Actual source code: parabolic.c
petsc-3.7.5 2017-01-01
1: #include <petsc/private/taoimpl.h>
3: /*T
4: Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
5: Routines: TaoCreate();
6: Routines: TaoSetType();
7: Routines: TaoSetInitialVector();
8: Routines: TaoSetObjectiveRoutine();
9: Routines: TaoSetGradientRoutine();
10: Routines: TaoSetConstraintsRoutine();
11: Routines: TaoSetJacobianStateRoutine();
12: Routines: TaoSetJacobianDesignRoutine();
13: Routines: TaoSetStateDesignIS();
14: Routines: TaoSetFromOptions();
15: Routines: TaoSetHistory(); TaoGetHistory();
16: Routines: TaoSolve();
17: Routines: TaoDestroy();
18: Processors: n
19: T*/
21: typedef struct {
22: PetscInt n; /* Number of 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: AppCtx user;
123: IS is_allstate,is_alldesign;
124: PetscInt lo,hi,hi2,lo2,ksp_old;
125: PetscInt ntests = 1;
126: PetscInt i;
127: #if defined(PETSC_USE_LOG)
128: PetscLogStage stages[1];
129: #endif
131: 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);
234: TaoDestroy(&tao);
235: VecDestroy(&x);
236: VecDestroy(&x0);
237: ParabolicDestroy(&user);
239: PetscFinalize();
240: return 0;
241: }
242: /* ------------------------------------------------------------------- */
245: /*
246: dwork = Qy - d
247: lwork = L*(u-ur)
248: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
249: */
250: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
251: {
253: PetscReal d1=0,d2=0;
254: PetscInt i,j;
255: AppCtx *user = (AppCtx*)ptr;
258: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
259: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
260: for (j=0; j<user->ns; j++){
261: i = user->sample_times[j];
262: MatMult(user->Qblock,user->yi[i],user->di[j]);
263: }
264: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
265: VecAXPY(user->dwork,-1.0,user->d);
266: VecDot(user->dwork,user->dwork,&d1);
268: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
269: MatMult(user->L,user->uwork,user->lwork);
270: VecDot(user->lwork,user->lwork,&d2);
272: *f = 0.5 * (d1 + user->alpha*d2);
273: return(0);
274: }
276: /* ------------------------------------------------------------------- */
279: /*
280: state: g_s = Q' *(Qy - d)
281: design: g_d = alpha*L'*L*(u-ur)
282: */
283: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
284: {
286: PetscInt i,j;
287: AppCtx *user = (AppCtx*)ptr;
290: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
291: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
292: for (j=0; j<user->ns; j++){
293: i = user->sample_times[j];
294: MatMult(user->Qblock,user->yi[i],user->di[j]);
295: }
296: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
297: VecAXPY(user->dwork,-1.0,user->d);
298: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
299: VecSet(user->ywork,0.0);
300: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
301: for (j=0; j<user->ns; j++){
302: i = user->sample_times[j];
303: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
304: }
305: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
307: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
308: MatMult(user->L,user->uwork,user->lwork);
309: MatMult(user->LT,user->lwork,user->uwork);
310: VecScale(user->uwork, user->alpha);
311: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
312: return(0);
313: }
317: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
318: {
320: PetscReal d1,d2;
321: PetscInt i,j;
322: AppCtx *user = (AppCtx*)ptr;
325: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
326: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
327: for (j=0; j<user->ns; j++){
328: i = user->sample_times[j];
329: MatMult(user->Qblock,user->yi[i],user->di[j]);
330: }
331: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
332: VecAXPY(user->dwork,-1.0,user->d);
333: VecDot(user->dwork,user->dwork,&d1);
334: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
335: VecSet(user->ywork,0.0);
336: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
337: for (j=0; j<user->ns; j++){
338: i = user->sample_times[j];
339: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
340: }
341: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
343: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
344: MatMult(user->L,user->uwork,user->lwork);
345: VecDot(user->lwork,user->lwork,&d2);
346: MatMult(user->LT,user->lwork,user->uwork);
347: VecScale(user->uwork, user->alpha);
348: *f = 0.5 * (d1 + user->alpha*d2);
350: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
351: return(0);
352: }
354: /* ------------------------------------------------------------------- */
357: /* A
358: MatShell object
359: */
360: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
361: {
363: AppCtx *user = (AppCtx*)ptr;
366: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
367: VecSet(user->uwork,0);
368: VecAXPY(user->uwork,-1.0,user->u);
369: VecExp(user->uwork);
370: MatMult(user->Av,user->uwork,user->Av_u);
371: VecCopy(user->Av_u,user->Swork);
372: VecReciprocal(user->Swork);
373: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
374: MatDiagonalScale(user->Divwork,NULL,user->Swork);
375: if (user->dsg_formed) {
376: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
377: } else {
378: MatMatMultSymbolic(user->Divwork,user->Grad,PETSC_DECIDE,&user->DSG);
379: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
380: user->dsg_formed = PETSC_TRUE;
381: }
383: /* B = speye(nx^3) + ht*DSG; */
384: MatScale(user->DSG,user->ht);
385: MatShift(user->DSG,1.0);
386: return(0);
387: }
389: /* ------------------------------------------------------------------- */
392: /* B */
393: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
394: {
396: AppCtx *user = (AppCtx*)ptr;
399: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
400: return(0);
401: }
405: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
406: {
408: PetscInt i;
409: AppCtx *user;
412: MatShellGetContext(J_shell,(void**)&user);
413: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
414: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
415: for (i=1; i<user->nt; i++){
416: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
417: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
418: }
419: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
420: return(0);
421: }
425: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
426: {
428: PetscInt i;
429: AppCtx *user;
432: MatShellGetContext(J_shell,(void**)&user);
433: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
434: for (i=0; i<user->nt-1; i++){
435: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
436: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
437: }
438: i = user->nt-1;
439: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
440: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
441: return(0);
442: }
446: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
447: {
449: AppCtx *user;
452: MatShellGetContext(J_shell,(void**)&user);
453: MatMult(user->Grad,X,user->Swork);
454: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
455: MatMult(user->Div,user->Swork,Y);
456: VecAYPX(Y,user->ht,X);
457: return(0);
458: }
462: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
463: {
465: PetscInt i;
466: AppCtx *user;
469: MatShellGetContext(J_shell,(void**)&user);
471: /* sdiag(1./v) */
472: VecSet(user->uwork,0);
473: VecAXPY(user->uwork,-1.0,user->u);
474: VecExp(user->uwork);
476: /* sdiag(1./((Av*(1./v)).^2)) */
477: MatMult(user->Av,user->uwork,user->Swork);
478: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
479: VecReciprocal(user->Swork);
481: /* (Av * (sdiag(1./v) * b)) */
482: VecPointwiseMult(user->uwork,user->uwork,X);
483: MatMult(user->Av,user->uwork,user->Twork);
485: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
486: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
488: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
489: for (i=0; i<user->nt; i++){
490: /* (sdiag(Grad*y(:,i)) */
491: MatMult(user->Grad,user->yi[i],user->Twork);
493: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
494: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
495: MatMult(user->Div,user->Twork,user->yiwork[i]);
496: VecScale(user->yiwork[i],user->ht);
497: }
498: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
500: return(0);
501: }
505: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
506: {
508: PetscInt i;
509: AppCtx *user;
512: MatShellGetContext(J_shell,(void**)&user);
514: /* sdiag(1./((Av*(1./v)).^2)) */
515: VecSet(user->uwork,0);
516: VecAXPY(user->uwork,-1.0,user->u);
517: VecExp(user->uwork);
518: MatMult(user->Av,user->uwork,user->Rwork);
519: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
520: VecReciprocal(user->Rwork);
522: VecSet(Y,0.0);
523: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
524: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
525: for (i=0; i<user->nt; i++){
526: /* (Div' * b(:,i)) */
527: MatMult(user->Grad,user->yiwork[i],user->Swork);
529: /* sdiag(Grad*y(:,i)) */
530: MatMult(user->Grad,user->yi[i],user->Twork);
532: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
533: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
535: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
536: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
538: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
539: MatMult(user->AvT,user->Twork,user->yiwork[i]);
541: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
542: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
543: VecAXPY(Y,user->ht,user->yiwork[i]);
544: }
545: return(0);
546: }
550: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
551: {
553: AppCtx *user;
556: PCShellGetContext(PC_shell,(void**)&user);
558: if (user->dsg_formed) {
559: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
560: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
561: return(0);
562: }
566: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
567: {
569: AppCtx *user;
570: PetscInt its,i;
573: MatShellGetContext(J_shell,(void**)&user);
575: if (Y == user->ytrue) {
576: /* First solve is done with true solution to set up problem */
577: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
578: } else {
579: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
580: }
582: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
583: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
584: KSPGetIterationNumber(user->solver,&its);
585: user->ksp_its = user->ksp_its + its;
587: for (i=1; i<user->nt; i++){
588: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
589: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
590: KSPGetIterationNumber(user->solver,&its);
591: user->ksp_its = user->ksp_its + its;
592: }
593: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
594: return(0);
595: }
599: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
600: {
602: AppCtx *user;
603: PetscInt its,i;
606: MatShellGetContext(J_shell,(void**)&user);
608: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
610: i = user->nt - 1;
611: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
613: KSPGetIterationNumber(user->solver,&its);
614: user->ksp_its = user->ksp_its + its;
616: for (i=user->nt-2; i>=0; i--){
617: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
618: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
620: KSPGetIterationNumber(user->solver,&its);
621: user->ksp_its = user->ksp_its + its;
623: }
625: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
626: return(0);
627: }
631: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
632: {
634: AppCtx *user;
637: MatShellGetContext(J_shell,(void**)&user);
639: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
640: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
641: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
642: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
643: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
644: return(0);
645: }
649: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
650: {
652: AppCtx *user;
655: MatShellGetContext(J_shell,(void**)&user);
656: VecCopy(user->js_diag,X);
657: return(0);
659: }
663: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
664: {
665: /* con = Ay - q, A = [B 0 0 ... 0;
666: -I B 0 ... 0;
667: 0 -I B ... 0;
668: ... ;
669: 0 ... -I B]
670: B = ht * Div * Sigma * Grad + eye */
672: PetscInt i;
673: AppCtx *user = (AppCtx*)ptr;
676: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
677: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
678: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
679: for (i=1; i<user->nt; i++){
680: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
681: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
682: }
683: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
684: VecAXPY(C,-1.0,user->q);
685: return(0);
686: }
691: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
692: {
696: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
697: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
698: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
699: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
700: return(0);
701: }
705: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
706: {
708: PetscInt i;
711: for (i=0; i<nt; i++){
712: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
713: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
714: }
715: return(0);
716: }
721: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
722: {
726: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
727: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
728: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
729: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
730: return(0);
731: }
735: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
736: {
738: PetscInt i;
741: for (i=0; i<nt; i++){
742: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
743: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
744: }
745: return(0);
746: }
750: PetscErrorCode ParabolicInitialize(AppCtx *user)
751: {
753: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
754: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
755: PetscReal *x, *y, *z;
756: PetscReal h,stime;
757: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
758: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
759: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
760: PetscScalar v,vx,vy,vz;
761: IS is_from_y,is_to_yi,is_from_d,is_to_di;
762: /* Data locations */
763: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
764: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
765: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
766: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
767: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
768: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
769: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
770: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
772: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
773: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
774: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
775: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
776: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
777: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
778: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
779: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
781: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
782: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
783: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
784: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
785: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
786: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
787: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
788: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
791: PetscMalloc1(user->mx,&x);
792: PetscMalloc1(user->mx,&y);
793: PetscMalloc1(user->mx,&z);
794: user->jformed = PETSC_FALSE;
795: user->dsg_formed = PETSC_FALSE;
797: n = user->mx * user->mx * user->mx;
798: m = 3 * user->mx * user->mx * (user->mx-1);
799: sqrt_beta = PetscSqrtScalar(user->beta);
801: user->ksp_its = 0;
802: user->ksp_its_initial = 0;
804: stime = (PetscReal)user->nt/user->ns;
805: PetscMalloc1(user->ns,&user->sample_times);
806: for (i=0; i<user->ns; i++){
807: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
808: }
810: VecCreate(PETSC_COMM_WORLD,&XX);
811: VecCreate(PETSC_COMM_WORLD,&user->q);
812: VecSetSizes(XX,PETSC_DECIDE,n);
813: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
814: VecSetFromOptions(XX);
815: VecSetFromOptions(user->q);
817: VecDuplicate(XX,&YY);
818: VecDuplicate(XX,&ZZ);
819: VecDuplicate(XX,&XXwork);
820: VecDuplicate(XX,&YYwork);
821: VecDuplicate(XX,&ZZwork);
822: VecDuplicate(XX,&UTwork);
823: VecDuplicate(XX,&user->utrue);
824: VecDuplicate(XX,&bc);
826: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
827: h = 1.0/user->mx;
828: hinv = user->mx;
829: neg_hinv = -hinv;
831: VecGetOwnershipRange(XX,&istart,&iend);
832: for (linear_index=istart; linear_index<iend; linear_index++){
833: i = linear_index % user->mx;
834: j = ((linear_index-i)/user->mx) % user->mx;
835: k = ((linear_index-i)/user->mx-j) / user->mx;
836: vx = h*(i+0.5);
837: vy = h*(j+0.5);
838: vz = h*(k+0.5);
839: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
840: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
841: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
842: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)){
843: v = 1000.0;
844: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
845: }
846: }
848: VecAssemblyBegin(XX);
849: VecAssemblyEnd(XX);
850: VecAssemblyBegin(YY);
851: VecAssemblyEnd(YY);
852: VecAssemblyBegin(ZZ);
853: VecAssemblyEnd(ZZ);
854: VecAssemblyBegin(bc);
855: VecAssemblyEnd(bc);
857: /* Compute true parameter function
858: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
859: VecCopy(XX,XXwork);
860: VecCopy(YY,YYwork);
861: VecCopy(ZZ,ZZwork);
863: VecShift(XXwork,-0.5);
864: VecShift(YYwork,-0.5);
865: VecShift(ZZwork,-0.5);
867: VecPointwiseMult(XXwork,XXwork,XXwork);
868: VecPointwiseMult(YYwork,YYwork,YYwork);
869: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
871: VecCopy(XXwork,user->utrue);
872: VecAXPY(user->utrue,1.0,YYwork);
873: VecAXPY(user->utrue,1.0,ZZwork);
874: VecScale(user->utrue,-10.0);
875: VecExp(user->utrue);
876: VecShift(user->utrue,0.5);
878: VecDestroy(&XX);
879: VecDestroy(&YY);
880: VecDestroy(&ZZ);
881: VecDestroy(&XXwork);
882: VecDestroy(&YYwork);
883: VecDestroy(&ZZwork);
884: VecDestroy(&UTwork);
886: /* Initial guess and reference model */
887: VecDuplicate(user->utrue,&user->ur);
888: VecSet(user->ur,0.0);
890: /* Generate Grad matrix */
891: MatCreate(PETSC_COMM_WORLD,&user->Grad);
892: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,m,n);
893: MatSetFromOptions(user->Grad);
894: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
895: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
896: MatGetOwnershipRange(user->Grad,&istart,&iend);
898: for (i=istart; i<iend; i++){
899: if (i<m/3){
900: iblock = i / (user->mx-1);
901: j = iblock*user->mx + (i % (user->mx-1));
902: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
903: j = j+1;
904: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
905: }
906: if (i>=m/3 && i<2*m/3){
907: iblock = (i-m/3) / (user->mx*(user->mx-1));
908: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
909: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
910: j = j + user->mx;
911: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
912: }
913: if (i>=2*m/3){
914: j = i-2*m/3;
915: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
916: j = j + user->mx*user->mx;
917: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
918: }
919: }
921: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
922: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
925: /* Generate arithmetic averaging matrix Av */
926: MatCreate(PETSC_COMM_WORLD,&user->Av);
927: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
928: MatSetFromOptions(user->Av);
929: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
930: MatSeqAIJSetPreallocation(user->Av,2,NULL);
931: MatGetOwnershipRange(user->Av,&istart,&iend);
933: for (i=istart; i<iend; i++){
934: if (i<m/3){
935: iblock = i / (user->mx-1);
936: j = iblock*user->mx + (i % (user->mx-1));
937: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
938: j = j+1;
939: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
940: }
941: if (i>=m/3 && i<2*m/3){
942: iblock = (i-m/3) / (user->mx*(user->mx-1));
943: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
944: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
945: j = j + user->mx;
946: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
947: }
948: if (i>=2*m/3){
949: j = i-2*m/3;
950: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
951: j = j + user->mx*user->mx;
952: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
953: }
954: }
956: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
957: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
959: /* Generate transpose of averaging matrix Av */
960: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
962: MatCreate(PETSC_COMM_WORLD,&user->L);
963: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
964: MatSetFromOptions(user->L);
965: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
966: MatSeqAIJSetPreallocation(user->L,2,NULL);
967: MatGetOwnershipRange(user->L,&istart,&iend);
969: for (i=istart; i<iend; i++){
970: if (i<m/3){
971: iblock = i / (user->mx-1);
972: j = iblock*user->mx + (i % (user->mx-1));
973: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
974: j = j+1;
975: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
976: }
977: if (i>=m/3 && i<2*m/3){
978: iblock = (i-m/3) / (user->mx*(user->mx-1));
979: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
980: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
981: j = j + user->mx;
982: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
983: }
984: if (i>=2*m/3 && i<m){
985: j = i-2*m/3;
986: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
987: j = j + user->mx*user->mx;
988: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
989: }
990: if (i>=m){
991: j = i - m;
992: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
993: }
994: }
996: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
997: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
999: MatScale(user->L,PetscPowScalar(h,1.5));
1001: /* Generate Div matrix */
1002: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
1004: /* Build work vectors and matrices */
1005: VecCreate(PETSC_COMM_WORLD,&user->S);
1006: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
1007: VecSetFromOptions(user->S);
1009: VecCreate(PETSC_COMM_WORLD,&user->lwork);
1010: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
1011: VecSetFromOptions(user->lwork);
1013: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1014: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
1016: VecCreate(PETSC_COMM_WORLD,&user->d);
1017: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
1018: VecSetFromOptions(user->d);
1020: VecDuplicate(user->S,&user->Swork);
1021: VecDuplicate(user->S,&user->Av_u);
1022: VecDuplicate(user->S,&user->Twork);
1023: VecDuplicate(user->S,&user->Rwork);
1024: VecDuplicate(user->y,&user->ywork);
1025: VecDuplicate(user->u,&user->uwork);
1026: VecDuplicate(user->u,&user->js_diag);
1027: VecDuplicate(user->c,&user->cwork);
1028: VecDuplicate(user->d,&user->dwork);
1030: /* Create matrix-free shell user->Js for computing A*x */
1031: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
1032: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1033: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1034: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1035: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
1037: /* Diagonal blocks of user->Js */
1038: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
1039: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1040: /* Blocks are symmetric */
1041: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
1043: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1044: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1045: This is an SSOR preconditioner for user->JsBlock. */
1046: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
1047: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1048: /* JsBlockPrec is symmetric */
1049: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1050: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1052: /* Create a matrix-free shell user->Jd for computing B*x */
1053: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1054: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1055: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1057: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1058: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1059: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1060: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1062: /* Solver options and tolerances */
1063: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1064: KSPSetType(user->solver,KSPCG);
1065: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1066: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1067: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1068: KSPSetFromOptions(user->solver);
1069: KSPGetPC(user->solver,&user->prec);
1070: PCSetType(user->prec,PCSHELL);
1072: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1073: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1074: PCShellSetContext(user->prec,user);
1076: /* Create scatter from y to y_1,y_2,...,y_nt */
1077: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1078: VecCreate(PETSC_COMM_WORLD,&yi);
1079: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1080: VecSetFromOptions(yi);
1081: VecDuplicateVecs(yi,user->nt,&user->yi);
1082: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1084: VecGetOwnershipRange(user->y,&lo2,&hi2);
1085: istart = 0;
1086: for (i=0; i<user->nt; i++){
1087: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1088: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1089: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1090: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1091: istart = istart + hi-lo;
1092: ISDestroy(&is_to_yi);
1093: ISDestroy(&is_from_y);
1094: }
1095: VecDestroy(&yi);
1097: /* Create scatter from d to d_1,d_2,...,d_ns */
1098: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1099: VecCreate(PETSC_COMM_WORLD,&di);
1100: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1101: VecSetFromOptions(di);
1102: VecDuplicateVecs(di,user->ns,&user->di);
1103: VecGetOwnershipRange(user->d,&lo2,&hi2);
1104: istart = 0;
1105: for (i=0; i<user->ns; i++){
1106: VecGetOwnershipRange(user->di[i],&lo,&hi);
1107: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1108: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1109: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1110: istart = istart + hi-lo;
1111: ISDestroy(&is_to_di);
1112: ISDestroy(&is_from_d);
1113: }
1114: VecDestroy(&di);
1116: /* Assemble RHS of forward problem */
1117: VecCopy(bc,user->yiwork[0]);
1118: for (i=1; i<user->nt; i++){
1119: VecSet(user->yiwork[i],0.0);
1120: }
1121: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1122: VecDestroy(&bc);
1124: /* Compute true state function yt given ut */
1125: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1126: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1127: VecSetFromOptions(user->ytrue);
1129: /* First compute Av_u = Av*exp(-u) */
1130: VecSet(user->uwork,0);
1131: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1132: VecExp(user->uwork);
1133: MatMult(user->Av,user->uwork,user->Av_u);
1135: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1136: user->dsg_formed = PETSC_TRUE;
1138: /* Next form DSG = Div*S*Grad */
1139: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1140: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1141: if (user->dsg_formed) {
1142: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1143: } else {
1144: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1145: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1146: user->dsg_formed = PETSC_TRUE;
1147: }
1148: /* B = speye(nx^3) + ht*DSG; */
1149: MatScale(user->DSG,user->ht);
1150: MatShift(user->DSG,1.0);
1152: /* Now solve for ytrue */
1153: StateMatInvMult(user->Js,user->q,user->ytrue);
1155: /* Initial guess y0 for state given u0 */
1157: /* First compute Av_u = Av*exp(-u) */
1158: VecSet(user->uwork,0);
1159: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1160: VecExp(user->uwork);
1161: MatMult(user->Av,user->uwork,user->Av_u);
1163: /* Next form DSG = Div*S*Grad */
1164: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1165: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1166: if (user->dsg_formed) {
1167: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1168: } else {
1169: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1170: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1171: user->dsg_formed = PETSC_TRUE;
1172: }
1173: /* B = speye(nx^3) + ht*DSG; */
1174: MatScale(user->DSG,user->ht);
1175: MatShift(user->DSG,1.0);
1177: /* Now solve for y */
1178: StateMatInvMult(user->Js,user->q,user->y);
1180: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1181: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1182: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1183: MatSetFromOptions(user->Qblock);
1184: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1185: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1187: for (i=0; i<user->mx; i++){
1188: x[i] = h*(i+0.5);
1189: y[i] = h*(i+0.5);
1190: z[i] = h*(i+0.5);
1191: }
1193: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1194: nx = user->mx; ny = user->mx; nz = user->mx;
1195: for (i=istart; i<iend; i++){
1196: xri = xr[i];
1197: im = 0;
1198: xim = x[im];
1199: while (xri>xim && im<nx){
1200: im = im+1;
1201: xim = x[im];
1202: }
1203: indx1 = im-1;
1204: indx2 = im;
1205: dx1 = xri - x[indx1];
1206: dx2 = x[indx2] - xri;
1208: yri = yr[i];
1209: im = 0;
1210: yim = y[im];
1211: while (yri>yim && im<ny){
1212: im = im+1;
1213: yim = y[im];
1214: }
1215: indy1 = im-1;
1216: indy2 = im;
1217: dy1 = yri - y[indy1];
1218: dy2 = y[indy2] - yri;
1220: zri = zr[i];
1221: im = 0;
1222: zim = z[im];
1223: while (zri>zim && im<nz){
1224: im = im+1;
1225: zim = z[im];
1226: }
1227: indz1 = im-1;
1228: indz2 = im;
1229: dz1 = zri - z[indz1];
1230: dz2 = z[indz2] - zri;
1232: Dx = x[indx2] - x[indx1];
1233: Dy = y[indy2] - y[indy1];
1234: Dz = z[indz2] - z[indz1];
1236: j = indx1 + indy1*nx + indz1*nx*ny;
1237: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1238: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1240: j = indx1 + indy1*nx + indz2*nx*ny;
1241: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1242: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1244: j = indx1 + indy2*nx + indz1*nx*ny;
1245: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1246: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1248: j = indx1 + indy2*nx + indz2*nx*ny;
1249: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1250: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1252: j = indx2 + indy1*nx + indz1*nx*ny;
1253: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1254: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1256: j = indx2 + indy1*nx + indz2*nx*ny;
1257: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1258: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1260: j = indx2 + indy2*nx + indz1*nx*ny;
1261: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1262: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1264: j = indx2 + indy2*nx + indz2*nx*ny;
1265: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1266: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1267: }
1268: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1269: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1271: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1272: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1274: /* Add noise to the measurement data */
1275: VecSet(user->ywork,1.0);
1276: VecAYPX(user->ywork,user->noise,user->ytrue);
1277: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1278: for (j=0; j<user->ns; j++){
1279: i = user->sample_times[j];
1280: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1281: }
1282: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1284: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1285: KSPSetFromOptions(user->solver);
1286: PetscFree(x);
1287: PetscFree(y);
1288: PetscFree(z);
1289: return(0);
1290: }
1294: PetscErrorCode ParabolicDestroy(AppCtx *user)
1295: {
1297: PetscInt i;
1300: MatDestroy(&user->Qblock);
1301: MatDestroy(&user->QblockT);
1302: MatDestroy(&user->Div);
1303: MatDestroy(&user->Divwork);
1304: MatDestroy(&user->Grad);
1305: MatDestroy(&user->Av);
1306: MatDestroy(&user->Avwork);
1307: MatDestroy(&user->AvT);
1308: MatDestroy(&user->DSG);
1309: MatDestroy(&user->L);
1310: MatDestroy(&user->LT);
1311: KSPDestroy(&user->solver);
1312: MatDestroy(&user->Js);
1313: MatDestroy(&user->Jd);
1314: MatDestroy(&user->JsInv);
1315: MatDestroy(&user->JsBlock);
1316: MatDestroy(&user->JsBlockPrec);
1317: VecDestroy(&user->u);
1318: VecDestroy(&user->uwork);
1319: VecDestroy(&user->utrue);
1320: VecDestroy(&user->y);
1321: VecDestroy(&user->ywork);
1322: VecDestroy(&user->ytrue);
1323: VecDestroyVecs(user->nt,&user->yi);
1324: VecDestroyVecs(user->nt,&user->yiwork);
1325: VecDestroyVecs(user->ns,&user->di);
1326: PetscFree(user->yi);
1327: PetscFree(user->yiwork);
1328: PetscFree(user->di);
1329: VecDestroy(&user->c);
1330: VecDestroy(&user->cwork);
1331: VecDestroy(&user->ur);
1332: VecDestroy(&user->q);
1333: VecDestroy(&user->d);
1334: VecDestroy(&user->dwork);
1335: VecDestroy(&user->lwork);
1336: VecDestroy(&user->S);
1337: VecDestroy(&user->Swork);
1338: VecDestroy(&user->Av_u);
1339: VecDestroy(&user->Twork);
1340: VecDestroy(&user->Rwork);
1341: VecDestroy(&user->js_diag);
1342: ISDestroy(&user->s_is);
1343: ISDestroy(&user->d_is);
1344: VecScatterDestroy(&user->state_scatter);
1345: VecScatterDestroy(&user->design_scatter);
1346: for (i=0; i<user->nt; i++){
1347: VecScatterDestroy(&user->yi_scatter[i]);
1348: }
1349: for (i=0; i<user->ns; i++){
1350: VecScatterDestroy(&user->di_scatter[i]);
1351: }
1352: PetscFree(user->yi_scatter);
1353: PetscFree(user->di_scatter);
1354: PetscFree(user->sample_times);
1355: return(0);
1356: }
1360: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1361: {
1363: Vec X;
1364: PetscReal unorm,ynorm;
1365: AppCtx *user = (AppCtx*)ptr;
1368: TaoGetSolutionVector(tao,&X);
1369: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1370: VecAXPY(user->ywork,-1.0,user->ytrue);
1371: VecAXPY(user->uwork,-1.0,user->utrue);
1372: VecNorm(user->uwork,NORM_2,&unorm);
1373: VecNorm(user->ywork,NORM_2,&ynorm);
1374: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1375: return(0);
1376: }