Actual source code: parabolic.c
petsc-3.8.4 2018-03-24
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[]="";
115: int main(int argc, char **argv)
116: {
117: PetscErrorCode ierr;
118: Vec x,x0;
119: Tao tao;
120: AppCtx user;
121: IS is_allstate,is_alldesign;
122: PetscInt lo,hi,hi2,lo2,ksp_old;
123: PetscInt ntests = 1;
124: PetscInt i;
125: #if defined(PETSC_USE_LOG)
126: PetscLogStage stages[1];
127: #endif
129: PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
130: user.mx = 8;
131: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,NULL,NULL);
132: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
133: user.nt = 8;
134: PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
135: user.ndata = 64;
136: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
137: user.ns = 8;
138: PetscOptionsInt("-ns","Number of samples","",user.ns,&user.ns,NULL);
139: user.alpha = 1.0;
140: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
141: user.beta = 0.01;
142: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
143: user.noise = 0.01;
144: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);
146: user.m = user.mx*user.mx*user.mx; /* number of constraints per time step */
147: user.n = user.m*(user.nt+1); /* number of variables */
148: user.ht = (PetscReal)1/user.nt;
150: VecCreate(PETSC_COMM_WORLD,&user.u);
151: VecCreate(PETSC_COMM_WORLD,&user.y);
152: VecCreate(PETSC_COMM_WORLD,&user.c);
153: VecSetSizes(user.u,PETSC_DECIDE,user.n-user.m*user.nt);
154: VecSetSizes(user.y,PETSC_DECIDE,user.m*user.nt);
155: VecSetSizes(user.c,PETSC_DECIDE,user.m*user.nt);
156: VecSetFromOptions(user.u);
157: VecSetFromOptions(user.y);
158: VecSetFromOptions(user.c);
160: /* Create scatters for reduced spaces.
161: If the state vector y and design vector u are partitioned as
162: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
163: then the solution vector x is organized as
164: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
165: The index sets user.s_is and user.d_is correspond to the indices of the
166: state and design variables owned by the current processor.
167: */
168: VecCreate(PETSC_COMM_WORLD,&x);
170: VecGetOwnershipRange(user.y,&lo,&hi);
171: VecGetOwnershipRange(user.u,&lo2,&hi2);
173: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
174: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user.s_is);
176: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
177: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user.d_is);
179: VecSetSizes(x,hi-lo+hi2-lo2,user.n);
180: VecSetFromOptions(x);
182: VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
183: VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
184: ISDestroy(&is_alldesign);
185: ISDestroy(&is_allstate);
187: /* Create TAO solver and set desired solution method */
188: TaoCreate(PETSC_COMM_WORLD,&tao);
189: TaoSetType(tao,TAOLCL);
191: /* Set up initial vectors and matrices */
192: ParabolicInitialize(&user);
194: Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
195: VecDuplicate(x,&x0);
196: VecCopy(x,x0);
198: /* Set solution vector with an initial guess */
199: TaoSetInitialVector(tao,x);
200: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
201: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
202: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
204: TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, (void *)&user);
205: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
207: TaoSetFromOptions(tao);
208: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
210: /* SOLVE THE APPLICATION */
211: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
212: PetscOptionsEnd();
213: PetscLogStageRegister("Trials",&stages[0]);
214: PetscLogStagePush(stages[0]);
215: user.ksp_its_initial = user.ksp_its;
216: ksp_old = user.ksp_its;
217: for (i=0; i<ntests; i++){
218: TaoSolve(tao);
219: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
220: VecCopy(x0,x);
221: TaoSetInitialVector(tao,x);
222: }
223: PetscLogStagePop();
224: PetscBarrier((PetscObject)x);
225: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
226: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
227: PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
228: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
229: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
230: PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);
232: TaoDestroy(&tao);
233: VecDestroy(&x);
234: VecDestroy(&x0);
235: ParabolicDestroy(&user);
237: PetscFinalize();
238: return ierr;
239: }
240: /* ------------------------------------------------------------------- */
241: /*
242: dwork = Qy - d
243: lwork = L*(u-ur)
244: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
245: */
246: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
247: {
249: PetscReal d1=0,d2=0;
250: PetscInt i,j;
251: AppCtx *user = (AppCtx*)ptr;
254: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
255: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
256: for (j=0; j<user->ns; j++){
257: i = user->sample_times[j];
258: MatMult(user->Qblock,user->yi[i],user->di[j]);
259: }
260: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
261: VecAXPY(user->dwork,-1.0,user->d);
262: VecDot(user->dwork,user->dwork,&d1);
264: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
265: MatMult(user->L,user->uwork,user->lwork);
266: VecDot(user->lwork,user->lwork,&d2);
268: *f = 0.5 * (d1 + user->alpha*d2);
269: return(0);
270: }
272: /* ------------------------------------------------------------------- */
273: /*
274: state: g_s = Q' *(Qy - d)
275: design: g_d = alpha*L'*L*(u-ur)
276: */
277: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
278: {
280: PetscInt i,j;
281: AppCtx *user = (AppCtx*)ptr;
284: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
285: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
286: for (j=0; j<user->ns; j++){
287: i = user->sample_times[j];
288: MatMult(user->Qblock,user->yi[i],user->di[j]);
289: }
290: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
291: VecAXPY(user->dwork,-1.0,user->d);
292: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
293: VecSet(user->ywork,0.0);
294: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
295: for (j=0; j<user->ns; j++){
296: i = user->sample_times[j];
297: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
298: }
299: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
301: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
302: MatMult(user->L,user->uwork,user->lwork);
303: MatMult(user->LT,user->lwork,user->uwork);
304: VecScale(user->uwork, user->alpha);
305: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
306: return(0);
307: }
309: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
310: {
312: PetscReal d1,d2;
313: PetscInt i,j;
314: AppCtx *user = (AppCtx*)ptr;
317: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
318: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
319: for (j=0; j<user->ns; j++){
320: i = user->sample_times[j];
321: MatMult(user->Qblock,user->yi[i],user->di[j]);
322: }
323: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
324: VecAXPY(user->dwork,-1.0,user->d);
325: VecDot(user->dwork,user->dwork,&d1);
326: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
327: VecSet(user->ywork,0.0);
328: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
329: for (j=0; j<user->ns; j++){
330: i = user->sample_times[j];
331: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
332: }
333: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
335: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
336: MatMult(user->L,user->uwork,user->lwork);
337: VecDot(user->lwork,user->lwork,&d2);
338: MatMult(user->LT,user->lwork,user->uwork);
339: VecScale(user->uwork, user->alpha);
340: *f = 0.5 * (d1 + user->alpha*d2);
342: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
343: return(0);
344: }
346: /* ------------------------------------------------------------------- */
347: /* A
348: MatShell object
349: */
350: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
351: {
353: AppCtx *user = (AppCtx*)ptr;
356: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
357: VecSet(user->uwork,0);
358: VecAXPY(user->uwork,-1.0,user->u);
359: VecExp(user->uwork);
360: MatMult(user->Av,user->uwork,user->Av_u);
361: VecCopy(user->Av_u,user->Swork);
362: VecReciprocal(user->Swork);
363: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
364: MatDiagonalScale(user->Divwork,NULL,user->Swork);
365: if (user->dsg_formed) {
366: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
367: } else {
368: MatMatMultSymbolic(user->Divwork,user->Grad,PETSC_DECIDE,&user->DSG);
369: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
370: user->dsg_formed = PETSC_TRUE;
371: }
373: /* B = speye(nx^3) + ht*DSG; */
374: MatScale(user->DSG,user->ht);
375: MatShift(user->DSG,1.0);
376: return(0);
377: }
379: /* ------------------------------------------------------------------- */
380: /* B */
381: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
382: {
384: AppCtx *user = (AppCtx*)ptr;
387: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
388: return(0);
389: }
391: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
392: {
394: PetscInt i;
395: AppCtx *user;
398: MatShellGetContext(J_shell,(void**)&user);
399: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
400: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
401: for (i=1; i<user->nt; i++){
402: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
403: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
404: }
405: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
406: return(0);
407: }
409: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
410: {
412: PetscInt i;
413: AppCtx *user;
416: MatShellGetContext(J_shell,(void**)&user);
417: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
418: for (i=0; i<user->nt-1; i++){
419: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
420: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
421: }
422: i = user->nt-1;
423: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
424: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
425: return(0);
426: }
428: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
429: {
431: AppCtx *user;
434: MatShellGetContext(J_shell,(void**)&user);
435: MatMult(user->Grad,X,user->Swork);
436: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
437: MatMult(user->Div,user->Swork,Y);
438: VecAYPX(Y,user->ht,X);
439: return(0);
440: }
442: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
443: {
445: PetscInt i;
446: AppCtx *user;
449: MatShellGetContext(J_shell,(void**)&user);
451: /* sdiag(1./v) */
452: VecSet(user->uwork,0);
453: VecAXPY(user->uwork,-1.0,user->u);
454: VecExp(user->uwork);
456: /* sdiag(1./((Av*(1./v)).^2)) */
457: MatMult(user->Av,user->uwork,user->Swork);
458: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
459: VecReciprocal(user->Swork);
461: /* (Av * (sdiag(1./v) * b)) */
462: VecPointwiseMult(user->uwork,user->uwork,X);
463: MatMult(user->Av,user->uwork,user->Twork);
465: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
466: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
468: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
469: for (i=0; i<user->nt; i++){
470: /* (sdiag(Grad*y(:,i)) */
471: MatMult(user->Grad,user->yi[i],user->Twork);
473: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
474: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
475: MatMult(user->Div,user->Twork,user->yiwork[i]);
476: VecScale(user->yiwork[i],user->ht);
477: }
478: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
480: return(0);
481: }
483: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
484: {
486: PetscInt i;
487: AppCtx *user;
490: MatShellGetContext(J_shell,(void**)&user);
492: /* sdiag(1./((Av*(1./v)).^2)) */
493: VecSet(user->uwork,0);
494: VecAXPY(user->uwork,-1.0,user->u);
495: VecExp(user->uwork);
496: MatMult(user->Av,user->uwork,user->Rwork);
497: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
498: VecReciprocal(user->Rwork);
500: VecSet(Y,0.0);
501: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
502: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
503: for (i=0; i<user->nt; i++){
504: /* (Div' * b(:,i)) */
505: MatMult(user->Grad,user->yiwork[i],user->Swork);
507: /* sdiag(Grad*y(:,i)) */
508: MatMult(user->Grad,user->yi[i],user->Twork);
510: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
511: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
513: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
514: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
516: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
517: MatMult(user->AvT,user->Twork,user->yiwork[i]);
519: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
520: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
521: VecAXPY(Y,user->ht,user->yiwork[i]);
522: }
523: return(0);
524: }
526: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
527: {
529: AppCtx *user;
532: PCShellGetContext(PC_shell,(void**)&user);
534: if (user->dsg_formed) {
535: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
536: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
537: return(0);
538: }
540: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
541: {
543: AppCtx *user;
544: PetscInt its,i;
547: MatShellGetContext(J_shell,(void**)&user);
549: if (Y == user->ytrue) {
550: /* First solve is done with true solution to set up problem */
551: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
552: } else {
553: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
554: }
556: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
557: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
558: KSPGetIterationNumber(user->solver,&its);
559: user->ksp_its = user->ksp_its + its;
561: for (i=1; i<user->nt; i++){
562: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
563: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
564: KSPGetIterationNumber(user->solver,&its);
565: user->ksp_its = user->ksp_its + its;
566: }
567: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
568: return(0);
569: }
571: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
572: {
574: AppCtx *user;
575: PetscInt its,i;
578: MatShellGetContext(J_shell,(void**)&user);
580: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
582: i = user->nt - 1;
583: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
585: KSPGetIterationNumber(user->solver,&its);
586: user->ksp_its = user->ksp_its + its;
588: for (i=user->nt-2; i>=0; i--){
589: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
590: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
592: KSPGetIterationNumber(user->solver,&its);
593: user->ksp_its = user->ksp_its + its;
595: }
597: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
598: return(0);
599: }
601: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
602: {
604: AppCtx *user;
607: MatShellGetContext(J_shell,(void**)&user);
609: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
610: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
611: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
612: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
613: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
614: return(0);
615: }
617: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
618: {
620: AppCtx *user;
623: MatShellGetContext(J_shell,(void**)&user);
624: VecCopy(user->js_diag,X);
625: return(0);
627: }
629: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
630: {
631: /* con = Ay - q, A = [B 0 0 ... 0;
632: -I B 0 ... 0;
633: 0 -I B ... 0;
634: ... ;
635: 0 ... -I B]
636: B = ht * Div * Sigma * Grad + eye */
638: PetscInt i;
639: AppCtx *user = (AppCtx*)ptr;
642: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
643: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
644: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
645: for (i=1; i<user->nt; i++){
646: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
647: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
648: }
649: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
650: VecAXPY(C,-1.0,user->q);
651: return(0);
652: }
655: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
656: {
660: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
661: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
662: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
663: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
664: return(0);
665: }
667: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
668: {
670: PetscInt i;
673: for (i=0; i<nt; i++){
674: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
675: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
676: }
677: return(0);
678: }
681: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
682: {
686: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
687: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
688: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
689: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
690: return(0);
691: }
693: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
694: {
696: PetscInt i;
699: for (i=0; i<nt; i++){
700: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
701: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
702: }
703: return(0);
704: }
706: PetscErrorCode ParabolicInitialize(AppCtx *user)
707: {
709: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
710: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
711: PetscReal *x, *y, *z;
712: PetscReal h,stime;
713: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
714: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
715: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
716: PetscScalar v,vx,vy,vz;
717: IS is_from_y,is_to_yi,is_from_d,is_to_di;
718: /* Data locations */
719: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
720: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
721: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
722: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
723: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
724: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
725: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
726: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
728: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
729: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
730: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
731: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
732: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
733: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
734: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
735: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
737: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
738: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
739: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
740: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
741: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
742: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
743: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
744: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
747: PetscMalloc1(user->mx,&x);
748: PetscMalloc1(user->mx,&y);
749: PetscMalloc1(user->mx,&z);
750: user->jformed = PETSC_FALSE;
751: user->dsg_formed = PETSC_FALSE;
753: n = user->mx * user->mx * user->mx;
754: m = 3 * user->mx * user->mx * (user->mx-1);
755: sqrt_beta = PetscSqrtScalar(user->beta);
757: user->ksp_its = 0;
758: user->ksp_its_initial = 0;
760: stime = (PetscReal)user->nt/user->ns;
761: PetscMalloc1(user->ns,&user->sample_times);
762: for (i=0; i<user->ns; i++){
763: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
764: }
766: VecCreate(PETSC_COMM_WORLD,&XX);
767: VecCreate(PETSC_COMM_WORLD,&user->q);
768: VecSetSizes(XX,PETSC_DECIDE,n);
769: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
770: VecSetFromOptions(XX);
771: VecSetFromOptions(user->q);
773: VecDuplicate(XX,&YY);
774: VecDuplicate(XX,&ZZ);
775: VecDuplicate(XX,&XXwork);
776: VecDuplicate(XX,&YYwork);
777: VecDuplicate(XX,&ZZwork);
778: VecDuplicate(XX,&UTwork);
779: VecDuplicate(XX,&user->utrue);
780: VecDuplicate(XX,&bc);
782: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
783: h = 1.0/user->mx;
784: hinv = user->mx;
785: neg_hinv = -hinv;
787: VecGetOwnershipRange(XX,&istart,&iend);
788: for (linear_index=istart; linear_index<iend; linear_index++){
789: i = linear_index % user->mx;
790: j = ((linear_index-i)/user->mx) % user->mx;
791: k = ((linear_index-i)/user->mx-j) / user->mx;
792: vx = h*(i+0.5);
793: vy = h*(j+0.5);
794: vz = h*(k+0.5);
795: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
796: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
797: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
798: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)){
799: v = 1000.0;
800: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
801: }
802: }
804: VecAssemblyBegin(XX);
805: VecAssemblyEnd(XX);
806: VecAssemblyBegin(YY);
807: VecAssemblyEnd(YY);
808: VecAssemblyBegin(ZZ);
809: VecAssemblyEnd(ZZ);
810: VecAssemblyBegin(bc);
811: VecAssemblyEnd(bc);
813: /* Compute true parameter function
814: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
815: VecCopy(XX,XXwork);
816: VecCopy(YY,YYwork);
817: VecCopy(ZZ,ZZwork);
819: VecShift(XXwork,-0.5);
820: VecShift(YYwork,-0.5);
821: VecShift(ZZwork,-0.5);
823: VecPointwiseMult(XXwork,XXwork,XXwork);
824: VecPointwiseMult(YYwork,YYwork,YYwork);
825: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
827: VecCopy(XXwork,user->utrue);
828: VecAXPY(user->utrue,1.0,YYwork);
829: VecAXPY(user->utrue,1.0,ZZwork);
830: VecScale(user->utrue,-10.0);
831: VecExp(user->utrue);
832: VecShift(user->utrue,0.5);
834: VecDestroy(&XX);
835: VecDestroy(&YY);
836: VecDestroy(&ZZ);
837: VecDestroy(&XXwork);
838: VecDestroy(&YYwork);
839: VecDestroy(&ZZwork);
840: VecDestroy(&UTwork);
842: /* Initial guess and reference model */
843: VecDuplicate(user->utrue,&user->ur);
844: VecSet(user->ur,0.0);
846: /* Generate Grad matrix */
847: MatCreate(PETSC_COMM_WORLD,&user->Grad);
848: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,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);
881: /* Generate arithmetic averaging matrix Av */
882: MatCreate(PETSC_COMM_WORLD,&user->Av);
883: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
884: MatSetFromOptions(user->Av);
885: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
886: MatSeqAIJSetPreallocation(user->Av,2,NULL);
887: MatGetOwnershipRange(user->Av,&istart,&iend);
889: for (i=istart; i<iend; i++){
890: if (i<m/3){
891: iblock = i / (user->mx-1);
892: j = iblock*user->mx + (i % (user->mx-1));
893: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
894: j = j+1;
895: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
896: }
897: if (i>=m/3 && i<2*m/3){
898: iblock = (i-m/3) / (user->mx*(user->mx-1));
899: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
900: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
901: j = j + user->mx;
902: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
903: }
904: if (i>=2*m/3){
905: j = i-2*m/3;
906: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
907: j = j + user->mx*user->mx;
908: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
909: }
910: }
912: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
913: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
915: /* Generate transpose of averaging matrix Av */
916: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
918: MatCreate(PETSC_COMM_WORLD,&user->L);
919: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
920: MatSetFromOptions(user->L);
921: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
922: MatSeqAIJSetPreallocation(user->L,2,NULL);
923: MatGetOwnershipRange(user->L,&istart,&iend);
925: for (i=istart; i<iend; i++){
926: if (i<m/3){
927: iblock = i / (user->mx-1);
928: j = iblock*user->mx + (i % (user->mx-1));
929: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
930: j = j+1;
931: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
932: }
933: if (i>=m/3 && i<2*m/3){
934: iblock = (i-m/3) / (user->mx*(user->mx-1));
935: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
936: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
937: j = j + user->mx;
938: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
939: }
940: if (i>=2*m/3 && i<m){
941: j = i-2*m/3;
942: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
943: j = j + user->mx*user->mx;
944: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
945: }
946: if (i>=m){
947: j = i - m;
948: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
949: }
950: }
952: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
953: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
955: MatScale(user->L,PetscPowScalar(h,1.5));
957: /* Generate Div matrix */
958: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
960: /* Build work vectors and matrices */
961: VecCreate(PETSC_COMM_WORLD,&user->S);
962: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
963: VecSetFromOptions(user->S);
965: VecCreate(PETSC_COMM_WORLD,&user->lwork);
966: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
967: VecSetFromOptions(user->lwork);
969: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
970: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
972: VecCreate(PETSC_COMM_WORLD,&user->d);
973: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
974: VecSetFromOptions(user->d);
976: VecDuplicate(user->S,&user->Swork);
977: VecDuplicate(user->S,&user->Av_u);
978: VecDuplicate(user->S,&user->Twork);
979: VecDuplicate(user->S,&user->Rwork);
980: VecDuplicate(user->y,&user->ywork);
981: VecDuplicate(user->u,&user->uwork);
982: VecDuplicate(user->u,&user->js_diag);
983: VecDuplicate(user->c,&user->cwork);
984: VecDuplicate(user->d,&user->dwork);
986: /* Create matrix-free shell user->Js for computing A*x */
987: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
988: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
989: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
990: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
991: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
993: /* Diagonal blocks of user->Js */
994: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
995: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
996: /* Blocks are symmetric */
997: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
999: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1000: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1001: This is an SSOR preconditioner for user->JsBlock. */
1002: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
1003: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1004: /* JsBlockPrec is symmetric */
1005: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1006: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1008: /* Create a matrix-free shell user->Jd for computing B*x */
1009: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1010: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1011: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1013: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1014: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1015: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1016: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1018: /* Solver options and tolerances */
1019: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1020: KSPSetType(user->solver,KSPCG);
1021: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1022: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1023: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1024: KSPSetFromOptions(user->solver);
1025: KSPGetPC(user->solver,&user->prec);
1026: PCSetType(user->prec,PCSHELL);
1028: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1029: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1030: PCShellSetContext(user->prec,user);
1032: /* Create scatter from y to y_1,y_2,...,y_nt */
1033: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1034: VecCreate(PETSC_COMM_WORLD,&yi);
1035: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1036: VecSetFromOptions(yi);
1037: VecDuplicateVecs(yi,user->nt,&user->yi);
1038: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1040: VecGetOwnershipRange(user->y,&lo2,&hi2);
1041: istart = 0;
1042: for (i=0; i<user->nt; i++){
1043: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1044: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1045: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1046: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1047: istart = istart + hi-lo;
1048: ISDestroy(&is_to_yi);
1049: ISDestroy(&is_from_y);
1050: }
1051: VecDestroy(&yi);
1053: /* Create scatter from d to d_1,d_2,...,d_ns */
1054: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1055: VecCreate(PETSC_COMM_WORLD,&di);
1056: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1057: VecSetFromOptions(di);
1058: VecDuplicateVecs(di,user->ns,&user->di);
1059: VecGetOwnershipRange(user->d,&lo2,&hi2);
1060: istart = 0;
1061: for (i=0; i<user->ns; i++){
1062: VecGetOwnershipRange(user->di[i],&lo,&hi);
1063: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1064: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1065: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1066: istart = istart + hi-lo;
1067: ISDestroy(&is_to_di);
1068: ISDestroy(&is_from_d);
1069: }
1070: VecDestroy(&di);
1072: /* Assemble RHS of forward problem */
1073: VecCopy(bc,user->yiwork[0]);
1074: for (i=1; i<user->nt; i++){
1075: VecSet(user->yiwork[i],0.0);
1076: }
1077: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1078: VecDestroy(&bc);
1080: /* Compute true state function yt given ut */
1081: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1082: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1083: VecSetFromOptions(user->ytrue);
1085: /* First compute Av_u = Av*exp(-u) */
1086: VecSet(user->uwork,0);
1087: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1088: VecExp(user->uwork);
1089: MatMult(user->Av,user->uwork,user->Av_u);
1091: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1092: user->dsg_formed = PETSC_TRUE;
1094: /* Next form DSG = Div*S*Grad */
1095: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1096: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1097: if (user->dsg_formed) {
1098: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1099: } else {
1100: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1101: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1102: user->dsg_formed = PETSC_TRUE;
1103: }
1104: /* B = speye(nx^3) + ht*DSG; */
1105: MatScale(user->DSG,user->ht);
1106: MatShift(user->DSG,1.0);
1108: /* Now solve for ytrue */
1109: StateMatInvMult(user->Js,user->q,user->ytrue);
1111: /* Initial guess y0 for state given u0 */
1113: /* First compute Av_u = Av*exp(-u) */
1114: VecSet(user->uwork,0);
1115: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1116: VecExp(user->uwork);
1117: MatMult(user->Av,user->uwork,user->Av_u);
1119: /* Next form DSG = Div*S*Grad */
1120: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1121: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1122: if (user->dsg_formed) {
1123: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1124: } else {
1125: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1126: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1127: user->dsg_formed = PETSC_TRUE;
1128: }
1129: /* B = speye(nx^3) + ht*DSG; */
1130: MatScale(user->DSG,user->ht);
1131: MatShift(user->DSG,1.0);
1133: /* Now solve for y */
1134: StateMatInvMult(user->Js,user->q,user->y);
1136: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1137: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1138: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1139: MatSetFromOptions(user->Qblock);
1140: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1141: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1143: for (i=0; i<user->mx; i++){
1144: x[i] = h*(i+0.5);
1145: y[i] = h*(i+0.5);
1146: z[i] = h*(i+0.5);
1147: }
1149: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1150: nx = user->mx; ny = user->mx; nz = user->mx;
1151: for (i=istart; i<iend; i++){
1152: xri = xr[i];
1153: im = 0;
1154: xim = x[im];
1155: while (xri>xim && im<nx){
1156: im = im+1;
1157: xim = x[im];
1158: }
1159: indx1 = im-1;
1160: indx2 = im;
1161: dx1 = xri - x[indx1];
1162: dx2 = x[indx2] - xri;
1164: yri = yr[i];
1165: im = 0;
1166: yim = y[im];
1167: while (yri>yim && im<ny){
1168: im = im+1;
1169: yim = y[im];
1170: }
1171: indy1 = im-1;
1172: indy2 = im;
1173: dy1 = yri - y[indy1];
1174: dy2 = y[indy2] - yri;
1176: zri = zr[i];
1177: im = 0;
1178: zim = z[im];
1179: while (zri>zim && im<nz){
1180: im = im+1;
1181: zim = z[im];
1182: }
1183: indz1 = im-1;
1184: indz2 = im;
1185: dz1 = zri - z[indz1];
1186: dz2 = z[indz2] - zri;
1188: Dx = x[indx2] - x[indx1];
1189: Dy = y[indy2] - y[indy1];
1190: Dz = z[indz2] - z[indz1];
1192: j = indx1 + indy1*nx + indz1*nx*ny;
1193: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1194: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1196: j = indx1 + indy1*nx + indz2*nx*ny;
1197: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1198: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1200: j = indx1 + indy2*nx + indz1*nx*ny;
1201: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1202: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1204: j = indx1 + indy2*nx + indz2*nx*ny;
1205: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1206: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1208: j = indx2 + indy1*nx + indz1*nx*ny;
1209: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1210: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1212: j = indx2 + indy1*nx + indz2*nx*ny;
1213: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1214: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1216: j = indx2 + indy2*nx + indz1*nx*ny;
1217: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1218: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1220: j = indx2 + indy2*nx + indz2*nx*ny;
1221: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1222: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1223: }
1224: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1225: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1227: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1228: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1230: /* Add noise to the measurement data */
1231: VecSet(user->ywork,1.0);
1232: VecAYPX(user->ywork,user->noise,user->ytrue);
1233: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1234: for (j=0; j<user->ns; j++){
1235: i = user->sample_times[j];
1236: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1237: }
1238: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1240: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1241: KSPSetFromOptions(user->solver);
1242: PetscFree(x);
1243: PetscFree(y);
1244: PetscFree(z);
1245: return(0);
1246: }
1248: PetscErrorCode ParabolicDestroy(AppCtx *user)
1249: {
1251: PetscInt i;
1254: MatDestroy(&user->Qblock);
1255: MatDestroy(&user->QblockT);
1256: MatDestroy(&user->Div);
1257: MatDestroy(&user->Divwork);
1258: MatDestroy(&user->Grad);
1259: MatDestroy(&user->Av);
1260: MatDestroy(&user->Avwork);
1261: MatDestroy(&user->AvT);
1262: MatDestroy(&user->DSG);
1263: MatDestroy(&user->L);
1264: MatDestroy(&user->LT);
1265: KSPDestroy(&user->solver);
1266: MatDestroy(&user->Js);
1267: MatDestroy(&user->Jd);
1268: MatDestroy(&user->JsInv);
1269: MatDestroy(&user->JsBlock);
1270: MatDestroy(&user->JsBlockPrec);
1271: VecDestroy(&user->u);
1272: VecDestroy(&user->uwork);
1273: VecDestroy(&user->utrue);
1274: VecDestroy(&user->y);
1275: VecDestroy(&user->ywork);
1276: VecDestroy(&user->ytrue);
1277: VecDestroyVecs(user->nt,&user->yi);
1278: VecDestroyVecs(user->nt,&user->yiwork);
1279: VecDestroyVecs(user->ns,&user->di);
1280: PetscFree(user->yi);
1281: PetscFree(user->yiwork);
1282: PetscFree(user->di);
1283: VecDestroy(&user->c);
1284: VecDestroy(&user->cwork);
1285: VecDestroy(&user->ur);
1286: VecDestroy(&user->q);
1287: VecDestroy(&user->d);
1288: VecDestroy(&user->dwork);
1289: VecDestroy(&user->lwork);
1290: VecDestroy(&user->S);
1291: VecDestroy(&user->Swork);
1292: VecDestroy(&user->Av_u);
1293: VecDestroy(&user->Twork);
1294: VecDestroy(&user->Rwork);
1295: VecDestroy(&user->js_diag);
1296: ISDestroy(&user->s_is);
1297: ISDestroy(&user->d_is);
1298: VecScatterDestroy(&user->state_scatter);
1299: VecScatterDestroy(&user->design_scatter);
1300: for (i=0; i<user->nt; i++){
1301: VecScatterDestroy(&user->yi_scatter[i]);
1302: }
1303: for (i=0; i<user->ns; i++){
1304: VecScatterDestroy(&user->di_scatter[i]);
1305: }
1306: PetscFree(user->yi_scatter);
1307: PetscFree(user->di_scatter);
1308: PetscFree(user->sample_times);
1309: return(0);
1310: }
1312: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1313: {
1315: Vec X;
1316: PetscReal unorm,ynorm;
1317: AppCtx *user = (AppCtx*)ptr;
1320: TaoGetSolutionVector(tao,&X);
1321: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1322: VecAXPY(user->ywork,-1.0,user->ytrue);
1323: VecAXPY(user->uwork,-1.0,user->utrue);
1324: VecNorm(user->uwork,NORM_2,&unorm);
1325: VecNorm(user->ywork,NORM_2,&ynorm);
1326: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1327: return(0);
1328: }