Actual source code: elliptic.c
petsc-3.5.4 2015-05-23
1: #include <petsc-private/taoimpl.h>
2: #include "../src/tao/pde_constrained/impls/lcl/lcl.h"
4: /*T
5: Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
6: Routines: TaoCreate();
7: Routines: TaoSetType();
8: Routines: TaoSetInitialVector();
9: Routines: TaoSetObjectiveRoutine();
10: Routines: TaoSetGradientRoutine();
11: Routines: TaoSetConstraintsRoutine();
12: Routines: TaoSetJacobianStateRoutine();
13: Routines: TaoSetJacobianDesignRoutine();
14: Routines: TaoSetStateDesignIS();
15: Routines: TaoSetFromOptions();
16: Routines: TaoSetHistory(); TaoGetHistory();
17: Routines: TaoSolve();
18: Routines: TaoGetConvergedReason(); TaoDestroy();
19: Processors: n
20: T*/
22: typedef struct {
23: PetscInt n; /* Number of total variables */
24: PetscInt m; /* Number of constraints */
25: PetscInt nstate;
26: PetscInt ndesign;
27: PetscInt mx; /* grid points in each direction */
28: PetscInt ns; /* Number of data samples (1<=ns<=8)
29: Currently only ns=1 is supported */
30: PetscInt ndata; /* Number of data points per sample */
31: IS s_is;
32: IS d_is;
34: VecScatter state_scatter;
35: VecScatter design_scatter;
36: VecScatter *yi_scatter, *di_scatter;
37: Vec suby,subq,subd;
38: Mat Js,Jd,JsPrec,JsInv,JsBlock;
40: PetscReal alpha; /* Regularization parameter */
41: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
42: PetscReal noise; /* Amount of noise to add to data */
43: PetscReal *ones;
44: Mat Q;
45: Mat MQ;
46: Mat L;
48: Mat Grad;
49: Mat Av,Avwork;
50: Mat Div, Divwork;
51: Mat DSG;
52: Mat Diag,Ones;
55: Vec q;
56: Vec ur; /* reference */
58: Vec d;
59: Vec dwork;
61: Vec x; /* super vec of y,u */
63: Vec y; /* state variables */
64: Vec ywork;
66: Vec ytrue;
68: Vec u; /* design variables */
69: Vec uwork;
71: Vec utrue;
73: Vec js_diag;
75: Vec c; /* constraint vector */
76: Vec cwork;
78: Vec lwork;
79: Vec S;
80: Vec Swork,Twork,Sdiag,Ywork;
81: Vec Av_u;
83: KSP solver;
84: PC prec;
86: PetscReal tola,tolb,tolc,told;
87: PetscInt ksp_its;
88: PetscInt ksp_its_initial;
89: int stages[10];
90: PetscBool use_ptap;
91: PetscBool use_lrc;
92: TAO_LCL* lcl;
93: } AppCtx;
95: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
96: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
97: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
98: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
99: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat,void*);
100: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
101: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
102: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
103: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
104: PetscErrorCode EllipticInitialize(AppCtx*);
105: PetscErrorCode EllipticDestroy(AppCtx*);
106: PetscErrorCode EllipticMonitor(Tao, void*);
108: PetscErrorCode StateBlockMatMult(Mat,Vec,Vec);
109: PetscErrorCode StateMatMult(Mat,Vec,Vec);
111: PetscErrorCode StateInvMatMult(Mat,Vec,Vec);
112: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
113: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
115: PetscErrorCode QMatMult(Mat,Vec,Vec);
116: PetscErrorCode QMatMultTranspose(Mat,Vec,Vec);
118: static char help[]="";
122: int main(int argc, char **argv)
123: {
124: PetscErrorCode ierr;
125: Vec x0;
126: Tao tao;
127: TaoConvergedReason reason;
128: AppCtx user;
129: PetscBool flag;
130: PetscInt ntests = 1;
131: PetscInt i;
133: PetscInitialize(&argc, &argv, (char*)0,help);
134: user.mx = 8;
135: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,&flag);
136: user.ns = 6;
137: PetscOptionsInt("-ns","Number of data samples (1<=ns<=8)","",user.ns,&user.ns,&flag);
138: user.ndata = 64;
139: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,&flag);
140: user.alpha = 0.1;
141: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,&flag);
142: user.beta = 0.00001;
143: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,&flag);
144: user.noise = 0.01;
145: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,&flag);
147: PetscOptionsBool("-use_ptap","Use ptap matrix for DSG","",PETSC_FALSE,&user.use_ptap,&flag);
148: PetscOptionsBool("-use_lrc","Use lrc matrix for Js","",PETSC_FALSE,&user.use_lrc,&flag);
150: user.m = user.ns*user.mx*user.mx*user.mx; /* number of constraints */
151: user.nstate = user.m;
152: user.ndesign = user.mx*user.mx*user.mx;
153: user.n = user.nstate + user.ndesign; /* number of variables */
155: /* Create TAO solver and set desired solution method */
156: TaoCreate(PETSC_COMM_WORLD,&tao);
157: TaoSetType(tao,TAOLCL);
158: user.lcl = (TAO_LCL*)(tao->data);
160: /* Set up initial vectors and matrices */
161: EllipticInitialize(&user);
163: Gather(user.x,user.y,user.state_scatter,user.u,user.design_scatter);
164: VecDuplicate(user.x,&x0);
165: VecCopy(user.x,x0);
167: /* Set solution vector with an initial guess */
168: TaoSetInitialVector(tao,user.x);
169: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
170: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
171: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
173: TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, (void *)&user);
174: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
176: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
177: TaoSetFromOptions(tao);
179: /* SOLVE THE APPLICATION */
180: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,&flag);
181: PetscLogStageRegister("Trials",&user.stages[1]);
182: PetscLogStagePush(user.stages[1]);
183: for (i=0; i<ntests; i++){
184: TaoSolve(tao);
185: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its);
186: VecCopy(x0,user.x);
187: }
188: PetscLogStagePop();
189: PetscBarrier((PetscObject)user.x);
190: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
191: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
193: TaoGetConvergedReason(tao,&reason);
194: if (reason < 0) {
195: PetscPrintf(MPI_COMM_WORLD, "TAO failed to converge.\n");
196: } else {
197: PetscPrintf(MPI_COMM_WORLD, "Optimization terminated with status %D.\n", reason);
198: }
200: TaoDestroy(&tao);
201: VecDestroy(&x0);
202: EllipticDestroy(&user);
203: PetscFinalize();
204: return 0;
205: }
206: /* ------------------------------------------------------------------- */
209: /*
210: dwork = Qy - d
211: lwork = L*(u-ur)
212: f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
213: */
214: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
215: {
217: PetscReal d1=0,d2=0;
218: AppCtx *user = (AppCtx*)ptr;
221: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
222: MatMult(user->MQ,user->y,user->dwork);
223: VecAXPY(user->dwork,-1.0,user->d);
224: VecDot(user->dwork,user->dwork,&d1);
225: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
226: MatMult(user->L,user->uwork,user->lwork);
227: VecDot(user->lwork,user->lwork,&d2);
228: *f = 0.5 * (d1 + user->alpha*d2);
229: return(0);
230: }
232: /* ------------------------------------------------------------------- */
235: /*
236: state: g_s = Q' *(Qy - d)
237: design: g_d = alpha*L'*L*(u-ur)
238: */
239: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
240: {
242: AppCtx *user = (AppCtx*)ptr;
245: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
246: MatMult(user->MQ,user->y,user->dwork);
247: VecAXPY(user->dwork,-1.0,user->d);
248: MatMultTranspose(user->MQ,user->dwork,user->ywork);
249: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
250: MatMult(user->L,user->uwork,user->lwork);
251: MatMultTranspose(user->L,user->lwork,user->uwork);
252: VecScale(user->uwork, user->alpha);
253: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
254: return(0);
255: }
259: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
260: {
262: PetscReal d1,d2;
263: AppCtx *user = (AppCtx*)ptr;
266: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
267: MatMult(user->MQ,user->y,user->dwork);
268: VecAXPY(user->dwork,-1.0,user->d);
269: VecDot(user->dwork,user->dwork,&d1);
270: MatMultTranspose(user->MQ,user->dwork,user->ywork);
272: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
273: MatMult(user->L,user->uwork,user->lwork);
274: VecDot(user->lwork,user->lwork,&d2);
275: MatMultTranspose(user->L,user->lwork,user->uwork);
276: VecScale(user->uwork, user->alpha);
277: *f = 0.5 * (d1 + user->alpha*d2);
278: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
279: return(0);
280: }
282: /* ------------------------------------------------------------------- */
285: /* A
286: MatShell object
287: */
288: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
289: {
291: AppCtx *user = (AppCtx*)ptr;
294: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
295: /* DSG = Div * (1/Av_u) * Grad */
296: VecSet(user->uwork,0);
297: VecAXPY(user->uwork,-1.0,user->u);
298: VecExp(user->uwork);
299: MatMult(user->Av,user->uwork,user->Av_u);
300: VecCopy(user->Av_u,user->Swork);
301: VecReciprocal(user->Swork);
302: if (user->use_ptap) {
303: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
304: MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
305: } else {
306: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
307: MatDiagonalScale(user->Divwork,NULL,user->Swork);
308: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
309: }
310: return(0);
311: }
312: /* ------------------------------------------------------------------- */
315: /* B */
316: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
317: {
319: AppCtx *user = (AppCtx*)ptr;
322: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
323: return(0);
324: }
328: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
329: {
331: PetscReal sum;
332: AppCtx *user;
335: MatShellGetContext(J_shell,(void**)&user);
336: MatMult(user->DSG,X,Y);
337: VecSum(X,&sum);
338: sum /= user->ndesign;
339: VecShift(Y,sum);
340: return(0);
341: }
345: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
346: {
348: PetscInt i;
349: AppCtx *user;
352: MatShellGetContext(J_shell,(void**)&user);
353: if (user->ns == 1) {
354: MatMult(user->JsBlock,X,Y);
355: } else {
356: for (i=0;i<user->ns;i++) {
357: Scatter(X,user->subq,user->yi_scatter[i],0,0);
358: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
359: MatMult(user->JsBlock,user->subq,user->suby);
360: Gather(X,user->subq,user->yi_scatter[i],0,0);
361: Gather(Y,user->suby,user->yi_scatter[i],0,0);
362: }
363: }
364: return(0);
365: }
369: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
370: {
372: PetscInt its,i;
373: PetscReal tau;
374: AppCtx *user;
377: MatShellGetContext(J_shell,(void**)&user);
378: KSPSetOperators(user->solver,user->JsBlock,user->DSG);
379: if (Y == user->ytrue) {
380: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
381: } else if (user->lcl) {
382: tau = user->lcl->tau[user->lcl->solve_type];
383: KSPSetTolerances(user->solver,tau,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
384: }
385: if (user->ns == 1) {
386: KSPSolve(user->solver,X,Y);
387: KSPGetIterationNumber(user->solver,&its);
388: user->ksp_its+=its;
389: } else {
390: for (i=0;i<user->ns;i++) {
391: Scatter(X,user->subq,user->yi_scatter[i],0,0);
392: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
393: KSPSolve(user->solver,user->subq,user->suby);
394: KSPGetIterationNumber(user->solver,&its);
395: user->ksp_its+=its;
396: Gather(X,user->subq,user->yi_scatter[i],0,0);
397: Gather(Y,user->suby,user->yi_scatter[i],0,0);
398: }
399: }
400: return(0);
401: }
404: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
405: {
407: AppCtx *user;
408: PetscInt i;
411: MatShellGetContext(J_shell,(void**)&user);
412: if (user->ns == 1) {
413: MatMult(user->Q,X,Y);
414: } else {
415: for (i=0;i<user->ns;i++) {
416: Scatter(X,user->subq,user->yi_scatter[i],0,0);
417: Scatter(Y,user->subd,user->di_scatter[i],0,0);
418: MatMult(user->Q,user->subq,user->subd);
419: Gather(X,user->subq,user->yi_scatter[i],0,0);
420: Gather(Y,user->subd,user->di_scatter[i],0,0);
421: }
422: }
423: return(0);
424: }
428: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
429: {
431: AppCtx *user;
432: PetscInt i;
435: MatShellGetContext(J_shell,(void**)&user);
436: if (user->ns == 1) {
437: MatMultTranspose(user->Q,X,Y);
438: } else {
439: for (i=0;i<user->ns;i++) {
440: Scatter(X,user->subd,user->di_scatter[i],0,0);
441: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
442: MatMultTranspose(user->Q,user->subd,user->suby);
443: Gather(X,user->subd,user->di_scatter[i],0,0);
444: Gather(Y,user->suby,user->yi_scatter[i],0,0);
445: }
446: }
447: return(0);
448: }
452: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
453: {
455: PetscInt i;
456: AppCtx *user;
459: MatShellGetContext(J_shell,(void**)&user);
461: /* sdiag(1./v) */
462: VecSet(user->uwork,0);
463: VecAXPY(user->uwork,-1.0,user->u);
464: VecExp(user->uwork);
466: /* sdiag(1./((Av*(1./v)).^2)) */
467: MatMult(user->Av,user->uwork,user->Swork);
468: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
469: VecReciprocal(user->Swork);
471: /* (Av * (sdiag(1./v) * b)) */
472: VecPointwiseMult(user->uwork,user->uwork,X);
473: MatMult(user->Av,user->uwork,user->Twork);
475: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
476: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
478: if (user->ns == 1) {
479: /* (sdiag(Grad*y(:,i)) */
480: MatMult(user->Grad,user->y,user->Twork);
482: /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
483: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
484: MatMultTranspose(user->Grad,user->Swork,Y);
485: } else {
486: for (i=0;i<user->ns;i++) {
487: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
488: Scatter(Y,user->subq,user->yi_scatter[i],0,0);
490: MatMult(user->Grad,user->suby,user->Twork);
491: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
492: MatMultTranspose(user->Grad,user->Twork,user->subq);
493: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
494: Gather(Y,user->subq,user->yi_scatter[i],0,0);
495: }
496: }
497: return(0);
498: }
502: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
503: {
505: PetscInt i;
506: AppCtx *user;
509: MatShellGetContext(J_shell,(void**)&user);
510: VecZeroEntries(Y);
512: /* Sdiag = 1./((Av*(1./v)).^2) */
513: VecSet(user->uwork,0);
514: VecAXPY(user->uwork,-1.0,user->u);
515: VecExp(user->uwork);
516: MatMult(user->Av,user->uwork,user->Swork);
517: VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
518: VecReciprocal(user->Sdiag);
520: for (i=0;i<user->ns;i++) {
521: Scatter(X,user->subq,user->yi_scatter[i],0,0);
522: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
524: /* Swork = (Div' * b(:,i)) */
525: MatMult(user->Grad,user->subq,user->Swork);
527: /* Twork = Grad*y(:,i) */
528: MatMult(user->Grad,user->suby,user->Twork);
530: /* Twork = sdiag(Twork) * Swork */
531: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
534: /* Swork = pointwisemult(Sdiag,Twork) */
535: VecPointwiseMult(user->Swork,user->Twork,user->Sdiag);
537: /* Ywork = Av' * Swork */
538: MatMultTranspose(user->Av,user->Swork,user->Ywork);
540: /* Ywork = pointwisemult(uwork,Ywork) */
541: VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
542: VecAXPY(Y,1.0,user->Ywork);
543: Gather(X,user->subq,user->yi_scatter[i],0,0);
544: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
545: }
546: return(0);
547: }
551: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
552: {
553: /* C=Ay - q A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
555: PetscReal sum;
556: PetscInt i;
557: AppCtx *user = (AppCtx*)ptr;
560: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
561: if (user->ns == 1) {
562: MatMult(user->Grad,user->y,user->Swork);
563: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
564: MatMultTranspose(user->Grad,user->Swork,C);
565: VecSum(user->y,&sum);
566: sum /= user->ndesign;
567: VecShift(C,sum);
568: } else {
569: for (i=0;i<user->ns;i++) {
570: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
571: Scatter(C,user->subq,user->yi_scatter[i],0,0);
572: MatMult(user->Grad,user->suby,user->Swork);
573: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
574: MatMultTranspose(user->Grad,user->Swork,user->subq);
576: VecSum(user->suby,&sum);
577: sum /= user->ndesign;
578: VecShift(user->subq,sum);
580: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
581: Gather(C,user->subq,user->yi_scatter[i],0,0);
582: }
583: }
584: VecAXPY(C,-1.0,user->q);
585: return(0);
586: }
590: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
591: {
595: VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
596: VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
597: if (sub2) {
598: VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
599: VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
600: }
601: return(0);
602: }
606: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
607: {
611: VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
612: VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
613: if (sub2) {
614: VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
615: VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
616: }
617: return(0);
618: }
622: PetscErrorCode EllipticInitialize(AppCtx *user)
623: {
625: PetscInt m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
626: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
627: PetscReal *x,*y,*z;
628: PetscReal h,meanut;
629: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
630: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
631: IS is_alldesign,is_allstate;
632: IS is_from_d;
633: IS is_from_y;
634: PetscInt lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
635: const PetscInt *ranges, *subranges;
636: PetscMPIInt size;
637: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
638: PetscScalar v,vx,vy,vz;
639: PetscInt offset,subindex,subvec,nrank,kk;
641: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
642: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
643: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
644: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
645: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
646: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
647: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
648: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
650: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
651: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
652: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
653: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
654: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
655: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
656: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
657: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
659: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
660: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
661: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
662: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
663: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
664: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
665: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
666: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
669: MPI_Comm_size(PETSC_COMM_WORLD,&size);
670: PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
671: PetscLogStagePush(user->stages[0]);
673: /* Create u,y,c,x */
674: VecCreate(PETSC_COMM_WORLD,&user->u);
675: VecCreate(PETSC_COMM_WORLD,&user->y);
676: VecCreate(PETSC_COMM_WORLD,&user->c);
677: VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
678: VecSetFromOptions(user->u);
679: VecGetLocalSize(user->u,&ysubnlocal);
680: VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
681: VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
682: VecSetFromOptions(user->y);
683: VecSetFromOptions(user->c);
685: /*
686: *******************************
687: Create scatters for x <-> y,u
688: *******************************
690: If the state vector y and design vector u are partitioned as
691: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
692: then the solution vector x is organized as
693: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
694: The index sets user->s_is and user->d_is correspond to the indices of the
695: state and design variables owned by the current processor.
696: */
697: VecCreate(PETSC_COMM_WORLD,&user->x);
699: VecGetOwnershipRange(user->y,&lo,&hi);
700: VecGetOwnershipRange(user->u,&lo2,&hi2);
702: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
703: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
704: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
705: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);
707: VecSetSizes(user->x,hi-lo+hi2-lo2,user->n);
708: VecSetFromOptions(user->x);
710: VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
711: VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
712: ISDestroy(&is_alldesign);
713: ISDestroy(&is_allstate);
714: /*
715: *******************************
716: Create scatter from y to y_1,y_2,...,y_ns
717: *******************************
718: */
719: PetscMalloc1(user->ns,&user->yi_scatter);
720: VecDuplicate(user->u,&user->suby);
721: VecDuplicate(user->u,&user->subq);
723: VecGetOwnershipRange(user->y,&lo2,&hi2);
724: istart = 0;
725: for (i=0; i<user->ns; i++){
726: VecGetOwnershipRange(user->suby,&lo,&hi);
727: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
728: VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
729: istart = istart + hi-lo;
730: ISDestroy(&is_from_y);
731: }
732: /*
733: *******************************
734: Create scatter from d to d_1,d_2,...,d_ns
735: *******************************
736: */
737: VecCreate(PETSC_COMM_WORLD,&user->subd);
738: VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
739: VecSetFromOptions(user->subd);
740: VecCreate(PETSC_COMM_WORLD,&user->d);
741: VecGetLocalSize(user->subd,&dsubnlocal);
742: VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
743: VecSetFromOptions(user->d);
744: PetscMalloc1(user->ns,&user->di_scatter);
746: VecGetOwnershipRange(user->d,&lo2,&hi2);
747: istart = 0;
748: for (i=0; i<user->ns; i++){
749: VecGetOwnershipRange(user->subd,&lo,&hi);
750: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
751: VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
752: istart = istart + hi-lo;
753: ISDestroy(&is_from_d);
754: }
756: PetscMalloc1(user->mx,&x);
757: PetscMalloc1(user->mx,&y);
758: PetscMalloc1(user->mx,&z);
760: user->ksp_its = 0;
761: user->ksp_its_initial = 0;
763: n = user->mx * user->mx * user->mx;
764: m = 3 * user->mx * user->mx * (user->mx-1);
765: sqrt_beta = PetscSqrtScalar(user->beta);
767: VecCreate(PETSC_COMM_WORLD,&XX);
768: VecCreate(PETSC_COMM_WORLD,&user->q);
769: VecSetSizes(XX,ysubnlocal,n);
770: VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
771: VecSetFromOptions(XX);
772: VecSetFromOptions(user->q);
774: VecDuplicate(XX,&YY);
775: VecDuplicate(XX,&ZZ);
776: VecDuplicate(XX,&XXwork);
777: VecDuplicate(XX,&YYwork);
778: VecDuplicate(XX,&ZZwork);
779: VecDuplicate(XX,&UTwork);
780: VecDuplicate(XX,&user->utrue);
782: /* map for striding q */
783: /*
784: PetscMalloc1((size+1),&ranges);
785: PetscMalloc1((size+1),&subranges); */
786: VecGetOwnershipRanges(user->q,&ranges);
787: VecGetOwnershipRanges(user->u,&subranges);
789: VecGetOwnershipRange(user->q,&lo2,&hi2);
790: VecGetOwnershipRange(user->u,&lo,&hi);
791: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
792: h = 1.0/user->mx;
793: hinv = user->mx;
794: neg_hinv = -hinv;
796: VecGetOwnershipRange(XX,&istart,&iend);
797: for (linear_index=istart; linear_index<iend; linear_index++){
798: i = linear_index % user->mx;
799: j = ((linear_index-i)/user->mx) % user->mx;
800: k = ((linear_index-i)/user->mx-j) / user->mx;
801: vx = h*(i+0.5);
802: vy = h*(j+0.5);
803: vz = h*(k+0.5);
804: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
805: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
806: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
807: for (is=0; is<2; is++){
808: for (js=0; js<2; js++){
809: for (ks=0; ks<2; ks++){
810: ls = is*4 + js*2 + ks;
811: if (ls<user->ns){
812: l =ls*n + linear_index;
813: /* remap */
814: subindex = l%n;
815: subvec = l/n;
816: nrank=0;
817: while (subindex >= subranges[nrank+1]) nrank++;
818: offset = subindex - subranges[nrank];
819: istart=0;
820: for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
821: istart += (subranges[nrank+1]-subranges[nrank])*subvec;
822: l = istart+offset;
823: 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));
824: VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
825: }
826: }
827: }
828: }
829: }
831: VecAssemblyBegin(XX);
832: VecAssemblyEnd(XX);
833: VecAssemblyBegin(YY);
834: VecAssemblyEnd(YY);
835: VecAssemblyBegin(ZZ);
836: VecAssemblyEnd(ZZ);
837: VecAssemblyBegin(user->q);
838: VecAssemblyEnd(user->q);
840: /* Compute true parameter function
841: 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) */
842: VecCopy(XX,XXwork);
843: VecCopy(YY,YYwork);
844: VecCopy(ZZ,ZZwork);
846: VecShift(XXwork,-0.25);
847: VecShift(YYwork,-0.25);
848: VecShift(ZZwork,-0.25);
850: VecPointwiseMult(XXwork,XXwork,XXwork);
851: VecPointwiseMult(YYwork,YYwork,YYwork);
852: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
854: VecCopy(XXwork,UTwork);
855: VecAXPY(UTwork,1.0,YYwork);
856: VecAXPY(UTwork,1.0,ZZwork);
857: VecScale(UTwork,-20.0);
858: VecExp(UTwork);
859: VecCopy(UTwork,user->utrue);
861: VecCopy(XX,XXwork);
862: VecCopy(YY,YYwork);
863: VecCopy(ZZ,ZZwork);
865: VecShift(XXwork,-0.75);
866: VecShift(YYwork,-0.75);
867: VecShift(ZZwork,-0.75);
869: VecPointwiseMult(XXwork,XXwork,XXwork);
870: VecPointwiseMult(YYwork,YYwork,YYwork);
871: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
873: VecCopy(XXwork,UTwork);
874: VecAXPY(UTwork,1.0,YYwork);
875: VecAXPY(UTwork,1.0,ZZwork);
876: VecScale(UTwork,-20.0);
877: VecExp(UTwork);
879: VecAXPY(user->utrue,-1.0,UTwork);
881: VecDestroy(&XX);
882: VecDestroy(&YY);
883: VecDestroy(&ZZ);
884: VecDestroy(&XXwork);
885: VecDestroy(&YYwork);
886: VecDestroy(&ZZwork);
887: VecDestroy(&UTwork);
889: /* Initial guess and reference model */
890: VecDuplicate(user->utrue,&user->ur);
891: VecSum(user->utrue,&meanut);
892: meanut = meanut / n;
893: VecSet(user->ur,meanut);
894: VecCopy(user->ur,user->u);
896: /* Generate Grad matrix */
897: MatCreate(PETSC_COMM_WORLD,&user->Grad);
898: MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
899: MatSetFromOptions(user->Grad);
900: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
901: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
902: MatGetOwnershipRange(user->Grad,&istart,&iend);
904: for (i=istart; i<iend; i++){
905: if (i<m/3){
906: iblock = i / (user->mx-1);
907: j = iblock*user->mx + (i % (user->mx-1));
908: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
909: j = j+1;
910: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
911: }
912: if (i>=m/3 && i<2*m/3){
913: iblock = (i-m/3) / (user->mx*(user->mx-1));
914: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
915: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
916: j = j + user->mx;
917: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
918: }
919: if (i>=2*m/3){
920: j = i-2*m/3;
921: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
922: j = j + user->mx*user->mx;
923: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
924: }
925: }
927: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
928: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
930: /* Generate arithmetic averaging matrix Av */
931: MatCreate(PETSC_COMM_WORLD,&user->Av);
932: MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
933: MatSetFromOptions(user->Av);
934: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
935: MatSeqAIJSetPreallocation(user->Av,2,NULL);
936: MatGetOwnershipRange(user->Av,&istart,&iend);
938: for (i=istart; i<iend; i++){
939: if (i<m/3){
940: iblock = i / (user->mx-1);
941: j = iblock*user->mx + (i % (user->mx-1));
942: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
943: j = j+1;
944: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
945: }
946: if (i>=m/3 && i<2*m/3){
947: iblock = (i-m/3) / (user->mx*(user->mx-1));
948: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
949: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
950: j = j + user->mx;
951: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
952: }
953: if (i>=2*m/3){
954: j = i-2*m/3;
955: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
956: j = j + user->mx*user->mx;
957: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
958: }
959: }
961: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
962: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
964: MatCreate(PETSC_COMM_WORLD,&user->L);
965: MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
966: MatSetFromOptions(user->L);
967: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
968: MatSeqAIJSetPreallocation(user->L,2,NULL);
969: MatGetOwnershipRange(user->L,&istart,&iend);
971: for (i=istart; i<iend; i++){
972: if (i<m/3){
973: iblock = i / (user->mx-1);
974: j = iblock*user->mx + (i % (user->mx-1));
975: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
976: j = j+1;
977: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
978: }
979: if (i>=m/3 && i<2*m/3){
980: iblock = (i-m/3) / (user->mx*(user->mx-1));
981: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
982: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
983: j = j + user->mx;
984: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
985: }
986: if (i>=2*m/3 && i<m){
987: j = i-2*m/3;
988: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
989: j = j + user->mx*user->mx;
990: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
991: }
992: if (i>=m){
993: j = i - m;
994: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
995: }
996: }
997: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
998: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
999: MatScale(user->L,PetscPowScalar(h,1.5));
1001: /* Generate Div matrix */
1002: if (!user->use_ptap) {
1003: /* Generate Div matrix */
1004: MatCreate(PETSC_COMM_WORLD,&user->Div);
1005: MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
1006: MatSetFromOptions(user->Div);
1007: MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
1008: MatSeqAIJSetPreallocation(user->Div,6,NULL);
1009: MatGetOwnershipRange(user->Grad,&istart,&iend);
1011: for (i=istart; i<iend; i++){
1012: if (i<m/3){
1013: iblock = i / (user->mx-1);
1014: j = iblock*user->mx + (i % (user->mx-1));
1015: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1016: j = j+1;
1017: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1018: }
1019: if (i>=m/3 && i<2*m/3){
1020: iblock = (i-m/3) / (user->mx*(user->mx-1));
1021: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
1022: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1023: j = j + user->mx;
1024: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1025: }
1026: if (i>=2*m/3){
1027: j = i-2*m/3;
1028: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
1029: j = j + user->mx*user->mx;
1030: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
1031: }
1032: }
1034: MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
1035: MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
1036: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1037: } else {
1038: MatCreate(PETSC_COMM_WORLD,&user->Diag);
1039: MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
1040: MatSetFromOptions(user->Diag);
1041: MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
1042: MatSeqAIJSetPreallocation(user->Diag,1,NULL);
1043: }
1045: /* Build work vectors and matrices */
1046: VecCreate(PETSC_COMM_WORLD,&user->S);
1047: VecSetSizes(user->S, PETSC_DECIDE, m);
1048: VecSetFromOptions(user->S);
1050: VecCreate(PETSC_COMM_WORLD,&user->lwork);
1051: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1052: VecSetFromOptions(user->lwork);
1054: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
1056: VecDuplicate(user->S,&user->Swork);
1057: VecDuplicate(user->S,&user->Sdiag);
1058: VecDuplicate(user->S,&user->Av_u);
1059: VecDuplicate(user->S,&user->Twork);
1060: VecDuplicate(user->y,&user->ywork);
1061: VecDuplicate(user->u,&user->Ywork);
1062: VecDuplicate(user->u,&user->uwork);
1063: VecDuplicate(user->u,&user->js_diag);
1064: VecDuplicate(user->c,&user->cwork);
1065: VecDuplicate(user->d,&user->dwork);
1067: /* Create a matrix-free shell user->Jd for computing B*x */
1068: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1069: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1070: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1072: /* Compute true state function ytrue given utrue */
1073: VecDuplicate(user->y,&user->ytrue);
1075: /* First compute Av_u = Av*exp(-u) */
1076: VecSet(user->uwork, 0);
1077: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1078: VecExp(user->uwork);
1079: MatMult(user->Av,user->uwork,user->Av_u);
1081: /* Next form DSG = Div*S*Grad */
1082: VecCopy(user->Av_u,user->Swork);
1083: VecReciprocal(user->Swork);
1084: if (user->use_ptap) {
1085: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1086: MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1087: } else {
1088: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1089: MatDiagonalScale(user->Divwork,NULL,user->Swork);
1090: MatMatMultSymbolic(user->Divwork,user->Grad,1.0,&user->DSG);
1091: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1092: }
1094: MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1095: MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1097: if (user->use_lrc == PETSC_TRUE) {
1098: v=PetscSqrtReal(1.0 /user->ndesign);
1099: PetscMalloc1(user->ndesign,&user->ones);
1101: for (i=0;i<user->ndesign;i++) {
1102: user->ones[i]=v;
1103: }
1104: MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1105: MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1106: MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1107: MatCreateLRC(user->DSG,user->Ones,user->Ones,&user->JsBlock);
1108: MatSetUp(user->JsBlock);
1109: } else {
1110: /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1111: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1112: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1113: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1114: }
1115: MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1116: MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1117: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1118: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1119: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1120: MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1121: MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1123: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1124: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1125: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1126: MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1127: MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1129: MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1130: MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1131: /* Now solve for ytrue */
1132: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1133: KSPSetFromOptions(user->solver);
1135: KSPSetOperators(user->solver,user->JsBlock,user->DSG);
1136: user->lcl->solve_type = LCL_FORWARD1;
1137: MatMult(user->JsInv,user->q,user->ytrue);
1138: /* First compute Av_u = Av*exp(-u) */
1139: VecSet(user->uwork,0);
1140: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1141: VecExp(user->uwork);
1142: MatMult(user->Av,user->uwork,user->Av_u);
1144: /* Next update DSG = Div*S*Grad with user->u */
1145: VecCopy(user->Av_u,user->Swork);
1146: VecReciprocal(user->Swork);
1147: if (user->use_ptap) {
1148: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1149: MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1150: } else {
1151: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1152: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1153: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1154: }
1156: /* Now solve for y */
1157: user->lcl->solve_type = LCL_FORWARD1;
1158: MatMult(user->JsInv,user->q,user->y);
1160: user->ksp_its_initial = user->ksp_its;
1161: user->ksp_its = 0;
1162: /* Construct projection matrix Q (blocks) */
1163: MatCreate(PETSC_COMM_WORLD,&user->Q);
1164: MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1165: MatSetFromOptions(user->Q);
1166: MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1167: MatSeqAIJSetPreallocation(user->Q,8,NULL);
1169: for (i=0; i<user->mx; i++){
1170: x[i] = h*(i+0.5);
1171: y[i] = h*(i+0.5);
1172: z[i] = h*(i+0.5);
1173: }
1174: MatGetOwnershipRange(user->Q,&istart,&iend);
1176: nx = user->mx; ny = user->mx; nz = user->mx;
1177: for (i=istart; i<iend; i++){
1179: xri = xr[i];
1180: im = 0;
1181: xim = x[im];
1182: while (xri>xim && im<nx){
1183: im = im+1;
1184: xim = x[im];
1185: }
1186: indx1 = im-1;
1187: indx2 = im;
1188: dx1 = xri - x[indx1];
1189: dx2 = x[indx2] - xri;
1191: yri = yr[i];
1192: im = 0;
1193: yim = y[im];
1194: while (yri>yim && im<ny){
1195: im = im+1;
1196: yim = y[im];
1197: }
1198: indy1 = im-1;
1199: indy2 = im;
1200: dy1 = yri - y[indy1];
1201: dy2 = y[indy2] - yri;
1203: zri = zr[i];
1204: im = 0;
1205: zim = z[im];
1206: while (zri>zim && im<nz){
1207: im = im+1;
1208: zim = z[im];
1209: }
1210: indz1 = im-1;
1211: indz2 = im;
1212: dz1 = zri - z[indz1];
1213: dz2 = z[indz2] - zri;
1215: Dx = x[indx2] - x[indx1];
1216: Dy = y[indy2] - y[indy1];
1217: Dz = z[indz2] - z[indz1];
1219: j = indx1 + indy1*nx + indz1*nx*ny;
1220: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1221: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1223: j = indx1 + indy1*nx + indz2*nx*ny;
1224: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1225: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1227: j = indx1 + indy2*nx + indz1*nx*ny;
1228: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1229: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1231: j = indx1 + indy2*nx + indz2*nx*ny;
1232: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1233: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1235: j = indx2 + indy1*nx + indz1*nx*ny;
1236: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1237: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1239: j = indx2 + indy1*nx + indz2*nx*ny;
1240: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1241: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1243: j = indx2 + indy2*nx + indz1*nx*ny;
1244: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1245: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1247: j = indx2 + indy2*nx + indz2*nx*ny;
1248: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1249: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1250: }
1252: MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1253: MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1254: /* Create MQ (composed of blocks of Q */
1255: MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1256: MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1257: MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);
1259: /* Add noise to the measurement data */
1260: VecSet(user->ywork,1.0);
1261: VecAYPX(user->ywork,user->noise,user->ytrue);
1262: MatMult(user->MQ,user->ywork,user->d);
1264: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1265: PetscFree(x);
1266: PetscFree(y);
1267: PetscFree(z);
1268: PetscLogStagePop();
1269: return(0);
1270: }
1274: PetscErrorCode EllipticDestroy(AppCtx *user)
1275: {
1277: PetscInt i;
1280: MatDestroy(&user->DSG);
1281: KSPDestroy(&user->solver);
1282: MatDestroy(&user->Q);
1283: MatDestroy(&user->MQ);
1284: if (!user->use_ptap) {
1285: MatDestroy(&user->Div);
1286: MatDestroy(&user->Divwork);
1287: } else {
1288: MatDestroy(&user->Diag);
1289: }
1290: if (user->use_lrc) {
1291: MatDestroy(&user->Ones);
1292: }
1294: MatDestroy(&user->Grad);
1295: MatDestroy(&user->Av);
1296: MatDestroy(&user->Avwork);
1297: MatDestroy(&user->L);
1298: MatDestroy(&user->Js);
1299: MatDestroy(&user->Jd);
1300: MatDestroy(&user->JsBlock);
1301: MatDestroy(&user->JsInv);
1303: VecDestroy(&user->x);
1304: VecDestroy(&user->u);
1305: VecDestroy(&user->uwork);
1306: VecDestroy(&user->utrue);
1307: VecDestroy(&user->y);
1308: VecDestroy(&user->ywork);
1309: VecDestroy(&user->ytrue);
1310: VecDestroy(&user->c);
1311: VecDestroy(&user->cwork);
1312: VecDestroy(&user->ur);
1313: VecDestroy(&user->q);
1314: VecDestroy(&user->d);
1315: VecDestroy(&user->dwork);
1316: VecDestroy(&user->lwork);
1317: VecDestroy(&user->S);
1318: VecDestroy(&user->Swork);
1319: VecDestroy(&user->Sdiag);
1320: VecDestroy(&user->Ywork);
1321: VecDestroy(&user->Twork);
1322: VecDestroy(&user->Av_u);
1323: VecDestroy(&user->js_diag);
1324: ISDestroy(&user->s_is);
1325: ISDestroy(&user->d_is);
1326: VecDestroy(&user->suby);
1327: VecDestroy(&user->subd);
1328: VecDestroy(&user->subq);
1329: VecScatterDestroy(&user->state_scatter);
1330: VecScatterDestroy(&user->design_scatter);
1331: for (i=0;i<user->ns;i++) {
1332: VecScatterDestroy(&user->yi_scatter[i]);
1333: VecScatterDestroy(&user->di_scatter[i]);
1334: }
1335: PetscFree(user->yi_scatter);
1336: PetscFree(user->di_scatter);
1337: if (user->use_lrc) {
1338: PetscFree(user->ones);
1339: MatDestroy(&user->Ones);
1340: }
1341: return(0);
1342: }
1346: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1347: {
1349: Vec X;
1350: PetscReal unorm,ynorm;
1351: AppCtx *user = (AppCtx*)ptr;
1354: TaoGetSolutionVector(tao,&X);
1355: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1356: VecAXPY(user->ywork,-1.0,user->ytrue);
1357: VecAXPY(user->uwork,-1.0,user->utrue);
1358: VecNorm(user->uwork,NORM_2,&unorm);
1359: VecNorm(user->ywork,NORM_2,&ynorm);
1360: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1361: return(0);
1362: }