Actual source code: elliptic.c
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: TaoSolve();
16: Routines: TaoDestroy();
17: Processors: n
18: 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: PetscLogStage stages[10];
90: PetscBool use_ptap;
91: PetscBool use_lrc;
92: } AppCtx;
94: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
95: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
96: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
97: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
98: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat,void*);
99: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
100: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
101: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
102: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
103: PetscErrorCode EllipticInitialize(AppCtx*);
104: PetscErrorCode EllipticDestroy(AppCtx*);
105: PetscErrorCode EllipticMonitor(Tao, void*);
107: PetscErrorCode StateBlockMatMult(Mat,Vec,Vec);
108: PetscErrorCode StateMatMult(Mat,Vec,Vec);
110: PetscErrorCode StateInvMatMult(Mat,Vec,Vec);
111: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
112: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
114: PetscErrorCode QMatMult(Mat,Vec,Vec);
115: PetscErrorCode QMatMultTranspose(Mat,Vec,Vec);
117: static char help[]="";
119: int main(int argc, char **argv)
120: {
121: PetscErrorCode ierr;
122: Vec x0;
123: Tao tao;
124: AppCtx user;
125: PetscInt ntests = 1;
126: PetscInt i;
128: PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
129: user.mx = 8;
130: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"elliptic example",NULL);
131: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
132: user.ns = 6;
133: PetscOptionsInt("-ns","Number of data samples (1<=ns<=8)","",user.ns,&user.ns,NULL);
134: user.ndata = 64;
135: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
136: user.alpha = 0.1;
137: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
138: user.beta = 0.00001;
139: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
140: user.noise = 0.01;
141: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);
143: user.use_ptap = PETSC_FALSE;
144: PetscOptionsBool("-use_ptap","Use ptap matrix for DSG","",user.use_ptap,&user.use_ptap,NULL);
145: user.use_lrc = PETSC_FALSE;
146: PetscOptionsBool("-use_lrc","Use lrc matrix for Js","",user.use_lrc,&user.use_lrc,NULL);
147: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
148: PetscOptionsEnd();
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);
159: /* Set up initial vectors and matrices */
160: EllipticInitialize(&user);
162: Gather(user.x,user.y,user.state_scatter,user.u,user.design_scatter);
163: VecDuplicate(user.x,&x0);
164: VecCopy(user.x,x0);
166: /* Set solution vector with an initial guess */
167: TaoSetInitialVector(tao,user.x);
168: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
169: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
170: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
172: TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, (void *)&user);
173: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
175: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
176: TaoSetFromOptions(tao);
178: /* SOLVE THE APPLICATION */
179: PetscLogStageRegister("Trials",&user.stages[1]);
180: PetscLogStagePush(user.stages[1]);
181: for (i=0; i<ntests; i++){
182: TaoSolve(tao);
183: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its);
184: VecCopy(x0,user.x);
185: }
186: PetscLogStagePop();
187: PetscBarrier((PetscObject)user.x);
188: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
189: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
191: TaoDestroy(&tao);
192: VecDestroy(&x0);
193: EllipticDestroy(&user);
194: PetscFinalize();
195: return ierr;
196: }
197: /* ------------------------------------------------------------------- */
198: /*
199: dwork = Qy - d
200: lwork = L*(u-ur)
201: f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
202: */
203: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
204: {
206: PetscReal d1=0,d2=0;
207: AppCtx *user = (AppCtx*)ptr;
210: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
211: MatMult(user->MQ,user->y,user->dwork);
212: VecAXPY(user->dwork,-1.0,user->d);
213: VecDot(user->dwork,user->dwork,&d1);
214: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
215: MatMult(user->L,user->uwork,user->lwork);
216: VecDot(user->lwork,user->lwork,&d2);
217: *f = 0.5 * (d1 + user->alpha*d2);
218: return(0);
219: }
221: /* ------------------------------------------------------------------- */
222: /*
223: state: g_s = Q' *(Qy - d)
224: design: g_d = alpha*L'*L*(u-ur)
225: */
226: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
227: {
229: AppCtx *user = (AppCtx*)ptr;
232: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
233: MatMult(user->MQ,user->y,user->dwork);
234: VecAXPY(user->dwork,-1.0,user->d);
235: MatMultTranspose(user->MQ,user->dwork,user->ywork);
236: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
237: MatMult(user->L,user->uwork,user->lwork);
238: MatMultTranspose(user->L,user->lwork,user->uwork);
239: VecScale(user->uwork, user->alpha);
240: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
241: return(0);
242: }
244: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
245: {
247: PetscReal d1,d2;
248: AppCtx *user = (AppCtx*)ptr;
251: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
252: MatMult(user->MQ,user->y,user->dwork);
253: VecAXPY(user->dwork,-1.0,user->d);
254: VecDot(user->dwork,user->dwork,&d1);
255: MatMultTranspose(user->MQ,user->dwork,user->ywork);
257: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
258: MatMult(user->L,user->uwork,user->lwork);
259: VecDot(user->lwork,user->lwork,&d2);
260: MatMultTranspose(user->L,user->lwork,user->uwork);
261: VecScale(user->uwork, user->alpha);
262: *f = 0.5 * (d1 + user->alpha*d2);
263: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
264: return(0);
265: }
267: /* ------------------------------------------------------------------- */
268: /* A
269: MatShell object
270: */
271: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
272: {
274: AppCtx *user = (AppCtx*)ptr;
277: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
278: /* DSG = Div * (1/Av_u) * Grad */
279: VecSet(user->uwork,0);
280: VecAXPY(user->uwork,-1.0,user->u);
281: VecExp(user->uwork);
282: MatMult(user->Av,user->uwork,user->Av_u);
283: VecCopy(user->Av_u,user->Swork);
284: VecReciprocal(user->Swork);
285: if (user->use_ptap) {
286: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
287: MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
288: } else {
289: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
290: MatDiagonalScale(user->Divwork,NULL,user->Swork);
291: MatProductNumeric(user->DSG);
292: }
293: return(0);
294: }
295: /* ------------------------------------------------------------------- */
296: /* B */
297: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
298: {
300: AppCtx *user = (AppCtx*)ptr;
303: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
304: return(0);
305: }
307: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
308: {
310: PetscReal sum;
311: AppCtx *user;
314: MatShellGetContext(J_shell,(void**)&user);
315: MatMult(user->DSG,X,Y);
316: VecSum(X,&sum);
317: sum /= user->ndesign;
318: VecShift(Y,sum);
319: return(0);
320: }
322: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
323: {
325: PetscInt i;
326: AppCtx *user;
329: MatShellGetContext(J_shell,(void**)&user);
330: if (user->ns == 1) {
331: MatMult(user->JsBlock,X,Y);
332: } else {
333: for (i=0;i<user->ns;i++) {
334: Scatter(X,user->subq,user->yi_scatter[i],0,0);
335: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
336: MatMult(user->JsBlock,user->subq,user->suby);
337: Gather(Y,user->suby,user->yi_scatter[i],0,0);
338: }
339: }
340: return(0);
341: }
343: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
344: {
346: PetscInt its,i;
347: AppCtx *user;
350: MatShellGetContext(J_shell,(void**)&user);
351: KSPSetOperators(user->solver,user->JsBlock,user->DSG);
352: if (Y == user->ytrue) {
353: /* First solve is done using true solution to set up problem */
354: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
355: } else {
356: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
357: }
358: if (user->ns == 1) {
359: KSPSolve(user->solver,X,Y);
360: KSPGetIterationNumber(user->solver,&its);
361: user->ksp_its+=its;
362: } else {
363: for (i=0;i<user->ns;i++) {
364: Scatter(X,user->subq,user->yi_scatter[i],0,0);
365: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
366: KSPSolve(user->solver,user->subq,user->suby);
367: KSPGetIterationNumber(user->solver,&its);
368: user->ksp_its+=its;
369: Gather(Y,user->suby,user->yi_scatter[i],0,0);
370: }
371: }
372: return(0);
373: }
374: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
375: {
377: AppCtx *user;
378: PetscInt i;
381: MatShellGetContext(J_shell,(void**)&user);
382: if (user->ns == 1) {
383: MatMult(user->Q,X,Y);
384: } else {
385: for (i=0;i<user->ns;i++) {
386: Scatter(X,user->subq,user->yi_scatter[i],0,0);
387: Scatter(Y,user->subd,user->di_scatter[i],0,0);
388: MatMult(user->Q,user->subq,user->subd);
389: Gather(Y,user->subd,user->di_scatter[i],0,0);
390: }
391: }
392: return(0);
393: }
395: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
396: {
398: AppCtx *user;
399: PetscInt i;
402: MatShellGetContext(J_shell,(void**)&user);
403: if (user->ns == 1) {
404: MatMultTranspose(user->Q,X,Y);
405: } else {
406: for (i=0;i<user->ns;i++) {
407: Scatter(X,user->subd,user->di_scatter[i],0,0);
408: Scatter(Y,user->suby,user->yi_scatter[i],0,0);
409: MatMultTranspose(user->Q,user->subd,user->suby);
410: Gather(Y,user->suby,user->yi_scatter[i],0,0);
411: }
412: }
413: return(0);
414: }
416: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
417: {
419: PetscInt i;
420: AppCtx *user;
423: MatShellGetContext(J_shell,(void**)&user);
425: /* sdiag(1./v) */
426: VecSet(user->uwork,0);
427: VecAXPY(user->uwork,-1.0,user->u);
428: VecExp(user->uwork);
430: /* sdiag(1./((Av*(1./v)).^2)) */
431: MatMult(user->Av,user->uwork,user->Swork);
432: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
433: VecReciprocal(user->Swork);
435: /* (Av * (sdiag(1./v) * b)) */
436: VecPointwiseMult(user->uwork,user->uwork,X);
437: MatMult(user->Av,user->uwork,user->Twork);
439: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
440: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
442: if (user->ns == 1) {
443: /* (sdiag(Grad*y(:,i)) */
444: MatMult(user->Grad,user->y,user->Twork);
446: /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
447: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
448: MatMultTranspose(user->Grad,user->Swork,Y);
449: } else {
450: for (i=0;i<user->ns;i++) {
451: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
452: Scatter(Y,user->subq,user->yi_scatter[i],0,0);
454: MatMult(user->Grad,user->suby,user->Twork);
455: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
456: MatMultTranspose(user->Grad,user->Twork,user->subq);
457: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
458: Gather(Y,user->subq,user->yi_scatter[i],0,0);
459: }
460: }
461: return(0);
462: }
464: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
465: {
467: PetscInt i;
468: AppCtx *user;
471: MatShellGetContext(J_shell,(void**)&user);
472: VecZeroEntries(Y);
474: /* Sdiag = 1./((Av*(1./v)).^2) */
475: VecSet(user->uwork,0);
476: VecAXPY(user->uwork,-1.0,user->u);
477: VecExp(user->uwork);
478: MatMult(user->Av,user->uwork,user->Swork);
479: VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
480: VecReciprocal(user->Sdiag);
482: for (i=0;i<user->ns;i++) {
483: Scatter(X,user->subq,user->yi_scatter[i],0,0);
484: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
486: /* Swork = (Div' * b(:,i)) */
487: MatMult(user->Grad,user->subq,user->Swork);
489: /* Twork = Grad*y(:,i) */
490: MatMult(user->Grad,user->suby,user->Twork);
492: /* Twork = sdiag(Twork) * Swork */
493: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
496: /* Swork = pointwisemult(Sdiag,Twork) */
497: VecPointwiseMult(user->Swork,user->Twork,user->Sdiag);
499: /* Ywork = Av' * Swork */
500: MatMultTranspose(user->Av,user->Swork,user->Ywork);
502: /* Ywork = pointwisemult(uwork,Ywork) */
503: VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
504: VecAXPY(Y,1.0,user->Ywork);
505: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
506: }
507: return(0);
508: }
510: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
511: {
512: /* C=Ay - q A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
514: PetscReal sum;
515: PetscInt i;
516: AppCtx *user = (AppCtx*)ptr;
519: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
520: if (user->ns == 1) {
521: MatMult(user->Grad,user->y,user->Swork);
522: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
523: MatMultTranspose(user->Grad,user->Swork,C);
524: VecSum(user->y,&sum);
525: sum /= user->ndesign;
526: VecShift(C,sum);
527: } else {
528: for (i=0;i<user->ns;i++) {
529: Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
530: Scatter(C,user->subq,user->yi_scatter[i],0,0);
531: MatMult(user->Grad,user->suby,user->Swork);
532: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
533: MatMultTranspose(user->Grad,user->Swork,user->subq);
535: VecSum(user->suby,&sum);
536: sum /= user->ndesign;
537: VecShift(user->subq,sum);
539: Gather(user->y,user->suby,user->yi_scatter[i],0,0);
540: Gather(C,user->subq,user->yi_scatter[i],0,0);
541: }
542: }
543: VecAXPY(C,-1.0,user->q);
544: return(0);
545: }
547: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
548: {
552: VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
553: VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
554: if (sub2) {
555: VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
556: VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
557: }
558: return(0);
559: }
561: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
562: {
566: VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
567: VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
568: if (sub2) {
569: VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
570: VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
571: }
572: return(0);
573: }
575: PetscErrorCode EllipticInitialize(AppCtx *user)
576: {
578: PetscInt m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
579: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
580: PetscReal *x,*y,*z;
581: PetscReal h,meanut;
582: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
583: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
584: IS is_alldesign,is_allstate;
585: IS is_from_d;
586: IS is_from_y;
587: PetscInt lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
588: const PetscInt *ranges, *subranges;
589: PetscMPIInt size;
590: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
591: PetscScalar v,vx,vy,vz;
592: PetscInt offset,subindex,subvec,nrank,kk;
594: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
595: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
596: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
597: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
598: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
599: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
600: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
601: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
603: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
604: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
605: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
606: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
607: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
608: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
609: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
610: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
612: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
613: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
614: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
615: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
616: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
617: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
618: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
619: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
622: MPI_Comm_size(PETSC_COMM_WORLD,&size);
623: PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
624: PetscLogStagePush(user->stages[0]);
626: /* Create u,y,c,x */
627: VecCreate(PETSC_COMM_WORLD,&user->u);
628: VecCreate(PETSC_COMM_WORLD,&user->y);
629: VecCreate(PETSC_COMM_WORLD,&user->c);
630: VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
631: VecSetFromOptions(user->u);
632: VecGetLocalSize(user->u,&ysubnlocal);
633: VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
634: VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
635: VecSetFromOptions(user->y);
636: VecSetFromOptions(user->c);
638: /*
639: *******************************
640: Create scatters for x <-> y,u
641: *******************************
643: If the state vector y and design vector u are partitioned as
644: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
645: then the solution vector x is organized as
646: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
647: The index sets user->s_is and user->d_is correspond to the indices of the
648: state and design variables owned by the current processor.
649: */
650: VecCreate(PETSC_COMM_WORLD,&user->x);
652: VecGetOwnershipRange(user->y,&lo,&hi);
653: VecGetOwnershipRange(user->u,&lo2,&hi2);
655: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
656: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
657: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
658: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);
660: VecSetSizes(user->x,hi-lo+hi2-lo2,user->n);
661: VecSetFromOptions(user->x);
663: VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
664: VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
665: ISDestroy(&is_alldesign);
666: ISDestroy(&is_allstate);
667: /*
668: *******************************
669: Create scatter from y to y_1,y_2,...,y_ns
670: *******************************
671: */
672: PetscMalloc1(user->ns,&user->yi_scatter);
673: VecDuplicate(user->u,&user->suby);
674: VecDuplicate(user->u,&user->subq);
676: VecGetOwnershipRange(user->y,&lo2,&hi2);
677: istart = 0;
678: for (i=0; i<user->ns; i++){
679: VecGetOwnershipRange(user->suby,&lo,&hi);
680: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
681: VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
682: istart = istart + hi-lo;
683: ISDestroy(&is_from_y);
684: }
685: /*
686: *******************************
687: Create scatter from d to d_1,d_2,...,d_ns
688: *******************************
689: */
690: VecCreate(PETSC_COMM_WORLD,&user->subd);
691: VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
692: VecSetFromOptions(user->subd);
693: VecCreate(PETSC_COMM_WORLD,&user->d);
694: VecGetLocalSize(user->subd,&dsubnlocal);
695: VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
696: VecSetFromOptions(user->d);
697: PetscMalloc1(user->ns,&user->di_scatter);
699: VecGetOwnershipRange(user->d,&lo2,&hi2);
700: istart = 0;
701: for (i=0; i<user->ns; i++){
702: VecGetOwnershipRange(user->subd,&lo,&hi);
703: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
704: VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
705: istart = istart + hi-lo;
706: ISDestroy(&is_from_d);
707: }
709: PetscMalloc1(user->mx,&x);
710: PetscMalloc1(user->mx,&y);
711: PetscMalloc1(user->mx,&z);
713: user->ksp_its = 0;
714: user->ksp_its_initial = 0;
716: n = user->mx * user->mx * user->mx;
717: m = 3 * user->mx * user->mx * (user->mx-1);
718: sqrt_beta = PetscSqrtScalar(user->beta);
720: VecCreate(PETSC_COMM_WORLD,&XX);
721: VecCreate(PETSC_COMM_WORLD,&user->q);
722: VecSetSizes(XX,ysubnlocal,n);
723: VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
724: VecSetFromOptions(XX);
725: VecSetFromOptions(user->q);
727: VecDuplicate(XX,&YY);
728: VecDuplicate(XX,&ZZ);
729: VecDuplicate(XX,&XXwork);
730: VecDuplicate(XX,&YYwork);
731: VecDuplicate(XX,&ZZwork);
732: VecDuplicate(XX,&UTwork);
733: VecDuplicate(XX,&user->utrue);
735: /* map for striding q */
736: VecGetOwnershipRanges(user->q,&ranges);
737: VecGetOwnershipRanges(user->u,&subranges);
739: VecGetOwnershipRange(user->q,&lo2,&hi2);
740: VecGetOwnershipRange(user->u,&lo,&hi);
741: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
742: h = 1.0/user->mx;
743: hinv = user->mx;
744: neg_hinv = -hinv;
746: VecGetOwnershipRange(XX,&istart,&iend);
747: for (linear_index=istart; linear_index<iend; linear_index++){
748: i = linear_index % user->mx;
749: j = ((linear_index-i)/user->mx) % user->mx;
750: k = ((linear_index-i)/user->mx-j) / user->mx;
751: vx = h*(i+0.5);
752: vy = h*(j+0.5);
753: vz = h*(k+0.5);
754: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
755: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
756: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
757: for (is=0; is<2; is++){
758: for (js=0; js<2; js++){
759: for (ks=0; ks<2; ks++){
760: ls = is*4 + js*2 + ks;
761: if (ls<user->ns){
762: l =ls*n + linear_index;
763: /* remap */
764: subindex = l%n;
765: subvec = l/n;
766: nrank=0;
767: while (subindex >= subranges[nrank+1]) nrank++;
768: offset = subindex - subranges[nrank];
769: istart=0;
770: for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
771: istart += (subranges[nrank+1]-subranges[nrank])*subvec;
772: l = istart+offset;
773: v = 100*PetscSinScalar(2*PETSC_PI*(vx+0.25*is))*PetscSinScalar(2*PETSC_PI*(vy+0.25*js))*PetscSinScalar(2*PETSC_PI*(vz+0.25*ks));
774: VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
775: }
776: }
777: }
778: }
779: }
781: VecAssemblyBegin(XX);
782: VecAssemblyEnd(XX);
783: VecAssemblyBegin(YY);
784: VecAssemblyEnd(YY);
785: VecAssemblyBegin(ZZ);
786: VecAssemblyEnd(ZZ);
787: VecAssemblyBegin(user->q);
788: VecAssemblyEnd(user->q);
790: /* Compute true parameter function
791: 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) */
792: VecCopy(XX,XXwork);
793: VecCopy(YY,YYwork);
794: VecCopy(ZZ,ZZwork);
796: VecShift(XXwork,-0.25);
797: VecShift(YYwork,-0.25);
798: VecShift(ZZwork,-0.25);
800: VecPointwiseMult(XXwork,XXwork,XXwork);
801: VecPointwiseMult(YYwork,YYwork,YYwork);
802: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
804: VecCopy(XXwork,UTwork);
805: VecAXPY(UTwork,1.0,YYwork);
806: VecAXPY(UTwork,1.0,ZZwork);
807: VecScale(UTwork,-20.0);
808: VecExp(UTwork);
809: VecCopy(UTwork,user->utrue);
811: VecCopy(XX,XXwork);
812: VecCopy(YY,YYwork);
813: VecCopy(ZZ,ZZwork);
815: VecShift(XXwork,-0.75);
816: VecShift(YYwork,-0.75);
817: VecShift(ZZwork,-0.75);
819: VecPointwiseMult(XXwork,XXwork,XXwork);
820: VecPointwiseMult(YYwork,YYwork,YYwork);
821: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
823: VecCopy(XXwork,UTwork);
824: VecAXPY(UTwork,1.0,YYwork);
825: VecAXPY(UTwork,1.0,ZZwork);
826: VecScale(UTwork,-20.0);
827: VecExp(UTwork);
829: VecAXPY(user->utrue,-1.0,UTwork);
831: VecDestroy(&XX);
832: VecDestroy(&YY);
833: VecDestroy(&ZZ);
834: VecDestroy(&XXwork);
835: VecDestroy(&YYwork);
836: VecDestroy(&ZZwork);
837: VecDestroy(&UTwork);
839: /* Initial guess and reference model */
840: VecDuplicate(user->utrue,&user->ur);
841: VecSum(user->utrue,&meanut);
842: meanut = meanut / n;
843: VecSet(user->ur,meanut);
844: VecCopy(user->ur,user->u);
846: /* Generate Grad matrix */
847: MatCreate(PETSC_COMM_WORLD,&user->Grad);
848: MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
849: MatSetFromOptions(user->Grad);
850: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
851: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
852: MatGetOwnershipRange(user->Grad,&istart,&iend);
854: for (i=istart; i<iend; i++){
855: if (i<m/3){
856: iblock = i / (user->mx-1);
857: j = iblock*user->mx + (i % (user->mx-1));
858: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
859: j = j+1;
860: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
861: }
862: if (i>=m/3 && i<2*m/3){
863: iblock = (i-m/3) / (user->mx*(user->mx-1));
864: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
865: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
866: j = j + user->mx;
867: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
868: }
869: if (i>=2*m/3){
870: j = i-2*m/3;
871: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
872: j = j + user->mx*user->mx;
873: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
874: }
875: }
877: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
878: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
880: /* Generate arithmetic averaging matrix Av */
881: MatCreate(PETSC_COMM_WORLD,&user->Av);
882: MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
883: MatSetFromOptions(user->Av);
884: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
885: MatSeqAIJSetPreallocation(user->Av,2,NULL);
886: MatGetOwnershipRange(user->Av,&istart,&iend);
888: for (i=istart; i<iend; i++){
889: if (i<m/3){
890: iblock = i / (user->mx-1);
891: j = iblock*user->mx + (i % (user->mx-1));
892: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
893: j = j+1;
894: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
895: }
896: if (i>=m/3 && i<2*m/3){
897: iblock = (i-m/3) / (user->mx*(user->mx-1));
898: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
899: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
900: j = j + user->mx;
901: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
902: }
903: if (i>=2*m/3){
904: j = i-2*m/3;
905: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
906: j = j + user->mx*user->mx;
907: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
908: }
909: }
911: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
912: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
914: MatCreate(PETSC_COMM_WORLD,&user->L);
915: MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
916: MatSetFromOptions(user->L);
917: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
918: MatSeqAIJSetPreallocation(user->L,2,NULL);
919: MatGetOwnershipRange(user->L,&istart,&iend);
921: for (i=istart; i<iend; i++){
922: if (i<m/3){
923: iblock = i / (user->mx-1);
924: j = iblock*user->mx + (i % (user->mx-1));
925: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
926: j = j+1;
927: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
928: }
929: if (i>=m/3 && i<2*m/3){
930: iblock = (i-m/3) / (user->mx*(user->mx-1));
931: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
932: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
933: j = j + user->mx;
934: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
935: }
936: if (i>=2*m/3 && i<m){
937: j = i-2*m/3;
938: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
939: j = j + user->mx*user->mx;
940: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
941: }
942: if (i>=m){
943: j = i - m;
944: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
945: }
946: }
947: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
948: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
949: MatScale(user->L,PetscPowScalar(h,1.5));
951: /* Generate Div matrix */
952: if (!user->use_ptap) {
953: /* Generate Div matrix */
954: MatCreate(PETSC_COMM_WORLD,&user->Div);
955: MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
956: MatSetFromOptions(user->Div);
957: MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
958: MatSeqAIJSetPreallocation(user->Div,6,NULL);
959: MatGetOwnershipRange(user->Grad,&istart,&iend);
961: for (i=istart; i<iend; i++){
962: if (i<m/3){
963: iblock = i / (user->mx-1);
964: j = iblock*user->mx + (i % (user->mx-1));
965: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
966: j = j+1;
967: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
968: }
969: if (i>=m/3 && i<2*m/3){
970: iblock = (i-m/3) / (user->mx*(user->mx-1));
971: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
972: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
973: j = j + user->mx;
974: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
975: }
976: if (i>=2*m/3){
977: j = i-2*m/3;
978: MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
979: j = j + user->mx*user->mx;
980: MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
981: }
982: }
984: MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
985: MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
986: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
987: } else {
988: MatCreate(PETSC_COMM_WORLD,&user->Diag);
989: MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
990: MatSetFromOptions(user->Diag);
991: MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
992: MatSeqAIJSetPreallocation(user->Diag,1,NULL);
993: }
995: /* Build work vectors and matrices */
996: VecCreate(PETSC_COMM_WORLD,&user->S);
997: VecSetSizes(user->S, PETSC_DECIDE, m);
998: VecSetFromOptions(user->S);
1000: VecCreate(PETSC_COMM_WORLD,&user->lwork);
1001: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1002: VecSetFromOptions(user->lwork);
1004: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
1006: VecDuplicate(user->S,&user->Swork);
1007: VecDuplicate(user->S,&user->Sdiag);
1008: VecDuplicate(user->S,&user->Av_u);
1009: VecDuplicate(user->S,&user->Twork);
1010: VecDuplicate(user->y,&user->ywork);
1011: VecDuplicate(user->u,&user->Ywork);
1012: VecDuplicate(user->u,&user->uwork);
1013: VecDuplicate(user->u,&user->js_diag);
1014: VecDuplicate(user->c,&user->cwork);
1015: VecDuplicate(user->d,&user->dwork);
1017: /* Create a matrix-free shell user->Jd for computing B*x */
1018: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
1019: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1020: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1022: /* Compute true state function ytrue given utrue */
1023: VecDuplicate(user->y,&user->ytrue);
1025: /* First compute Av_u = Av*exp(-u) */
1026: VecSet(user->uwork, 0);
1027: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1028: VecExp(user->uwork);
1029: MatMult(user->Av,user->uwork,user->Av_u);
1031: /* Next form DSG = Div*S*Grad */
1032: VecCopy(user->Av_u,user->Swork);
1033: VecReciprocal(user->Swork);
1034: if (user->use_ptap) {
1035: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1036: MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1037: } else {
1038: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1039: MatDiagonalScale(user->Divwork,NULL,user->Swork);
1041: MatMatMult(user->Divwork,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
1042: }
1044: MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1045: MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1047: if (user->use_lrc == PETSC_TRUE) {
1048: v=PetscSqrtReal(1.0 /user->ndesign);
1049: PetscMalloc1(user->ndesign,&user->ones);
1051: for (i=0;i<user->ndesign;i++) {
1052: user->ones[i]=v;
1053: }
1054: MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
1055: MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
1056: MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
1057: MatCreateLRC(user->DSG,user->Ones,NULL,user->Ones,&user->JsBlock);
1058: MatSetUp(user->JsBlock);
1059: } else {
1060: /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1061: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
1062: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
1063: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
1064: }
1065: MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
1066: MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1067: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
1068: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1069: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
1070: MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
1071: MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1073: MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
1074: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
1075: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
1076: MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
1077: MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1079: MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
1080: MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1081: /* Now solve for ytrue */
1082: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1083: KSPSetFromOptions(user->solver);
1085: KSPSetOperators(user->solver,user->JsBlock,user->DSG);
1087: MatMult(user->JsInv,user->q,user->ytrue);
1088: /* First compute Av_u = Av*exp(-u) */
1089: VecSet(user->uwork,0);
1090: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1091: VecExp(user->uwork);
1092: MatMult(user->Av,user->uwork,user->Av_u);
1094: /* Next update DSG = Div*S*Grad with user->u */
1095: VecCopy(user->Av_u,user->Swork);
1096: VecReciprocal(user->Swork);
1097: if (user->use_ptap) {
1098: MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
1099: MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
1100: } else {
1101: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1102: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1103: MatProductNumeric(user->DSG);
1104: }
1106: /* Now solve for y */
1108: MatMult(user->JsInv,user->q,user->y);
1110: user->ksp_its_initial = user->ksp_its;
1111: user->ksp_its = 0;
1112: /* Construct projection matrix Q (blocks) */
1113: MatCreate(PETSC_COMM_WORLD,&user->Q);
1114: MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
1115: MatSetFromOptions(user->Q);
1116: MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
1117: MatSeqAIJSetPreallocation(user->Q,8,NULL);
1119: for (i=0; i<user->mx; i++){
1120: x[i] = h*(i+0.5);
1121: y[i] = h*(i+0.5);
1122: z[i] = h*(i+0.5);
1123: }
1124: MatGetOwnershipRange(user->Q,&istart,&iend);
1126: nx = user->mx; ny = user->mx; nz = user->mx;
1127: for (i=istart; i<iend; i++){
1129: xri = xr[i];
1130: im = 0;
1131: xim = x[im];
1132: while (xri>xim && im<nx){
1133: im = im+1;
1134: xim = x[im];
1135: }
1136: indx1 = im-1;
1137: indx2 = im;
1138: dx1 = xri - x[indx1];
1139: dx2 = x[indx2] - xri;
1141: yri = yr[i];
1142: im = 0;
1143: yim = y[im];
1144: while (yri>yim && im<ny){
1145: im = im+1;
1146: yim = y[im];
1147: }
1148: indy1 = im-1;
1149: indy2 = im;
1150: dy1 = yri - y[indy1];
1151: dy2 = y[indy2] - yri;
1153: zri = zr[i];
1154: im = 0;
1155: zim = z[im];
1156: while (zri>zim && im<nz){
1157: im = im+1;
1158: zim = z[im];
1159: }
1160: indz1 = im-1;
1161: indz2 = im;
1162: dz1 = zri - z[indz1];
1163: dz2 = z[indz2] - zri;
1165: Dx = x[indx2] - x[indx1];
1166: Dy = y[indy2] - y[indy1];
1167: Dz = z[indz2] - z[indz1];
1169: j = indx1 + indy1*nx + indz1*nx*ny;
1170: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1171: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1173: j = indx1 + indy1*nx + indz2*nx*ny;
1174: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1175: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1177: j = indx1 + indy2*nx + indz1*nx*ny;
1178: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1179: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1181: j = indx1 + indy2*nx + indz2*nx*ny;
1182: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1183: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1185: j = indx2 + indy1*nx + indz1*nx*ny;
1186: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1187: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1189: j = indx2 + indy1*nx + indz2*nx*ny;
1190: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1191: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1193: j = indx2 + indy2*nx + indz1*nx*ny;
1194: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1195: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1197: j = indx2 + indy2*nx + indz2*nx*ny;
1198: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1199: MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
1200: }
1202: MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1203: MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1204: /* Create MQ (composed of blocks of Q */
1205: MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
1206: MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
1207: MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);
1209: /* Add noise to the measurement data */
1210: VecSet(user->ywork,1.0);
1211: VecAYPX(user->ywork,user->noise,user->ytrue);
1212: MatMult(user->MQ,user->ywork,user->d);
1214: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1215: PetscFree(x);
1216: PetscFree(y);
1217: PetscFree(z);
1218: PetscLogStagePop();
1219: return(0);
1220: }
1222: PetscErrorCode EllipticDestroy(AppCtx *user)
1223: {
1225: PetscInt i;
1228: MatDestroy(&user->DSG);
1229: KSPDestroy(&user->solver);
1230: MatDestroy(&user->Q);
1231: MatDestroy(&user->MQ);
1232: if (!user->use_ptap) {
1233: MatDestroy(&user->Div);
1234: MatDestroy(&user->Divwork);
1235: } else {
1236: MatDestroy(&user->Diag);
1237: }
1238: if (user->use_lrc) {
1239: MatDestroy(&user->Ones);
1240: }
1242: MatDestroy(&user->Grad);
1243: MatDestroy(&user->Av);
1244: MatDestroy(&user->Avwork);
1245: MatDestroy(&user->L);
1246: MatDestroy(&user->Js);
1247: MatDestroy(&user->Jd);
1248: MatDestroy(&user->JsBlock);
1249: MatDestroy(&user->JsInv);
1251: VecDestroy(&user->x);
1252: VecDestroy(&user->u);
1253: VecDestroy(&user->uwork);
1254: VecDestroy(&user->utrue);
1255: VecDestroy(&user->y);
1256: VecDestroy(&user->ywork);
1257: VecDestroy(&user->ytrue);
1258: VecDestroy(&user->c);
1259: VecDestroy(&user->cwork);
1260: VecDestroy(&user->ur);
1261: VecDestroy(&user->q);
1262: VecDestroy(&user->d);
1263: VecDestroy(&user->dwork);
1264: VecDestroy(&user->lwork);
1265: VecDestroy(&user->S);
1266: VecDestroy(&user->Swork);
1267: VecDestroy(&user->Sdiag);
1268: VecDestroy(&user->Ywork);
1269: VecDestroy(&user->Twork);
1270: VecDestroy(&user->Av_u);
1271: VecDestroy(&user->js_diag);
1272: ISDestroy(&user->s_is);
1273: ISDestroy(&user->d_is);
1274: VecDestroy(&user->suby);
1275: VecDestroy(&user->subd);
1276: VecDestroy(&user->subq);
1277: VecScatterDestroy(&user->state_scatter);
1278: VecScatterDestroy(&user->design_scatter);
1279: for (i=0;i<user->ns;i++) {
1280: VecScatterDestroy(&user->yi_scatter[i]);
1281: VecScatterDestroy(&user->di_scatter[i]);
1282: }
1283: PetscFree(user->yi_scatter);
1284: PetscFree(user->di_scatter);
1285: if (user->use_lrc) {
1286: PetscFree(user->ones);
1287: MatDestroy(&user->Ones);
1288: }
1289: return(0);
1290: }
1292: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1293: {
1295: Vec X;
1296: PetscReal unorm,ynorm;
1297: AppCtx *user = (AppCtx*)ptr;
1300: TaoGetSolutionVector(tao,&X);
1301: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1302: VecAXPY(user->ywork,-1.0,user->ytrue);
1303: VecAXPY(user->uwork,-1.0,user->utrue);
1304: VecNorm(user->uwork,NORM_2,&unorm);
1305: VecNorm(user->ywork,NORM_2,&ynorm);
1306: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1307: return(0);
1308: }
1313: /*TEST
1315: build:
1316: requires: !complex
1318: test:
1319: args: -tao_cmonitor -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
1320: requires: !single
1322: test:
1323: suffix: 2
1324: args: -tao_cmonitor -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
1325: requires: !single
1327: TEST*/