Actual source code: parabolic.c
petsc-3.6.4 2016-04-12
1: #include <petsc/private/taoimpl.h>
3: /*T
4: Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
5: Routines: TaoCreate();
6: Routines: TaoSetType();
7: Routines: TaoSetInitialVector();
8: Routines: TaoSetObjectiveRoutine();
9: Routines: TaoSetGradientRoutine();
10: Routines: TaoSetConstraintsRoutine();
11: Routines: TaoSetJacobianStateRoutine();
12: Routines: TaoSetJacobianDesignRoutine();
13: Routines: TaoSetStateDesignIS();
14: Routines: TaoSetFromOptions();
15: Routines: TaoSetHistory(); TaoGetHistory();
16: Routines: TaoSolve();
17: Routines: TaoGetConvergedReason(); TaoDestroy();
18: Processors: n
19: T*/
21: typedef struct {
22: PetscInt n; /* Number of variables */
23: PetscInt m; /* Number of constraints per time step */
24: PetscInt mx; /* grid points in each direction */
25: PetscInt nt; /* Number of time steps; as of now, must be divisible by 8 */
26: PetscInt ndata; /* Number of data points per sample */
27: PetscInt ns; /* Number of samples */
28: PetscInt *sample_times; /* Times of samples */
29: IS s_is;
30: IS d_is;
32: VecScatter state_scatter;
33: VecScatter design_scatter;
34: VecScatter *yi_scatter;
35: VecScatter *di_scatter;
37: Mat Js,Jd,JsBlockPrec,JsInv,JsBlock;
38: PetscBool jformed,dsg_formed;
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 ht; /* Time step */
45: Mat Qblock,QblockT;
46: Mat L,LT;
47: Mat Div,Divwork;
48: Mat Grad;
49: Mat Av,Avwork,AvT;
50: Mat DSG;
51: Vec q;
52: Vec ur; /* reference */
54: Vec d;
55: Vec dwork;
56: Vec *di;
58: Vec y; /* state variables */
59: Vec ywork;
61: Vec ytrue;
62: Vec *yi,*yiwork;
64: Vec u; /* design variables */
65: Vec uwork;
67: Vec utrue;
68: Vec js_diag;
69: Vec c; /* constraint vector */
70: Vec cwork;
72: Vec lwork;
73: Vec S;
74: Vec Rwork,Swork,Twork;
75: Vec Av_u;
77: KSP solver;
78: PC prec;
80: PetscInt ksp_its;
81: PetscInt ksp_its_initial;
82: } AppCtx;
85: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
86: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
87: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
88: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
89: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void*);
90: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
91: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
92: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
93: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
94: PetscErrorCode ParabolicInitialize(AppCtx *user);
95: PetscErrorCode ParabolicDestroy(AppCtx *user);
96: PetscErrorCode ParabolicMonitor(Tao, void*);
98: PetscErrorCode StateMatMult(Mat,Vec,Vec);
99: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
100: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
101: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
102: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
103: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
104: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
105: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);
107: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
108: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
110: PetscErrorCode Gather_i(Vec,Vec*,VecScatter*,PetscInt);
111: PetscErrorCode Scatter_i(Vec,Vec*,VecScatter*,PetscInt);
113: static char help[]="";
117: int main(int argc, char **argv)
118: {
119: PetscErrorCode ierr;
120: Vec x,x0;
121: Tao tao;
122: TaoConvergedReason reason;
123: AppCtx user;
124: IS is_allstate,is_alldesign;
125: PetscInt lo,hi,hi2,lo2,ksp_old;
126: PetscInt ntests = 1;
127: PetscInt i;
128: int stages[1];
130: PetscInitialize(&argc, &argv, (char*)0,help);
132: user.mx = 8;
133: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,NULL,NULL);
134: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
135: user.nt = 8;
136: PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
137: user.ndata = 64;
138: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
139: user.ns = 8;
140: PetscOptionsInt("-ns","Number of samples","",user.ns,&user.ns,NULL);
141: user.alpha = 1.0;
142: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
143: user.beta = 0.01;
144: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
145: user.noise = 0.01;
146: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);
148: user.m = user.mx*user.mx*user.mx; /* number of constraints per time step */
149: user.n = user.m*(user.nt+1); /* number of variables */
150: user.ht = (PetscReal)1/user.nt;
152: VecCreate(PETSC_COMM_WORLD,&user.u);
153: VecCreate(PETSC_COMM_WORLD,&user.y);
154: VecCreate(PETSC_COMM_WORLD,&user.c);
155: VecSetSizes(user.u,PETSC_DECIDE,user.n-user.m*user.nt);
156: VecSetSizes(user.y,PETSC_DECIDE,user.m*user.nt);
157: VecSetSizes(user.c,PETSC_DECIDE,user.m*user.nt);
158: VecSetFromOptions(user.u);
159: VecSetFromOptions(user.y);
160: VecSetFromOptions(user.c);
162: /* Create scatters for reduced spaces.
163: If the state vector y and design vector u are partitioned as
164: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
165: then the solution vector x is organized as
166: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
167: The index sets user.s_is and user.d_is correspond to the indices of the
168: state and design variables owned by the current processor.
169: */
170: VecCreate(PETSC_COMM_WORLD,&x);
172: VecGetOwnershipRange(user.y,&lo,&hi);
173: VecGetOwnershipRange(user.u,&lo2,&hi2);
175: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
176: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user.s_is);
178: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
179: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user.d_is);
181: VecSetSizes(x,hi-lo+hi2-lo2,user.n);
182: VecSetFromOptions(x);
184: VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
185: VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
186: ISDestroy(&is_alldesign);
187: ISDestroy(&is_allstate);
189: /* Create TAO solver and set desired solution method */
190: TaoCreate(PETSC_COMM_WORLD,&tao);
191: TaoSetType(tao,TAOLCL);
193: /* Set up initial vectors and matrices */
194: ParabolicInitialize(&user);
196: Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
197: VecDuplicate(x,&x0);
198: VecCopy(x,x0);
200: /* Set solution vector with an initial guess */
201: TaoSetInitialVector(tao,x);
202: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
203: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
204: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
206: TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, (void *)&user);
207: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
209: TaoSetFromOptions(tao);
210: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
212: /* SOLVE THE APPLICATION */
213: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
214: PetscOptionsEnd();
215: PetscLogStageRegister("Trials",&stages[0]);
216: PetscLogStagePush(stages[0]);
217: user.ksp_its_initial = user.ksp_its;
218: ksp_old = user.ksp_its;
219: for (i=0; i<ntests; i++){
220: TaoSolve(tao);
221: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
222: VecCopy(x0,x);
223: TaoSetInitialVector(tao,x);
224: }
225: PetscLogStagePop();
226: PetscBarrier((PetscObject)x);
227: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
228: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
229: PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
230: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
231: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
232: PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);
233: TaoGetConvergedReason(tao,&reason);
235: if (reason < 0) {
236: PetscPrintf(MPI_COMM_WORLD, "TAO failed to converge.\n");
237: } else {
238: PetscPrintf(MPI_COMM_WORLD, "Optimization terminated with status %D.\n", reason);
239: }
240: TaoDestroy(&tao);
241: VecDestroy(&x);
242: VecDestroy(&x0);
243: ParabolicDestroy(&user);
245: PetscFinalize();
246: return 0;
247: }
248: /* ------------------------------------------------------------------- */
251: /*
252: dwork = Qy - d
253: lwork = L*(u-ur)
254: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
255: */
256: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
257: {
259: PetscReal d1=0,d2=0;
260: PetscInt i,j;
261: AppCtx *user = (AppCtx*)ptr;
264: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
265: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
266: for (j=0; j<user->ns; j++){
267: i = user->sample_times[j];
268: MatMult(user->Qblock,user->yi[i],user->di[j]);
269: }
270: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
271: VecAXPY(user->dwork,-1.0,user->d);
272: VecDot(user->dwork,user->dwork,&d1);
274: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
275: MatMult(user->L,user->uwork,user->lwork);
276: VecDot(user->lwork,user->lwork,&d2);
278: *f = 0.5 * (d1 + user->alpha*d2);
279: return(0);
280: }
282: /* ------------------------------------------------------------------- */
285: /*
286: state: g_s = Q' *(Qy - d)
287: design: g_d = alpha*L'*L*(u-ur)
288: */
289: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
290: {
292: PetscInt i,j;
293: AppCtx *user = (AppCtx*)ptr;
296: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
297: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
298: for (j=0; j<user->ns; j++){
299: i = user->sample_times[j];
300: MatMult(user->Qblock,user->yi[i],user->di[j]);
301: }
302: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
303: VecAXPY(user->dwork,-1.0,user->d);
304: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
305: VecSet(user->ywork,0.0);
306: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
307: for (j=0; j<user->ns; j++){
308: i = user->sample_times[j];
309: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
310: }
311: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
313: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
314: MatMult(user->L,user->uwork,user->lwork);
315: MatMult(user->LT,user->lwork,user->uwork);
316: VecScale(user->uwork, user->alpha);
317: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
318: return(0);
319: }
323: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
324: {
326: PetscReal d1,d2;
327: PetscInt i,j;
328: AppCtx *user = (AppCtx*)ptr;
331: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
332: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
333: for (j=0; j<user->ns; j++){
334: i = user->sample_times[j];
335: MatMult(user->Qblock,user->yi[i],user->di[j]);
336: }
337: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
338: VecAXPY(user->dwork,-1.0,user->d);
339: VecDot(user->dwork,user->dwork,&d1);
340: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
341: VecSet(user->ywork,0.0);
342: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
343: for (j=0; j<user->ns; j++){
344: i = user->sample_times[j];
345: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
346: }
347: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
349: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
350: MatMult(user->L,user->uwork,user->lwork);
351: VecDot(user->lwork,user->lwork,&d2);
352: MatMult(user->LT,user->lwork,user->uwork);
353: VecScale(user->uwork, user->alpha);
354: *f = 0.5 * (d1 + user->alpha*d2);
356: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
357: return(0);
358: }
360: /* ------------------------------------------------------------------- */
363: /* A
364: MatShell object
365: */
366: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
367: {
369: AppCtx *user = (AppCtx*)ptr;
372: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
373: VecSet(user->uwork,0);
374: VecAXPY(user->uwork,-1.0,user->u);
375: VecExp(user->uwork);
376: MatMult(user->Av,user->uwork,user->Av_u);
377: VecCopy(user->Av_u,user->Swork);
378: VecReciprocal(user->Swork);
379: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
380: MatDiagonalScale(user->Divwork,NULL,user->Swork);
381: if (user->dsg_formed) {
382: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
383: } else {
384: MatMatMultSymbolic(user->Divwork,user->Grad,PETSC_DECIDE,&user->DSG);
385: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
386: user->dsg_formed = PETSC_TRUE;
387: }
389: /* B = speye(nx^3) + ht*DSG; */
390: MatScale(user->DSG,user->ht);
391: MatShift(user->DSG,1.0);
392: return(0);
393: }
395: /* ------------------------------------------------------------------- */
398: /* B */
399: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
400: {
402: AppCtx *user = (AppCtx*)ptr;
405: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
406: return(0);
407: }
411: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
412: {
414: PetscInt i;
415: AppCtx *user;
418: MatShellGetContext(J_shell,(void**)&user);
419: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
420: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
421: for (i=1; i<user->nt; i++){
422: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
423: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
424: }
425: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
426: return(0);
427: }
431: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
432: {
434: PetscInt i;
435: AppCtx *user;
438: MatShellGetContext(J_shell,(void**)&user);
439: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
440: for (i=0; i<user->nt-1; i++){
441: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
442: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
443: }
444: i = user->nt-1;
445: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
446: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
447: return(0);
448: }
452: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
453: {
455: AppCtx *user;
458: MatShellGetContext(J_shell,(void**)&user);
459: MatMult(user->Grad,X,user->Swork);
460: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
461: MatMult(user->Div,user->Swork,Y);
462: VecAYPX(Y,user->ht,X);
463: return(0);
464: }
468: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
469: {
471: PetscInt i;
472: AppCtx *user;
475: MatShellGetContext(J_shell,(void**)&user);
477: /* sdiag(1./v) */
478: VecSet(user->uwork,0);
479: VecAXPY(user->uwork,-1.0,user->u);
480: VecExp(user->uwork);
482: /* sdiag(1./((Av*(1./v)).^2)) */
483: MatMult(user->Av,user->uwork,user->Swork);
484: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
485: VecReciprocal(user->Swork);
487: /* (Av * (sdiag(1./v) * b)) */
488: VecPointwiseMult(user->uwork,user->uwork,X);
489: MatMult(user->Av,user->uwork,user->Twork);
491: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
492: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
494: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
495: for (i=0; i<user->nt; i++){
496: /* (sdiag(Grad*y(:,i)) */
497: MatMult(user->Grad,user->yi[i],user->Twork);
499: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
500: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
501: MatMult(user->Div,user->Twork,user->yiwork[i]);
502: VecScale(user->yiwork[i],user->ht);
503: }
504: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
506: return(0);
507: }
511: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
512: {
514: PetscInt i;
515: AppCtx *user;
518: MatShellGetContext(J_shell,(void**)&user);
520: /* sdiag(1./((Av*(1./v)).^2)) */
521: VecSet(user->uwork,0);
522: VecAXPY(user->uwork,-1.0,user->u);
523: VecExp(user->uwork);
524: MatMult(user->Av,user->uwork,user->Rwork);
525: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
526: VecReciprocal(user->Rwork);
528: VecSet(Y,0.0);
529: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
530: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
531: for (i=0; i<user->nt; i++){
532: /* (Div' * b(:,i)) */
533: MatMult(user->Grad,user->yiwork[i],user->Swork);
535: /* sdiag(Grad*y(:,i)) */
536: MatMult(user->Grad,user->yi[i],user->Twork);
538: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
539: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
541: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
542: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
544: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
545: MatMult(user->AvT,user->Twork,user->yiwork[i]);
547: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
548: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
549: VecAXPY(Y,user->ht,user->yiwork[i]);
550: }
551: return(0);
552: }
556: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
557: {
559: AppCtx *user;
562: PCShellGetContext(PC_shell,(void**)&user);
564: if (user->dsg_formed) {
565: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
566: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
567: return(0);
568: }
572: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
573: {
575: AppCtx *user;
576: PetscInt its,i;
579: MatShellGetContext(J_shell,(void**)&user);
581: if (Y == user->ytrue) {
582: /* First solve is done with true solution to set up problem */
583: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
584: } else {
585: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
586: }
588: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
589: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
590: KSPGetIterationNumber(user->solver,&its);
591: user->ksp_its = user->ksp_its + its;
593: for (i=1; i<user->nt; i++){
594: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
595: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
596: KSPGetIterationNumber(user->solver,&its);
597: user->ksp_its = user->ksp_its + its;
598: }
599: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
600: return(0);
601: }
605: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
606: {
608: AppCtx *user;
609: PetscInt its,i;
612: MatShellGetContext(J_shell,(void**)&user);
614: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
616: i = user->nt - 1;
617: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
619: KSPGetIterationNumber(user->solver,&its);
620: user->ksp_its = user->ksp_its + its;
622: for (i=user->nt-2; i>=0; i--){
623: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
624: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
626: KSPGetIterationNumber(user->solver,&its);
627: user->ksp_its = user->ksp_its + its;
629: }
631: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
632: return(0);
633: }
637: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
638: {
640: AppCtx *user;
643: MatShellGetContext(J_shell,(void**)&user);
645: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
646: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
647: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
648: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
649: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
650: return(0);
651: }
655: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
656: {
658: AppCtx *user;
661: MatShellGetContext(J_shell,(void**)&user);
662: VecCopy(user->js_diag,X);
663: return(0);
665: }
669: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
670: {
671: /* con = Ay - q, A = [B 0 0 ... 0;
672: -I B 0 ... 0;
673: 0 -I B ... 0;
674: ... ;
675: 0 ... -I B]
676: B = ht * Div * Sigma * Grad + eye */
678: PetscInt i;
679: AppCtx *user = (AppCtx*)ptr;
682: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
683: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
684: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
685: for (i=1; i<user->nt; i++){
686: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
687: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
688: }
689: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
690: VecAXPY(C,-1.0,user->q);
691: return(0);
692: }
697: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
698: {
702: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
703: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
704: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
705: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
706: return(0);
707: }
711: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
712: {
714: PetscInt i;
717: for (i=0; i<nt; i++){
718: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
719: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
720: }
721: return(0);
722: }
727: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
728: {
732: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
733: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
734: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
735: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
736: return(0);
737: }
741: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
742: {
744: PetscInt i;
747: for (i=0; i<nt; i++){
748: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
749: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
750: }
751: return(0);
752: }
756: PetscErrorCode ParabolicInitialize(AppCtx *user)
757: {
759: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
760: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
761: PetscReal *x, *y, *z;
762: PetscReal h,stime;
763: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
764: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
765: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
766: PetscScalar v,vx,vy,vz;
767: IS is_from_y,is_to_yi,is_from_d,is_to_di;
768: /* Data locations */
769: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
770: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
771: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
772: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
773: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
774: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
775: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
776: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
778: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
779: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
780: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
781: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
782: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
783: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
784: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
785: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
787: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
788: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
789: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
790: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
791: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
792: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
793: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
794: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
797: PetscMalloc1(user->mx,&x);
798: PetscMalloc1(user->mx,&y);
799: PetscMalloc1(user->mx,&z);
800: user->jformed = PETSC_FALSE;
801: user->dsg_formed = PETSC_FALSE;
803: n = user->mx * user->mx * user->mx;
804: m = 3 * user->mx * user->mx * (user->mx-1);
805: sqrt_beta = PetscSqrtScalar(user->beta);
807: user->ksp_its = 0;
808: user->ksp_its_initial = 0;
810: stime = (PetscReal)user->nt/user->ns;
811: PetscMalloc1(user->ns,&user->sample_times);
812: for (i=0; i<user->ns; i++){
813: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
814: }
816: VecCreate(PETSC_COMM_WORLD,&XX);
817: VecCreate(PETSC_COMM_WORLD,&user->q);
818: VecSetSizes(XX,PETSC_DECIDE,n);
819: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
820: VecSetFromOptions(XX);
821: VecSetFromOptions(user->q);
823: VecDuplicate(XX,&YY);
824: VecDuplicate(XX,&ZZ);
825: VecDuplicate(XX,&XXwork);
826: VecDuplicate(XX,&YYwork);
827: VecDuplicate(XX,&ZZwork);
828: VecDuplicate(XX,&UTwork);
829: VecDuplicate(XX,&user->utrue);
830: VecDuplicate(XX,&bc);
832: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
833: h = 1.0/user->mx;
834: hinv = user->mx;
835: neg_hinv = -hinv;
837: VecGetOwnershipRange(XX,&istart,&iend);
838: for (linear_index=istart; linear_index<iend; linear_index++){
839: i = linear_index % user->mx;
840: j = ((linear_index-i)/user->mx) % user->mx;
841: k = ((linear_index-i)/user->mx-j) / user->mx;
842: vx = h*(i+0.5);
843: vy = h*(j+0.5);
844: vz = h*(k+0.5);
845: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
846: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
847: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
848: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)){
849: v = 1000.0;
850: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
851: }
852: }
854: VecAssemblyBegin(XX);
855: VecAssemblyEnd(XX);
856: VecAssemblyBegin(YY);
857: VecAssemblyEnd(YY);
858: VecAssemblyBegin(ZZ);
859: VecAssemblyEnd(ZZ);
860: VecAssemblyBegin(bc);
861: VecAssemblyEnd(bc);
863: /* Compute true parameter function
864: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
865: VecCopy(XX,XXwork);
866: VecCopy(YY,YYwork);
867: VecCopy(ZZ,ZZwork);
869: VecShift(XXwork,-0.5);
870: VecShift(YYwork,-0.5);
871: VecShift(ZZwork,-0.5);
873: VecPointwiseMult(XXwork,XXwork,XXwork);
874: VecPointwiseMult(YYwork,YYwork,YYwork);
875: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
877: VecCopy(XXwork,user->utrue);
878: VecAXPY(user->utrue,1.0,YYwork);
879: VecAXPY(user->utrue,1.0,ZZwork);
880: VecScale(user->utrue,-10.0);
881: VecExp(user->utrue);
882: VecShift(user->utrue,0.5);
884: VecDestroy(&XX);
885: VecDestroy(&YY);
886: VecDestroy(&ZZ);
887: VecDestroy(&XXwork);
888: VecDestroy(&YYwork);
889: VecDestroy(&ZZwork);
890: VecDestroy(&UTwork);
892: /* Initial guess and reference model */
893: VecDuplicate(user->utrue,&user->ur);
894: VecSet(user->ur,0.0);
896: /* Generate Grad matrix */
897: MatCreate(PETSC_COMM_WORLD,&user->Grad);
898: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,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);
931: /* Generate arithmetic averaging matrix Av */
932: MatCreate(PETSC_COMM_WORLD,&user->Av);
933: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
934: MatSetFromOptions(user->Av);
935: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
936: MatSeqAIJSetPreallocation(user->Av,2,NULL);
937: MatGetOwnershipRange(user->Av,&istart,&iend);
939: for (i=istart; i<iend; i++){
940: if (i<m/3){
941: iblock = i / (user->mx-1);
942: j = iblock*user->mx + (i % (user->mx-1));
943: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
944: j = j+1;
945: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
946: }
947: if (i>=m/3 && i<2*m/3){
948: iblock = (i-m/3) / (user->mx*(user->mx-1));
949: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
950: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
951: j = j + user->mx;
952: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
953: }
954: if (i>=2*m/3){
955: j = i-2*m/3;
956: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
957: j = j + user->mx*user->mx;
958: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
959: }
960: }
962: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
963: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
965: /* Generate transpose of averaging matrix Av */
966: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
968: MatCreate(PETSC_COMM_WORLD,&user->L);
969: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
970: MatSetFromOptions(user->L);
971: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
972: MatSeqAIJSetPreallocation(user->L,2,NULL);
973: MatGetOwnershipRange(user->L,&istart,&iend);
975: for (i=istart; i<iend; i++){
976: if (i<m/3){
977: iblock = i / (user->mx-1);
978: j = iblock*user->mx + (i % (user->mx-1));
979: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
980: j = j+1;
981: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
982: }
983: if (i>=m/3 && i<2*m/3){
984: iblock = (i-m/3) / (user->mx*(user->mx-1));
985: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
986: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
987: j = j + user->mx;
988: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
989: }
990: if (i>=2*m/3 && i<m){
991: j = i-2*m/3;
992: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
993: j = j + user->mx*user->mx;
994: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
995: }
996: if (i>=m){
997: j = i - m;
998: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
999: }
1000: }
1002: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
1003: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
1005: MatScale(user->L,PetscPowScalar(h,1.5));
1007: /* Generate Div matrix */
1008: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
1010: /* Build work vectors and matrices */
1011: VecCreate(PETSC_COMM_WORLD,&user->S);
1012: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
1013: VecSetFromOptions(user->S);
1015: VecCreate(PETSC_COMM_WORLD,&user->lwork);
1016: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1017: VecSetFromOptions(user->lwork);
1019: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1020: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
1022: VecCreate(PETSC_COMM_WORLD,&user->d);
1023: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
1024: VecSetFromOptions(user->d);
1026: VecDuplicate(user->S,&user->Swork);
1027: VecDuplicate(user->S,&user->Av_u);
1028: VecDuplicate(user->S,&user->Twork);
1029: VecDuplicate(user->S,&user->Rwork);
1030: VecDuplicate(user->y,&user->ywork);
1031: VecDuplicate(user->u,&user->uwork);
1032: VecDuplicate(user->u,&user->js_diag);
1033: VecDuplicate(user->c,&user->cwork);
1034: VecDuplicate(user->d,&user->dwork);
1036: /* Create matrix-free shell user->Js for computing A*x */
1037: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
1038: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1039: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1040: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1041: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
1043: /* Diagonal blocks of user->Js */
1044: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
1045: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1046: /* Blocks are symmetric */
1047: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
1049: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1050: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1051: This is an SSOR preconditioner for user->JsBlock. */
1052: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
1053: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1054: /* JsBlockPrec is symmetric */
1055: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1056: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1058: /* Create a matrix-free shell user->Jd for computing B*x */
1059: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1060: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1061: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1063: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1064: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1065: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1066: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1068: /* Solver options and tolerances */
1069: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1070: KSPSetType(user->solver,KSPCG);
1071: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1072: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1073: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1074: KSPGetPC(user->solver,&user->prec);
1075: PCSetType(user->prec,PCSHELL);
1077: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1078: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1079: PCShellSetContext(user->prec,user);
1081: /* Create scatter from y to y_1,y_2,...,y_nt */
1082: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1083: VecCreate(PETSC_COMM_WORLD,&yi);
1084: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1085: VecSetFromOptions(yi);
1086: VecDuplicateVecs(yi,user->nt,&user->yi);
1087: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1089: VecGetOwnershipRange(user->y,&lo2,&hi2);
1090: istart = 0;
1091: for (i=0; i<user->nt; i++){
1092: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1093: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1094: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1095: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1096: istart = istart + hi-lo;
1097: ISDestroy(&is_to_yi);
1098: ISDestroy(&is_from_y);
1099: }
1100: VecDestroy(&yi);
1102: /* Create scatter from d to d_1,d_2,...,d_ns */
1103: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1104: VecCreate(PETSC_COMM_WORLD,&di);
1105: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1106: VecSetFromOptions(di);
1107: VecDuplicateVecs(di,user->ns,&user->di);
1108: VecGetOwnershipRange(user->d,&lo2,&hi2);
1109: istart = 0;
1110: for (i=0; i<user->ns; i++){
1111: VecGetOwnershipRange(user->di[i],&lo,&hi);
1112: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1113: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1114: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1115: istart = istart + hi-lo;
1116: ISDestroy(&is_to_di);
1117: ISDestroy(&is_from_d);
1118: }
1119: VecDestroy(&di);
1121: /* Assemble RHS of forward problem */
1122: VecCopy(bc,user->yiwork[0]);
1123: for (i=1; i<user->nt; i++){
1124: VecSet(user->yiwork[i],0.0);
1125: }
1126: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1127: VecDestroy(&bc);
1129: /* Compute true state function yt given ut */
1130: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1131: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1132: VecSetFromOptions(user->ytrue);
1134: /* First compute Av_u = Av*exp(-u) */
1135: VecSet(user->uwork,0);
1136: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1137: VecExp(user->uwork);
1138: MatMult(user->Av,user->uwork,user->Av_u);
1140: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1141: user->dsg_formed = PETSC_TRUE;
1143: /* Next form DSG = Div*S*Grad */
1144: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1145: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1146: if (user->dsg_formed) {
1147: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1148: } else {
1149: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1150: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1151: user->dsg_formed = PETSC_TRUE;
1152: }
1153: /* B = speye(nx^3) + ht*DSG; */
1154: MatScale(user->DSG,user->ht);
1155: MatShift(user->DSG,1.0);
1157: /* Now solve for ytrue */
1158: StateMatInvMult(user->Js,user->q,user->ytrue);
1160: /* Initial guess y0 for state given u0 */
1162: /* First compute Av_u = Av*exp(-u) */
1163: VecSet(user->uwork,0);
1164: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1165: VecExp(user->uwork);
1166: MatMult(user->Av,user->uwork,user->Av_u);
1168: /* Next form DSG = Div*S*Grad */
1169: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1170: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1171: if (user->dsg_formed) {
1172: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1173: } else {
1174: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1175: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1176: user->dsg_formed = PETSC_TRUE;
1177: }
1178: /* B = speye(nx^3) + ht*DSG; */
1179: MatScale(user->DSG,user->ht);
1180: MatShift(user->DSG,1.0);
1182: /* Now solve for y */
1183: StateMatInvMult(user->Js,user->q,user->y);
1185: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1186: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1187: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1188: MatSetFromOptions(user->Qblock);
1189: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1190: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1192: for (i=0; i<user->mx; i++){
1193: x[i] = h*(i+0.5);
1194: y[i] = h*(i+0.5);
1195: z[i] = h*(i+0.5);
1196: }
1198: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1199: nx = user->mx; ny = user->mx; nz = user->mx;
1200: for (i=istart; i<iend; i++){
1201: xri = xr[i];
1202: im = 0;
1203: xim = x[im];
1204: while (xri>xim && im<nx){
1205: im = im+1;
1206: xim = x[im];
1207: }
1208: indx1 = im-1;
1209: indx2 = im;
1210: dx1 = xri - x[indx1];
1211: dx2 = x[indx2] - xri;
1213: yri = yr[i];
1214: im = 0;
1215: yim = y[im];
1216: while (yri>yim && im<ny){
1217: im = im+1;
1218: yim = y[im];
1219: }
1220: indy1 = im-1;
1221: indy2 = im;
1222: dy1 = yri - y[indy1];
1223: dy2 = y[indy2] - yri;
1225: zri = zr[i];
1226: im = 0;
1227: zim = z[im];
1228: while (zri>zim && im<nz){
1229: im = im+1;
1230: zim = z[im];
1231: }
1232: indz1 = im-1;
1233: indz2 = im;
1234: dz1 = zri - z[indz1];
1235: dz2 = z[indz2] - zri;
1237: Dx = x[indx2] - x[indx1];
1238: Dy = y[indy2] - y[indy1];
1239: Dz = z[indz2] - z[indz1];
1241: j = indx1 + indy1*nx + indz1*nx*ny;
1242: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1243: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1245: j = indx1 + indy1*nx + indz2*nx*ny;
1246: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1247: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1249: j = indx1 + indy2*nx + indz1*nx*ny;
1250: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1251: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1253: j = indx1 + indy2*nx + indz2*nx*ny;
1254: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1255: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1257: j = indx2 + indy1*nx + indz1*nx*ny;
1258: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1259: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1261: j = indx2 + indy1*nx + indz2*nx*ny;
1262: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1263: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1265: j = indx2 + indy2*nx + indz1*nx*ny;
1266: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1267: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1269: j = indx2 + indy2*nx + indz2*nx*ny;
1270: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1271: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1272: }
1273: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1274: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1276: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1277: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1279: /* Add noise to the measurement data */
1280: VecSet(user->ywork,1.0);
1281: VecAYPX(user->ywork,user->noise,user->ytrue);
1282: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1283: for (j=0; j<user->ns; j++){
1284: i = user->sample_times[j];
1285: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1286: }
1287: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1289: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1290: KSPSetFromOptions(user->solver);
1291: PetscFree(x);
1292: PetscFree(y);
1293: PetscFree(z);
1294: return(0);
1295: }
1299: PetscErrorCode ParabolicDestroy(AppCtx *user)
1300: {
1302: PetscInt i;
1305: MatDestroy(&user->Qblock);
1306: MatDestroy(&user->QblockT);
1307: MatDestroy(&user->Div);
1308: MatDestroy(&user->Divwork);
1309: MatDestroy(&user->Grad);
1310: MatDestroy(&user->Av);
1311: MatDestroy(&user->Avwork);
1312: MatDestroy(&user->AvT);
1313: MatDestroy(&user->DSG);
1314: MatDestroy(&user->L);
1315: MatDestroy(&user->LT);
1316: KSPDestroy(&user->solver);
1317: MatDestroy(&user->Js);
1318: MatDestroy(&user->Jd);
1319: MatDestroy(&user->JsInv);
1320: MatDestroy(&user->JsBlock);
1321: MatDestroy(&user->JsBlockPrec);
1322: VecDestroy(&user->u);
1323: VecDestroy(&user->uwork);
1324: VecDestroy(&user->utrue);
1325: VecDestroy(&user->y);
1326: VecDestroy(&user->ywork);
1327: VecDestroy(&user->ytrue);
1328: VecDestroyVecs(user->nt,&user->yi);
1329: VecDestroyVecs(user->nt,&user->yiwork);
1330: VecDestroyVecs(user->ns,&user->di);
1331: PetscFree(user->yi);
1332: PetscFree(user->yiwork);
1333: PetscFree(user->di);
1334: VecDestroy(&user->c);
1335: VecDestroy(&user->cwork);
1336: VecDestroy(&user->ur);
1337: VecDestroy(&user->q);
1338: VecDestroy(&user->d);
1339: VecDestroy(&user->dwork);
1340: VecDestroy(&user->lwork);
1341: VecDestroy(&user->S);
1342: VecDestroy(&user->Swork);
1343: VecDestroy(&user->Av_u);
1344: VecDestroy(&user->Twork);
1345: VecDestroy(&user->Rwork);
1346: VecDestroy(&user->js_diag);
1347: ISDestroy(&user->s_is);
1348: ISDestroy(&user->d_is);
1349: VecScatterDestroy(&user->state_scatter);
1350: VecScatterDestroy(&user->design_scatter);
1351: for (i=0; i<user->nt; i++){
1352: VecScatterDestroy(&user->yi_scatter[i]);
1353: }
1354: for (i=0; i<user->ns; i++){
1355: VecScatterDestroy(&user->di_scatter[i]);
1356: }
1357: PetscFree(user->yi_scatter);
1358: PetscFree(user->di_scatter);
1359: PetscFree(user->sample_times);
1360: return(0);
1361: }
1365: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1366: {
1368: Vec X;
1369: PetscReal unorm,ynorm;
1370: AppCtx *user = (AppCtx*)ptr;
1373: TaoGetSolutionVector(tao,&X);
1374: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1375: VecAXPY(user->ywork,-1.0,user->ytrue);
1376: VecAXPY(user->uwork,-1.0,user->utrue);
1377: VecNorm(user->uwork,NORM_2,&unorm);
1378: VecNorm(user->ywork,NORM_2,&ynorm);
1379: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1380: return(0);
1381: }