Actual source code: elliptic.c

petsc-dev 2014-02-02
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  1: #include <petsc-private/taoimpl.h>
  2: #include "../src/tao/pde_constrained/impls/lcl/lcl.h"

  4: /*T
  5:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
  6:    Routines: TaoCreate();
  7:    Routines: TaoSetType();
  8:    Routines: TaoSetInitialVector();
  9:    Routines: TaoSetObjectiveRoutine();
 10:    Routines: TaoSetGradientRoutine();
 11:    Routines: TaoSetConstraintsRoutine();
 12:    Routines: TaoSetJacobianStateRoutine();
 13:    Routines: TaoSetJacobianDesignRoutine();
 14:    Routines: TaoSetStateDesignIS();
 15:    Routines: TaoSetFromOptions();
 16:    Routines: TaoSetHistory(); TaoGetHistory();
 17:    Routines: TaoSolve();
 18:    Routines: TaoGetTerminationReason(); TaoDestroy();
 19:    Processors: n
 20: 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:   int       stages[10];
 90:   PetscBool use_ptap;
 91:   PetscBool use_lrc;
 92:   TAO_LCL*  lcl;
 93: } AppCtx;

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

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

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

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

118: static  char help[]="";

122: int main(int argc, char **argv)
123: {
124:   PetscErrorCode       ierr;
125:   Vec                  x0;
126:   Tao                  tao;
127:   TaoTerminationReason reason;
128:   AppCtx               user;
129:   PetscBool            flag;
130:   PetscInt             ntests = 1;
131:   PetscInt             i;

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

147:   PetscOptionsBool("-use_ptap","Use ptap matrix for DSG","",PETSC_FALSE,&user.use_ptap,&flag);
148:   PetscOptionsBool("-use_lrc","Use lrc matrix for Js","",PETSC_FALSE,&user.use_lrc,&flag);

150:   user.m = user.ns*user.mx*user.mx*user.mx; /* number of constraints */
151:   user.nstate =  user.m;
152:   user.ndesign = user.mx*user.mx*user.mx;
153:   user.n = user.nstate + user.ndesign; /* number of variables */

155:   /* Create TAO solver and set desired solution method */
156:   TaoCreate(PETSC_COMM_WORLD,&tao);
157:   TaoSetType(tao,"tao_lcl");
158:   user.lcl = (TAO_LCL*)(tao->data);

160:   /* Set up initial vectors and matrices */
161:   EllipticInitialize(&user);

163:   Gather(user.x,user.y,user.state_scatter,user.u,user.design_scatter);
164:   VecDuplicate(user.x,&x0);
165:   VecCopy(user.x,x0);

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

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

176:   TaoSetStateDesignIS(tao,user.s_is,user.d_is);
177:   TaoSetFromOptions(tao);

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

193:   TaoGetTerminationReason(tao,&reason);
194:   if (reason < 0) {
195:     PetscPrintf(MPI_COMM_WORLD, "TAO failed to converge.\n");
196:   } else {
197:     PetscPrintf(MPI_COMM_WORLD, "Optimization terminated with status %D.\n", reason);
198:   }

200:   TaoDestroy(&tao);
201:   VecDestroy(&x0);
202:   EllipticDestroy(&user);
203:   PetscFinalize();
204:   return 0;
205: }
206: /* ------------------------------------------------------------------- */
209: /*
210:    dwork = Qy - d
211:    lwork = L*(u-ur)
212:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
213: */
214: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
215: {
217:   PetscReal      d1=0,d2=0;
218:   AppCtx         *user = (AppCtx*)ptr;

221:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
222:   MatMult(user->MQ,user->y,user->dwork);
223:   VecAXPY(user->dwork,-1.0,user->d);
224:   VecDot(user->dwork,user->dwork,&d1);
225:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
226:   MatMult(user->L,user->uwork,user->lwork);
227:   VecDot(user->lwork,user->lwork,&d2);
228:   *f = 0.5 * (d1 + user->alpha*d2);
229:   return(0);
230: }

232: /* ------------------------------------------------------------------- */
235: /*
236:     state: g_s = Q' *(Qy - d)
237:     design: g_d = alpha*L'*L*(u-ur)
238: */
239: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
240: {
242:   AppCtx         *user = (AppCtx*)ptr;

245:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
246:   MatMult(user->MQ,user->y,user->dwork);
247:   VecAXPY(user->dwork,-1.0,user->d);
248:   MatMultTranspose(user->MQ,user->dwork,user->ywork);
249:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
250:   MatMult(user->L,user->uwork,user->lwork);
251:   MatMultTranspose(user->L,user->lwork,user->uwork);
252:   VecScale(user->uwork, user->alpha);
253:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
254:   return(0);
255: }

259: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
260: {
262:   PetscReal      d1,d2;
263:   AppCtx         *user = (AppCtx*)ptr;

266:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
267:   MatMult(user->MQ,user->y,user->dwork);
268:   VecAXPY(user->dwork,-1.0,user->d);
269:   VecDot(user->dwork,user->dwork,&d1);
270:   MatMultTranspose(user->MQ,user->dwork,user->ywork);

272:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
273:   MatMult(user->L,user->uwork,user->lwork);
274:   VecDot(user->lwork,user->lwork,&d2);
275:   MatMultTranspose(user->L,user->lwork,user->uwork);
276:   VecScale(user->uwork, user->alpha);
277:   *f = 0.5 * (d1 + user->alpha*d2);
278:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
279:   return(0);
280: }

282: /* ------------------------------------------------------------------- */
285: /* A
286: MatShell object
287: */
288: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat *J, Mat* JPre, Mat* JInv, MatStructure* flag, void *ptr)
289: {
291:   AppCtx         *user = (AppCtx*)ptr;

294:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
295:   /* DSG = Div * (1/Av_u) * Grad */
296:   VecSet(user->uwork,0);
297:   VecAXPY(user->uwork,-1.0,user->u);
298:   VecExp(user->uwork);
299:   MatMult(user->Av,user->uwork,user->Av_u);
300:   VecCopy(user->Av_u,user->Swork);
301:   VecReciprocal(user->Swork);
302:   if (user->use_ptap) {
303:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
304:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
305:   } else {
306:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
307:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
308:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
309:   }
310:   *flag = SAME_NONZERO_PATTERN;
311:   return(0);
312: }
313: /* ------------------------------------------------------------------- */
316: /* B */
317: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat *J, void *ptr)
318: {
320:   AppCtx         *user = (AppCtx*)ptr;

323:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
324:   *J = user->Jd;
325:   return(0);
326: }

330: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
331: {
333:   PetscReal      sum;
334:   AppCtx         *user;

337:   MatShellGetContext(J_shell,(void**)&user);
338:   MatMult(user->DSG,X,Y);
339:   VecSum(X,&sum);
340:   sum /= user->ndesign;
341:   VecShift(Y,sum);
342:   return(0);
343: }

347: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
348: {
350:   PetscInt       i;
351:   AppCtx         *user;

354:   MatShellGetContext(J_shell,(void**)&user);
355:   if (user->ns == 1) {
356:     MatMult(user->JsBlock,X,Y);
357:   } else {
358:     for (i=0;i<user->ns;i++) {
359:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
360:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
361:       MatMult(user->JsBlock,user->subq,user->suby);
362:       Gather(X,user->subq,user->yi_scatter[i],0,0);
363:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
364:     }
365:   }
366:   return(0);
367: }

371: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
372: {
374:   PetscInt       its,i;
375:   PetscReal      tau;
376:   AppCtx         *user;

379:   MatShellGetContext(J_shell,(void**)&user);
380:   KSPSetOperators(user->solver,user->JsBlock,user->DSG,SAME_NONZERO_PATTERN);
381:   if (Y == user->ytrue) {
382:     KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
383:   } else if (user->lcl) {
384:     tau = user->lcl->tau[user->lcl->solve_type];
385:     KSPSetTolerances(user->solver,tau,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
386:   }
387:   if (user->ns == 1) {
388:     KSPSolve(user->solver,X,Y);
389:     KSPGetIterationNumber(user->solver,&its);
390:     user->ksp_its+=its;
391:   } else {
392:     for (i=0;i<user->ns;i++) {
393:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
394:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
395:       KSPSolve(user->solver,user->subq,user->suby);
396:       KSPGetIterationNumber(user->solver,&its);
397:       user->ksp_its+=its;
398:       Gather(X,user->subq,user->yi_scatter[i],0,0);
399:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
400:     }
401:   }
402:   return(0);
403: }
406: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
407: {
409:   AppCtx         *user;
410:   PetscInt       i;

413:   MatShellGetContext(J_shell,(void**)&user);
414:   if (user->ns == 1) {
415:     MatMult(user->Q,X,Y);
416:   } else {
417:     for (i=0;i<user->ns;i++) {
418:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
419:       Scatter(Y,user->subd,user->di_scatter[i],0,0);
420:       MatMult(user->Q,user->subq,user->subd);
421:       Gather(X,user->subq,user->yi_scatter[i],0,0);
422:       Gather(Y,user->subd,user->di_scatter[i],0,0);
423:     }
424:   }
425:   return(0);
426: }

430: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
431: {
433:   AppCtx         *user;
434:   PetscInt       i;

437:   MatShellGetContext(J_shell,(void**)&user);
438:   if (user->ns == 1) {
439:     MatMultTranspose(user->Q,X,Y);
440:   } else {
441:     for (i=0;i<user->ns;i++) {
442:       Scatter(X,user->subd,user->di_scatter[i],0,0);
443:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
444:       MatMultTranspose(user->Q,user->subd,user->suby);
445:       Gather(X,user->subd,user->di_scatter[i],0,0);
446:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
447:     }
448:   }
449:   return(0);
450: }

454: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
455: {
457:   PetscInt       i;
458:   AppCtx         *user;

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

463:   /* sdiag(1./v) */
464:   VecSet(user->uwork,0);
465:   VecAXPY(user->uwork,-1.0,user->u);
466:   VecExp(user->uwork);

468:   /* sdiag(1./((Av*(1./v)).^2)) */
469:   MatMult(user->Av,user->uwork,user->Swork);
470:   VecPointwiseMult(user->Swork,user->Swork,user->Swork);
471:   VecReciprocal(user->Swork);

473:   /* (Av * (sdiag(1./v) * b)) */
474:   VecPointwiseMult(user->uwork,user->uwork,X);
475:   MatMult(user->Av,user->uwork,user->Twork);

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

480:   if (user->ns == 1) {
481:     /* (sdiag(Grad*y(:,i)) */
482:     MatMult(user->Grad,user->y,user->Twork);

484:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
485:     VecPointwiseMult(user->Swork,user->Twork,user->Swork);
486:     MatMultTranspose(user->Grad,user->Swork,Y);
487:   } else {
488:     for (i=0;i<user->ns;i++) {
489:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
490:       Scatter(Y,user->subq,user->yi_scatter[i],0,0);

492:       MatMult(user->Grad,user->suby,user->Twork);
493:       VecPointwiseMult(user->Twork,user->Twork,user->Swork);
494:       MatMultTranspose(user->Grad,user->Twork,user->subq);
495:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
496:       Gather(Y,user->subq,user->yi_scatter[i],0,0);
497:     }
498:   }
499:   return(0);
500: }

504: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
505: {
507:   PetscInt       i;
508:   AppCtx         *user;

511:   MatShellGetContext(J_shell,(void**)&user);
512:   VecZeroEntries(Y);

514:   /* Sdiag = 1./((Av*(1./v)).^2) */
515:   VecSet(user->uwork,0);
516:   VecAXPY(user->uwork,-1.0,user->u);
517:   VecExp(user->uwork);
518:   MatMult(user->Av,user->uwork,user->Swork);
519:   VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
520:   VecReciprocal(user->Sdiag);

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

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

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

532:     /* Twork = sdiag(Twork) * Swork */
533:     VecPointwiseMult(user->Twork,user->Swork,user->Twork);


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

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

542:     /* Ywork = pointwisemult(uwork,Ywork) */
543:     VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
544:     VecAXPY(Y,1.0,user->Ywork);
545:     Gather(X,user->subq,user->yi_scatter[i],0,0);
546:     Gather(user->y,user->suby,user->yi_scatter[i],0,0);
547:   }
548:   return(0);
549: }

553: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
554: {
555:    /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
557:    PetscReal      sum;
558:    PetscInt       i;
559:    AppCtx         *user = (AppCtx*)ptr;

562:    Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
563:    if (user->ns == 1) {
564:      MatMult(user->Grad,user->y,user->Swork);
565:      VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
566:      MatMultTranspose(user->Grad,user->Swork,C);
567:      VecSum(user->y,&sum);
568:      sum /= user->ndesign;
569:      VecShift(C,sum);
570:    } else {
571:      for (i=0;i<user->ns;i++) {
572:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
573:       Scatter(C,user->subq,user->yi_scatter[i],0,0);
574:       MatMult(user->Grad,user->suby,user->Swork);
575:       VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
576:       MatMultTranspose(user->Grad,user->Swork,user->subq);

578:       VecSum(user->suby,&sum);
579:       sum /= user->ndesign;
580:       VecShift(user->subq,sum);

582:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
583:       Gather(C,user->subq,user->yi_scatter[i],0,0);
584:      }
585:    }
586:    VecAXPY(C,-1.0,user->q);
587:    return(0);
588: }

592: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
593: {

597:   VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
598:   VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
599:   if (sub2) {
600:     VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
601:     VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
602:   }
603:   return(0);
604: }

608: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
609: {

613:   VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
614:   VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
615:   if (sub2) {
616:     VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
617:     VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
618:   }
619:   return(0);
620: }

624: PetscErrorCode EllipticInitialize(AppCtx *user)
625: {
627:   PetscInt       m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
628:   Vec            XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
629:   PetscReal      *x,*y,*z;
630:   PetscReal      h,meanut;
631:   PetscScalar    hinv,neg_hinv,half = 0.5,sqrt_beta;
632:   PetscInt       im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
633:   IS             is_alldesign,is_allstate;
634:   IS             is_from_d;
635:   IS             is_from_y;
636:   PetscInt       lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
637:   const PetscInt *ranges, *subranges;
638:   PetscMPIInt    size;
639:   PetscReal      xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
640:   PetscScalar    v,vx,vy,vz;
641:   PetscInt       offset,subindex,subvec,nrank,kk;

643:   PetscScalar xr[64] = {0.4970,     0.8498,     0.7814,     0.6268,     0.7782,     0.6402,     0.3617,     0.3160,
644:                         0.3610,     0.5298,     0.6987,     0.3331,     0.7962,     0.5596,     0.3866,     0.6774,
645:                         0.5407,     0.4518,     0.6702,     0.6061,     0.7580,     0.8997,     0.5198,     0.8326,
646:                         0.2138,     0.9198,     0.3000,     0.2833,     0.8288,     0.7076,     0.1820,     0.0728,
647:                         0.8447,     0.2367,     0.3239,     0.6413,     0.3114,     0.4731,     0.1192,     0.9273,
648:                         0.5724,     0.4331,     0.5136,     0.3547,     0.4413,     0.2602,     0.5698,     0.7278,
649:                         0.5261,     0.6230,     0.2454,     0.3948,     0.7479,     0.6582,     0.4660,     0.5594,
650:                         0.7574,     0.1143,     0.5900,     0.1065,     0.4260,     0.3294,     0.8276,     0.0756};

652:   PetscScalar yr[64] = {0.7345,     0.9120,     0.9288,     0.7528,     0.4463,     0.4985,     0.2497,     0.6256,
653:                         0.3425,     0.9026,     0.6983,     0.4230,     0.7140,     0.2970,     0.4474,     0.8792,
654:                         0.6604,     0.2485,     0.7968,     0.6127,     0.1796,     0.2437,     0.5938,     0.6137,
655:                         0.3867,     0.5658,     0.4575,     0.1009,     0.0863,     0.3361,     0.0738,     0.3985,
656:                         0.6602,     0.1437,     0.0934,     0.5983,     0.5950,     0.0763,     0.0768,     0.2288,
657:                         0.5761,     0.1129,     0.3841,     0.6150,     0.6904,     0.6686,     0.1361,     0.4601,
658:                         0.4491,     0.3716,     0.1969,     0.6537,     0.6743,     0.6991,     0.4811,     0.5480,
659:                         0.1684,     0.4569,     0.6889,     0.8437,     0.3015,     0.2854,     0.8199,     0.2658};

661:   PetscScalar zr[64] = {0.7668,     0.8573,     0.2654,     0.2719,     0.1060,     0.1311,     0.6232,     0.2295,
662:                         0.8009,     0.2147,     0.2119,     0.9325,     0.4473,     0.3600,     0.3374,     0.3819,
663:                         0.4066,     0.5801,     0.1673,     0.0959,     0.4638,     0.8236,     0.8800,     0.2939,
664:                         0.2028,     0.8262,     0.2706,     0.6276,     0.9085,     0.6443,     0.8241,     0.0712,
665:                         0.1824,     0.7789,     0.4389,     0.8415,     0.7055,     0.6639,     0.3653,     0.2078,
666:                         0.1987,     0.2297,     0.4321,     0.8115,     0.4915,     0.7764,     0.4657,     0.4627,
667:                         0.4569,     0.4232,     0.8514,     0.0674,     0.3227,     0.1055,     0.6690,     0.6313,
668:                         0.9226,     0.5461,     0.4126,     0.2364,     0.6096,     0.7042,     0.3914,     0.0711};

671:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
672:   PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
673:   PetscLogStagePush(user->stages[0]);

675:   /* Create u,y,c,x */
676:   VecCreate(PETSC_COMM_WORLD,&user->u);
677:   VecCreate(PETSC_COMM_WORLD,&user->y);
678:   VecCreate(PETSC_COMM_WORLD,&user->c);
679:   VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
680:   VecSetFromOptions(user->u);
681:   VecGetLocalSize(user->u,&ysubnlocal);
682:   VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
683:   VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
684:   VecSetFromOptions(user->y);
685:   VecSetFromOptions(user->c);

687:   /*
688:      *******************************
689:      Create scatters for x <-> y,u
690:      *******************************

692:      If the state vector y and design vector u are partitioned as
693:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
694:      then the solution vector x is organized as
695:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
696:      The index sets user->s_is and user->d_is correspond to the indices of the
697:      state and design variables owned by the current processor.
698:   */
699:   VecCreate(PETSC_COMM_WORLD,&user->x);

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

704:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
705:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
706:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
707:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);

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

712:   VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
713:   VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
714:   ISDestroy(&is_alldesign);
715:   ISDestroy(&is_allstate);
716:   /*
717:      *******************************
718:      Create scatter from y to y_1,y_2,...,y_ns
719:      *******************************
720:   */
721:   PetscMalloc1(user->ns,&user->yi_scatter);
722:   VecDuplicate(user->u,&user->suby);
723:   VecDuplicate(user->u,&user->subq);

725:   VecGetOwnershipRange(user->y,&lo2,&hi2);
726:   istart = 0;
727:   for (i=0; i<user->ns; i++){
728:     VecGetOwnershipRange(user->suby,&lo,&hi);
729:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
730:     VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
731:     istart = istart + hi-lo;
732:     ISDestroy(&is_from_y);
733:   }
734:   /*
735:      *******************************
736:      Create scatter from d to d_1,d_2,...,d_ns
737:      *******************************
738:   */
739:   VecCreate(PETSC_COMM_WORLD,&user->subd);
740:   VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
741:   VecSetFromOptions(user->subd);
742:   VecCreate(PETSC_COMM_WORLD,&user->d);
743:   VecGetLocalSize(user->subd,&dsubnlocal);
744:   VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
745:   VecSetFromOptions(user->d);
746:   PetscMalloc1(user->ns,&user->di_scatter);

748:   VecGetOwnershipRange(user->d,&lo2,&hi2);
749:   istart = 0;
750:   for (i=0; i<user->ns; i++){
751:     VecGetOwnershipRange(user->subd,&lo,&hi);
752:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
753:     VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
754:     istart = istart + hi-lo;
755:     ISDestroy(&is_from_d);
756:   }

758:   PetscMalloc1(user->mx,&x);
759:   PetscMalloc1(user->mx,&y);
760:   PetscMalloc1(user->mx,&z);

762:   user->ksp_its = 0;
763:   user->ksp_its_initial = 0;

765:   n = user->mx * user->mx * user->mx;
766:   m = 3 * user->mx * user->mx * (user->mx-1);
767:   sqrt_beta = PetscSqrtScalar(user->beta);

769:   VecCreate(PETSC_COMM_WORLD,&XX);
770:   VecCreate(PETSC_COMM_WORLD,&user->q);
771:   VecSetSizes(XX,ysubnlocal,n);
772:   VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
773:   VecSetFromOptions(XX);
774:   VecSetFromOptions(user->q);

776:   VecDuplicate(XX,&YY);
777:   VecDuplicate(XX,&ZZ);
778:   VecDuplicate(XX,&XXwork);
779:   VecDuplicate(XX,&YYwork);
780:   VecDuplicate(XX,&ZZwork);
781:   VecDuplicate(XX,&UTwork);
782:   VecDuplicate(XX,&user->utrue);

784:   /* map for striding q */
785:   /*
786:   PetscMalloc1((size+1),&ranges);
787:   PetscMalloc1((size+1),&subranges); */
788:   VecGetOwnershipRanges(user->q,&ranges);
789:   VecGetOwnershipRanges(user->u,&subranges);

791:   VecGetOwnershipRange(user->q,&lo2,&hi2);
792:   VecGetOwnershipRange(user->u,&lo,&hi);
793:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
794:   h = 1.0/user->mx;
795:   hinv = user->mx;
796:   neg_hinv = -hinv;

798:   VecGetOwnershipRange(XX,&istart,&iend);
799:   for (linear_index=istart; linear_index<iend; linear_index++){
800:     i = linear_index % user->mx;
801:     j = ((linear_index-i)/user->mx) % user->mx;
802:     k = ((linear_index-i)/user->mx-j) / user->mx;
803:     vx = h*(i+0.5);
804:     vy = h*(j+0.5);
805:     vz = h*(k+0.5);
806:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
807:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
808:     VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
809:     for (is=0; is<2; is++){
810:       for (js=0; js<2; js++){
811:         for (ks=0; ks<2; ks++){
812:           ls = is*4 + js*2 + ks;
813:           if (ls<user->ns){
814:             l =ls*n + linear_index;
815:             /* remap */
816:             subindex = l%n;
817:             subvec = l/n;
818:             nrank=0;
819:             while (subindex >= subranges[nrank+1]) nrank++;
820:             offset = subindex - subranges[nrank];
821:             istart=0;
822:             for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
823:             istart += (subranges[nrank+1]-subranges[nrank])*subvec;
824:             l = istart+offset;
825:             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));
826:             VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
827:           }
828:         }
829:       }
830:     }
831:   }

833:   VecAssemblyBegin(XX);
834:   VecAssemblyEnd(XX);
835:   VecAssemblyBegin(YY);
836:   VecAssemblyEnd(YY);
837:   VecAssemblyBegin(ZZ);
838:   VecAssemblyEnd(ZZ);
839:   VecAssemblyBegin(user->q);
840:   VecAssemblyEnd(user->q);

842:   /* Compute true parameter function
843:      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) */
844:   VecCopy(XX,XXwork);
845:   VecCopy(YY,YYwork);
846:   VecCopy(ZZ,ZZwork);

848:   VecShift(XXwork,-0.25);
849:   VecShift(YYwork,-0.25);
850:   VecShift(ZZwork,-0.25);

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

856:   VecCopy(XXwork,UTwork);
857:   VecAXPY(UTwork,1.0,YYwork);
858:   VecAXPY(UTwork,1.0,ZZwork);
859:   VecScale(UTwork,-20.0);
860:   VecExp(UTwork);
861:   VecCopy(UTwork,user->utrue);

863:   VecCopy(XX,XXwork);
864:   VecCopy(YY,YYwork);
865:   VecCopy(ZZ,ZZwork);

867:   VecShift(XXwork,-0.75);
868:   VecShift(YYwork,-0.75);
869:   VecShift(ZZwork,-0.75);

871:   VecPointwiseMult(XXwork,XXwork,XXwork);
872:   VecPointwiseMult(YYwork,YYwork,YYwork);
873:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

875:   VecCopy(XXwork,UTwork);
876:   VecAXPY(UTwork,1.0,YYwork);
877:   VecAXPY(UTwork,1.0,ZZwork);
878:   VecScale(UTwork,-20.0);
879:   VecExp(UTwork);

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

883:   VecDestroy(&XX);
884:   VecDestroy(&YY);
885:   VecDestroy(&ZZ);
886:   VecDestroy(&XXwork);
887:   VecDestroy(&YYwork);
888:   VecDestroy(&ZZwork);
889:   VecDestroy(&UTwork);

891:   /* Initial guess and reference model */
892:   VecDuplicate(user->utrue,&user->ur);
893:   VecSum(user->utrue,&meanut);
894:   meanut = meanut / n;
895:   VecSet(user->ur,meanut);
896:   VecCopy(user->ur,user->u);

898:   /* Generate Grad matrix */
899:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
900:   MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
901:   MatSetFromOptions(user->Grad);
902:   MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
903:   MatSeqAIJSetPreallocation(user->Grad,2,NULL);
904:   MatGetOwnershipRange(user->Grad,&istart,&iend);

906:   for (i=istart; i<iend; i++){
907:     if (i<m/3){
908:       iblock = i / (user->mx-1);
909:       j = iblock*user->mx + (i % (user->mx-1));
910:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
911:       j = j+1;
912:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
913:     }
914:     if (i>=m/3 && i<2*m/3){
915:       iblock = (i-m/3) / (user->mx*(user->mx-1));
916:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
917:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
918:       j = j + user->mx;
919:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
920:     }
921:     if (i>=2*m/3){
922:       j = i-2*m/3;
923:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
924:       j = j + user->mx*user->mx;
925:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
926:     }
927:   }

929:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
930:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

932:   /* Generate arithmetic averaging matrix Av */
933:   MatCreate(PETSC_COMM_WORLD,&user->Av);
934:   MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
935:   MatSetFromOptions(user->Av);
936:   MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
937:   MatSeqAIJSetPreallocation(user->Av,2,NULL);
938:   MatGetOwnershipRange(user->Av,&istart,&iend);

940:   for (i=istart; i<iend; i++){
941:     if (i<m/3){
942:       iblock = i / (user->mx-1);
943:       j = iblock*user->mx + (i % (user->mx-1));
944:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
945:       j = j+1;
946:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
947:     }
948:     if (i>=m/3 && i<2*m/3){
949:       iblock = (i-m/3) / (user->mx*(user->mx-1));
950:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
951:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
952:       j = j + user->mx;
953:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
954:     }
955:     if (i>=2*m/3){
956:       j = i-2*m/3;
957:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
958:       j = j + user->mx*user->mx;
959:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
960:     }
961:   }

963:   MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
964:   MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);

966:   MatCreate(PETSC_COMM_WORLD,&user->L);
967:   MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
968:   MatSetFromOptions(user->L);
969:   MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
970:   MatSeqAIJSetPreallocation(user->L,2,NULL);
971:   MatGetOwnershipRange(user->L,&istart,&iend);

973:   for (i=istart; i<iend; i++){
974:     if (i<m/3){
975:       iblock = i / (user->mx-1);
976:       j = iblock*user->mx + (i % (user->mx-1));
977:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
978:       j = j+1;
979:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
980:     }
981:     if (i>=m/3 && i<2*m/3){
982:       iblock = (i-m/3) / (user->mx*(user->mx-1));
983:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
984:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
985:       j = j + user->mx;
986:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
987:     }
988:     if (i>=2*m/3 && i<m){
989:       j = i-2*m/3;
990:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
991:       j = j + user->mx*user->mx;
992:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
993:     }
994:     if (i>=m){
995:       j = i - m;
996:       MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
997:     }
998:   }
999:   MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
1000:   MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
1001:   MatScale(user->L,PetscPowScalar(h,1.5));

1003:   /* Generate Div matrix */
1004:   if (!user->use_ptap) {
1005:     /* Generate Div matrix */
1006:     MatCreate(PETSC_COMM_WORLD,&user->Div);
1007:     MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
1008:     MatSetFromOptions(user->Div);
1009:     MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
1010:     MatSeqAIJSetPreallocation(user->Div,6,NULL);
1011:     MatGetOwnershipRange(user->Grad,&istart,&iend);

1013:     for (i=istart; i<iend; i++){
1014:       if (i<m/3){
1015:         iblock = i / (user->mx-1);
1016:         j = iblock*user->mx + (i % (user->mx-1));
1017:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1018:         j = j+1;
1019:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1020:       }
1021:       if (i>=m/3 && i<2*m/3){
1022:         iblock = (i-m/3) / (user->mx*(user->mx-1));
1023:         j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
1024:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1025:         j = j + user->mx;
1026:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1027:       }
1028:       if (i>=2*m/3){
1029:         j = i-2*m/3;
1030:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1031:         j = j + user->mx*user->mx;
1032:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1033:       }
1034:     }

1036:     MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
1037:     MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
1038:     MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1039:   } else {
1040:     MatCreate(PETSC_COMM_WORLD,&user->Diag);
1041:     MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
1042:     MatSetFromOptions(user->Diag);
1043:     MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
1044:     MatSeqAIJSetPreallocation(user->Diag,1,NULL);
1045:   }

1047:   /* Build work vectors and matrices */
1048:   VecCreate(PETSC_COMM_WORLD,&user->S);
1049:   VecSetSizes(user->S, PETSC_DECIDE, m);
1050:   VecSetFromOptions(user->S);

1052:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1053:   VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1054:   VecSetFromOptions(user->lwork);

1056:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

1058:   VecDuplicate(user->S,&user->Swork);
1059:   VecDuplicate(user->S,&user->Sdiag);
1060:   VecDuplicate(user->S,&user->Av_u);
1061:   VecDuplicate(user->S,&user->Twork);
1062:   VecDuplicate(user->y,&user->ywork);
1063:   VecDuplicate(user->u,&user->Ywork);
1064:   VecDuplicate(user->u,&user->uwork);
1065:   VecDuplicate(user->u,&user->js_diag);
1066:   VecDuplicate(user->c,&user->cwork);
1067:   VecDuplicate(user->d,&user->dwork);

1069:   /* Create a matrix-free shell user->Jd for computing B*x */
1070:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1071:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1072:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1074:   /* Compute true state function ytrue given utrue */
1075:   VecDuplicate(user->y,&user->ytrue);

1077:   /* First compute Av_u = Av*exp(-u) */
1078:   VecSet(user->uwork, 0);
1079:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1080:   VecExp(user->uwork);
1081:   MatMult(user->Av,user->uwork,user->Av_u);

1083:   /* Next form DSG = Div*S*Grad */
1084:   VecCopy(user->Av_u,user->Swork);
1085:   VecReciprocal(user->Swork);
1086:   if (user->use_ptap) {
1087:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1088:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1089:   } else {
1090:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1091:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
1092:     MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1093:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1094:   }

1096:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1097:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1099:   if (user->use_lrc == PETSC_TRUE) {
1100:     v=PetscSqrtReal(1.0 /user->ndesign);
1101:     PetscMalloc1(user->ndesign,&user->ones);

1103:     for (i=0;i<user->ndesign;i++) {
1104:       user->ones[i]=v;
1105:     }
1106:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1107:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1108:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1109:     MatCreateLRC(user->DSG,user->Ones,user->Ones,&user->JsBlock);
1110:     MatSetUp(user->JsBlock);
1111:   } else {
1112:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1113:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1114:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1115:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1116:   }
1117:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1118:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1119:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1120:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1121:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1122:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1123:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1125:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1126:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1127:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1128:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1129:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1131:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1132:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1133:   /* Now solve for ytrue */
1134:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1135:   KSPSetFromOptions(user->solver);

1137:   KSPSetOperators(user->solver,user->JsBlock,user->DSG,SAME_NONZERO_PATTERN);
1138:   user->lcl->solve_type = LCL_FORWARD1;
1139:   MatMult(user->JsInv,user->q,user->ytrue);
1140:   /* First compute Av_u = Av*exp(-u) */
1141:   VecSet(user->uwork,0);
1142:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1143:   VecExp(user->uwork);
1144:   MatMult(user->Av,user->uwork,user->Av_u);

1146:   /* Next update DSG = Div*S*Grad  with user->u */
1147:   VecCopy(user->Av_u,user->Swork);
1148:   VecReciprocal(user->Swork);
1149:   if (user->use_ptap) {
1150:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1151:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1152:   } else {
1153:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1154:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1155:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1156:   }

1158:   /* Now solve for y */
1159:   user->lcl->solve_type = LCL_FORWARD1;
1160:   MatMult(user->JsInv,user->q,user->y);

1162:   user->ksp_its_initial = user->ksp_its;
1163:   user->ksp_its = 0;
1164:   /* Construct projection matrix Q (blocks) */
1165:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1166:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1167:   MatSetFromOptions(user->Q);
1168:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1169:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

1171:   for (i=0; i<user->mx; i++){
1172:     x[i] = h*(i+0.5);
1173:     y[i] = h*(i+0.5);
1174:     z[i] = h*(i+0.5);
1175:   }
1176:   MatGetOwnershipRange(user->Q,&istart,&iend);

1178:   nx = user->mx; ny = user->mx; nz = user->mx;
1179:   for (i=istart; i<iend; i++){

1181:     xri = xr[i];
1182:     im = 0;
1183:     xim = x[im];
1184:     while (xri>xim && im<nx){
1185:       im = im+1;
1186:       xim = x[im];
1187:     }
1188:     indx1 = im-1;
1189:     indx2 = im;
1190:     dx1 = xri - x[indx1];
1191:     dx2 = x[indx2] - xri;

1193:     yri = yr[i];
1194:     im = 0;
1195:     yim = y[im];
1196:     while (yri>yim && im<ny){
1197:       im = im+1;
1198:       yim = y[im];
1199:     }
1200:     indy1 = im-1;
1201:     indy2 = im;
1202:     dy1 = yri - y[indy1];
1203:     dy2 = y[indy2] - yri;

1205:     zri = zr[i];
1206:     im = 0;
1207:     zim = z[im];
1208:     while (zri>zim && im<nz){
1209:       im = im+1;
1210:       zim = z[im];
1211:     }
1212:     indz1 = im-1;
1213:     indz2 = im;
1214:     dz1 = zri - z[indz1];
1215:     dz2 = z[indz2] - zri;

1217:     Dx = x[indx2] - x[indx1];
1218:     Dy = y[indy2] - y[indy1];
1219:     Dz = z[indz2] - z[indz1];

1221:     j = indx1 + indy1*nx + indz1*nx*ny;
1222:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1223:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1225:     j = indx1 + indy1*nx + indz2*nx*ny;
1226:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1227:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1229:     j = indx1 + indy2*nx + indz1*nx*ny;
1230:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1231:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1233:     j = indx1 + indy2*nx + indz2*nx*ny;
1234:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1235:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1237:     j = indx2 + indy1*nx + indz1*nx*ny;
1238:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1239:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1241:     j = indx2 + indy1*nx + indz2*nx*ny;
1242:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1243:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1245:     j = indx2 + indy2*nx + indz1*nx*ny;
1246:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1247:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1249:     j = indx2 + indy2*nx + indz2*nx*ny;
1250:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1251:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1252:   }

1254:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1255:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1256:   /* Create MQ (composed of blocks of Q */
1257:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1258:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1259:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

1261:   /* Add noise to the measurement data */
1262:   VecSet(user->ywork,1.0);
1263:   VecAYPX(user->ywork,user->noise,user->ytrue);
1264:   MatMult(user->MQ,user->ywork,user->d);

1266:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1267:   PetscFree(x);
1268:   PetscFree(y);
1269:   PetscFree(z);
1270:   PetscLogStagePop();
1271:   return(0);
1272: }

1276: PetscErrorCode EllipticDestroy(AppCtx *user)
1277: {
1279:   PetscInt       i;

1282:   MatDestroy(&user->DSG);
1283:   KSPDestroy(&user->solver);
1284:   MatDestroy(&user->Q);
1285:   MatDestroy(&user->MQ);
1286:   if (!user->use_ptap) {
1287:     MatDestroy(&user->Div);
1288:     MatDestroy(&user->Divwork);
1289:   } else {
1290:     MatDestroy(&user->Diag);
1291:   }
1292:   if (user->use_lrc) {
1293:     MatDestroy(&user->Ones);
1294:   }

1296:   MatDestroy(&user->Grad);
1297:   MatDestroy(&user->Av);
1298:   MatDestroy(&user->Avwork);
1299:   MatDestroy(&user->L);
1300:   MatDestroy(&user->Js);
1301:   MatDestroy(&user->Jd);
1302:   MatDestroy(&user->JsBlock);
1303:   MatDestroy(&user->JsInv);

1305:   VecDestroy(&user->x);
1306:   VecDestroy(&user->u);
1307:   VecDestroy(&user->uwork);
1308:   VecDestroy(&user->utrue);
1309:   VecDestroy(&user->y);
1310:   VecDestroy(&user->ywork);
1311:   VecDestroy(&user->ytrue);
1312:   VecDestroy(&user->c);
1313:   VecDestroy(&user->cwork);
1314:   VecDestroy(&user->ur);
1315:   VecDestroy(&user->q);
1316:   VecDestroy(&user->d);
1317:   VecDestroy(&user->dwork);
1318:   VecDestroy(&user->lwork);
1319:   VecDestroy(&user->S);
1320:   VecDestroy(&user->Swork);
1321:   VecDestroy(&user->Sdiag);
1322:   VecDestroy(&user->Ywork);
1323:   VecDestroy(&user->Twork);
1324:   VecDestroy(&user->Av_u);
1325:   VecDestroy(&user->js_diag);
1326:   ISDestroy(&user->s_is);
1327:   ISDestroy(&user->d_is);
1328:   VecDestroy(&user->suby);
1329:   VecDestroy(&user->subd);
1330:   VecDestroy(&user->subq);
1331:   VecScatterDestroy(&user->state_scatter);
1332:   VecScatterDestroy(&user->design_scatter);
1333:   for (i=0;i<user->ns;i++) {
1334:     VecScatterDestroy(&user->yi_scatter[i]);
1335:     VecScatterDestroy(&user->di_scatter[i]);
1336:   }
1337:   PetscFree(user->yi_scatter);
1338:   PetscFree(user->di_scatter);
1339:   if (user->use_lrc) {
1340:     PetscFree(user->ones);
1341:     MatDestroy(&user->Ones);
1342:   }
1343:   return(0);
1344: }

1348: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1349: {
1351:   Vec            X;
1352:   PetscReal      unorm,ynorm;
1353:   AppCtx         *user = (AppCtx*)ptr;

1356:   TaoGetSolutionVector(tao,&X);
1357:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1358:   VecAXPY(user->ywork,-1.0,user->ytrue);
1359:   VecAXPY(user->uwork,-1.0,user->utrue);
1360:   VecNorm(user->uwork,NORM_2,&unorm);
1361:   VecNorm(user->ywork,NORM_2,&ynorm);
1362:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1363:   return(0);
1364: }