Actual source code: parabolic.c
1: #include <petsc/private/taoimpl.h>
3: /*T
4: Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
5: Routines: TaoCreate();
6: Routines: TaoSetType();
7: Routines: TaoSetInitialVector();
8: Routines: TaoSetObjectiveRoutine();
9: Routines: TaoSetGradientRoutine();
10: Routines: TaoSetConstraintsRoutine();
11: Routines: TaoSetJacobianStateRoutine();
12: Routines: TaoSetJacobianDesignRoutine();
13: Routines: TaoSetStateDesignIS();
14: Routines: TaoSetFromOptions();
15: Routines: TaoSolve();
16: Routines: TaoDestroy();
17: Processors: n
18: T*/
20: typedef struct {
21: PetscInt n; /* Number of variables */
22: PetscInt m; /* Number of constraints per time step */
23: PetscInt mx; /* grid points in each direction */
24: PetscInt nt; /* Number of time steps; as of now, must be divisible by 8 */
25: PetscInt ndata; /* Number of data points per sample */
26: PetscInt ns; /* Number of samples */
27: PetscInt *sample_times; /* Times of samples */
28: IS s_is;
29: IS d_is;
31: VecScatter state_scatter;
32: VecScatter design_scatter;
33: VecScatter *yi_scatter;
34: VecScatter *di_scatter;
36: Mat Js,Jd,JsBlockPrec,JsInv,JsBlock;
37: PetscBool jformed,dsg_formed;
39: PetscReal alpha; /* Regularization parameter */
40: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
41: PetscReal noise; /* Amount of noise to add to data */
42: PetscReal ht; /* Time step */
44: Mat Qblock,QblockT;
45: Mat L,LT;
46: Mat Div,Divwork;
47: Mat Grad;
48: Mat Av,Avwork,AvT;
49: Mat DSG;
50: Vec q;
51: Vec ur; /* reference */
53: Vec d;
54: Vec dwork;
55: Vec *di;
57: Vec y; /* state variables */
58: Vec ywork;
60: Vec ytrue;
61: Vec *yi,*yiwork;
63: Vec u; /* design variables */
64: Vec uwork;
66: Vec utrue;
67: Vec js_diag;
68: Vec c; /* constraint vector */
69: Vec cwork;
71: Vec lwork;
72: Vec S;
73: Vec Rwork,Swork,Twork;
74: Vec Av_u;
76: KSP solver;
77: PC prec;
79: PetscInt ksp_its;
80: PetscInt ksp_its_initial;
81: } AppCtx;
83: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
84: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
85: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
86: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
87: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void*);
88: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
89: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
90: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
91: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
92: PetscErrorCode ParabolicInitialize(AppCtx *user);
93: PetscErrorCode ParabolicDestroy(AppCtx *user);
94: PetscErrorCode ParabolicMonitor(Tao, void*);
96: PetscErrorCode StateMatMult(Mat,Vec,Vec);
97: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
98: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
99: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
100: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
101: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
102: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
103: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);
105: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
106: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
108: PetscErrorCode Gather_i(Vec,Vec*,VecScatter*,PetscInt);
109: PetscErrorCode Scatter_i(Vec,Vec*,VecScatter*,PetscInt);
111: static char help[]="";
113: int main(int argc, char **argv)
114: {
115: PetscErrorCode ierr;
116: Vec x,x0;
117: Tao tao;
118: AppCtx user;
119: IS is_allstate,is_alldesign;
120: PetscInt lo,hi,hi2,lo2,ksp_old;
121: PetscInt ntests = 1;
122: PetscInt i;
123: #if defined(PETSC_USE_LOG)
124: PetscLogStage stages[1];
125: #endif
127: PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
128: user.mx = 8;
129: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"parabolic example",NULL);
130: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
131: user.nt = 8;
132: PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
133: user.ndata = 64;
134: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
135: user.ns = 8;
136: PetscOptionsInt("-ns","Number of samples","",user.ns,&user.ns,NULL);
137: user.alpha = 1.0;
138: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
139: user.beta = 0.01;
140: PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
141: user.noise = 0.01;
142: PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);
143: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
144: PetscOptionsEnd();
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, &user);
201: TaoSetGradientRoutine(tao, FormGradient, &user);
202: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user);
204: TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, &user);
205: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user);
207: TaoSetFromOptions(tao);
208: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
210: /* SOLVE THE APPLICATION */
211: PetscLogStageRegister("Trials",&stages[0]);
212: PetscLogStagePush(stages[0]);
213: user.ksp_its_initial = user.ksp_its;
214: ksp_old = user.ksp_its;
215: for (i=0; i<ntests; i++) {
216: TaoSolve(tao);
217: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
218: VecCopy(x0,x);
219: TaoSetInitialVector(tao,x);
220: }
221: PetscLogStagePop();
222: PetscBarrier((PetscObject)x);
223: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
224: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
225: PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
226: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
227: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
228: PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);
230: TaoDestroy(&tao);
231: VecDestroy(&x);
232: VecDestroy(&x0);
233: ParabolicDestroy(&user);
235: PetscFinalize();
236: return ierr;
237: }
238: /* ------------------------------------------------------------------- */
239: /*
240: dwork = Qy - d
241: lwork = L*(u-ur)
242: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
243: */
244: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
245: {
247: PetscReal d1=0,d2=0;
248: PetscInt i,j;
249: AppCtx *user = (AppCtx*)ptr;
252: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
253: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
254: for (j=0; j<user->ns; j++) {
255: i = user->sample_times[j];
256: MatMult(user->Qblock,user->yi[i],user->di[j]);
257: }
258: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
259: VecAXPY(user->dwork,-1.0,user->d);
260: VecDot(user->dwork,user->dwork,&d1);
262: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
263: MatMult(user->L,user->uwork,user->lwork);
264: VecDot(user->lwork,user->lwork,&d2);
266: *f = 0.5 * (d1 + user->alpha*d2);
267: return(0);
268: }
270: /* ------------------------------------------------------------------- */
271: /*
272: state: g_s = Q' *(Qy - d)
273: design: g_d = alpha*L'*L*(u-ur)
274: */
275: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
276: {
278: PetscInt i,j;
279: AppCtx *user = (AppCtx*)ptr;
282: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
283: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
284: for (j=0; j<user->ns; j++) {
285: i = user->sample_times[j];
286: MatMult(user->Qblock,user->yi[i],user->di[j]);
287: }
288: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
289: VecAXPY(user->dwork,-1.0,user->d);
290: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
291: VecSet(user->ywork,0.0);
292: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
293: for (j=0; j<user->ns; j++) {
294: i = user->sample_times[j];
295: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
296: }
297: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
299: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
300: MatMult(user->L,user->uwork,user->lwork);
301: MatMult(user->LT,user->lwork,user->uwork);
302: VecScale(user->uwork, user->alpha);
303: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
304: return(0);
305: }
307: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
308: {
310: PetscReal d1,d2;
311: PetscInt i,j;
312: AppCtx *user = (AppCtx*)ptr;
315: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
316: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
317: for (j=0; j<user->ns; j++) {
318: i = user->sample_times[j];
319: MatMult(user->Qblock,user->yi[i],user->di[j]);
320: }
321: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
322: VecAXPY(user->dwork,-1.0,user->d);
323: VecDot(user->dwork,user->dwork,&d1);
324: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
325: VecSet(user->ywork,0.0);
326: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
327: for (j=0; j<user->ns; j++) {
328: i = user->sample_times[j];
329: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
330: }
331: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
333: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
334: MatMult(user->L,user->uwork,user->lwork);
335: VecDot(user->lwork,user->lwork,&d2);
336: MatMult(user->LT,user->lwork,user->uwork);
337: VecScale(user->uwork, user->alpha);
338: *f = 0.5 * (d1 + user->alpha*d2);
340: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
341: return(0);
342: }
344: /* ------------------------------------------------------------------- */
345: /* A
346: MatShell object
347: */
348: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
349: {
351: AppCtx *user = (AppCtx*)ptr;
354: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
355: VecSet(user->uwork,0);
356: VecAXPY(user->uwork,-1.0,user->u);
357: VecExp(user->uwork);
358: MatMult(user->Av,user->uwork,user->Av_u);
359: VecCopy(user->Av_u,user->Swork);
360: VecReciprocal(user->Swork);
361: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
362: MatDiagonalScale(user->Divwork,NULL,user->Swork);
363: if (user->dsg_formed) {
364: MatProductNumeric(user->DSG);
365: } else {
366: MatMatMult(user->Divwork,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&user->DSG);
367: user->dsg_formed = PETSC_TRUE;
368: }
370: /* B = speye(nx^3) + ht*DSG; */
371: MatScale(user->DSG,user->ht);
372: MatShift(user->DSG,1.0);
373: return(0);
374: }
376: /* ------------------------------------------------------------------- */
377: /* B */
378: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
379: {
381: AppCtx *user = (AppCtx*)ptr;
384: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
385: return(0);
386: }
388: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
389: {
391: PetscInt i;
392: AppCtx *user;
395: MatShellGetContext(J_shell,&user);
396: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
397: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
398: for (i=1; i<user->nt; i++) {
399: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
400: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
401: }
402: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
403: return(0);
404: }
406: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
407: {
409: PetscInt i;
410: AppCtx *user;
413: MatShellGetContext(J_shell,&user);
414: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
415: for (i=0; i<user->nt-1; i++) {
416: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
417: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
418: }
419: i = user->nt-1;
420: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
421: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
422: return(0);
423: }
425: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
426: {
428: AppCtx *user;
431: MatShellGetContext(J_shell,&user);
432: MatMult(user->Grad,X,user->Swork);
433: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
434: MatMult(user->Div,user->Swork,Y);
435: VecAYPX(Y,user->ht,X);
436: return(0);
437: }
439: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
440: {
442: PetscInt i;
443: AppCtx *user;
446: MatShellGetContext(J_shell,&user);
448: /* sdiag(1./v) */
449: VecSet(user->uwork,0);
450: VecAXPY(user->uwork,-1.0,user->u);
451: VecExp(user->uwork);
453: /* sdiag(1./((Av*(1./v)).^2)) */
454: MatMult(user->Av,user->uwork,user->Swork);
455: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
456: VecReciprocal(user->Swork);
458: /* (Av * (sdiag(1./v) * b)) */
459: VecPointwiseMult(user->uwork,user->uwork,X);
460: MatMult(user->Av,user->uwork,user->Twork);
462: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
463: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
465: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
466: for (i=0; i<user->nt; i++) {
467: /* (sdiag(Grad*y(:,i)) */
468: MatMult(user->Grad,user->yi[i],user->Twork);
470: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
471: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
472: MatMult(user->Div,user->Twork,user->yiwork[i]);
473: VecScale(user->yiwork[i],user->ht);
474: }
475: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
477: return(0);
478: }
480: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
481: {
483: PetscInt i;
484: AppCtx *user;
487: MatShellGetContext(J_shell,&user);
489: /* sdiag(1./((Av*(1./v)).^2)) */
490: VecSet(user->uwork,0);
491: VecAXPY(user->uwork,-1.0,user->u);
492: VecExp(user->uwork);
493: MatMult(user->Av,user->uwork,user->Rwork);
494: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
495: VecReciprocal(user->Rwork);
497: VecSet(Y,0.0);
498: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
499: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
500: for (i=0; i<user->nt; i++) {
501: /* (Div' * b(:,i)) */
502: MatMult(user->Grad,user->yiwork[i],user->Swork);
504: /* sdiag(Grad*y(:,i)) */
505: MatMult(user->Grad,user->yi[i],user->Twork);
507: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
508: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
510: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
511: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
513: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
514: MatMult(user->AvT,user->Twork,user->yiwork[i]);
516: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
517: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
518: VecAXPY(Y,user->ht,user->yiwork[i]);
519: }
520: return(0);
521: }
523: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
524: {
526: AppCtx *user;
529: PCShellGetContext(PC_shell,&user);
531: if (user->dsg_formed) {
532: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
533: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
534: return(0);
535: }
537: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
538: {
540: AppCtx *user;
541: PetscInt its,i;
544: MatShellGetContext(J_shell,&user);
546: if (Y == user->ytrue) {
547: /* First solve is done with true solution to set up problem */
548: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
549: } else {
550: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
551: }
553: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
554: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
555: KSPGetIterationNumber(user->solver,&its);
556: user->ksp_its = user->ksp_its + its;
558: for (i=1; i<user->nt; i++) {
559: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
560: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
561: KSPGetIterationNumber(user->solver,&its);
562: user->ksp_its = user->ksp_its + its;
563: }
564: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
565: return(0);
566: }
568: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
569: {
571: AppCtx *user;
572: PetscInt its,i;
575: MatShellGetContext(J_shell,&user);
577: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
579: i = user->nt - 1;
580: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
582: KSPGetIterationNumber(user->solver,&its);
583: user->ksp_its = user->ksp_its + its;
585: for (i=user->nt-2; i>=0; i--) {
586: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
587: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
589: KSPGetIterationNumber(user->solver,&its);
590: user->ksp_its = user->ksp_its + its;
592: }
594: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
595: return(0);
596: }
598: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
599: {
601: AppCtx *user;
604: MatShellGetContext(J_shell,&user);
606: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
607: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
608: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
609: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
610: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
611: return(0);
612: }
614: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
615: {
617: AppCtx *user;
620: MatShellGetContext(J_shell,&user);
621: VecCopy(user->js_diag,X);
622: return(0);
624: }
626: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
627: {
628: /* con = Ay - q, A = [B 0 0 ... 0;
629: -I B 0 ... 0;
630: 0 -I B ... 0;
631: ... ;
632: 0 ... -I B]
633: B = ht * Div * Sigma * Grad + eye */
635: PetscInt i;
636: AppCtx *user = (AppCtx*)ptr;
639: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
640: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
641: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
642: for (i=1; i<user->nt; i++) {
643: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
644: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
645: }
646: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
647: VecAXPY(C,-1.0,user->q);
648: return(0);
649: }
651: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
652: {
656: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
657: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
658: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
659: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
660: return(0);
661: }
663: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
664: {
666: PetscInt i;
669: for (i=0; i<nt; i++) {
670: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
671: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
672: }
673: return(0);
674: }
676: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
677: {
681: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
682: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
683: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
684: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
685: return(0);
686: }
688: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
689: {
691: PetscInt i;
694: for (i=0; i<nt; i++) {
695: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
696: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
697: }
698: return(0);
699: }
701: PetscErrorCode ParabolicInitialize(AppCtx *user)
702: {
704: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
705: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
706: PetscReal *x, *y, *z;
707: PetscReal h,stime;
708: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
709: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
710: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
711: PetscScalar v,vx,vy,vz;
712: IS is_from_y,is_to_yi,is_from_d,is_to_di;
713: /* Data locations */
714: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
715: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
716: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
717: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
718: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
719: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
720: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
721: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
723: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
724: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
725: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
726: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
727: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
728: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
729: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
730: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
732: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
733: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
734: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
735: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
736: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
737: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
738: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
739: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
742: PetscMalloc1(user->mx,&x);
743: PetscMalloc1(user->mx,&y);
744: PetscMalloc1(user->mx,&z);
745: user->jformed = PETSC_FALSE;
746: user->dsg_formed = PETSC_FALSE;
748: n = user->mx * user->mx * user->mx;
749: m = 3 * user->mx * user->mx * (user->mx-1);
750: sqrt_beta = PetscSqrtScalar(user->beta);
752: user->ksp_its = 0;
753: user->ksp_its_initial = 0;
755: stime = (PetscReal)user->nt/user->ns;
756: PetscMalloc1(user->ns,&user->sample_times);
757: for (i=0; i<user->ns; i++) {
758: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
759: }
761: VecCreate(PETSC_COMM_WORLD,&XX);
762: VecCreate(PETSC_COMM_WORLD,&user->q);
763: VecSetSizes(XX,PETSC_DECIDE,n);
764: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
765: VecSetFromOptions(XX);
766: VecSetFromOptions(user->q);
768: VecDuplicate(XX,&YY);
769: VecDuplicate(XX,&ZZ);
770: VecDuplicate(XX,&XXwork);
771: VecDuplicate(XX,&YYwork);
772: VecDuplicate(XX,&ZZwork);
773: VecDuplicate(XX,&UTwork);
774: VecDuplicate(XX,&user->utrue);
775: VecDuplicate(XX,&bc);
777: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
778: h = 1.0/user->mx;
779: hinv = user->mx;
780: neg_hinv = -hinv;
782: VecGetOwnershipRange(XX,&istart,&iend);
783: for (linear_index=istart; linear_index<iend; linear_index++) {
784: i = linear_index % user->mx;
785: j = ((linear_index-i)/user->mx) % user->mx;
786: k = ((linear_index-i)/user->mx-j) / user->mx;
787: vx = h*(i+0.5);
788: vy = h*(j+0.5);
789: vz = h*(k+0.5);
790: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
791: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
792: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
793: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)) {
794: v = 1000.0;
795: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
796: }
797: }
799: VecAssemblyBegin(XX);
800: VecAssemblyEnd(XX);
801: VecAssemblyBegin(YY);
802: VecAssemblyEnd(YY);
803: VecAssemblyBegin(ZZ);
804: VecAssemblyEnd(ZZ);
805: VecAssemblyBegin(bc);
806: VecAssemblyEnd(bc);
808: /* Compute true parameter function
809: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
810: VecCopy(XX,XXwork);
811: VecCopy(YY,YYwork);
812: VecCopy(ZZ,ZZwork);
814: VecShift(XXwork,-0.5);
815: VecShift(YYwork,-0.5);
816: VecShift(ZZwork,-0.5);
818: VecPointwiseMult(XXwork,XXwork,XXwork);
819: VecPointwiseMult(YYwork,YYwork,YYwork);
820: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
822: VecCopy(XXwork,user->utrue);
823: VecAXPY(user->utrue,1.0,YYwork);
824: VecAXPY(user->utrue,1.0,ZZwork);
825: VecScale(user->utrue,-10.0);
826: VecExp(user->utrue);
827: VecShift(user->utrue,0.5);
829: VecDestroy(&XX);
830: VecDestroy(&YY);
831: VecDestroy(&ZZ);
832: VecDestroy(&XXwork);
833: VecDestroy(&YYwork);
834: VecDestroy(&ZZwork);
835: VecDestroy(&UTwork);
837: /* Initial guess and reference model */
838: VecDuplicate(user->utrue,&user->ur);
839: VecSet(user->ur,0.0);
841: /* Generate Grad matrix */
842: MatCreate(PETSC_COMM_WORLD,&user->Grad);
843: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,m,n);
844: MatSetFromOptions(user->Grad);
845: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
846: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
847: MatGetOwnershipRange(user->Grad,&istart,&iend);
849: for (i=istart; i<iend; i++) {
850: if (i<m/3) {
851: iblock = i / (user->mx-1);
852: j = iblock*user->mx + (i % (user->mx-1));
853: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
854: j = j+1;
855: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
856: }
857: if (i>=m/3 && i<2*m/3) {
858: iblock = (i-m/3) / (user->mx*(user->mx-1));
859: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
860: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
861: j = j + user->mx;
862: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
863: }
864: if (i>=2*m/3) {
865: j = i-2*m/3;
866: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
867: j = j + user->mx*user->mx;
868: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
869: }
870: }
872: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
873: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
875: /* Generate arithmetic averaging matrix Av */
876: MatCreate(PETSC_COMM_WORLD,&user->Av);
877: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
878: MatSetFromOptions(user->Av);
879: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
880: MatSeqAIJSetPreallocation(user->Av,2,NULL);
881: MatGetOwnershipRange(user->Av,&istart,&iend);
883: for (i=istart; i<iend; i++) {
884: if (i<m/3) {
885: iblock = i / (user->mx-1);
886: j = iblock*user->mx + (i % (user->mx-1));
887: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
888: j = j+1;
889: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
890: }
891: if (i>=m/3 && i<2*m/3) {
892: iblock = (i-m/3) / (user->mx*(user->mx-1));
893: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
894: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
895: j = j + user->mx;
896: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
897: }
898: if (i>=2*m/3) {
899: j = i-2*m/3;
900: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
901: j = j + user->mx*user->mx;
902: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
903: }
904: }
906: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
907: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
909: /* Generate transpose of averaging matrix Av */
910: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
912: MatCreate(PETSC_COMM_WORLD,&user->L);
913: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
914: MatSetFromOptions(user->L);
915: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
916: MatSeqAIJSetPreallocation(user->L,2,NULL);
917: MatGetOwnershipRange(user->L,&istart,&iend);
919: for (i=istart; i<iend; i++) {
920: if (i<m/3) {
921: iblock = i / (user->mx-1);
922: j = iblock*user->mx + (i % (user->mx-1));
923: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
924: j = j+1;
925: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
926: }
927: if (i>=m/3 && i<2*m/3) {
928: iblock = (i-m/3) / (user->mx*(user->mx-1));
929: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
930: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
931: j = j + user->mx;
932: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
933: }
934: if (i>=2*m/3 && i<m) {
935: j = i-2*m/3;
936: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
937: j = j + user->mx*user->mx;
938: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
939: }
940: if (i>=m) {
941: j = i - m;
942: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
943: }
944: }
946: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
947: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
949: MatScale(user->L,PetscPowScalar(h,1.5));
951: /* Generate Div matrix */
952: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
954: /* Build work vectors and matrices */
955: VecCreate(PETSC_COMM_WORLD,&user->S);
956: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
957: VecSetFromOptions(user->S);
959: VecCreate(PETSC_COMM_WORLD,&user->lwork);
960: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
961: VecSetFromOptions(user->lwork);
963: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
964: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
966: VecCreate(PETSC_COMM_WORLD,&user->d);
967: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
968: VecSetFromOptions(user->d);
970: VecDuplicate(user->S,&user->Swork);
971: VecDuplicate(user->S,&user->Av_u);
972: VecDuplicate(user->S,&user->Twork);
973: VecDuplicate(user->S,&user->Rwork);
974: VecDuplicate(user->y,&user->ywork);
975: VecDuplicate(user->u,&user->uwork);
976: VecDuplicate(user->u,&user->js_diag);
977: VecDuplicate(user->c,&user->cwork);
978: VecDuplicate(user->d,&user->dwork);
980: /* Create matrix-free shell user->Js for computing A*x */
981: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
982: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
983: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
984: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
985: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
987: /* Diagonal blocks of user->Js */
988: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
989: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
990: /* Blocks are symmetric */
991: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
993: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
994: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
995: This is an SSOR preconditioner for user->JsBlock. */
996: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
997: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
998: /* JsBlockPrec is symmetric */
999: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
1000: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
1002: /* Create a matrix-free shell user->Jd for computing B*x */
1003: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
1004: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1005: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1007: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1008: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
1009: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1010: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1012: /* Solver options and tolerances */
1013: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1014: KSPSetType(user->solver,KSPCG);
1015: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1016: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
1017: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1018: KSPSetFromOptions(user->solver);
1019: KSPGetPC(user->solver,&user->prec);
1020: PCSetType(user->prec,PCSHELL);
1022: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1023: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
1024: PCShellSetContext(user->prec,user);
1026: /* Create scatter from y to y_1,y_2,...,y_nt */
1027: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
1028: VecCreate(PETSC_COMM_WORLD,&yi);
1029: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
1030: VecSetFromOptions(yi);
1031: VecDuplicateVecs(yi,user->nt,&user->yi);
1032: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1034: VecGetOwnershipRange(user->y,&lo2,&hi2);
1035: istart = 0;
1036: for (i=0; i<user->nt; i++) {
1037: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1038: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1039: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
1040: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1041: istart = istart + hi-lo;
1042: ISDestroy(&is_to_yi);
1043: ISDestroy(&is_from_y);
1044: }
1045: VecDestroy(&yi);
1047: /* Create scatter from d to d_1,d_2,...,d_ns */
1048: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1049: VecCreate(PETSC_COMM_WORLD,&di);
1050: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1051: VecSetFromOptions(di);
1052: VecDuplicateVecs(di,user->ns,&user->di);
1053: VecGetOwnershipRange(user->d,&lo2,&hi2);
1054: istart = 0;
1055: for (i=0; i<user->ns; i++) {
1056: VecGetOwnershipRange(user->di[i],&lo,&hi);
1057: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1058: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1059: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1060: istart = istart + hi-lo;
1061: ISDestroy(&is_to_di);
1062: ISDestroy(&is_from_d);
1063: }
1064: VecDestroy(&di);
1066: /* Assemble RHS of forward problem */
1067: VecCopy(bc,user->yiwork[0]);
1068: for (i=1; i<user->nt; i++) {
1069: VecSet(user->yiwork[i],0.0);
1070: }
1071: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1072: VecDestroy(&bc);
1074: /* Compute true state function yt given ut */
1075: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1076: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1077: VecSetFromOptions(user->ytrue);
1079: /* First compute Av_u = Av*exp(-u) */
1080: VecSet(user->uwork,0);
1081: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1082: VecExp(user->uwork);
1083: MatMult(user->Av,user->uwork,user->Av_u);
1085: /* Symbolic DSG = Div * Grad */
1086: MatProductCreate(user->Div,user->Grad,NULL,&user->DSG);
1087: MatProductSetType(user->DSG,MATPRODUCT_AB);
1088: MatProductSetAlgorithm(user->DSG,"default");
1089: MatProductSetFill(user->DSG,PETSC_DEFAULT);
1090: MatProductSetFromOptions(user->DSG);
1091: MatProductSymbolic(user->DSG);
1093: user->dsg_formed = PETSC_TRUE;
1095: /* Next form DSG = Div*Grad */
1096: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1097: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1098: if (user->dsg_formed) {
1099: MatProductNumeric(user->DSG);
1100: } else {
1101: MatMatMult(user->Div,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&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: MatProductNumeric(user->DSG);
1124: } else {
1125: MatMatMult(user->Div,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&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: }
1330: /*TEST
1332: build:
1333: requires: !complex
1335: test:
1336: args: -tao_cmonitor -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1337: requires: !single
1339: TEST*/