha);
239:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
240:   return(0);
241: }

243: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
244: {
246:   PetscReal      d1,d2;
247:   AppCtx         *user = (AppCtx*)ptr;

250:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
251:   MatMult(user->MQ,user->y,user->dwork);
252:   VecAXPY(user->dwork,-1.0,user->d);
253:   VecDot(user->dwork,user->dwork,&d1);
254:   MatMultTranspose(user->MQ,user->dwork,user->ywork);

256:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
257:   MatMult(user->L,user->uwork,user->lwork);
258:   VecDot(user->lwork,user->lwork,&d2);
259:   MatMultTranspose(user->L,user->lwork,user->uwork);
260:   VecScale(user->uwork, user->alpha);
261:   *f = 0.5 * (d1 + user->alpha*d2);
262:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
263:   return(0);
264: }

266: /* ------------------------------------------------------------------- */
267: /* A
268: MatShell object
269: */
270: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
271: {
273:   AppCtx         *user = (AppCtx*)ptr;

276:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
277:   /* DSG = Div * (1/Av_u) * Grad */
278:   VecSet(user->uwork,0);
279:   VecAXPY(user->uwork,-1.0,user->u);
280:   VecExp(user->uwork);
281:   MatMult(user->Av,user->uwork,user->Av_u);
282:   VecCopy(user->Av_u,user->Swork);
283:   VecReciprocal(user->Swork);
284:   if (user->use_ptap) {
285:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
286:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
287:   } else {
288:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
289:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
290:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
291:   }
292:   return(0);
293: }
294: /* ------------------------------------------------------------------- */
295: /* B */
296: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
297: {
299:   AppCtx         *user = (AppCtx*)ptr;

302:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
303:   return(0);
304: }

306: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
307: {
309:   PetscReal      sum;
310:   AppCtx         *user;

313:   MatShellGetContext(J_shell,(void**)&user);
314:   MatMult(user->DSG,X,Y);
315:   VecSum(X,&sum);
316:   sum /= user->ndesign;
317:   VecShift(Y,sum);
318:   return(0);
319: }

321: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
322: {
324:   PetscInt       i;
325:   AppCtx         *user;

328:   MatShellGetContext(J_shell,(void**)&user);
329:   if (user->ns == 1) {
330:     MatMult(user->JsBlock,X,Y);
331:   } else {
332:     for (i=0;i<user->ns;i++) {
333:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
334:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
335:       MatMult(user->JsBlock,user->subq,user->suby);
336:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
337:     }
338:   }
339:   return(0);
340: }

342: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
343: {
345:   PetscInt       its,i;
346:   AppCtx         *user;

349:   MatShellGetContext(J_shell,(void**)&user);
350:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);
351:   if (Y == user->ytrue) {
352:     /* First solve is done using true solution to set up problem */
353:     KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
354:   } else {
355:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
356:   }
357:   if (user->ns == 1) {
358:     KSPSolve(user->solver,X,Y);
359:     KSPGetIterationNumber(user->solver,&its);
360:     user->ksp_its+=its;
361:   } else {
362:     for (i=0;i<user->ns;i++) {
363:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
364:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
365:       KSPSolve(user->solver,user->subq,user->suby);
366:       KSPGetIterationNumber(user->solver,&its);
367:       user->ksp_its+=its;
368:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
369:     }
370:   }
371:   return(0);
372: }
373: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
374: {
376:   AppCtx         *user;
377:   PetscInt       i;

380:   MatShellGetContext(J_shell,(void**)&user);
381:   if (user->ns == 1) {
382:     MatMult(user->Q,X,Y);
383:   } else {
384:     for (i=0;i<user->ns;i++) {
385:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
386:       Scatter(Y,user->subd,user->di_scatter[i],0,0);
387:       MatMult(user->Q,user->subq,user->subd);
388:       Gather(Y,user->subd,user->di_scatter[i],0,0);
389:     }
390:   }
391:   return(0);
392: }

394: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
395: {
397:   AppCtx         *user;
398:   PetscInt       i;

401:   MatShellGetContext(J_shell,(void**)&user);
402:   if (user->ns == 1) {
403:     MatMultTranspose(user->Q,X,Y);
404:   } else {
405:     for (i=0;i<user->ns;i++) {
406:       Scatter(X,user->subd,user->di_scatter[i],0,0);
407:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
408:       MatMultTranspose(user->Q,user->subd,user->suby);
409:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
410:     }
411:   }
412:   return(0);
413: }

415: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
416: {
418:   PetscInt       i;
419:   AppCtx         *user;

422:   MatShellGetContext(J_shell,(void**)&user);

424:   /* sdiag(1./v) */
425:   VecSet(user->uwork,0);
426:   VecAXPY(user->uwork,-1.0,user->u);
427:   VecExp(user->uwork);

429:   /* sdiag(1./((Av*(1./v)).^2)) */
430:   MatMult(user->Av,user->uwork,user->Swork);
431:   VecPointwiseMult(user->Swork,user->Swork,user->Swork);
432:   VecReciprocal(user->Swork);

434:   /* (Av * (sdiag(1./v) * b)) */
435:   VecPointwiseMult(user->uwork,user->uwork,X);
436:   MatMult(user->Av,user->uwork,user->Twork);

438:   /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
439:   VecPointwiseMult(user->Swork,user->Twork,user->Swork);

441:   if (user->ns == 1) {
442:     /* (sdiag(Grad*y(:,i)) */
443:     MatMult(user->Grad,user->y,user->Twork);

445:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
446:     VecPointwiseMult(user->Swork,user->Twork,user->Swork);
447:     MatMultTranspose(user->Grad,user->Swork,Y);
448:   } else {
449:     for (i=0;i<user->ns;i++) {
450:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
451:       Scatter(Y,user->subq,user->yi_scatter[i],0,0);

453:       MatMult(user->Grad,user->suby,user->Twork);
454:       VecPointwiseMult(user->Twork,user->Twork,user->Swork);
455:       MatMultTranspose(user->Grad,user->Twork,user->subq);
456:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
457:       Gather(Y,user->subq,user->yi_scatter[i],0,0);
458:     }
459:   }
460:   return(0);
461: }

463: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
464: {
466:   PetscInt       i;
467:   AppCtx         *user;

470:   MatShellGetContext(J_shell,(void**)&user);
471:   VecZeroEntries(Y);

473:   /* Sdiag = 1./((Av*(1./v)).^2) */
474:   VecSet(user->uwork,0);
475:   VecAXPY(user->uwork,-1.0,user->u);
476:   VecExp(user->uwork);
477:   MatMult(user->Av,user->uwork,user->Swork);
478:   VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
479:   VecReciprocal(user->Sdiag);

481:   for (i=0;i<user->ns;i++) {
482:     Scatter(X,user->subq,user->yi_scatter[i],0,0);
483:     Scatter(user->y,user->suby,user->yi_scatter[i],0,0);

485:     /* Swork = (Div' * b(:,i)) */
486:     MatMult(user->Grad,user->subq,user->Swork);

488:     /* Twork = Grad*y(:,i) */
489:     MatMult(user->Grad,user->suby,user->Twork);

491:     /* Twork = sdiag(Twork) * Swork */
492:     VecPointwiseMult(user->Twork,user->Swork,user->Twork);


495:     /* Swork = pointwisemult(Sdiag,Twork) */
496:     VecPointwiseMult(user->Swork,user->Twork,user->Sdiag);

498:     /* Ywork = Av' * Swork */
499:     MatMultTranspose(user->Av,user->Swork,user->Ywork);

501:     /* Ywork = pointwisemult(uwork,Ywork) */
502:     VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
503:     VecAXPY(Y,1.0,user->Ywork);
504:     Gather(user->y,user->suby,user->yi_scatter[i],0,0);
505:   }
506:   return(0);
507: }

509: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
510: {
511:    /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
513:    PetscReal      sum;
514:    PetscInt       i;
515:    AppCtx         *user = (AppCtx*)ptr;

518:    Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
519:    if (user->ns == 1) {
520:      MatMult(user->Grad,user->y,user->Swork);
521:      VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
522:      MatMultTranspose(user->Grad,user->Swork,C);
523:      VecSum(user->y,&sum);
524:      sum /= user->ndesign;
525:      VecShift(C,sum);
526:    } else {
527:      for (i=0;i<user->ns;i++) {
528:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
529:       Scatter(C,user->subq,user->yi_scatter[i],0,0);
530:       MatMult(user->Grad,user->suby,user->Swork);
531:       VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
532:       MatMultTranspose(user->Grad,user->Swork,user->subq);

534:       VecSum(user->suby,&sum);
535:       sum /= user->ndesign;
536:       VecShift(user->subq,sum);

538:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
539:       Gather(C,user->subq,user->yi_scatter[i],0,0);
540:      }
541:    }
542:    VecAXPY(C,-1.0,user->q);
543:    return(0);
544: }

546: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
547: {

551:   VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
552:   VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
553:   if (sub2) {
554:     VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
555:     VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
556:   }
557:   return(0);
558: }

560: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
561: {

565:   VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
566:   VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
567:   if (sub2) {
568:     VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
569:     VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
570:   }
571:   return(0);
572: }

574: PetscErrorCode EllipticInitialize(AppCtx *user)
575: {
577:   PetscInt       m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
578:   Vec            XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
579:   PetscReal      *x,*y,*z;
580:   PetscReal      h,meanut;
581:   PetscScalar    hinv,neg_hinv,half = 0.5,sqrt_beta;
582:   PetscInt       im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
583:   IS             is_alldesign,is_allstate;
584:   IS             is_from_d;
585:   IS             is_from_y;
586:   PetscInt       lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
587:   const PetscInt *ranges, *subranges;
588:   PetscMPIInt    size;
589:   PetscReal      xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
590:   PetscScalar    v,vx,vy,vz;
591:   PetscInt       offset,subindex,subvec,nrank,kk;

593:   PetscScalar xr[64] = {0.4970,     0.8498,     0.7814,     0.6268,     0.7782,     0.6402,     0.3617,     0.3160,
594:                         0.3610,     0.5298,     0.6987,     0.3331,     0.7962,     0.5596,     0.3866,     0.6774,
595:                         0.5407,     0.4518,     0.6702,     0.6061,     0.7580,     0.8997,     0.5198,     0.8326,
596:                         0.2138,     0.9198,     0.3000,     0.2833,     0.8288,     0.7076,     0.1820,     0.0728,
597:                         0.8447,     0.2367,     0.3239,     0.6413,     0.3114,     0.4731,     0.1192,     0.9273,
598:                         0.5724,     0.4331,     0.5136,     0.3547,     0.4413,     0.2602,     0.5698,     0.7278,
599:                         0.5261,     0.6230,     0.2454,     0.3948,     0.7479,     0.6582,     0.4660,     0.5594,
600:                         0.7574,     0.1143,     0.5900,     0.1065,     0.4260,     0.3294,     0.8276,     0.0756};

602:   PetscScalar yr[64] = {0.7345,     0.9120,     0.9288,     0.7528,     0.4463,     0.4985,     0.2497,     0.6256,
603:                         0.3425,     0.9026,     0.6983,     0.4230,     0.7140,     0.2970,     0.4474,     0.8792,
604:                         0.6604,     0.2485,     0.7968,     0.6127,     0.1796,     0.2437,     0.5938,     0.6137,
605:                         0.3867,     0.5658,     0.4575,     0.1009,     0.0863,     0.3361,     0.0738,     0.3985,
606:                         0.6602,     0.1437,     0.0934,     0.5983,     0.5950,     0.0763,     0.0768,     0.2288,
607:                         0.5761,     0.1129,     0.3841,     0.6150,     0.6904,     0.6686,     0.1361,     0.4601,
608:                         0.4491,     0.3716,     0.1969,     0.6537,     0.6743,     0.6991,     0.4811,     0.5480,
609:                         0.1684,     0.4569,     0.6889,     0.8437,     0.3015,     0.2854,     0.8199,     0.2658};

611:   PetscScalar zr[64] = {0.7668,     0.8573,     0.2654,     0.2719,     0.1060,     0.1311,     0.6232,     0.2295,
612:                         0.8009,     0.2147,     0.2119,     0.9325,     0.4473,     0.3600,     0.3374,     0.3819,
613:                         0.4066,     0.5801,     0.1673,     0.0959,     0.4638,     0.8236,     0.8800,     0.2939,
614:                         0.2028,     0.8262,     0.2706,     0.6276,     0.9085,     0.6443,     0.8241,     0.0712,
615:                         0.1824,     0.7789,     0.4389,     0.8415,     0.7055,     0.6639,     0.3653,     0.2078,
616:                         0.1987,     0.2297,     0.4321,     0.8115,     0.4915,     0.7764,     0.4657,     0.4627,
617:                         0.4569,     0.4232,     0.8514,     0.0674,     0.3227,     0.1055,     0.6690,     0.6313,
618:                         0.9226,     0.5461,     0.4126,     0.2364,     0.6096,     0.7042,     0.3914,     0.0711};

621:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
622:   PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
623:   PetscLogStagePush(user->stages[0]);

625:   /* Create u,y,c,x */
626:   VecCreate(PETSC_COMM_WORLD,&user->u);
627:   VecCreate(PETSC_COMM_WORLD,&user->y);
628:   VecCreate(PETSC_COMM_WORLD,&user->c);
629:   VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
630:   VecSetFromOptions(user->u);
631:   VecGetLocalSize(user->u,&ysubnlocal);
632:   VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
633:   VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
634:   VecSetFromOptions(user->y);
635:   VecSetFromOptions(user->c);

637:   /*
638:      *******************************
639:      Create scatters for x <-> y,u
640:      *******************************

642:      If the state vector y and design vector u are partitioned as
643:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
644:      then the solution vector x is organized as
645:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
646:      The index sets user->s_is and user->d_is correspond to the indices of the
647:      state and design variables owned by the current processor.
648:   */
649:   VecCreate(PETSC_COMM_WORLD,&user->x);

651:   VecGetOwnershipRange(user->y,&lo,&hi);
652:   VecGetOwnershipRange(user->u,&lo2,&hi2);

654:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
655:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
656:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
657:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);

659:   VecSetSizes(user->x,hi-lo+hi2-lo2,user->n);
660:   VecSetFromOptions(user->x);

662:   VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
663:   VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
664:   ISDestroy(&is_alldesign);
665:   ISDestroy(&is_allstate);
666:   /*
667:      *******************************
668:      Create scatter from y to y_1,y_2,...,y_ns
669:      *******************************
670:   */
671:   PetscMalloc1(user->ns,&user->yi_scatter);
672:   VecDuplicate(user->u,&user->suby);
673:   VecDuplicate(user->u,&user->subq);

675:   VecGetOwnershipRange(user->y,&lo2,&hi2);
676:   istart = 0;
677:   for (i=0; i<user->ns; i++){
678:     VecGetOwnershipRange(user->suby,&lo,&hi);
679:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
680:     VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
681:     istart = istart + hi-lo;
682:     ISDestroy(&is_from_y);
683:   }
684:   /*
685:      *******************************
686:      Create scatter from d to d_1,d_2,...,d_ns
687:      *******************************
688:   */
689:   VecCreate(PETSC_COMM_WORLD,&user->subd);
690:   VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
691:   VecSetFromOptions(user->subd);
692:   VecCreate(PETSC_COMM_WORLD,&user->d);
693:   VecGetLocalSize(user->subd,&dsubnlocal);
694:   VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
695:   VecSetFromOptions(user->d);
696:   PetscMalloc1(user->ns,&user->di_scatter);

698:   VecGetOwnershipRange(user->d,&lo2,&hi2);
699:   istart = 0;
700:   for (i=0; i<user->ns; i++){
701:     VecGetOwnershipRange(user->subd,&lo,&hi);
702:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
703:     VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
704:     istart = istart + hi-lo;
705:     ISDestroy(&is_from_d);
706:   }

708:   PetscMalloc1(user->mx,&x);
709:   PetscMalloc1(user->mx,&y);
710:   PetscMalloc1(user->mx,&z);

712:   user->ksp_its = 0;
713:   user->ksp_its_initial = 0;

715:   n = user->mx * user->mx * user->mx;
716:   m = 3 * user->mx * user->mx * (user->mx-1);
717:   sqrt_beta = PetscSqrtScalar(user->beta);

719:   VecCreate(PETSC_COMM_WORLD,&XX);
720:   VecCreate(PETSC_COMM_WORLD,&user->q);
721:   VecSetSizes(XX,ysubnlocal,n);
722:   VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
723:   VecSetFromOptions(XX);
724:   VecSetFromOptions(user->q);

726:   VecDuplicate(XX,&YY);
727:   VecDuplicate(XX,&ZZ);
728:   VecDuplicate(XX,&XXwork);
729:   VecDuplicate(XX,&YYwork);
730:   VecDuplicate(XX,&ZZwork);
731:   VecDuplicate(XX,&UTwork);
732:   VecDuplicate(XX,&user->utrue);

734:   /* map for striding q */
735:   VecGetOwnershipRanges(user->q,&ranges);
736:   VecGetOwnershipRanges(user->u,&subranges);

738:   VecGetOwnershipRange(user->q,&lo2,&hi2);
739:   VecGetOwnershipRange(user->u,&lo,&hi);
740:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
741:   h = 1.0/user->mx;
742:   hinv = user->mx;
743:   neg_hinv = -hinv;

745:   VecGetOwnershipRange(XX,&istart,&iend);
746:   for (linear_index=istart; linear_index<iend; linear_index++){
747:     i = linear_index % user->mx;
748:     j = ((linear_index-i)/user->mx) % user->mx;
749:     k = ((linear_index-i)/user->mx-j) / user->mx;
750:     vx = h*(i+0.5);
751:     vy = h*(j+0.5);
752:     vz = h*(k+0.5);
753:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
754:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
755:     VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
756:     for (is=0; is<2; is++){
757:       for (js=0; js<2; js++){
758:         for (ks=0; ks<2; ks++){
759:           ls = is*4 + js*2 + ks;
760:           if (ls<user->ns){
761:             l =ls*n + linear_index;
762:             /* remap */
763:             subindex = l%n;
764:             subvec = l/n;
765:             nrank=0;
766:             while (subindex >= subranges[nrank+1]) nrank++;
767:             offset = subindex - subranges[nrank];
768:             istart=0;
769:             for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
770:             istart += (subranges[nrank+1]-subranges[nrank])*subvec;
771:             l = istart+offset;
772:             v = 100*PetscSinScalar(2*PETSC_PI*(vx+0.25*is))*PetscSinScalar(2*PETSC_PI*(vy+0.25*js))*PetscSinScalar(2*PETSC_PI*(vz+0.25*ks));
773:             VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
774:           }
775:         }
776:       }
777:     }
778:   }

780:   VecAssemblyBegin(XX);
781:   VecAssemblyEnd(XX);
782:   VecAssemblyBegin(YY);
783:   VecAssemblyEnd(YY);
784:   VecAssemblyBegin(ZZ);
785:   VecAssemblyEnd(ZZ);
786:   VecAssemblyBegin(user->q);
787:   VecAssemblyEnd(user->q);

789:   /* Compute true parameter function
790:      ut = exp(-((x-0.25)^2+(y-0.25)^2+(z-0.25)^2)/0.05) - exp((x-0.75)^2-(y-0.75)^2-(z-0.75))^2/0.05) */
791:   VecCopy(XX,XXwork);
792:   VecCopy(YY,YYwork);
793:   VecCopy(ZZ,ZZwork);

795:   VecShift(XXwork,-0.25);
796:   VecShift(YYwork,-0.25);
797:   VecShift(ZZwork,-0.25);

799:   VecPointwiseMult(XXwork,XXwork,XXwork);
800:   VecPointwiseMult(YYwork,YYwork,YYwork);
801:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

803:   VecCopy(XXwork,UTwork);
804:   VecAXPY(UTwork,1.0,YYwork);
805:   VecAXPY(UTwork,1.0,ZZwork);
806:   VecScale(UTwork,-20.0);
807:   VecExp(UTwork);
808:   VecCopy(UTwork,user->utrue);

810:   VecCopy(XX,XXwork);
811:   VecCopy(YY,YYwork);
812:   VecCopy(ZZ,ZZwork);

814:   VecShift(XXwork,-0.75);
815:   VecShift(YYwork,-0.75);
816:   VecShift(ZZwork,-0.75);

818:   VecPointwiseMult(XXwork,XXwork,XXwork);
819:   VecPointwiseMult(YYwork,YYwork,YYwork);
820:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

822:   VecCopy(XXwork,UTwork);
823:   VecAXPY(UTwork,1.0,YYwork);
824:   VecAXPY(UTwork,1.0,ZZwork);
825:   VecScale(UTwork,-20.0);
826:   VecExp(UTwork);

828:   VecAXPY(user->utrue,-1.0,UTwork);

830:   VecDestroy(&XX);
831:   VecDestroy(&YY);
832:   VecDestroy(&ZZ);
833:   VecDestroy(&XXwork);
834:   VecDestroy(&YYwork);
835:   VecDestroy(&ZZwork);
836:   VecDestroy(&UTwork);

838:   /* Initial guess and reference model */
839:   VecDuplicate(user->utrue,&user->ur);
840:   VecSum(user->utrue,&meanut);
841:   meanut = meanut / n;
842:   VecSet(user->ur,meanut);
843:   VecCopy(user->ur,user->u);

845:   /* Generate Grad matrix */
846:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
847:   MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
848:   MatSetFromOptions(user->Grad);
849:   MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
850:   MatSeqAIJSetPreallocation(user->Grad,2,NULL);
851:   MatGetOwnershipRange(user->Grad,&istart,&iend);

853:   for (i=istart; i<iend; i++){
854:     if (i<m/3){
855:       iblock = i / (user->mx-1);
856:       j = iblock*user->mx + (i % (user->mx-1));
857:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
858:       j = j+1;
859:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
860:     }
861:     if (i>=m/3 && i<2*m/3){
862:       iblock = (i-m/3) / (user->mx*(user->mx-1));
863:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
864:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
865:       j = j + user->mx;
866:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
867:     }
868:     if (i>=2*m/3){
869:       j = i-2*m/3;
870:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
871:       j = j + user->mx*user->mx;
872:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
873:     }
874:   }

876:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
877:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

879:   /* Generate arithmetic averaging matrix Av */
880:   MatCreate(PETSC_COMM_WORLD,&user->Av);
881:   MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
882:   MatSetFromOptions(user->Av);
883:   MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
884:   MatSeqAIJSetPreallocation(user->Av,2,NULL);
885:   MatGetOwnershipRange(user->Av,&istart,&iend);

887:   for (i=istart; i<iend; i++){
888:     if (i<m/3){
889:       iblock = i / (user->mx-1);
890:       j = iblock*user->mx + (i % (user->mx-1));
891:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
892:       j = j+1;
893:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
894:     }
895:     if (i>=m/3 && i<2*m/3){
896:       iblock = (i-m/3) / (user->mx*(user->mx-1));
897:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
898:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
899:       j = j + user->mx;
900:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
901:     }
902:     if (i>=2*m/3){
903:       j = i-2*m/3;
904:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
905:       j = j + user->mx*user->mx;
906:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
907:     }
908:   }

910:   MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
911:   MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);

913:   MatCreate(PETSC_COMM_WORLD,&user->L);
914:   MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
915:   MatSetFromOptions(user->L);
916:   MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
917:   MatSeqAIJSetPreallocation(user->L,2,NULL);
918:   MatGetOwnershipRange(user->L,&istart,&iend);

920:   for (i=istart; i<iend; i++){
921:     if (i<m/3){
922:       iblock = i / (user->mx-1);
923:       j = iblock*user->mx + (i % (user->mx-1));
924:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
925:       j = j+1;
926:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
927:     }
928:     if (i>=m/3 && i<2*m/3){
929:       iblock = (i-m/3) / (user->mx*(user->mx-1));
930:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
931:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
932:       j = j + user->mx;
933:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
934:     }
935:     if (i>=2*m/3 && i<m){
936:       j = i-2*m/3;
937:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
938:       j = j + user->mx*user->mx;
939:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
940:     }
941:     if (i>=m){
942:       j = i - m;
943:       MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
944:     }
945:   }
946:   MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
947:   MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
948:   MatScale(user->L,PetscPowScalar(h,1.5));

950:   /* Generate Div matrix */
951:   if (!user->use_ptap) {
952:     /* Generate Div matrix */
953:     MatCreate(PETSC_COMM_WORLD,&user->Div);
954:     MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
955:     MatSetFromOptions(user->Div);
956:     MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
957:     MatSeqAIJSetPreallocation(user->Div,6,NULL);
958:     MatGetOwnershipRange(user->Grad,&istart,&iend);

960:     for (i=istart; i<iend; i++){
961:       if (i<m/3){
962:         iblock = i / (user->mx-1);
963:         j = iblock*user->mx + (i % (user->mx-1));
964:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
965:         j = j+1;
966:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
967:       }
968:       if (i>=m/3 && i<2*m/3){
969:         iblock = (i-m/3) / (user->mx*(user->mx-1));
970:         j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
971:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
972:         j = j + user->mx;
973:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
974:       }
975:       if (i>=2*m/3){
976:         j = i-2*m/3;
977:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
978:         j = j + user->mx*user->mx;
979:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
980:       }
981:     }

983:     MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
984:     MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
985:     MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
986:   } else {
987:     MatCreate(PETSC_COMM_WORLD,&user->Diag);
988:     MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
989:     MatSetFromOptions(user->Diag);
990:     MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
991:     MatSeqAIJSetPreallocation(user->Diag,1,NULL);
992:   }

994:   /* Build work vectors and matrices */
995:   VecCreate(PETSC_COMM_WORLD,&user->S);
996:   VecSetSizes(user->S, PETSC_DECIDE, m);
997:   VecSetFromOptions(user->S);

999:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1000:   VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1001:   VecSetFromOptions(user->lwork);

1003:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

1005:   VecDuplicate(user->S,&user->Swork);
1006:   VecDuplicate(user->S,&user->Sdiag);
1007:   VecDuplicate(user->S,&user->Av_u);
1008:   VecDuplicate(user->S,&user->Twork);
1009:   VecDuplicate(user->y,&user->ywork);
1010:   VecDuplicate(user->u,&user->Ywork);
1011:   VecDuplicate(user->u,&user->uwork);
1012:   VecDuplicate(user->u,&user->js_diag);
1013:   VecDuplicate(user->c,&user->cwork);
1014:   VecDuplicate(user->d,&user->dwork);

1016:   /* Create a matrix-free shell user->Jd for computing B*x */
1017:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1018:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1019:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1021:   /* Compute true state function ytrue given utrue */
1022:   VecDuplicate(user->y,&user->ytrue);

1024:   /* First compute Av_u = Av*exp(-u) */
1025:   VecSet(user->uwork, 0);
1026:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1027:   VecExp(user->uwork);
1028:   MatMult(user->Av,user->uwork,user->Av_u);

1030:   /* Next form DSG = Div*S*Grad */
1031:   VecCopy(user->Av_u,user->Swork);
1032:   VecReciprocal(user->Swork);
1033:   if (user->use_ptap) {
1034:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1035:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1036:   } else {
1037:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1038:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
1039:     MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1040:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1041:   }

1043:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1044:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1046:   if (user->use_lrc == PETSC_TRUE) {
1047:     v=PetscSqrtReal(1.0 /user->ndesign);
1048:     PetscMalloc1(user->ndesign,&user->ones);

1050:     for (i=0;i<user->ndesign;i++) {
1051:       user->ones[i]=v;
1052:     }
1053:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1054:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1055:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1056:     MatCreateLRC(user->DSG,user->Ones,NULL,user->Ones,&user->JsBlock);
1057:     MatSetUp(user->JsBlock);
1058:   } else {
1059:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1060:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1061:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1062:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1063:   }
1064:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1065:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1066:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1067:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1068:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1069:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1070:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1072:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1073:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1074:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1075:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1076:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1078:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1079:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1080:   /* Now solve for ytrue */
1081:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1082:   KSPSetFromOptions(user->solver);

1084:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);

1086:   MatMult(user->JsInv,user->q,user->ytrue);
1087:   /* First compute Av_u = Av*exp(-u) */
1088:   VecSet(user->uwork,0);
1089:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1090:   VecExp(user->uwork);
1091:   MatMult(user->Av,user->uwork,user->Av_u);

1093:   /* Next update DSG = Div*S*Grad  with user->u */
1094:   VecCopy(user->Av_u,user->Swork);
1095:   VecReciprocal(user->Swork);
1096:   if (user->use_ptap) {
1097:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1098:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1099:   } else {
1100:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1101:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1102:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1103:   }

1105:   /* Now solve for y */

1107:   MatMult(user->JsInv,user->q,user->y);

1109:   user->ksp_its_initial = user->ksp_its;
1110:   user->ksp_its = 0;
1111:   /* Construct projection matrix Q (blocks) */
1112:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1113:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1114:   MatSetFromOptions(user->Q);
1115:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1116:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

1118:   for (i=0; i<user->mx; i++){
1119:     x[i] = h*(i+0.5);
1120:     y[i] = h*(i+0.5);
1121:     z[i] = h*(i+0.5);
1122:   }
1123:   MatGetOwnershipRange(user->Q,&istart,&iend);

1125:   nx = user->mx; ny = user->mx; nz = user->mx;
1126:   for (i=istart; i<iend; i++){

1128:     xri = xr[i];
1129:     im = 0;
1130:     xim = x[im];
1131:     while (xri>xim && im<nx){
1132:       im = im+1;
1133:       xim = x[im];
1134:     }
1135:     indx1 = im-1;
1136:     indx2 = im;
1137:     dx1 = xri - x[indx1];
1138:     dx2 = x[indx2] - xri;

1140:     yri = yr[i];
1141:     im = 0;
1142:     yim = y[im];
1143:     while (yri>yim && im<ny){
1144:       im = im+1;
1145:       yim = y[im];
1146:     }
1147:     indy1 = im-1;
1148:     indy2 = im;
1149:     dy1 = yri - y[indy1];
1150:     dy2 = y[indy2] - yri;

1152:     zri = zr[i];
1153:     im = 0;
1154:     zim = z[im];
1155:     while (zri>zim && im<nz){
1156:       im = im+1;
1157:       zim = z[im];
1158:     }
1159:     indz1 = im-1;
1160:     indz2 = im;
1161:     dz1 = zri - z[indz1];
1162:     dz2 = z[indz2] - zri;

1164:     Dx = x[indx2] - x[indx1];
1165:     Dy = y[indy2] - y[indy1];
1166:     Dz = z[indz2] - z[indz1];

1168:     j = indx1 + indy1*nx + indz1*nx*ny;
1169:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1170:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1172:     j = indx1 + indy1*nx + indz2*nx*ny;
1173:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1174:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1176:     j = indx1 + indy2*nx + indz1*nx*ny;
1177:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1178:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1180:     j = indx1 + indy2*nx + indz2*nx*ny;
1181:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1182:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1184:     j = indx2 + indy1*nx + indz1*nx*ny;
1185:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1186:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1188:     j = indx2 + indy1*nx + indz2*nx*ny;
1189:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1190:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1192:     j = indx2 + indy2*nx + indz1*nx*ny;
1193:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1194:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1196:     j = indx2 + indy2*nx + indz2*nx*ny;
1197:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1198:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1199:   }

1201:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1202:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1203:   /* Create MQ (composed of blocks of Q */
1204:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1205:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1206:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

1208:   /* Add noise to the measurement data */
1209:   VecSet(user->ywork,1.0);
1210:   VecAYPX(user->ywork,user->noise,user->ytrue);
1211:   MatMult(user->MQ,user->ywork,user->d);

1213:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1214:   PetscFree(x);
1215:   PetscFree(y);
1216:   PetscFree(z);
1217:   PetscLogStagePop();
1218:   return(0);
1219: }

1221: PetscErrorCode EllipticDestroy(AppCtx *user)
1222: {
1224:   PetscInt       i;

1227:   MatDestroy(&user->DSG);
1228:   KSPDestroy(&user->solver);
1229:   MatDestroy(&user->Q);
1230:   MatDestroy(&user->MQ);
1231:   if (!user->use_ptap) {
1232:     MatDestroy(&user->Div);
1233:     MatDestroy(&user->Divwork);
1234:   } else {
1235:     MatDestroy(&user->Diag);
1236:   }
1237:   if (user->use_lrc) {
1238:     MatDestroy(&user->Ones);
1239:   }

1241:   MatDestroy(&user->Grad);
1242:   MatDestroy(&user->Av);
1243:   MatDestroy(&user->Avwork);
1244:   MatDestroy(&user->L);
1245:   MatDestroy(&user->Js);
1246:   MatDestroy(&user->Jd);
1247:   MatDestroy(&user->JsBlock);
1248:   MatDestroy(&user->JsInv);

1250:   VecDestroy(&user->x);
1251:   VecDestroy(&user->u);
1252:   VecDestroy(&user->uwork);
1253:   VecDestroy(&user->utrue);
1254:   VecDestroy(&user->y);
1255:   VecDestroy(&user->ywork);
1256:   VecDestroy(&user->ytrue);
1257:   VecDestroy(&user->c);
1258:   VecDestroy(&user->cwork);
1259:   VecDestroy(&user->ur);
1260:   VecDestroy(&user->q);
1261:   VecDestroy(&user->d);
1262:   VecDestroy(&user->dwork);
1263:   VecDestroy(&user->lwork);
1264:   VecDestroy(&user->S);
1265:   VecDestroy(&user->Swork);
1266:   VecDestroy(&user->Sdiag);
1267:   VecDestroy(&user->Ywork);
1268:   VecDestroy(&user->Twork);
1269:   VecDestroy(&user->Av_u);
1270:   VecDestroy(&user->js_diag);
1271:   ISDestroy(&user->s_is);
1272:   ISDestroy(&user->d_is);
1273:   VecDestroy(&user->suby);
1274:   VecDestroy(&user->subd);
1275:   VecDestroy(&user->subq);
1276:   VecScatterDestroy(&user->state_scatter);
1277:   VecScatterDestroy(&user->design_scatter);
1278:   for (i=0;i<user->ns;i++) {
1279:     VecScatterDestroy(&user->yi_scatter[i]);
1280:     VecScatterDestroy(&user->di_scatter[i]);
1281:   }
1282:   PetscFree(user->yi_scatter);
1283:   PetscFree(user->di_scatter);
1284:   if (user->use_lrc) {
1285:     PetscFree(user->ones);
1286:     MatDestroy(&user->Ones);
1287:   }
1288:   return(0);
1289: }

1291: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1292: {
1294:   Vec            X;
1295:   PetscReal      unorm,ynorm;
1296:   AppCtx         *user = (AppCtx*)ptr;

1299:   TaoGetSolutionVector(tao,&X);
1300:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1301:   VecAXPY(user->ywork,-1.0,user->ytrue);
1302:   VecAXPY(user->uwork,-1.0,user->utrue);
1303:   VecNorm(user->uwork,NORM_2,&unorm);
1304:   VecNorm(user->ywork,NORM_2,&ynorm);
1305:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1306:   return(0);
1307: }




1312: /*TEST

1314:    build:
1315:       requires: !complex

1317:    test:
1318:       args: -tao_cmonitor -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
1319:       requires: !single

1321:    test:
1322:       suffix: 2
1323:       args: -tao_cmonitor -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
1324:       requires: !single

1326: TEST*/