Actual source code: parabolic.c
petsc-3.11.4 2019-09-28
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*/
23: typedef struct {
24: PetscInt n; /* Number of variables */
25: PetscInt m; /* Number of constraints per time step */
26: PetscInt mx; /* grid points in each direction */
27: PetscInt nt; /* Number of time steps; as of now, must be divisible by 8 */
28: PetscInt ndata; /* Number of data points per sample */
29: PetscInt ns; /* Number of samples */
30: PetscInt *sample_times; /* Times of samples */
31: IS s_is;
32: IS d_is;
34: VecScatter state_scatter;
35: VecScatter design_scatter;
36: VecScatter *yi_scatter;
37: VecScatter *di_scatter;
39: Mat Js,Jd,JsBlockPrec,JsInv,JsBlock;
40: PetscBool jformed,dsg_formed;
42: PetscReal alpha; /* Regularization parameter */
43: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
44: PetscReal noise; /* Amount of noise to add to data */
45: PetscReal ht; /* Time step */
47: Mat Qblock,QblockT;
48: Mat L,LT;
49: Mat Div,Divwork;
50: Mat Grad;
51: Mat Av,Avwork,AvT;
52: Mat DSG;
53: Vec q;
54: Vec ur; /* reference */
56: Vec d;
57: Vec dwork;
58: Vec *di;
60: Vec y; /* state variables */
61: Vec ywork;
63: Vec ytrue;
64: Vec *yi,*yiwork;
66: Vec u; /* design variables */
67: Vec uwork;
69: Vec utrue;
70: Vec js_diag;
71: Vec c; /* constraint vector */
72: Vec cwork;
74: Vec lwork;
75: Vec S;
76: Vec Rwork,Swork,Twork;
77: Vec Av_u;
79: KSP solver;
80: PC prec;
82: PetscInt ksp_its;
83: PetscInt ksp_its_initial;
84: } AppCtx;
87: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
88: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
89: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
90: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
91: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void*);
92: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
93: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
94: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
95: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
96: PetscErrorCode ParabolicInitialize(AppCtx *user);
97: PetscErrorCode ParabolicDestroy(AppCtx *user);
98: PetscErrorCode ParabolicMonitor(Tao, void*);
100: PetscErrorCode StateMatMult(Mat,Vec,Vec);
101: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
102: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
103: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
104: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
105: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
106: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
107: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);
109: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
110: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
112: PetscErrorCode Gather_i(Vec,Vec*,VecScatter*,PetscInt);
113: PetscErrorCode Scatter_i(Vec,Vec*,VecScatter*,PetscInt);
115: 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);if (ierr) return ierr;
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 ierr;
241: }
242: /* ------------------------------------------------------------------- */
243: /*
244: dwork = Qy - d
245: lwork = L*(u-ur)
246: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
247: */
248: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
249: {
251: PetscReal d1=0,d2=0;
252: PetscInt i,j;
253: AppCtx *user = (AppCtx*)ptr;
256: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
257: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
258: for (j=0; j<user->ns; j++){
259: i = user->sample_times[j];
260: MatMult(user->Qblock,user->yi[i],user->di[j]);
261: }
262: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
263: VecAXPY(user->dwork,-1.0,user->d);
264: VecDot(user->dwork,user->dwork,&d1);
266: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
267: MatMult(user->L,user->uwork,user->lwork);
268: VecDot(user->lwork,user->lwork,&d2);
270: *f = 0.5 * (d1 + user->alpha*d2);
271: return(0);
272: }
274: /* ------------------------------------------------------------------- */
275: /*
276: state: g_s = Q' *(Qy - d)
277: design: g_d = alpha*L'*L*(u-ur)
278: */
279: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
280: {
282: PetscInt i,j;
283: AppCtx *user = (AppCtx*)ptr;
286: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
287: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
288: for (j=0; j<user->ns; j++){
289: i = user->sample_times[j];
290: MatMult(user->Qblock,user->yi[i],user->di[j]);
291: }
292: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
293: VecAXPY(user->dwork,-1.0,user->d);
294: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
295: VecSet(user->ywork,0.0);
296: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
297: for (j=0; j<user->ns; j++){
298: i = user->sample_times[j];
299: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
300: }
301: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
303: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
304: MatMult(user->L,user->uwork,user->lwork);
305: MatMult(user->LT,user->lwork,user->uwork);
306: VecScale(user->uwork, user->alpha);
307: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
308: return(0);
309: }
311: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
312: {
314: PetscReal d1,d2;
315: PetscInt i,j;
316: AppCtx *user = (AppCtx*)ptr;
319: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
320: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
321: for (j=0; j<user->ns; j++){
322: i = user->sample_times[j];
323: MatMult(user->Qblock,user->yi[i],user->di[j]);
324: }
325: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
326: VecAXPY(user->dwork,-1.0,user->d);
327: VecDot(user->dwork,user->dwork,&d1);
328: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
329: VecSet(user->ywork,0.0);
330: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
331: for (j=0; j<user->ns; j++){
332: i = user->sample_times[j];
333: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
334: }
335: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
337: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
338: MatMult(user->L,user->uwork,user->lwork);
339: VecDot(user->lwork,user->lwork,&d2);
340: MatMult(user->LT,user->lwork,user->uwork);
341: VecScale(user->uwork, user->alpha);
342: *f = 0.5 * (d1 + user->alpha*d2);
344: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
345: return(0);
346: }
348: /* ------------------------------------------------------------------- */
349: /* A
350: MatShell object
351: */
352: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
353: {
355: AppCtx *user = (AppCtx*)ptr;
358: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
359: VecSet(user->uwork,0);
360: VecAXPY(user->uwork,-1.0,user->u);
361: VecExp(user->uwork);
362: MatMult(user->Av,user->uwork,user->Av_u);
363: VecCopy(user->Av_u,user->Swork);
364: VecReciprocal(user->Swork);
365: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
366: MatDiagonalScale(user->Divwork,NULL,user->Swork);
367: if (user->dsg_formed) {
368: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
369: } else {
370: MatMatMultSymbolic(user->Divwork,user->Grad,PETSC_DECIDE,&user->DSG);
371: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
372: user->dsg_formed = PETSC_TRUE;
373: }
375: /* B = speye(nx^3) + ht*DSG; */
376: MatScale(user->DSG,user->ht);
377: MatShift(user->DSG,1.0);
378: return(0);
379: }
381: /* ------------------------------------------------------------------- */
382: /* B */
383: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
384: {
386: AppCtx *user = (AppCtx*)ptr;
389: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
390: return(0);
391: }
393: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
394: {
396: PetscInt i;
397: AppCtx *user;
400: MatShellGetContext(J_shell,(void**)&user);
401: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
402: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
403: for (i=1; i<user->nt; i++){
404: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
405: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
406: }
407: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
408: return(0);
409: }
411: PetscErrorCode StateMatMultTranspose(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: for (i=0; i<user->nt-1; i++){
421: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
422: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
423: }
424: i = user->nt-1;
425: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
426: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
427: return(0);
428: }
430: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
431: {
433: AppCtx *user;
436: MatShellGetContext(J_shell,(void**)&user);
437: MatMult(user->Grad,X,user->Swork);
438: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
439: MatMult(user->Div,user->Swork,Y);
440: VecAYPX(Y,user->ht,X);
441: return(0);
442: }
444: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
445: {
447: PetscInt i;
448: AppCtx *user;
451: MatShellGetContext(J_shell,(void**)&user);
453: /* sdiag(1./v) */
454: VecSet(user->uwork,0);
455: VecAXPY(user->uwork,-1.0,user->u);
456: VecExp(user->uwork);
458: /* sdiag(1./((Av*(1./v)).^2)) */
459: MatMult(user->Av,user->uwork,user->Swork);
460: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
461: VecReciprocal(user->Swork);
463: /* (Av * (sdiag(1./v) * b)) */
464: VecPointwiseMult(user->uwork,user->uwork,X);
465: MatMult(user->Av,user->uwork,user->Twork);
467: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
468: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
470: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
471: for (i=0; i<user->nt; i++){
472: /* (sdiag(Grad*y(:,i)) */
473: MatMult(user->Grad,user->yi[i],user->Twork);
475: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
476: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
477: MatMult(user->Div,user->Twork,user->yiwork[i]);
478: VecScale(user->yiwork[i],user->ht);
479: }
480: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
482: return(0);
483: }
485: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
486: {
488: PetscInt i;
489: AppCtx *user;
492: MatShellGetContext(J_shell,(void**)&user);
494: /* sdiag(1./((Av*(1./v)).^2)) */
495: VecSet(user->uwork,0);
496: VecAXPY(user->uwork,-1.0,user->u);
497: VecExp(user->uwork);
498: MatMult(user->Av,user->uwork,user->Rwork);
499: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
500: VecReciprocal(user->Rwork);
502: VecSet(Y,0.0);
503: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
504: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
505: for (i=0; i<user->nt; i++){
506: /* (Div' * b(:,i)) */
507: MatMult(user->Grad,user->yiwork[i],user->Swork);
509: /* sdiag(Grad*y(:,i)) */
510: MatMult(user->Grad,user->yi[i],user->Twork);
512: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
513: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
515: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
516: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
518: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
519: MatMult(user->AvT,user->Twork,user->yiwork[i]);
521: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
522: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
523: VecAXPY(Y,user->ht,user->yiwork[i]);
524: }
525: return(0);
526: }
528: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
529: {
531: AppCtx *user;
534: PCShellGetContext(PC_shell,(void**)&user);
536: if (user->dsg_formed) {
537: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
538: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
539: return(0);
540: }
542: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
543: {
545: AppCtx *user;
546: PetscInt its,i;
549: MatShellGetContext(J_shell,(void**)&user);
551: if (Y == user->ytrue) {
552: /* First solve is done with true solution to set up problem */
553: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
554: } else {
555: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
556: }
558: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
559: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
560: KSPGetIterationNumber(user->solver,&its);
561: user->ksp_its = user->ksp_its + its;
563: for (i=1; i<user->nt; i++){
564: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
565: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
566: KSPGetIterationNumber(user->solver,&its);
567: user->ksp_its = user->ksp_its + its;
568: }
569: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
570: return(0);
571: }
573: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
574: {
576: AppCtx *user;
577: PetscInt its,i;
580: MatShellGetContext(J_shell,(void**)&user);
582: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
584: i = user->nt - 1;
585: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
587: KSPGetIterationNumber(user->solver,&its);
588: user->ksp_its = user->ksp_its + its;
590: for (i=user->nt-2; i>=0; i--){
591: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
592: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
594: KSPGetIterationNumber(user->solver,&its);
595: user->ksp_its = user->ksp_its + its;
597: }
599: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
600: return(0);
601: }
603: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
604: {
606: AppCtx *user;
609: MatShellGetContext(J_shell,(void**)&user);
611: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
612: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
613: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
614: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
615: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
616: return(0);
617: }
619: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
620: {
622: AppCtx *user;
625: MatShellGetContext(J_shell,(void**)&user);
626: VecCopy(user->js_diag,X);
627: return(0);
629: }
631: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
632: {
633: /* con = Ay - q, A = [B 0 0 ... 0;
634: -I B 0 ... 0;
635: 0 -I B ... 0;
636: ... ;
637: 0 ... -I B]
638: B = ht * Div * Sigma * Grad + eye */
640: PetscInt i;
641: AppCtx *user = (AppCtx*)ptr;
644: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
645: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
646: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
647: for (i=1; i<user->nt; i++){
648: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
649: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
650: }
651: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
652: VecAXPY(C,-1.0,user->q);
653: return(0);
654: }
657: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
658: {
662: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
663: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
664: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
665: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
666: return(0);
667: }
669: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
670: {
672: PetscInt i;
675: for (i=0; i<nt; i++){
676: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
677: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
678: }
679: return(0);
680: }
683: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
684: {
688: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
689: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
690: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
691: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
692: return(0);
693: }
695: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
696: {
698: PetscInt i;
701: for (i=0; i<nt; i++){
702: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
703: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
704: }
705: return(0);
706: }
708: PetscErrorCode ParabolicInitialize(AppCtx *user)
709: {
711: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
712: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
713: PetscReal *x, *y, *z;
714: PetscReal h,stime;
715: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
716: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
717: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
718: PetscScalar v,vx,vy,vz;
719: IS is_from_y,is_to_yi,is_from_d,is_to_di;
720: /* Data locations */
721: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
722: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
723: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
724: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
725: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
726: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
727: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
728: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
730: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
731: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
732: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
733: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
734: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
735: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
736: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
737: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
739: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
740: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
741: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
742: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
743: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
744: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
745: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
746: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
749: PetscMalloc1(user->mx,&x);
750: PetscMalloc1(user->mx,&y);
751: PetscMalloc1(user->mx,&z);
752: user->jformed = PETSC_FALSE;
753: user->dsg_formed = PETSC_FALSE;
755: n = user->mx * user->mx * user->mx;
756: m = 3 * user->mx * user->mx * (user->mx-1);
757: sqrt_beta = PetscSqrtScalar(user->beta);
759: user->ksp_its = 0;
760: user->ksp_its_initial = 0;
762: stime = (PetscReal)user->nt/user->ns;
763: PetscMalloc1(user->ns,&user->sample_times);
764: for (i=0; i<user->ns; i++){
765: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
766: }
768: VecCreate(PETSC_COMM_WORLD,&XX);
769: VecCreate(PETSC_COMM_WORLD,&user->q);
770: VecSetSizes(XX,PETSC_DECIDE,n);
771: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
772: VecSetFromOptions(XX);
773: VecSetFromOptions(user->q);
775: VecDuplicate(XX,&YY);
776: VecDuplicate(XX,&ZZ);
777: VecDuplicate(XX,&XXwork);
778: VecDuplicate(XX,&YYwork);
779: VecDuplicate(XX,&ZZwork);
780: VecDuplicate(XX,&UTwork);
781: VecDuplicate(XX,&user->utrue);
782: VecDuplicate(XX,&bc);
784: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
785: h = 1.0/user->mx;
786: hinv = user->mx;
787: neg_hinv = -hinv;
789: VecGetOwnershipRange(XX,&istart,&iend);
790: for (linear_index=istart; linear_index<iend; linear_index++){
791: i = linear_index % user->mx;
792: j = ((linear_index-i)/user->mx) % user->mx;
793: k = ((linear_index-i)/user->mx-j) / user->mx;
794: vx = h*(i+0.5);
795: vy = h*(j+0.5);
796: vz = h*(k+0.5);
797: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
798: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
799: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
800: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)){
801: v = 1000.0;
802: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
803: }
804: }
806: VecAssemblyBegin(XX);
807: VecAssemblyEnd(XX);
808: VecAssemblyBegin(YY);
809: VecAssemblyEnd(YY);
810: VecAssemblyBegin(ZZ);
811: VecAssemblyEnd(ZZ);
812: VecAssemblyBegin(bc);
813: VecAssemblyEnd(bc);
815: /* Compute true parameter function
816: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
817: VecCopy(XX,XXwork);
818: VecCopy(YY,YYwork);
819: VecCopy(ZZ,ZZwork);
821: VecShift(XXwork,-0.5);
822: VecShift(YYwork,-0.5);
823: VecShift(ZZwork,-0.5);
825: VecPointwiseMult(XXwork,XXwork,XXwork);
826: VecPointwiseMult(YYwork,YYwork,YYwork);
827: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
829: VecCopy(XXwork,user->utrue);
830: VecAXPY(user->utrue,1.0,YYwork);
831: VecAXPY(user->utrue,1.0,ZZwork);
832: VecScale(user->utrue,-10.0);
833: VecExp(user->utrue);
834: VecShift(user->utrue,0.5);
836: VecDestroy(&XX);
837: VecDestroy(&YY);
838: VecDestroy(&ZZ);
839: VecDestroy(&XXwork);
840: VecDestroy(&YYwork);
841: VecDestroy(&ZZwork);
842: VecDestroy(&UTwork);
844: /* Initial guess and reference model */
845: VecDuplicate(user->utrue,&user->ur);
846: VecSet(user->ur,0.0);
848: /* Generate Grad matrix */
849: MatCreate(PETSC_COMM_WORLD,&user->Grad);
850: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,m,n);
851: MatSetFromOptions(user->Grad);
852: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
853: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
854: MatGetOwnershipRange(user->Grad,&istart,&iend);
856: for (i=istart; i<iend; i++){
857: if (i<m/3){
858: iblock = i / (user->mx-1);
859: j = iblock*user->mx + (i % (user->mx-1));
860: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
861: j = j+1;
862: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
863: }
864: if (i>=m/3 && i<2*m/3){
865: iblock = (i-m/3) / (user->mx*(user->mx-1));
866: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
867: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
868: j = j + user->mx;
869: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
870: }
871: if (i>=2*m/3){
872: j = i-2*m/3;
873: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
874: j = j + user->mx*user->mx;
875: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
876: }
877: }
879: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
880: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
883: /* Generate arithmetic averaging matrix Av */
884: MatCreate(PETSC_COMM_WORLD,&user->Av);
885: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
886: MatSetFromOptions(user->Av);
887: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
888: MatSeqAIJSetPreallocation(user->Av,2,NULL);
889: MatGetOwnershipRange(user->Av,&istart,&iend);
891: for (i=istart; i<iend; i++){
892: if (i<m/3){
893: iblock = i / (user->mx-1);
894: j = iblock*user->mx + (i % (user->mx-1));
895: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
896: j = j+1;
897: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
898: }
899: if (i>=m/3 && i<2*m/3){
900: iblock = (i-m/3) / (user->mx*(user->mx-1));
901: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
902: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
903: j = j + user->mx;
904: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
905: }
906: if (i>=2*m/3){
907: j = i-2*m/3;
908: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
909: j = j + user->mx*user->mx;
910: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
911: }
912: }
914: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
915: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
917: /* Generate transpose of averaging matrix Av */
918: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
920: MatCreate(PETSC_COMM_WORLD,&user->L);
921: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
922: MatSetFromOptions(user->L);
923: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
924: MatSeqAIJSetPreallocation(user->L,2,NULL);
925: MatGetOwnershipRange(user->L,&istart,&iend);
927: for (i=istart; i<iend; i++){
928: if (i<m/3){
929: iblock = i / (user->mx-1);
930: j = iblock*user->mx + (i % (user->mx-1));
931: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
932: j = j+1;
933: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
934: }
935: if (i>=m/3 && i<2*m/3){
936: iblock = (i-m/3) / (user->mx*(user->mx-1));
937: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
938: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
939: j = j + user->mx;
940: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
941: }
942: if (i>=2*m/3 && i<m){
943: j = i-2*m/3;
944: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
945: j = j + user->mx*user->mx;
946: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
947: }
948: if (i>=m){
949: j = i - m;
950: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
951: }
952: }
954: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
955: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
957: MatScale(user->L,PetscPowScalar(h,1.5));
959: /* Generate Div matrix */
960: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
962: /* Build work vectors and matrices */
963: VecCreate(PETSC_COMM_WORLD,&user->S);
964: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
965: VecSetFromOptions(user->S);
967: VecCreate(PETSC_COMM_WORLD,&user->lwork);
968: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
969: VecSetFromOptions(user->lwork);
971: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
972: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
974: VecCreate(PETSC_COMM_WORLD,&user->d);
975: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
976: VecSetFromOptions(user->d);
978: VecDuplicate(user->S,&user->Swork);
979: VecDuplicate(user->S,&user->Av_u);
980: VecDuplicate(user->S,&user->Twork);
981: VecDuplicate(user->S,&user->Rwork);
982: VecDuplicate(user->y,&user->ywork);
983: VecDuplicate(user->u,&user->uwork);
984: VecDuplicate(user->u,&user->js_diag);
985: VecDuplicate(user->c,&user->cwork);
986: VecDuplicate(user->d,&user->dwork);
988: /* Create matrix-free shell user->Js for computing A*x */
989: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
990: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
991: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
992: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
993: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
995: /* Diagonal blocks of user->Js */
996: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
997: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
998: /* Blocks are symmetric */
999: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
1001: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1002: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1003: This is an SSOR preconditioner for user->JsBlock. */
1004: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
1005: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1006: /* JsBlockPrec is symmetric */
1007: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1008: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1010: /* Create a matrix-free shell user->Jd for computing B*x */
1011: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1012: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1013: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1015: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1016: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1017: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1018: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1020: /* Solver options and tolerances */
1021: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1022: KSPSetType(user->solver,KSPCG);
1023: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1024: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1025: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1026: KSPSetFromOptions(user->solver);
1027: KSPGetPC(user->solver,&user->prec);
1028: PCSetType(user->prec,PCSHELL);
1030: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1031: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1032: PCShellSetContext(user->prec,user);
1034: /* Create scatter from y to y_1,y_2,...,y_nt */
1035: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1036: VecCreate(PETSC_COMM_WORLD,&yi);
1037: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1038: VecSetFromOptions(yi);
1039: VecDuplicateVecs(yi,user->nt,&user->yi);
1040: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1042: VecGetOwnershipRange(user->y,&lo2,&hi2);
1043: istart = 0;
1044: for (i=0; i<user->nt; i++){
1045: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1046: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1047: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1048: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1049: istart = istart + hi-lo;
1050: ISDestroy(&is_to_yi);
1051: ISDestroy(&is_from_y);
1052: }
1053: VecDestroy(&yi);
1055: /* Create scatter from d to d_1,d_2,...,d_ns */
1056: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1057: VecCreate(PETSC_COMM_WORLD,&di);
1058: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1059: VecSetFromOptions(di);
1060: VecDuplicateVecs(di,user->ns,&user->di);
1061: VecGetOwnershipRange(user->d,&lo2,&hi2);
1062: istart = 0;
1063: for (i=0; i<user->ns; i++){
1064: VecGetOwnershipRange(user->di[i],&lo,&hi);
1065: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1066: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1067: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1068: istart = istart + hi-lo;
1069: ISDestroy(&is_to_di);
1070: ISDestroy(&is_from_d);
1071: }
1072: VecDestroy(&di);
1074: /* Assemble RHS of forward problem */
1075: VecCopy(bc,user->yiwork[0]);
1076: for (i=1; i<user->nt; i++){
1077: VecSet(user->yiwork[i],0.0);
1078: }
1079: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1080: VecDestroy(&bc);
1082: /* Compute true state function yt given ut */
1083: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1084: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1085: VecSetFromOptions(user->ytrue);
1087: /* First compute Av_u = Av*exp(-u) */
1088: VecSet(user->uwork,0);
1089: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1090: VecExp(user->uwork);
1091: MatMult(user->Av,user->uwork,user->Av_u);
1093: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1094: user->dsg_formed = PETSC_TRUE;
1096: /* Next form DSG = Div*S*Grad */
1097: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1098: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1099: if (user->dsg_formed) {
1100: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1101: } else {
1102: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1103: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1104: user->dsg_formed = PETSC_TRUE;
1105: }
1106: /* B = speye(nx^3) + ht*DSG; */
1107: MatScale(user->DSG,user->ht);
1108: MatShift(user->DSG,1.0);
1110: /* Now solve for ytrue */
1111: StateMatInvMult(user->Js,user->q,user->ytrue);
1113: /* Initial guess y0 for state given u0 */
1115: /* First compute Av_u = Av*exp(-u) */
1116: VecSet(user->uwork,0);
1117: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1118: VecExp(user->uwork);
1119: MatMult(user->Av,user->uwork,user->Av_u);
1121: /* Next form DSG = Div*S*Grad */
1122: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1123: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1124: if (user->dsg_formed) {
1125: MatMatMultNumeric(user->Divwork,user->Grad,user->DSG);
1126: } else {
1127: MatMatMultSymbolic(user->Div,user->Grad,PETSC_DEFAULT,&user->DSG);
1128: MatMatMultNumeric(user->Div,user->Grad,user->DSG);
1129: user->dsg_formed = PETSC_TRUE;
1130: }
1131: /* B = speye(nx^3) + ht*DSG; */
1132: MatScale(user->DSG,user->ht);
1133: MatShift(user->DSG,1.0);
1135: /* Now solve for y */
1136: StateMatInvMult(user->Js,user->q,user->y);
1138: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1139: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1140: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1141: MatSetFromOptions(user->Qblock);
1142: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1143: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1145: for (i=0; i<user->mx; i++){
1146: x[i] = h*(i+0.5);
1147: y[i] = h*(i+0.5);
1148: z[i] = h*(i+0.5);
1149: }
1151: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1152: nx = user->mx; ny = user->mx; nz = user->mx;
1153: for (i=istart; i<iend; i++){
1154: xri = xr[i];
1155: im = 0;
1156: xim = x[im];
1157: while (xri>xim && im<nx){
1158: im = im+1;
1159: xim = x[im];
1160: }
1161: indx1 = im-1;
1162: indx2 = im;
1163: dx1 = xri - x[indx1];
1164: dx2 = x[indx2] - xri;
1166: yri = yr[i];
1167: im = 0;
1168: yim = y[im];
1169: while (yri>yim && im<ny){
1170: im = im+1;
1171: yim = y[im];
1172: }
1173: indy1 = im-1;
1174: indy2 = im;
1175: dy1 = yri - y[indy1];
1176: dy2 = y[indy2] - yri;
1178: zri = zr[i];
1179: im = 0;
1180: zim = z[im];
1181: while (zri>zim && im<nz){
1182: im = im+1;
1183: zim = z[im];
1184: }
1185: indz1 = im-1;
1186: indz2 = im;
1187: dz1 = zri - z[indz1];
1188: dz2 = z[indz2] - zri;
1190: Dx = x[indx2] - x[indx1];
1191: Dy = y[indy2] - y[indy1];
1192: Dz = z[indz2] - z[indz1];
1194: j = indx1 + indy1*nx + indz1*nx*ny;
1195: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1196: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1198: j = indx1 + indy1*nx + indz2*nx*ny;
1199: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1200: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1202: j = indx1 + indy2*nx + indz1*nx*ny;
1203: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1204: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1206: j = indx1 + indy2*nx + indz2*nx*ny;
1207: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1208: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1210: j = indx2 + indy1*nx + indz1*nx*ny;
1211: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1212: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1214: j = indx2 + indy1*nx + indz2*nx*ny;
1215: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1216: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1218: j = indx2 + indy2*nx + indz1*nx*ny;
1219: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1220: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1222: j = indx2 + indy2*nx + indz2*nx*ny;
1223: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1224: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1225: }
1226: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1227: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1229: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1230: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1232: /* Add noise to the measurement data */
1233: VecSet(user->ywork,1.0);
1234: VecAYPX(user->ywork,user->noise,user->ytrue);
1235: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1236: for (j=0; j<user->ns; j++){
1237: i = user->sample_times[j];
1238: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1239: }
1240: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1242: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1243: KSPSetFromOptions(user->solver);
1244: PetscFree(x);
1245: PetscFree(y);
1246: PetscFree(z);
1247: return(0);
1248: }
1250: PetscErrorCode ParabolicDestroy(AppCtx *user)
1251: {
1253: PetscInt i;
1256: MatDestroy(&user->Qblock);
1257: MatDestroy(&user->QblockT);
1258: MatDestroy(&user->Div);
1259: MatDestroy(&user->Divwork);
1260: MatDestroy(&user->Grad);
1261: MatDestroy(&user->Av);
1262: MatDestroy(&user->Avwork);
1263: MatDestroy(&user->AvT);
1264: MatDestroy(&user->DSG);
1265: MatDestroy(&user->L);
1266: MatDestroy(&user->LT);
1267: KSPDestroy(&user->solver);
1268: MatDestroy(&user->Js);
1269: MatDestroy(&user->Jd);
1270: MatDestroy(&user->JsInv);
1271: MatDestroy(&user->JsBlock);
1272: MatDestroy(&user->JsBlockPrec);
1273: VecDestroy(&user->u);
1274: VecDestroy(&user->uwork);
1275: VecDestroy(&user->utrue);
1276: VecDestroy(&user->y);
1277: VecDestroy(&user->ywork);
1278: VecDestroy(&user->ytrue);
1279: VecDestroyVecs(user->nt,&user->yi);
1280: VecDestroyVecs(user->nt,&user->yiwork);
1281: VecDestroyVecs(user->ns,&user->di);
1282: PetscFree(user->yi);
1283: PetscFree(user->yiwork);
1284: PetscFree(user->di);
1285: VecDestroy(&user->c);
1286: VecDestroy(&user->cwork);
1287: VecDestroy(&user->ur);
1288: VecDestroy(&user->q);
1289: VecDestroy(&user->d);
1290: VecDestroy(&user->dwork);
1291: VecDestroy(&user->lwork);
1292: VecDestroy(&user->S);
1293: VecDestroy(&user->Swork);
1294: VecDestroy(&user->Av_u);
1295: VecDestroy(&user->Twork);
1296: VecDestroy(&user->Rwork);
1297: VecDestroy(&user->js_diag);
1298: ISDestroy(&user->s_is);
1299: ISDestroy(&user->d_is);
1300: VecScatterDestroy(&user->state_scatter);
1301: VecScatterDestroy(&user->design_scatter);
1302: for (i=0; i<user->nt; i++){
1303: VecScatterDestroy(&user->yi_scatter[i]);
1304: }
1305: for (i=0; i<user->ns; i++){
1306: VecScatterDestroy(&user->di_scatter[i]);
1307: }
1308: PetscFree(user->yi_scatter);
1309: PetscFree(user->di_scatter);
1310: PetscFree(user->sample_times);
1311: return(0);
1312: }
1314: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1315: {
1317: Vec X;
1318: PetscReal unorm,ynorm;
1319: AppCtx *user = (AppCtx*)ptr;
1322: TaoGetSolutionVector(tao,&X);
1323: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1324: VecAXPY(user->ywork,-1.0,user->ytrue);
1325: VecAXPY(user->uwork,-1.0,user->utrue);
1326: VecNorm(user->uwork,NORM_2,&unorm);
1327: VecNorm(user->ywork,NORM_2,&ynorm);
1328: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1329: return(0);
1330: }
1333: /*TEST
1335: build:
1336: requires: !complex
1338: test:
1339: args: -tao_cmonitor -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1340: requires: !single
1342: TEST*/