Actual source code: elliptic.c

petsc-master 2017-04-20
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  1: #include <petsc/private/taoimpl.h>

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

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

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

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

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


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

 57:   Vec d;
 58:   Vec dwork;

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

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

 65:   Vec ytrue;

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

 70:   Vec utrue;

 72:   Vec js_diag;

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

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

 82:   KSP solver;
 83:   PC  prec;

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

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

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

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

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

116: static  char help[]="";

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

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

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

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

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

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

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

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

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

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

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

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

219: /* ------------------------------------------------------------------- */
220: /*
221:     state: g_s = Q' *(Qy - d)
222:     design: g_d = alpha*L'*L*(u-ur)
223: */
224: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
225: {
227:   AppCtx         *user = (AppCtx*)ptr;

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

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

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

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

265: /* ------------------------------------------------------------------- */
266: /* A
267: MatShell object
268: */
269: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
270: {
272:   AppCtx         *user = (AppCtx*)ptr;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

636:   /*
637:      *******************************
638:      Create scatters for x <-> y,u
639:      *******************************

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

788:   /* Compute true parameter function
789:      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) */
790:   VecCopy(XX,XXwork);
791:   VecCopy(YY,YYwork);
792:   VecCopy(ZZ,ZZwork);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1002:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

1004:   VecDuplicate(user->S,&user->Swork);
1005:   VecDuplicate(user->S,&user->Sdiag);
1006:   VecDuplicate(user->S,&user->Av_u);
1007:   VecDuplicate(user->S,&user->Twork);
1008:   VecDuplicate(user->y,&user->ywork);
1009:   VecDuplicate(user->u,&user->Ywork);
1010:   VecDuplicate(user->u,&user->uwork);
1011:   VecDuplicate(user->u,&user->js_diag);
1012:   VecDuplicate(user->c,&user->cwork);
1013:   VecDuplicate(user->d,&user->dwork);

1015:   /* Create a matrix-free shell user->Jd for computing B*x */
1016:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1017:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1018:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1020:   /* Compute true state function ytrue given utrue */
1021:   VecDuplicate(user->y,&user->ytrue);

1023:   /* First compute Av_u = Av*exp(-u) */
1024:   VecSet(user->uwork, 0);
1025:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1026:   VecExp(user->uwork);
1027:   MatMult(user->Av,user->uwork,user->Av_u);

1029:   /* Next form DSG = Div*S*Grad */
1030:   VecCopy(user->Av_u,user->Swork);
1031:   VecReciprocal(user->Swork);
1032:   if (user->use_ptap) {
1033:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1034:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1035:   } else {
1036:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1037:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
1038:     MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1039:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1040:   }

1042:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1043:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1045:   if (user->use_lrc == PETSC_TRUE) {
1046:     v=PetscSqrtReal(1.0 /user->ndesign);
1047:     PetscMalloc1(user->ndesign,&user->ones);

1049:     for (i=0;i<user->ndesign;i++) {
1050:       user->ones[i]=v;
1051:     }
1052:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1053:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1054:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1055:     MatCreateLRC(user->DSG,user->Ones,NULL,user->Ones,&user->JsBlock);
1056:     MatSetUp(user->JsBlock);
1057:   } else {
1058:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1059:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1060:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1061:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1062:   }
1063:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1064:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1065:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1066:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1067:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1068:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1069:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1071:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1072:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1073:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1074:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1075:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

1077:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1078:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1079:   /* Now solve for ytrue */
1080:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1081:   KSPSetFromOptions(user->solver);

1083:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);

1085:   MatMult(user->JsInv,user->q,user->ytrue);
1086:   /* First compute Av_u = Av*exp(-u) */
1087:   VecSet(user->uwork,0);
1088:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1089:   VecExp(user->uwork);
1090:   MatMult(user->Av,user->uwork,user->Av_u);

1092:   /* Next update DSG = Div*S*Grad  with user->u */
1093:   VecCopy(user->Av_u,user->Swork);
1094:   VecReciprocal(user->Swork);
1095:   if (user->use_ptap) {
1096:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1097:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1098:   } else {
1099:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1100:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1101:     MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1102:   }

1104:   /* Now solve for y */

1106:   MatMult(user->JsInv,user->q,user->y);

1108:   user->ksp_its_initial = user->ksp_its;
1109:   user->ksp_its = 0;
1110:   /* Construct projection matrix Q (blocks) */
1111:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1112:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1113:   MatSetFromOptions(user->Q);
1114:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1115:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

1117:   for (i=0; i<user->mx; i++){
1118:     x[i] = h*(i+0.5);
1119:     y[i] = h*(i+0.5);
1120:     z[i] = h*(i+0.5);
1121:   }
1122:   MatGetOwnershipRange(user->Q,&istart,&iend);

1124:   nx = user->mx; ny = user->mx; nz = user->mx;
1125:   for (i=istart; i<iend; i++){

1127:     xri = xr[i];
1128:     im = 0;
1129:     xim = x[im];
1130:     while (xri>xim && im<nx){
1131:       im = im+1;
1132:       xim = x[im];
1133:     }
1134:     indx1 = im-1;
1135:     indx2 = im;
1136:     dx1 = xri - x[indx1];
1137:     dx2 = x[indx2] - xri;

1139:     yri = yr[i];
1140:     im = 0;
1141:     yim = y[im];
1142:     while (yri>yim && im<ny){
1143:       im = im+1;
1144:       yim = y[im];
1145:     }
1146:     indy1 = im-1;
1147:     indy2 = im;
1148:     dy1 = yri - y[indy1];
1149:     dy2 = y[indy2] - yri;

1151:     zri = zr[i];
1152:     im = 0;
1153:     zim = z[im];
1154:     while (zri>zim && im<nz){
1155:       im = im+1;
1156:       zim = z[im];
1157:     }
1158:     indz1 = im-1;
1159:     indz2 = im;
1160:     dz1 = zri - z[indz1];
1161:     dz2 = z[indz2] - zri;

1163:     Dx = x[indx2] - x[indx1];
1164:     Dy = y[indy2] - y[indy1];
1165:     Dz = z[indz2] - z[indz1];

1167:     j = indx1 + indy1*nx + indz1*nx*ny;
1168:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1169:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1171:     j = indx1 + indy1*nx + indz2*nx*ny;
1172:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1173:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1175:     j = indx1 + indy2*nx + indz1*nx*ny;
1176:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1177:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1179:     j = indx1 + indy2*nx + indz2*nx*ny;
1180:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1181:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1183:     j = indx2 + indy1*nx + indz1*nx*ny;
1184:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1185:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1187:     j = indx2 + indy1*nx + indz2*nx*ny;
1188:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1189:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1191:     j = indx2 + indy2*nx + indz1*nx*ny;
1192:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1193:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

1195:     j = indx2 + indy2*nx + indz2*nx*ny;
1196:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1197:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1198:   }

1200:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1201:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1202:   /* Create MQ (composed of blocks of Q */
1203:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1204:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1205:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

1207:   /* Add noise to the measurement data */
1208:   VecSet(user->ywork,1.0);
1209:   VecAYPX(user->ywork,user->noise,user->ytrue);
1210:   MatMult(user->MQ,user->ywork,user->d);

1212:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1213:   PetscFree(x);
1214:   PetscFree(y);
1215:   PetscFree(z);
1216:   PetscLogStagePop();
1217:   return(0);
1218: }

1220: PetscErrorCode EllipticDestroy(AppCtx *user)
1221: {
1223:   PetscInt       i;

1226:   MatDestroy(&user->DSG);
1227:   KSPDestroy(&user->solver);
1228:   MatDestroy(&user->Q);
1229:   MatDestroy(&user->MQ);
1230:   if (!user->use_ptap) {
1231:     MatDestroy(&user->Div);
1232:     MatDestroy(&user->Divwork);
1233:   } else {
1234:     MatDestroy(&user->Diag);
1235:   }
1236:   if (user->use_lrc) {
1237:     MatDestroy(&user->Ones);
1238:   }

1240:   MatDestroy(&user->Grad);
1241:   MatDestroy(&user->Av);
1242:   MatDestroy(&user->Avwork);
1243:   MatDestroy(&user->L);
1244:   MatDestroy(&user->Js);
1245:   MatDestroy(&user->Jd);
1246:   MatDestroy(&user->JsBlock);
1247:   MatDestroy(&user->JsInv);

1249:   VecDestroy(&user->x);
1250:   VecDestroy(&user->u);
1251:   VecDestroy(&user->uwork);
1252:   VecDestroy(&user->utrue);
1253:   VecDestroy(&user->y);
1254:   VecDestroy(&user->ywork);
1255:   VecDestroy(&user->ytrue);
1256:   VecDestroy(&user->c);
1257:   VecDestroy(&user->cwork);
1258:   VecDestroy(&user->ur);
1259:   VecDestroy(&user->q);
1260:   VecDestroy(&user->d);
1261:   VecDestroy(&user->dwork);
1262:   VecDestroy(&user->lwork);
1263:   VecDestroy(&user->S);
1264:   VecDestroy(&user->Swork);
1265:   VecDestroy(&user->Sdiag);
1266:   VecDestroy(&user->Ywork);
1267:   VecDestroy(&user->Twork);
1268:   VecDestroy(&user->Av_u);
1269:   VecDestroy(&user->js_diag);
1270:   ISDestroy(&user->s_is);
1271:   ISDestroy(&user->d_is);
1272:   VecDestroy(&user->suby);
1273:   VecDestroy(&user->subd);
1274:   VecDestroy(&user->subq);
1275:   VecScatterDestroy(&user->state_scatter);
1276:   VecScatterDestroy(&user->design_scatter);
1277:   for (i=0;i<user->ns;i++) {
1278:     VecScatterDestroy(&user->yi_scatter[i]);
1279:     VecScatterDestroy(&user->di_scatter[i]);
1280:   }
1281:   PetscFree(user->yi_scatter);
1282:   PetscFree(user->di_scatter);
1283:   if (user->use_lrc) {
1284:     PetscFree(user->ones);
1285:     MatDestroy(&user->Ones);
1286:   }
1287:   return(0);
1288: }

1290: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1291: {
1293:   Vec            X;
1294:   PetscReal      unorm,ynorm;
1295:   AppCtx         *user = (AppCtx*)ptr;

1298:   TaoGetSolutionVector(tao,&X);
1299:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1300:   VecAXPY(user->ywork,-1.0,user->ytrue);
1301:   VecAXPY(user->uwork,-1.0,user->utrue);
1302:   VecNorm(user->uwork,NORM_2,&unorm);
1303:   VecNorm(user->ywork,NORM_2,&ynorm);
1304:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1305:   return(0);
1306: }