Actual source code: elliptic.c

petsc-master 2015-07-31
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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: TaoGetConvergedReason(); 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:   TaoConvergedReason reason;
126:   AppCtx             user;
127:   PetscInt           ntests = 1;
128:   PetscInt           i;

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

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

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

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

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

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

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

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

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

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

199:   TaoDestroy(&tao);
200:   VecDestroy(&x0);
201:   EllipticDestroy(&user);
202:   PetscFinalize();
203:   return 0;
204: }
205: /* ------------------------------------------------------------------- */
208: /*
209:    dwork = Qy - d
210:    lwork = L*(u-ur)
211:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
212: */
213: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
214: {
216:   PetscReal      d1=0,d2=0;
217:   AppCtx         *user = (AppCtx*)ptr;

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

231: /* ------------------------------------------------------------------- */
234: /*
235:     state: g_s = Q' *(Qy - d)
236:     design: g_d = alpha*L'*L*(u-ur)
237: */
238: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
239: {
241:   AppCtx         *user = (AppCtx*)ptr;

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

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

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

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

281: /* ------------------------------------------------------------------- */
284: /* A
285: MatShell object
286: */
287: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
288: {
290:   AppCtx         *user = (AppCtx*)ptr;

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

321:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
322:   return(0);
323: }

327: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
328: {
330:   PetscReal      sum;
331:   AppCtx         *user;

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

344: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
345: {
347:   PetscInt       i;
348:   AppCtx         *user;

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

367: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
368: {
370:   PetscInt       its,i;
371:   AppCtx         *user;

374:   MatShellGetContext(J_shell,(void**)&user);
375:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);
376:   if (Y == user->ytrue) {
377:     /* First solve is done using true solution to set up problem */
378:     KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
379:   } else {
380:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
381:   }
382:   if (user->ns == 1) {
383:     KSPSolve(user->solver,X,Y);
384:     KSPGetIterationNumber(user->solver,&its);
385:     user->ksp_its+=its;
386:   } else {
387:     for (i=0;i<user->ns;i++) {
388:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
389:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
390:       KSPSolve(user->solver,user->subq,user->suby);
391:       KSPGetIterationNumber(user->solver,&its);
392:       user->ksp_its+=its;
393:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
394:     }
395:   }
396:   return(0);
397: }
400: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
401: {
403:   AppCtx         *user;
404:   PetscInt       i;

407:   MatShellGetContext(J_shell,(void**)&user);
408:   if (user->ns == 1) {
409:     MatMult(user->Q,X,Y);
410:   } else {
411:     for (i=0;i<user->ns;i++) {
412:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
413:       Scatter(Y,user->subd,user->di_scatter[i],0,0);
414:       MatMult(user->Q,user->subq,user->subd);
415:       Gather(Y,user->subd,user->di_scatter[i],0,0);
416:     }
417:   }
418:   return(0);
419: }

423: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
424: {
426:   AppCtx         *user;
427:   PetscInt       i;

430:   MatShellGetContext(J_shell,(void**)&user);
431:   if (user->ns == 1) {
432:     MatMultTranspose(user->Q,X,Y);
433:   } else {
434:     for (i=0;i<user->ns;i++) {
435:       Scatter(X,user->subd,user->di_scatter[i],0,0);
436:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
437:       MatMultTranspose(user->Q,user->subd,user->suby);
438:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
439:     }
440:   }
441:   return(0);
442: }

446: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
447: {
449:   PetscInt       i;
450:   AppCtx         *user;

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

455:   /* sdiag(1./v) */
456:   VecSet(user->uwork,0);
457:   VecAXPY(user->uwork,-1.0,user->u);
458:   VecExp(user->uwork);

460:   /* sdiag(1./((Av*(1./v)).^2)) */
461:   MatMult(user->Av,user->uwork,user->Swork);
462:   VecPointwiseMult(user->Swork,user->Swork,user->Swork);
463:   VecReciprocal(user->Swork);

465:   /* (Av * (sdiag(1./v) * b)) */
466:   VecPointwiseMult(user->uwork,user->uwork,X);
467:   MatMult(user->Av,user->uwork,user->Twork);

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

472:   if (user->ns == 1) {
473:     /* (sdiag(Grad*y(:,i)) */
474:     MatMult(user->Grad,user->y,user->Twork);

476:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
477:     VecPointwiseMult(user->Swork,user->Twork,user->Swork);
478:     MatMultTranspose(user->Grad,user->Swork,Y);
479:   } else {
480:     for (i=0;i<user->ns;i++) {
481:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
482:       Scatter(Y,user->subq,user->yi_scatter[i],0,0);

484:       MatMult(user->Grad,user->suby,user->Twork);
485:       VecPointwiseMult(user->Twork,user->Twork,user->Swork);
486:       MatMultTranspose(user->Grad,user->Twork,user->subq);
487:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
488:       Gather(Y,user->subq,user->yi_scatter[i],0,0);
489:     }
490:   }
491:   return(0);
492: }

496: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
497: {
499:   PetscInt       i;
500:   AppCtx         *user;

503:   MatShellGetContext(J_shell,(void**)&user);
504:   VecZeroEntries(Y);

506:   /* Sdiag = 1./((Av*(1./v)).^2) */
507:   VecSet(user->uwork,0);
508:   VecAXPY(user->uwork,-1.0,user->u);
509:   VecExp(user->uwork);
510:   MatMult(user->Av,user->uwork,user->Swork);
511:   VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
512:   VecReciprocal(user->Sdiag);

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

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

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

524:     /* Twork = sdiag(Twork) * Swork */
525:     VecPointwiseMult(user->Twork,user->Swork,user->Twork);


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

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

534:     /* Ywork = pointwisemult(uwork,Ywork) */
535:     VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
536:     VecAXPY(Y,1.0,user->Ywork);
537:     Gather(user->y,user->suby,user->yi_scatter[i],0,0);
538:   }
539:   return(0);
540: }

544: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
545: {
546:    /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
548:    PetscReal      sum;
549:    PetscInt       i;
550:    AppCtx         *user = (AppCtx*)ptr;

553:    Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
554:    if (user->ns == 1) {
555:      MatMult(user->Grad,user->y,user->Swork);
556:      VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
557:      MatMultTranspose(user->Grad,user->Swork,C);
558:      VecSum(user->y,&sum);
559:      sum /= user->ndesign;
560:      VecShift(C,sum);
561:    } else {
562:      for (i=0;i<user->ns;i++) {
563:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
564:       Scatter(C,user->subq,user->yi_scatter[i],0,0);
565:       MatMult(user->Grad,user->suby,user->Swork);
566:       VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
567:       MatMultTranspose(user->Grad,user->Swork,user->subq);

569:       VecSum(user->suby,&sum);
570:       sum /= user->ndesign;
571:       VecShift(user->subq,sum);

573:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
574:       Gather(C,user->subq,user->yi_scatter[i],0,0);
575:      }
576:    }
577:    VecAXPY(C,-1.0,user->q);
578:    return(0);
579: }

583: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
584: {

588:   VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
589:   VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
590:   if (sub2) {
591:     VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
592:     VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
593:   }
594:   return(0);
595: }

599: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
600: {

604:   VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
605:   VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
606:   if (sub2) {
607:     VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
608:     VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
609:   }
610:   return(0);
611: }

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

634:   PetscScalar xr[64] = {0.4970,     0.8498,     0.7814,     0.6268,     0.7782,     0.6402,     0.3617,     0.3160,
635:                         0.3610,     0.5298,     0.6987,     0.3331,     0.7962,     0.5596,     0.3866,     0.6774,
636:                         0.5407,     0.4518,     0.6702,     0.6061,     0.7580,     0.8997,     0.5198,     0.8326,
637:                         0.2138,     0.9198,     0.3000,     0.2833,     0.8288,     0.7076,     0.1820,     0.0728,
638:                         0.8447,     0.2367,     0.3239,     0.6413,     0.3114,     0.4731,     0.1192,     0.9273,
639:                         0.5724,     0.4331,     0.5136,     0.3547,     0.4413,     0.2602,     0.5698,     0.7278,
640:                         0.5261,     0.6230,     0.2454,     0.3948,     0.7479,     0.6582,     0.4660,     0.5594,
641:                         0.7574,     0.1143,     0.5900,     0.1065,     0.4260,     0.3294,     0.8276,     0.0756};

643:   PetscScalar yr[64] = {0.7345,     0.9120,     0.9288,     0.7528,     0.4463,     0.4985,     0.2497,     0.6256,
644:                         0.3425,     0.9026,     0.6983,     0.4230,     0.7140,     0.2970,     0.4474,     0.8792,
645:                         0.6604,     0.2485,     0.7968,     0.6127,     0.1796,     0.2437,     0.5938,     0.6137,
646:                         0.3867,     0.5658,     0.4575,     0.1009,     0.0863,     0.3361,     0.0738,     0.3985,
647:                         0.6602,     0.1437,     0.0934,     0.5983,     0.5950,     0.0763,     0.0768,     0.2288,
648:                         0.5761,     0.1129,     0.3841,     0.6150,     0.6904,     0.6686,     0.1361,     0.4601,
649:                         0.4491,     0.3716,     0.1969,     0.6537,     0.6743,     0.6991,     0.4811,     0.5480,
650:                         0.1684,     0.4569,     0.6889,     0.8437,     0.3015,     0.2854,     0.8199,     0.2658};

652:   PetscScalar zr[64] = {0.7668,     0.8573,     0.2654,     0.2719,     0.1060,     0.1311,     0.6232,     0.2295,
653:                         0.8009,     0.2147,     0.2119,     0.9325,     0.4473,     0.3600,     0.3374,     0.3819,
654:                         0.4066,     0.5801,     0.1673,     0.0959,     0.4638,     0.8236,     0.8800,     0.2939,
655:                         0.2028,     0.8262,     0.2706,     0.6276,     0.9085,     0.6443,     0.8241,     0.0712,
656:                         0.1824,     0.7789,     0.4389,     0.8415,     0.7055,     0.6639,     0.3653,     0.2078,
657:                         0.1987,     0.2297,     0.4321,     0.8115,     0.4915,     0.7764,     0.4657,     0.4627,
658:                         0.4569,     0.4232,     0.8514,     0.0674,     0.3227,     0.1055,     0.6690,     0.6313,
659:                         0.9226,     0.5461,     0.4126,     0.2364,     0.6096,     0.7042,     0.3914,     0.0711};

662:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
663:   PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
664:   PetscLogStagePush(user->stages[0]);

666:   /* Create u,y,c,x */
667:   VecCreate(PETSC_COMM_WORLD,&user->u);
668:   VecCreate(PETSC_COMM_WORLD,&user->y);
669:   VecCreate(PETSC_COMM_WORLD,&user->c);
670:   VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
671:   VecSetFromOptions(user->u);
672:   VecGetLocalSize(user->u,&ysubnlocal);
673:   VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
674:   VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
675:   VecSetFromOptions(user->y);
676:   VecSetFromOptions(user->c);

678:   /*
679:      *******************************
680:      Create scatters for x <-> y,u
681:      *******************************

683:      If the state vector y and design vector u are partitioned as
684:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
685:      then the solution vector x is organized as
686:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
687:      The index sets user->s_is and user->d_is correspond to the indices of the
688:      state and design variables owned by the current processor.
689:   */
690:   VecCreate(PETSC_COMM_WORLD,&user->x);

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

695:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
696:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
697:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
698:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);

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

703:   VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
704:   VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
705:   ISDestroy(&is_alldesign);
706:   ISDestroy(&is_allstate);
707:   /*
708:      *******************************
709:      Create scatter from y to y_1,y_2,...,y_ns
710:      *******************************
711:   */
712:   PetscMalloc1(user->ns,&user->yi_scatter);
713:   VecDuplicate(user->u,&user->suby);
714:   VecDuplicate(user->u,&user->subq);

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

739:   VecGetOwnershipRange(user->d,&lo2,&hi2);
740:   istart = 0;
741:   for (i=0; i<user->ns; i++){
742:     VecGetOwnershipRange(user->subd,&lo,&hi);
743:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
744:     VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
745:     istart = istart + hi-lo;
746:     ISDestroy(&is_from_d);
747:   }

749:   PetscMalloc1(user->mx,&x);
750:   PetscMalloc1(user->mx,&y);
751:   PetscMalloc1(user->mx,&z);

753:   user->ksp_its = 0;
754:   user->ksp_its_initial = 0;

756:   n = user->mx * user->mx * user->mx;
757:   m = 3 * user->mx * user->mx * (user->mx-1);
758:   sqrt_beta = PetscSqrtScalar(user->beta);

760:   VecCreate(PETSC_COMM_WORLD,&XX);
761:   VecCreate(PETSC_COMM_WORLD,&user->q);
762:   VecSetSizes(XX,ysubnlocal,n);
763:   VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
764:   VecSetFromOptions(XX);
765:   VecSetFromOptions(user->q);

767:   VecDuplicate(XX,&YY);
768:   VecDuplicate(XX,&ZZ);
769:   VecDuplicate(XX,&XXwork);
770:   VecDuplicate(XX,&YYwork);
771:   VecDuplicate(XX,&ZZwork);
772:   VecDuplicate(XX,&UTwork);
773:   VecDuplicate(XX,&user->utrue);

775:   /* map for striding q */
776:   VecGetOwnershipRanges(user->q,&ranges);
777:   VecGetOwnershipRanges(user->u,&subranges);

779:   VecGetOwnershipRange(user->q,&lo2,&hi2);
780:   VecGetOwnershipRange(user->u,&lo,&hi);
781:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
782:   h = 1.0/user->mx;
783:   hinv = user->mx;
784:   neg_hinv = -hinv;

786:   VecGetOwnershipRange(XX,&istart,&iend);
787:   for (linear_index=istart; linear_index<iend; linear_index++){
788:     i = linear_index % user->mx;
789:     j = ((linear_index-i)/user->mx) % user->mx;
790:     k = ((linear_index-i)/user->mx-j) / user->mx;
791:     vx = h*(i+0.5);
792:     vy = h*(j+0.5);
793:     vz = h*(k+0.5);
794:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
795:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
796:     VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
797:     for (is=0; is<2; is++){
798:       for (js=0; js<2; js++){
799:         for (ks=0; ks<2; ks++){
800:           ls = is*4 + js*2 + ks;
801:           if (ls<user->ns){
802:             l =ls*n + linear_index;
803:             /* remap */
804:             subindex = l%n;
805:             subvec = l/n;
806:             nrank=0;
807:             while (subindex >= subranges[nrank+1]) nrank++;
808:             offset = subindex - subranges[nrank];
809:             istart=0;
810:             for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
811:             istart += (subranges[nrank+1]-subranges[nrank])*subvec;
812:             l = istart+offset;
813:             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));
814:             VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
815:           }
816:         }
817:       }
818:     }
819:   }

821:   VecAssemblyBegin(XX);
822:   VecAssemblyEnd(XX);
823:   VecAssemblyBegin(YY);
824:   VecAssemblyEnd(YY);
825:   VecAssemblyBegin(ZZ);
826:   VecAssemblyEnd(ZZ);
827:   VecAssemblyBegin(user->q);
828:   VecAssemblyEnd(user->q);

830:   /* Compute true parameter function
831:      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) */
832:   VecCopy(XX,XXwork);
833:   VecCopy(YY,YYwork);
834:   VecCopy(ZZ,ZZwork);

836:   VecShift(XXwork,-0.25);
837:   VecShift(YYwork,-0.25);
838:   VecShift(ZZwork,-0.25);

840:   VecPointwiseMult(XXwork,XXwork,XXwork);
841:   VecPointwiseMult(YYwork,YYwork,YYwork);
842:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

844:   VecCopy(XXwork,UTwork);
845:   VecAXPY(UTwork,1.0,YYwork);
846:   VecAXPY(UTwork,1.0,ZZwork);
847:   VecScale(UTwork,-20.0);
848:   VecExp(UTwork);
849:   VecCopy(UTwork,user->utrue);

851:   VecCopy(XX,XXwork);
852:   VecCopy(YY,YYwork);
853:   VecCopy(ZZ,ZZwork);

855:   VecShift(XXwork,-0.75);
856:   VecShift(YYwork,-0.75);
857:   VecShift(ZZwork,-0.75);

859:   VecPointwiseMult(XXwork,XXwork,XXwork);
860:   VecPointwiseMult(YYwork,YYwork,YYwork);
861:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

863:   VecCopy(XXwork,UTwork);
864:   VecAXPY(UTwork,1.0,YYwork);
865:   VecAXPY(UTwork,1.0,ZZwork);
866:   VecScale(UTwork,-20.0);
867:   VecExp(UTwork);

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

871:   VecDestroy(&XX);
872:   VecDestroy(&YY);
873:   VecDestroy(&ZZ);
874:   VecDestroy(&XXwork);
875:   VecDestroy(&YYwork);
876:   VecDestroy(&ZZwork);
877:   VecDestroy(&UTwork);

879:   /* Initial guess and reference model */
880:   VecDuplicate(user->utrue,&user->ur);
881:   VecSum(user->utrue,&meanut);
882:   meanut = meanut / n;
883:   VecSet(user->ur,meanut);
884:   VecCopy(user->ur,user->u);

886:   /* Generate Grad matrix */
887:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
888:   MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
889:   MatSetFromOptions(user->Grad);
890:   MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
891:   MatSeqAIJSetPreallocation(user->Grad,2,NULL);
892:   MatGetOwnershipRange(user->Grad,&istart,&iend);

894:   for (i=istart; i<iend; i++){
895:     if (i<m/3){
896:       iblock = i / (user->mx-1);
897:       j = iblock*user->mx + (i % (user->mx-1));
898:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
899:       j = j+1;
900:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
901:     }
902:     if (i>=m/3 && i<2*m/3){
903:       iblock = (i-m/3) / (user->mx*(user->mx-1));
904:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
905:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
906:       j = j + user->mx;
907:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
908:     }
909:     if (i>=2*m/3){
910:       j = i-2*m/3;
911:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
912:       j = j + user->mx*user->mx;
913:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
914:     }
915:   }

917:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
918:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

920:   /* Generate arithmetic averaging matrix Av */
921:   MatCreate(PETSC_COMM_WORLD,&user->Av);
922:   MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
923:   MatSetFromOptions(user->Av);
924:   MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
925:   MatSeqAIJSetPreallocation(user->Av,2,NULL);
926:   MatGetOwnershipRange(user->Av,&istart,&iend);

928:   for (i=istart; i<iend; i++){
929:     if (i<m/3){
930:       iblock = i / (user->mx-1);
931:       j = iblock*user->mx + (i % (user->mx-1));
932:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
933:       j = j+1;
934:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
935:     }
936:     if (i>=m/3 && i<2*m/3){
937:       iblock = (i-m/3) / (user->mx*(user->mx-1));
938:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
939:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
940:       j = j + user->mx;
941:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
942:     }
943:     if (i>=2*m/3){
944:       j = i-2*m/3;
945:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
946:       j = j + user->mx*user->mx;
947:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
948:     }
949:   }

951:   MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
952:   MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);

954:   MatCreate(PETSC_COMM_WORLD,&user->L);
955:   MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
956:   MatSetFromOptions(user->L);
957:   MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
958:   MatSeqAIJSetPreallocation(user->L,2,NULL);
959:   MatGetOwnershipRange(user->L,&istart,&iend);

961:   for (i=istart; i<iend; i++){
962:     if (i<m/3){
963:       iblock = i / (user->mx-1);
964:       j = iblock*user->mx + (i % (user->mx-1));
965:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
966:       j = j+1;
967:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
968:     }
969:     if (i>=m/3 && i<2*m/3){
970:       iblock = (i-m/3) / (user->mx*(user->mx-1));
971:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
972:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
973:       j = j + user->mx;
974:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
975:     }
976:     if (i>=2*m/3 && i<m){
977:       j = i-2*m/3;
978:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
979:       j = j + user->mx*user->mx;
980:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
981:     }
982:     if (i>=m){
983:       j = i - m;
984:       MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
985:     }
986:   }
987:   MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
988:   MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
989:   MatScale(user->L,PetscPowScalar(h,1.5));

991:   /* Generate Div matrix */
992:   if (!user->use_ptap) {
993:     /* Generate Div matrix */
994:     MatCreate(PETSC_COMM_WORLD,&user->Div);
995:     MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
996:     MatSetFromOptions(user->Div);
997:     MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
998:     MatSeqAIJSetPreallocation(user->Div,6,NULL);
999:     MatGetOwnershipRange(user->Grad,&istart,&iend);

1001:     for (i=istart; i<iend; i++){
1002:       if (i<m/3){
1003:         iblock = i / (user->mx-1);
1004:         j = iblock*user->mx + (i % (user->mx-1));
1005:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1006:         j = j+1;
1007:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1008:       }
1009:       if (i>=m/3 && i<2*m/3){
1010:         iblock = (i-m/3) / (user->mx*(user->mx-1));
1011:         j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
1012:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1013:         j = j + user->mx;
1014:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1015:       }
1016:       if (i>=2*m/3){
1017:         j = i-2*m/3;
1018:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1019:         j = j + user->mx*user->mx;
1020:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1021:       }
1022:     }

1024:     MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
1025:     MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
1026:     MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1027:   } else {
1028:     MatCreate(PETSC_COMM_WORLD,&user->Diag);
1029:     MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
1030:     MatSetFromOptions(user->Diag);
1031:     MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
1032:     MatSeqAIJSetPreallocation(user->Diag,1,NULL);
1033:   }

1035:   /* Build work vectors and matrices */
1036:   VecCreate(PETSC_COMM_WORLD,&user->S);
1037:   VecSetSizes(user->S, PETSC_DECIDE, m);
1038:   VecSetFromOptions(user->S);

1040:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1041:   VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1042:   VecSetFromOptions(user->lwork);

1044:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

1046:   VecDuplicate(user->S,&user->Swork);
1047:   VecDuplicate(user->S,&user->Sdiag);
1048:   VecDuplicate(user->S,&user->Av_u);
1049:   VecDuplicate(user->S,&user->Twork);
1050:   VecDuplicate(user->y,&user->ywork);
1051:   VecDuplicate(user->u,&user->Ywork);
1052:   VecDuplicate(user->u,&user->uwork);
1053:   VecDuplicate(user->u,&user->js_diag);
1054:   VecDuplicate(user->c,&user->cwork);
1055:   VecDuplicate(user->d,&user->dwork);

1057:   /* Create a matrix-free shell user->Jd for computing B*x */
1058:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1059:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1060:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1062:   /* Compute true state function ytrue given utrue */
1063:   VecDuplicate(user->y,&user->ytrue);

1065:   /* First compute Av_u = Av*exp(-u) */
1066:   VecSet(user->uwork, 0);
1067:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1068:   VecExp(user->uwork);
1069:   MatMult(user->Av,user->uwork,user->Av_u);

1071:   /* Next form DSG = Div*S*Grad */
1072:   VecCopy(user->Av_u,user->Swork);
1073:   VecReciprocal(user->Swork);
1074:   if (user->use_ptap) {
1075:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1076:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1077:   } else {
1078:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1079:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
1080:     MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1081:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1082:   }

1084:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1085:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1087:   if (user->use_lrc == PETSC_TRUE) {
1088:     v=PetscSqrtReal(1.0 /user->ndesign);
1089:     PetscMalloc1(user->ndesign,&user->ones);

1091:     for (i=0;i<user->ndesign;i++) {
1092:       user->ones[i]=v;
1093:     }
1094:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1095:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1096:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1097:     MatCreateLRC(user->DSG,user->Ones,user->Ones,&user->JsBlock);
1098:     MatSetUp(user->JsBlock);
1099:   } else {
1100:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1101:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1102:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1103:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1104:   }
1105:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1106:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1107:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1108:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1109:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1110:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1111:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1113:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1114:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1115:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1116:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1117:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1119:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1120:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1121:   /* Now solve for ytrue */
1122:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1123:   KSPSetFromOptions(user->solver);

1125:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);

1127:   MatMult(user->JsInv,user->q,user->ytrue);
1128:   /* First compute Av_u = Av*exp(-u) */
1129:   VecSet(user->uwork,0);
1130:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1131:   VecExp(user->uwork);
1132:   MatMult(user->Av,user->uwork,user->Av_u);

1134:   /* Next update DSG = Div*S*Grad  with user->u */
1135:   VecCopy(user->Av_u,user->Swork);
1136:   VecReciprocal(user->Swork);
1137:   if (user->use_ptap) {
1138:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1139:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1140:   } else {
1141:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1142:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1143:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1144:   }

1146:   /* Now solve for y */

1148:   MatMult(user->JsInv,user->q,user->y);

1150:   user->ksp_its_initial = user->ksp_its;
1151:   user->ksp_its = 0;
1152:   /* Construct projection matrix Q (blocks) */
1153:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1154:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1155:   MatSetFromOptions(user->Q);
1156:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1157:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

1159:   for (i=0; i<user->mx; i++){
1160:     x[i] = h*(i+0.5);
1161:     y[i] = h*(i+0.5);
1162:     z[i] = h*(i+0.5);
1163:   }
1164:   MatGetOwnershipRange(user->Q,&istart,&iend);

1166:   nx = user->mx; ny = user->mx; nz = user->mx;
1167:   for (i=istart; i<iend; i++){

1169:     xri = xr[i];
1170:     im = 0;
1171:     xim = x[im];
1172:     while (xri>xim && im<nx){
1173:       im = im+1;
1174:       xim = x[im];
1175:     }
1176:     indx1 = im-1;
1177:     indx2 = im;
1178:     dx1 = xri - x[indx1];
1179:     dx2 = x[indx2] - xri;

1181:     yri = yr[i];
1182:     im = 0;
1183:     yim = y[im];
1184:     while (yri>yim && im<ny){
1185:       im = im+1;
1186:       yim = y[im];
1187:     }
1188:     indy1 = im-1;
1189:     indy2 = im;
1190:     dy1 = yri - y[indy1];
1191:     dy2 = y[indy2] - yri;

1193:     zri = zr[i];
1194:     im = 0;
1195:     zim = z[im];
1196:     while (zri>zim && im<nz){
1197:       im = im+1;
1198:       zim = z[im];
1199:     }
1200:     indz1 = im-1;
1201:     indz2 = im;
1202:     dz1 = zri - z[indz1];
1203:     dz2 = z[indz2] - zri;

1205:     Dx = x[indx2] - x[indx1];
1206:     Dy = y[indy2] - y[indy1];
1207:     Dz = z[indz2] - z[indz1];

1209:     j = indx1 + indy1*nx + indz1*nx*ny;
1210:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1211:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1213:     j = indx1 + indy1*nx + indz2*nx*ny;
1214:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1215:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1217:     j = indx1 + indy2*nx + indz1*nx*ny;
1218:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1219:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1221:     j = indx1 + indy2*nx + indz2*nx*ny;
1222:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1223:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1225:     j = indx2 + indy1*nx + indz1*nx*ny;
1226:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1227:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1229:     j = indx2 + indy1*nx + indz2*nx*ny;
1230:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1231:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1233:     j = indx2 + indy2*nx + indz1*nx*ny;
1234:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1235:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1237:     j = indx2 + indy2*nx + indz2*nx*ny;
1238:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1239:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1240:   }

1242:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1243:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1244:   /* Create MQ (composed of blocks of Q */
1245:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1246:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1247:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

1249:   /* Add noise to the measurement data */
1250:   VecSet(user->ywork,1.0);
1251:   VecAYPX(user->ywork,user->noise,user->ytrue);
1252:   MatMult(user->MQ,user->ywork,user->d);

1254:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1255:   PetscFree(x);
1256:   PetscFree(y);
1257:   PetscFree(z);
1258:   PetscLogStagePop();
1259:   return(0);
1260: }

1264: PetscErrorCode EllipticDestroy(AppCtx *user)
1265: {
1267:   PetscInt       i;

1270:   MatDestroy(&user->DSG);
1271:   KSPDestroy(&user->solver);
1272:   MatDestroy(&user->Q);
1273:   MatDestroy(&user->MQ);
1274:   if (!user->use_ptap) {
1275:     MatDestroy(&user->Div);
1276:     MatDestroy(&user->Divwork);
1277:   } else {
1278:     MatDestroy(&user->Diag);
1279:   }
1280:   if (user->use_lrc) {
1281:     MatDestroy(&user->Ones);
1282:   }

1284:   MatDestroy(&user->Grad);
1285:   MatDestroy(&user->Av);
1286:   MatDestroy(&user->Avwork);
1287:   MatDestroy(&user->L);
1288:   MatDestroy(&user->Js);
1289:   MatDestroy(&user->Jd);
1290:   MatDestroy(&user->JsBlock);
1291:   MatDestroy(&user->JsInv);

1293:   VecDestroy(&user->x);
1294:   VecDestroy(&user->u);
1295:   VecDestroy(&user->uwork);
1296:   VecDestroy(&user->utrue);
1297:   VecDestroy(&user->y);
1298:   VecDestroy(&user->ywork);
1299:   VecDestroy(&user->ytrue);
1300:   VecDestroy(&user->c);
1301:   VecDestroy(&user->cwork);
1302:   VecDestroy(&user->ur);
1303:   VecDestroy(&user->q);
1304:   VecDestroy(&user->d);
1305:   VecDestroy(&user->dwork);
1306:   VecDestroy(&user->lwork);
1307:   VecDestroy(&user->S);
1308:   VecDestroy(&user->Swork);
1309:   VecDestroy(&user->Sdiag);
1310:   VecDestroy(&user->Ywork);
1311:   VecDestroy(&user->Twork);
1312:   VecDestroy(&user->Av_u);
1313:   VecDestroy(&user->js_diag);
1314:   ISDestroy(&user->s_is);
1315:   ISDestroy(&user->d_is);
1316:   VecDestroy(&user->suby);
1317:   VecDestroy(&user->subd);
1318:   VecDestroy(&user->subq);
1319:   VecScatterDestroy(&user->state_scatter);
1320:   VecScatterDestroy(&user->design_scatter);
1321:   for (i=0;i<user->ns;i++) {
1322:     VecScatterDestroy(&user->yi_scatter[i]);
1323:     VecScatterDestroy(&user->di_scatter[i]);
1324:   }
1325:   PetscFree(user->yi_scatter);
1326:   PetscFree(user->di_scatter);
1327:   if (user->use_lrc) {
1328:     PetscFree(user->ones);
1329:     MatDestroy(&user->Ones);
1330:   }
1331:   return(0);
1332: }

1336: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1337: {
1339:   Vec            X;
1340:   PetscReal      unorm,ynorm;
1341:   AppCtx         *user = (AppCtx*)ptr;

1344:   TaoGetSolutionVector(tao,&X);
1345:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1346:   VecAXPY(user->ywork,-1.0,user->ytrue);
1347:   VecAXPY(user->uwork,-1.0,user->utrue);
1348:   VecNorm(user->uwork,NORM_2,&unorm);
1349:   VecNorm(user->ywork,NORM_2,&ynorm);
1350:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1351:   return(0);
1352: }