Actual source code: elliptic.c

petsc-master 2016-05-29
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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: TaoSetHistory(); TaoGetHistory();
 16:    Routines: TaoSolve();
 17:    Routines: TaoDestroy();
 18:    Processors: n
 19: T*/

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

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

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

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


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

 57:   Vec d;
 58:   Vec dwork;

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

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

 65:   Vec ytrue;

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

 70:   Vec utrue;

 72:   Vec js_diag;

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

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

 82:   KSP solver;
 83:   PC  prec;

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

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

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

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

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

116: static  char help[]="";

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

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

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

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

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

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

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

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

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

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

191:   TaoDestroy(&tao);
192:   VecDestroy(&x0);
193:   EllipticDestroy(&user);
194:   PetscFinalize();
195:   return ierr;
196: }
197: /* ------------------------------------------------------------------- */
200: /*
201:    dwork = Qy - d
202:    lwork = L*(u-ur)
203:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
204: */
205: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
206: {
208:   PetscReal      d1=0,d2=0;
209:   AppCtx         *user = (AppCtx*)ptr;

212:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
213:   MatMult(user->MQ,user->y,user->dwork);
214:   VecAXPY(user->dwork,-1.0,user->d);
215:   VecDot(user->dwork,user->dwork,&d1);
216:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
217:   MatMult(user->L,user->uwork,user->lwork);
218:   VecDot(user->lwork,user->lwork,&d2);
219:   *f = 0.5 * (d1 + user->alpha*d2);
220:   return(0);
221: }

223: /* ------------------------------------------------------------------- */
226: /*
227:     state: g_s = Q' *(Qy - d)
228:     design: g_d = alpha*L'*L*(u-ur)
229: */
230: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
231: {
233:   AppCtx         *user = (AppCtx*)ptr;

236:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
237:   MatMult(user->MQ,user->y,user->dwork);
238:   VecAXPY(user->dwork,-1.0,user->d);
239:   MatMultTranspose(user->MQ,user->dwork,user->ywork);
240:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
241:   MatMult(user->L,user->uwork,user->lwork);
242:   MatMultTranspose(user->L,user->lwork,user->uwork);
243:   VecScale(user->uwork, user->alpha);
244:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
245:   return(0);
246: }

250: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
251: {
253:   PetscReal      d1,d2;
254:   AppCtx         *user = (AppCtx*)ptr;

257:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
258:   MatMult(user->MQ,user->y,user->dwork);
259:   VecAXPY(user->dwork,-1.0,user->d);
260:   VecDot(user->dwork,user->dwork,&d1);
261:   MatMultTranspose(user->MQ,user->dwork,user->ywork);

263:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
264:   MatMult(user->L,user->uwork,user->lwork);
265:   VecDot(user->lwork,user->lwork,&d2);
266:   MatMultTranspose(user->L,user->lwork,user->uwork);
267:   VecScale(user->uwork, user->alpha);
268:   *f = 0.5 * (d1 + user->alpha*d2);
269:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
270:   return(0);
271: }

273: /* ------------------------------------------------------------------- */
276: /* A
277: MatShell object
278: */
279: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
280: {
282:   AppCtx         *user = (AppCtx*)ptr;

285:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
286:   /* DSG = Div * (1/Av_u) * Grad */
287:   VecSet(user->uwork,0);
288:   VecAXPY(user->uwork,-1.0,user->u);
289:   VecExp(user->uwork);
290:   MatMult(user->Av,user->uwork,user->Av_u);
291:   VecCopy(user->Av_u,user->Swork);
292:   VecReciprocal(user->Swork);
293:   if (user->use_ptap) {
294:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
295:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
296:   } else {
297:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
298:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
299:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
300:   }
301:   return(0);
302: }
303: /* ------------------------------------------------------------------- */
306: /* B */
307: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
308: {
310:   AppCtx         *user = (AppCtx*)ptr;

313:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
314:   return(0);
315: }

319: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
320: {
322:   PetscReal      sum;
323:   AppCtx         *user;

326:   MatShellGetContext(J_shell,(void**)&user);
327:   MatMult(user->DSG,X,Y);
328:   VecSum(X,&sum);
329:   sum /= user->ndesign;
330:   VecShift(Y,sum);
331:   return(0);
332: }

336: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
337: {
339:   PetscInt       i;
340:   AppCtx         *user;

343:   MatShellGetContext(J_shell,(void**)&user);
344:   if (user->ns == 1) {
345:     MatMult(user->JsBlock,X,Y);
346:   } else {
347:     for (i=0;i<user->ns;i++) {
348:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
349:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
350:       MatMult(user->JsBlock,user->subq,user->suby);
351:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
352:     }
353:   }
354:   return(0);
355: }

359: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
360: {
362:   PetscInt       its,i;
363:   AppCtx         *user;

366:   MatShellGetContext(J_shell,(void**)&user);
367:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);
368:   if (Y == user->ytrue) {
369:     /* First solve is done using true solution to set up problem */
370:     KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
371:   } else {
372:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
373:   }
374:   if (user->ns == 1) {
375:     KSPSolve(user->solver,X,Y);
376:     KSPGetIterationNumber(user->solver,&its);
377:     user->ksp_its+=its;
378:   } else {
379:     for (i=0;i<user->ns;i++) {
380:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
381:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
382:       KSPSolve(user->solver,user->subq,user->suby);
383:       KSPGetIterationNumber(user->solver,&its);
384:       user->ksp_its+=its;
385:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
386:     }
387:   }
388:   return(0);
389: }
392: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
393: {
395:   AppCtx         *user;
396:   PetscInt       i;

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

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

422:   MatShellGetContext(J_shell,(void**)&user);
423:   if (user->ns == 1) {
424:     MatMultTranspose(user->Q,X,Y);
425:   } else {
426:     for (i=0;i<user->ns;i++) {
427:       Scatter(X,user->subd,user->di_scatter[i],0,0);
428:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
429:       MatMultTranspose(user->Q,user->subd,user->suby);
430:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
431:     }
432:   }
433:   return(0);
434: }

438: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
439: {
441:   PetscInt       i;
442:   AppCtx         *user;

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

447:   /* sdiag(1./v) */
448:   VecSet(user->uwork,0);
449:   VecAXPY(user->uwork,-1.0,user->u);
450:   VecExp(user->uwork);

452:   /* sdiag(1./((Av*(1./v)).^2)) */
453:   MatMult(user->Av,user->uwork,user->Swork);
454:   VecPointwiseMult(user->Swork,user->Swork,user->Swork);
455:   VecReciprocal(user->Swork);

457:   /* (Av * (sdiag(1./v) * b)) */
458:   VecPointwiseMult(user->uwork,user->uwork,X);
459:   MatMult(user->Av,user->uwork,user->Twork);

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

464:   if (user->ns == 1) {
465:     /* (sdiag(Grad*y(:,i)) */
466:     MatMult(user->Grad,user->y,user->Twork);

468:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
469:     VecPointwiseMult(user->Swork,user->Twork,user->Swork);
470:     MatMultTranspose(user->Grad,user->Swork,Y);
471:   } else {
472:     for (i=0;i<user->ns;i++) {
473:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
474:       Scatter(Y,user->subq,user->yi_scatter[i],0,0);

476:       MatMult(user->Grad,user->suby,user->Twork);
477:       VecPointwiseMult(user->Twork,user->Twork,user->Swork);
478:       MatMultTranspose(user->Grad,user->Twork,user->subq);
479:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
480:       Gather(Y,user->subq,user->yi_scatter[i],0,0);
481:     }
482:   }
483:   return(0);
484: }

488: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
489: {
491:   PetscInt       i;
492:   AppCtx         *user;

495:   MatShellGetContext(J_shell,(void**)&user);
496:   VecZeroEntries(Y);

498:   /* Sdiag = 1./((Av*(1./v)).^2) */
499:   VecSet(user->uwork,0);
500:   VecAXPY(user->uwork,-1.0,user->u);
501:   VecExp(user->uwork);
502:   MatMult(user->Av,user->uwork,user->Swork);
503:   VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
504:   VecReciprocal(user->Sdiag);

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

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

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

516:     /* Twork = sdiag(Twork) * Swork */
517:     VecPointwiseMult(user->Twork,user->Swork,user->Twork);


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

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

526:     /* Ywork = pointwisemult(uwork,Ywork) */
527:     VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
528:     VecAXPY(Y,1.0,user->Ywork);
529:     Gather(user->y,user->suby,user->yi_scatter[i],0,0);
530:   }
531:   return(0);
532: }

536: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
537: {
538:    /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
540:    PetscReal      sum;
541:    PetscInt       i;
542:    AppCtx         *user = (AppCtx*)ptr;

545:    Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
546:    if (user->ns == 1) {
547:      MatMult(user->Grad,user->y,user->Swork);
548:      VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
549:      MatMultTranspose(user->Grad,user->Swork,C);
550:      VecSum(user->y,&sum);
551:      sum /= user->ndesign;
552:      VecShift(C,sum);
553:    } else {
554:      for (i=0;i<user->ns;i++) {
555:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
556:       Scatter(C,user->subq,user->yi_scatter[i],0,0);
557:       MatMult(user->Grad,user->suby,user->Swork);
558:       VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
559:       MatMultTranspose(user->Grad,user->Swork,user->subq);

561:       VecSum(user->suby,&sum);
562:       sum /= user->ndesign;
563:       VecShift(user->subq,sum);

565:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
566:       Gather(C,user->subq,user->yi_scatter[i],0,0);
567:      }
568:    }
569:    VecAXPY(C,-1.0,user->q);
570:    return(0);
571: }

575: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
576: {

580:   VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
581:   VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
582:   if (sub2) {
583:     VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
584:     VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
585:   }
586:   return(0);
587: }

591: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
592: {

596:   VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
597:   VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
598:   if (sub2) {
599:     VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
600:     VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
601:   }
602:   return(0);
603: }

607: PetscErrorCode EllipticInitialize(AppCtx *user)
608: {
610:   PetscInt       m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
611:   Vec            XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
612:   PetscReal      *x,*y,*z;
613:   PetscReal      h,meanut;
614:   PetscScalar    hinv,neg_hinv,half = 0.5,sqrt_beta;
615:   PetscInt       im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
616:   IS             is_alldesign,is_allstate;
617:   IS             is_from_d;
618:   IS             is_from_y;
619:   PetscInt       lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
620:   const PetscInt *ranges, *subranges;
621:   PetscMPIInt    size;
622:   PetscReal      xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
623:   PetscScalar    v,vx,vy,vz;
624:   PetscInt       offset,subindex,subvec,nrank,kk;

626:   PetscScalar xr[64] = {0.4970,     0.8498,     0.7814,     0.6268,     0.7782,     0.6402,     0.3617,     0.3160,
627:                         0.3610,     0.5298,     0.6987,     0.3331,     0.7962,     0.5596,     0.3866,     0.6774,
628:                         0.5407,     0.4518,     0.6702,     0.6061,     0.7580,     0.8997,     0.5198,     0.8326,
629:                         0.2138,     0.9198,     0.3000,     0.2833,     0.8288,     0.7076,     0.1820,     0.0728,
630:                         0.8447,     0.2367,     0.3239,     0.6413,     0.3114,     0.4731,     0.1192,     0.9273,
631:                         0.5724,     0.4331,     0.5136,     0.3547,     0.4413,     0.2602,     0.5698,     0.7278,
632:                         0.5261,     0.6230,     0.2454,     0.3948,     0.7479,     0.6582,     0.4660,     0.5594,
633:                         0.7574,     0.1143,     0.5900,     0.1065,     0.4260,     0.3294,     0.8276,     0.0756};

635:   PetscScalar yr[64] = {0.7345,     0.9120,     0.9288,     0.7528,     0.4463,     0.4985,     0.2497,     0.6256,
636:                         0.3425,     0.9026,     0.6983,     0.4230,     0.7140,     0.2970,     0.4474,     0.8792,
637:                         0.6604,     0.2485,     0.7968,     0.6127,     0.1796,     0.2437,     0.5938,     0.6137,
638:                         0.3867,     0.5658,     0.4575,     0.1009,     0.0863,     0.3361,     0.0738,     0.3985,
639:                         0.6602,     0.1437,     0.0934,     0.5983,     0.5950,     0.0763,     0.0768,     0.2288,
640:                         0.5761,     0.1129,     0.3841,     0.6150,     0.6904,     0.6686,     0.1361,     0.4601,
641:                         0.4491,     0.3716,     0.1969,     0.6537,     0.6743,     0.6991,     0.4811,     0.5480,
642:                         0.1684,     0.4569,     0.6889,     0.8437,     0.3015,     0.2854,     0.8199,     0.2658};

644:   PetscScalar zr[64] = {0.7668,     0.8573,     0.2654,     0.2719,     0.1060,     0.1311,     0.6232,     0.2295,
645:                         0.8009,     0.2147,     0.2119,     0.9325,     0.4473,     0.3600,     0.3374,     0.3819,
646:                         0.4066,     0.5801,     0.1673,     0.0959,     0.4638,     0.8236,     0.8800,     0.2939,
647:                         0.2028,     0.8262,     0.2706,     0.6276,     0.9085,     0.6443,     0.8241,     0.0712,
648:                         0.1824,     0.7789,     0.4389,     0.8415,     0.7055,     0.6639,     0.3653,     0.2078,
649:                         0.1987,     0.2297,     0.4321,     0.8115,     0.4915,     0.7764,     0.4657,     0.4627,
650:                         0.4569,     0.4232,     0.8514,     0.0674,     0.3227,     0.1055,     0.6690,     0.6313,
651:                         0.9226,     0.5461,     0.4126,     0.2364,     0.6096,     0.7042,     0.3914,     0.0711};

654:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
655:   PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
656:   PetscLogStagePush(user->stages[0]);

658:   /* Create u,y,c,x */
659:   VecCreate(PETSC_COMM_WORLD,&user->u);
660:   VecCreate(PETSC_COMM_WORLD,&user->y);
661:   VecCreate(PETSC_COMM_WORLD,&user->c);
662:   VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
663:   VecSetFromOptions(user->u);
664:   VecGetLocalSize(user->u,&ysubnlocal);
665:   VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
666:   VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
667:   VecSetFromOptions(user->y);
668:   VecSetFromOptions(user->c);

670:   /*
671:      *******************************
672:      Create scatters for x <-> y,u
673:      *******************************

675:      If the state vector y and design vector u are partitioned as
676:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
677:      then the solution vector x is organized as
678:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
679:      The index sets user->s_is and user->d_is correspond to the indices of the
680:      state and design variables owned by the current processor.
681:   */
682:   VecCreate(PETSC_COMM_WORLD,&user->x);

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

687:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
688:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
689:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
690:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);

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

695:   VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
696:   VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
697:   ISDestroy(&is_alldesign);
698:   ISDestroy(&is_allstate);
699:   /*
700:      *******************************
701:      Create scatter from y to y_1,y_2,...,y_ns
702:      *******************************
703:   */
704:   PetscMalloc1(user->ns,&user->yi_scatter);
705:   VecDuplicate(user->u,&user->suby);
706:   VecDuplicate(user->u,&user->subq);

708:   VecGetOwnershipRange(user->y,&lo2,&hi2);
709:   istart = 0;
710:   for (i=0; i<user->ns; i++){
711:     VecGetOwnershipRange(user->suby,&lo,&hi);
712:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
713:     VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
714:     istart = istart + hi-lo;
715:     ISDestroy(&is_from_y);
716:   }
717:   /*
718:      *******************************
719:      Create scatter from d to d_1,d_2,...,d_ns
720:      *******************************
721:   */
722:   VecCreate(PETSC_COMM_WORLD,&user->subd);
723:   VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
724:   VecSetFromOptions(user->subd);
725:   VecCreate(PETSC_COMM_WORLD,&user->d);
726:   VecGetLocalSize(user->subd,&dsubnlocal);
727:   VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
728:   VecSetFromOptions(user->d);
729:   PetscMalloc1(user->ns,&user->di_scatter);

731:   VecGetOwnershipRange(user->d,&lo2,&hi2);
732:   istart = 0;
733:   for (i=0; i<user->ns; i++){
734:     VecGetOwnershipRange(user->subd,&lo,&hi);
735:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
736:     VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
737:     istart = istart + hi-lo;
738:     ISDestroy(&is_from_d);
739:   }

741:   PetscMalloc1(user->mx,&x);
742:   PetscMalloc1(user->mx,&y);
743:   PetscMalloc1(user->mx,&z);

745:   user->ksp_its = 0;
746:   user->ksp_its_initial = 0;

748:   n = user->mx * user->mx * user->mx;
749:   m = 3 * user->mx * user->mx * (user->mx-1);
750:   sqrt_beta = PetscSqrtScalar(user->beta);

752:   VecCreate(PETSC_COMM_WORLD,&XX);
753:   VecCreate(PETSC_COMM_WORLD,&user->q);
754:   VecSetSizes(XX,ysubnlocal,n);
755:   VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
756:   VecSetFromOptions(XX);
757:   VecSetFromOptions(user->q);

759:   VecDuplicate(XX,&YY);
760:   VecDuplicate(XX,&ZZ);
761:   VecDuplicate(XX,&XXwork);
762:   VecDuplicate(XX,&YYwork);
763:   VecDuplicate(XX,&ZZwork);
764:   VecDuplicate(XX,&UTwork);
765:   VecDuplicate(XX,&user->utrue);

767:   /* map for striding q */
768:   VecGetOwnershipRanges(user->q,&ranges);
769:   VecGetOwnershipRanges(user->u,&subranges);

771:   VecGetOwnershipRange(user->q,&lo2,&hi2);
772:   VecGetOwnershipRange(user->u,&lo,&hi);
773:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
774:   h = 1.0/user->mx;
775:   hinv = user->mx;
776:   neg_hinv = -hinv;

778:   VecGetOwnershipRange(XX,&istart,&iend);
779:   for (linear_index=istart; linear_index<iend; linear_index++){
780:     i = linear_index % user->mx;
781:     j = ((linear_index-i)/user->mx) % user->mx;
782:     k = ((linear_index-i)/user->mx-j) / user->mx;
783:     vx = h*(i+0.5);
784:     vy = h*(j+0.5);
785:     vz = h*(k+0.5);
786:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
787:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
788:     VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
789:     for (is=0; is<2; is++){
790:       for (js=0; js<2; js++){
791:         for (ks=0; ks<2; ks++){
792:           ls = is*4 + js*2 + ks;
793:           if (ls<user->ns){
794:             l =ls*n + linear_index;
795:             /* remap */
796:             subindex = l%n;
797:             subvec = l/n;
798:             nrank=0;
799:             while (subindex >= subranges[nrank+1]) nrank++;
800:             offset = subindex - subranges[nrank];
801:             istart=0;
802:             for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
803:             istart += (subranges[nrank+1]-subranges[nrank])*subvec;
804:             l = istart+offset;
805:             v = 100*PetscSinScalar(2*PETSC_PI*(vx+0.25*is))*sin(2*PETSC_PI*(vy+0.25*js))*sin(2*PETSC_PI*(vz+0.25*ks));
806:             VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
807:           }
808:         }
809:       }
810:     }
811:   }

813:   VecAssemblyBegin(XX);
814:   VecAssemblyEnd(XX);
815:   VecAssemblyBegin(YY);
816:   VecAssemblyEnd(YY);
817:   VecAssemblyBegin(ZZ);
818:   VecAssemblyEnd(ZZ);
819:   VecAssemblyBegin(user->q);
820:   VecAssemblyEnd(user->q);

822:   /* Compute true parameter function
823:      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) */
824:   VecCopy(XX,XXwork);
825:   VecCopy(YY,YYwork);
826:   VecCopy(ZZ,ZZwork);

828:   VecShift(XXwork,-0.25);
829:   VecShift(YYwork,-0.25);
830:   VecShift(ZZwork,-0.25);

832:   VecPointwiseMult(XXwork,XXwork,XXwork);
833:   VecPointwiseMult(YYwork,YYwork,YYwork);
834:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

836:   VecCopy(XXwork,UTwork);
837:   VecAXPY(UTwork,1.0,YYwork);
838:   VecAXPY(UTwork,1.0,ZZwork);
839:   VecScale(UTwork,-20.0);
840:   VecExp(UTwork);
841:   VecCopy(UTwork,user->utrue);

843:   VecCopy(XX,XXwork);
844:   VecCopy(YY,YYwork);
845:   VecCopy(ZZ,ZZwork);

847:   VecShift(XXwork,-0.75);
848:   VecShift(YYwork,-0.75);
849:   VecShift(ZZwork,-0.75);

851:   VecPointwiseMult(XXwork,XXwork,XXwork);
852:   VecPointwiseMult(YYwork,YYwork,YYwork);
853:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

855:   VecCopy(XXwork,UTwork);
856:   VecAXPY(UTwork,1.0,YYwork);
857:   VecAXPY(UTwork,1.0,ZZwork);
858:   VecScale(UTwork,-20.0);
859:   VecExp(UTwork);

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

863:   VecDestroy(&XX);
864:   VecDestroy(&YY);
865:   VecDestroy(&ZZ);
866:   VecDestroy(&XXwork);
867:   VecDestroy(&YYwork);
868:   VecDestroy(&ZZwork);
869:   VecDestroy(&UTwork);

871:   /* Initial guess and reference model */
872:   VecDuplicate(user->utrue,&user->ur);
873:   VecSum(user->utrue,&meanut);
874:   meanut = meanut / n;
875:   VecSet(user->ur,meanut);
876:   VecCopy(user->ur,user->u);

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

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

909:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
910:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

912:   /* Generate arithmetic averaging matrix Av */
913:   MatCreate(PETSC_COMM_WORLD,&user->Av);
914:   MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
915:   MatSetFromOptions(user->Av);
916:   MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
917:   MatSeqAIJSetPreallocation(user->Av,2,NULL);
918:   MatGetOwnershipRange(user->Av,&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->Av,1,&i,1,&j,&half,INSERT_VALUES);
925:       j = j+1;
926:       MatSetValues(user->Av,1,&i,1,&j,&half,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->Av,1,&i,1,&j,&half,INSERT_VALUES);
932:       j = j + user->mx;
933:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
934:     }
935:     if (i>=2*m/3){
936:       j = i-2*m/3;
937:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
938:       j = j + user->mx*user->mx;
939:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
940:     }
941:   }

943:   MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
944:   MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);

946:   MatCreate(PETSC_COMM_WORLD,&user->L);
947:   MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
948:   MatSetFromOptions(user->L);
949:   MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
950:   MatSeqAIJSetPreallocation(user->L,2,NULL);
951:   MatGetOwnershipRange(user->L,&istart,&iend);

953:   for (i=istart; i<iend; i++){
954:     if (i<m/3){
955:       iblock = i / (user->mx-1);
956:       j = iblock*user->mx + (i % (user->mx-1));
957:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
958:       j = j+1;
959:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
960:     }
961:     if (i>=m/3 && i<2*m/3){
962:       iblock = (i-m/3) / (user->mx*(user->mx-1));
963:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
964:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
965:       j = j + user->mx;
966:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
967:     }
968:     if (i>=2*m/3 && i<m){
969:       j = i-2*m/3;
970:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
971:       j = j + user->mx*user->mx;
972:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
973:     }
974:     if (i>=m){
975:       j = i - m;
976:       MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
977:     }
978:   }
979:   MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
980:   MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
981:   MatScale(user->L,PetscPowScalar(h,1.5));

983:   /* Generate Div matrix */
984:   if (!user->use_ptap) {
985:     /* Generate Div matrix */
986:     MatCreate(PETSC_COMM_WORLD,&user->Div);
987:     MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
988:     MatSetFromOptions(user->Div);
989:     MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
990:     MatSeqAIJSetPreallocation(user->Div,6,NULL);
991:     MatGetOwnershipRange(user->Grad,&istart,&iend);

993:     for (i=istart; i<iend; i++){
994:       if (i<m/3){
995:         iblock = i / (user->mx-1);
996:         j = iblock*user->mx + (i % (user->mx-1));
997:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
998:         j = j+1;
999:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1000:       }
1001:       if (i>=m/3 && i<2*m/3){
1002:         iblock = (i-m/3) / (user->mx*(user->mx-1));
1003:         j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
1004:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1005:         j = j + user->mx;
1006:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1007:       }
1008:       if (i>=2*m/3){
1009:         j = i-2*m/3;
1010:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1011:         j = j + user->mx*user->mx;
1012:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1013:       }
1014:     }

1016:     MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
1017:     MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
1018:     MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1019:   } else {
1020:     MatCreate(PETSC_COMM_WORLD,&user->Diag);
1021:     MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
1022:     MatSetFromOptions(user->Diag);
1023:     MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
1024:     MatSeqAIJSetPreallocation(user->Diag,1,NULL);
1025:   }

1027:   /* Build work vectors and matrices */
1028:   VecCreate(PETSC_COMM_WORLD,&user->S);
1029:   VecSetSizes(user->S, PETSC_DECIDE, m);
1030:   VecSetFromOptions(user->S);

1032:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1033:   VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1034:   VecSetFromOptions(user->lwork);

1036:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

1038:   VecDuplicate(user->S,&user->Swork);
1039:   VecDuplicate(user->S,&user->Sdiag);
1040:   VecDuplicate(user->S,&user->Av_u);
1041:   VecDuplicate(user->S,&user->Twork);
1042:   VecDuplicate(user->y,&user->ywork);
1043:   VecDuplicate(user->u,&user->Ywork);
1044:   VecDuplicate(user->u,&user->uwork);
1045:   VecDuplicate(user->u,&user->js_diag);
1046:   VecDuplicate(user->c,&user->cwork);
1047:   VecDuplicate(user->d,&user->dwork);

1049:   /* Create a matrix-free shell user->Jd for computing B*x */
1050:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1051:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1052:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1054:   /* Compute true state function ytrue given utrue */
1055:   VecDuplicate(user->y,&user->ytrue);

1057:   /* First compute Av_u = Av*exp(-u) */
1058:   VecSet(user->uwork, 0);
1059:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1060:   VecExp(user->uwork);
1061:   MatMult(user->Av,user->uwork,user->Av_u);

1063:   /* Next form DSG = Div*S*Grad */
1064:   VecCopy(user->Av_u,user->Swork);
1065:   VecReciprocal(user->Swork);
1066:   if (user->use_ptap) {
1067:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1068:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1069:   } else {
1070:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1071:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
1072:     MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1073:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1074:   }

1076:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1077:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1079:   if (user->use_lrc == PETSC_TRUE) {
1080:     v=PetscSqrtReal(1.0 /user->ndesign);
1081:     PetscMalloc1(user->ndesign,&user->ones);

1083:     for (i=0;i<user->ndesign;i++) {
1084:       user->ones[i]=v;
1085:     }
1086:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1087:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1088:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1089:     MatCreateLRC(user->DSG,user->Ones,user->Ones,&user->JsBlock);
1090:     MatSetUp(user->JsBlock);
1091:   } else {
1092:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1093:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1094:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1095:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1096:   }
1097:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1098:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1099:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1100:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1101:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1102:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1103:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1105:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1106:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1107:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1108:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1109:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1111:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1112:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1113:   /* Now solve for ytrue */
1114:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1115:   KSPSetFromOptions(user->solver);

1117:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);

1119:   MatMult(user->JsInv,user->q,user->ytrue);
1120:   /* First compute Av_u = Av*exp(-u) */
1121:   VecSet(user->uwork,0);
1122:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1123:   VecExp(user->uwork);
1124:   MatMult(user->Av,user->uwork,user->Av_u);

1126:   /* Next update DSG = Div*S*Grad  with user->u */
1127:   VecCopy(user->Av_u,user->Swork);
1128:   VecReciprocal(user->Swork);
1129:   if (user->use_ptap) {
1130:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1131:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1132:   } else {
1133:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1134:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1135:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1136:   }

1138:   /* Now solve for y */

1140:   MatMult(user->JsInv,user->q,user->y);

1142:   user->ksp_its_initial = user->ksp_its;
1143:   user->ksp_its = 0;
1144:   /* Construct projection matrix Q (blocks) */
1145:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1146:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1147:   MatSetFromOptions(user->Q);
1148:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1149:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

1151:   for (i=0; i<user->mx; i++){
1152:     x[i] = h*(i+0.5);
1153:     y[i] = h*(i+0.5);
1154:     z[i] = h*(i+0.5);
1155:   }
1156:   MatGetOwnershipRange(user->Q,&istart,&iend);

1158:   nx = user->mx; ny = user->mx; nz = user->mx;
1159:   for (i=istart; i<iend; i++){

1161:     xri = xr[i];
1162:     im = 0;
1163:     xim = x[im];
1164:     while (xri>xim && im<nx){
1165:       im = im+1;
1166:       xim = x[im];
1167:     }
1168:     indx1 = im-1;
1169:     indx2 = im;
1170:     dx1 = xri - x[indx1];
1171:     dx2 = x[indx2] - xri;

1173:     yri = yr[i];
1174:     im = 0;
1175:     yim = y[im];
1176:     while (yri>yim && im<ny){
1177:       im = im+1;
1178:       yim = y[im];
1179:     }
1180:     indy1 = im-1;
1181:     indy2 = im;
1182:     dy1 = yri - y[indy1];
1183:     dy2 = y[indy2] - yri;

1185:     zri = zr[i];
1186:     im = 0;
1187:     zim = z[im];
1188:     while (zri>zim && im<nz){
1189:       im = im+1;
1190:       zim = z[im];
1191:     }
1192:     indz1 = im-1;
1193:     indz2 = im;
1194:     dz1 = zri - z[indz1];
1195:     dz2 = z[indz2] - zri;

1197:     Dx = x[indx2] - x[indx1];
1198:     Dy = y[indy2] - y[indy1];
1199:     Dz = z[indz2] - z[indz1];

1201:     j = indx1 + indy1*nx + indz1*nx*ny;
1202:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1203:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1205:     j = indx1 + indy1*nx + indz2*nx*ny;
1206:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1207:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1209:     j = indx1 + indy2*nx + indz1*nx*ny;
1210:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1211:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1213:     j = indx1 + indy2*nx + indz2*nx*ny;
1214:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1215:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1217:     j = indx2 + indy1*nx + indz1*nx*ny;
1218:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1219:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1221:     j = indx2 + indy1*nx + indz2*nx*ny;
1222:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1223:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1225:     j = indx2 + indy2*nx + indz1*nx*ny;
1226:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1227:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1229:     j = indx2 + indy2*nx + indz2*nx*ny;
1230:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1231:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1232:   }

1234:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1235:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1236:   /* Create MQ (composed of blocks of Q */
1237:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1238:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1239:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

1241:   /* Add noise to the measurement data */
1242:   VecSet(user->ywork,1.0);
1243:   VecAYPX(user->ywork,user->noise,user->ytrue);
1244:   MatMult(user->MQ,user->ywork,user->d);

1246:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1247:   PetscFree(x);
1248:   PetscFree(y);
1249:   PetscFree(z);
1250:   PetscLogStagePop();
1251:   return(0);
1252: }

1256: PetscErrorCode EllipticDestroy(AppCtx *user)
1257: {
1259:   PetscInt       i;

1262:   MatDestroy(&user->DSG);
1263:   KSPDestroy(&user->solver);
1264:   MatDestroy(&user->Q);
1265:   MatDestroy(&user->MQ);
1266:   if (!user->use_ptap) {
1267:     MatDestroy(&user->Div);
1268:     MatDestroy(&user->Divwork);
1269:   } else {
1270:     MatDestroy(&user->Diag);
1271:   }
1272:   if (user->use_lrc) {
1273:     MatDestroy(&user->Ones);
1274:   }

1276:   MatDestroy(&user->Grad);
1277:   MatDestroy(&user->Av);
1278:   MatDestroy(&user->Avwork);
1279:   MatDestroy(&user->L);
1280:   MatDestroy(&user->Js);
1281:   MatDestroy(&user->Jd);
1282:   MatDestroy(&user->JsBlock);
1283:   MatDestroy(&user->JsInv);

1285:   VecDestroy(&user->x);
1286:   VecDestroy(&user->u);
1287:   VecDestroy(&user->uwork);
1288:   VecDestroy(&user->utrue);
1289:   VecDestroy(&user->y);
1290:   VecDestroy(&user->ywork);
1291:   VecDestroy(&user->ytrue);
1292:   VecDestroy(&user->c);
1293:   VecDestroy(&user->cwork);
1294:   VecDestroy(&user->ur);
1295:   VecDestroy(&user->q);
1296:   VecDestroy(&user->d);
1297:   VecDestroy(&user->dwork);
1298:   VecDestroy(&user->lwork);
1299:   VecDestroy(&user->S);
1300:   VecDestroy(&user->Swork);
1301:   VecDestroy(&user->Sdiag);
1302:   VecDestroy(&user->Ywork);
1303:   VecDestroy(&user->Twork);
1304:   VecDestroy(&user->Av_u);
1305:   VecDestroy(&user->js_diag);
1306:   ISDestroy(&user->s_is);
1307:   ISDestroy(&user->d_is);
1308:   VecDestroy(&user->suby);
1309:   VecDestroy(&user->subd);
1310:   VecDestroy(&user->subq);
1311:   VecScatterDestroy(&user->state_scatter);
1312:   VecScatterDestroy(&user->design_scatter);
1313:   for (i=0;i<user->ns;i++) {
1314:     VecScatterDestroy(&user->yi_scatter[i]);
1315:     VecScatterDestroy(&user->di_scatter[i]);
1316:   }
1317:   PetscFree(user->yi_scatter);
1318:   PetscFree(user->di_scatter);
1319:   if (user->use_lrc) {
1320:     PetscFree(user->ones);
1321:     MatDestroy(&user->Ones);
1322:   }
1323:   return(0);
1324: }

1328: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1329: {
1331:   Vec            X;
1332:   PetscReal      unorm,ynorm;
1333:   AppCtx         *user = (AppCtx*)ptr;

1336:   TaoGetSolutionVector(tao,&X);
1337:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1338:   VecAXPY(user->ywork,-1.0,user->ytrue);
1339:   VecAXPY(user->uwork,-1.0,user->utrue);
1340:   VecNorm(user->uwork,NORM_2,&unorm);
1341:   VecNorm(user->ywork,NORM_2,&ynorm);
1342:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1343:   return(0);
1344: }