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: TaoSetSolution();
8: Routines: TaoSetObjective();
9: Routines: TaoSetGradient();
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);
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: TaoSetSolution(tao,x);
200: TaoSetObjective(tao, FormFunction, &user);
201: TaoSetGradient(tao, NULL, 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: TaoSetSolution(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 0;
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: {
246: PetscReal d1=0,d2=0;
247: PetscInt i,j;
248: AppCtx *user = (AppCtx*)ptr;
250: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
251: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
252: for (j=0; j<user->ns; j++) {
253: i = user->sample_times[j];
254: MatMult(user->Qblock,user->yi[i],user->di[j]);
255: }
256: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
257: VecAXPY(user->dwork,-1.0,user->d);
258: VecDot(user->dwork,user->dwork,&d1);
260: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
261: MatMult(user->L,user->uwork,user->lwork);
262: VecDot(user->lwork,user->lwork,&d2);
264: *f = 0.5 * (d1 + user->alpha*d2);
265: return 0;
266: }
268: /* ------------------------------------------------------------------- */
269: /*
270: state: g_s = Q' *(Qy - d)
271: design: g_d = alpha*L'*L*(u-ur)
272: */
273: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
274: {
275: PetscInt i,j;
276: AppCtx *user = (AppCtx*)ptr;
278: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
279: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
280: for (j=0; j<user->ns; j++) {
281: i = user->sample_times[j];
282: MatMult(user->Qblock,user->yi[i],user->di[j]);
283: }
284: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
285: VecAXPY(user->dwork,-1.0,user->d);
286: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
287: VecSet(user->ywork,0.0);
288: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
289: for (j=0; j<user->ns; j++) {
290: i = user->sample_times[j];
291: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
292: }
293: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
295: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
296: MatMult(user->L,user->uwork,user->lwork);
297: MatMult(user->LT,user->lwork,user->uwork);
298: VecScale(user->uwork, user->alpha);
299: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
300: return 0;
301: }
303: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
304: {
305: PetscReal d1,d2;
306: PetscInt i,j;
307: AppCtx *user = (AppCtx*)ptr;
309: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
310: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
311: for (j=0; j<user->ns; j++) {
312: i = user->sample_times[j];
313: MatMult(user->Qblock,user->yi[i],user->di[j]);
314: }
315: Gather_i(user->dwork,user->di,user->di_scatter,user->ns);
316: VecAXPY(user->dwork,-1.0,user->d);
317: VecDot(user->dwork,user->dwork,&d1);
318: Scatter_i(user->dwork,user->di,user->di_scatter,user->ns);
319: VecSet(user->ywork,0.0);
320: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
321: for (j=0; j<user->ns; j++) {
322: i = user->sample_times[j];
323: MatMult(user->QblockT,user->di[j],user->yiwork[i]);
324: }
325: Gather_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
327: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
328: MatMult(user->L,user->uwork,user->lwork);
329: VecDot(user->lwork,user->lwork,&d2);
330: MatMult(user->LT,user->lwork,user->uwork);
331: VecScale(user->uwork, user->alpha);
332: *f = 0.5 * (d1 + user->alpha*d2);
334: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
335: return 0;
336: }
338: /* ------------------------------------------------------------------- */
339: /* A
340: MatShell object
341: */
342: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
343: {
344: AppCtx *user = (AppCtx*)ptr;
346: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
347: VecSet(user->uwork,0);
348: VecAXPY(user->uwork,-1.0,user->u);
349: VecExp(user->uwork);
350: MatMult(user->Av,user->uwork,user->Av_u);
351: VecCopy(user->Av_u,user->Swork);
352: VecReciprocal(user->Swork);
353: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
354: MatDiagonalScale(user->Divwork,NULL,user->Swork);
355: if (user->dsg_formed) {
356: MatProductNumeric(user->DSG);
357: } else {
358: MatMatMult(user->Divwork,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&user->DSG);
359: user->dsg_formed = PETSC_TRUE;
360: }
362: /* B = speye(nx^3) + ht*DSG; */
363: MatScale(user->DSG,user->ht);
364: MatShift(user->DSG,1.0);
365: return 0;
366: }
368: /* ------------------------------------------------------------------- */
369: /* B */
370: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
371: {
372: AppCtx *user = (AppCtx*)ptr;
374: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
375: return 0;
376: }
378: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
379: {
380: PetscInt i;
381: AppCtx *user;
383: MatShellGetContext(J_shell,&user);
384: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
385: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
386: for (i=1; i<user->nt; i++) {
387: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
388: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
389: }
390: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
391: return 0;
392: }
394: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
395: {
396: PetscInt i;
397: AppCtx *user;
399: MatShellGetContext(J_shell,&user);
400: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
401: for (i=0; i<user->nt-1; i++) {
402: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
403: VecAXPY(user->yiwork[i],-1.0,user->yi[i+1]);
404: }
405: i = user->nt-1;
406: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
407: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
408: return 0;
409: }
411: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
412: {
413: AppCtx *user;
415: MatShellGetContext(J_shell,&user);
416: MatMult(user->Grad,X,user->Swork);
417: VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
418: MatMult(user->Div,user->Swork,Y);
419: VecAYPX(Y,user->ht,X);
420: return 0;
421: }
423: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
424: {
425: PetscInt i;
426: AppCtx *user;
428: MatShellGetContext(J_shell,&user);
430: /* sdiag(1./v) */
431: VecSet(user->uwork,0);
432: VecAXPY(user->uwork,-1.0,user->u);
433: VecExp(user->uwork);
435: /* sdiag(1./((Av*(1./v)).^2)) */
436: MatMult(user->Av,user->uwork,user->Swork);
437: VecPointwiseMult(user->Swork,user->Swork,user->Swork);
438: VecReciprocal(user->Swork);
440: /* (Av * (sdiag(1./v) * b)) */
441: VecPointwiseMult(user->uwork,user->uwork,X);
442: MatMult(user->Av,user->uwork,user->Twork);
444: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
445: VecPointwiseMult(user->Swork,user->Twork,user->Swork);
447: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
448: for (i=0; i<user->nt; i++) {
449: /* (sdiag(Grad*y(:,i)) */
450: MatMult(user->Grad,user->yi[i],user->Twork);
452: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
453: VecPointwiseMult(user->Twork,user->Twork,user->Swork);
454: MatMult(user->Div,user->Twork,user->yiwork[i]);
455: VecScale(user->yiwork[i],user->ht);
456: }
457: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
459: return 0;
460: }
462: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
463: {
464: PetscInt i;
465: AppCtx *user;
467: MatShellGetContext(J_shell,&user);
469: /* sdiag(1./((Av*(1./v)).^2)) */
470: VecSet(user->uwork,0);
471: VecAXPY(user->uwork,-1.0,user->u);
472: VecExp(user->uwork);
473: MatMult(user->Av,user->uwork,user->Rwork);
474: VecPointwiseMult(user->Rwork,user->Rwork,user->Rwork);
475: VecReciprocal(user->Rwork);
477: VecSet(Y,0.0);
478: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
479: Scatter_i(X,user->yiwork,user->yi_scatter,user->nt);
480: for (i=0; i<user->nt; i++) {
481: /* (Div' * b(:,i)) */
482: MatMult(user->Grad,user->yiwork[i],user->Swork);
484: /* sdiag(Grad*y(:,i)) */
485: MatMult(user->Grad,user->yi[i],user->Twork);
487: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
488: VecPointwiseMult(user->Twork,user->Swork,user->Twork);
490: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
491: VecPointwiseMult(user->Twork,user->Rwork,user->Twork);
493: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
494: MatMult(user->AvT,user->Twork,user->yiwork[i]);
496: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
497: VecPointwiseMult(user->yiwork[i],user->uwork,user->yiwork[i]);
498: VecAXPY(Y,user->ht,user->yiwork[i]);
499: }
500: return 0;
501: }
503: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
504: {
505: AppCtx *user;
507: PCShellGetContext(PC_shell,&user);
509: if (user->dsg_formed) {
510: MatSOR(user->DSG,X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
511: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DSG not formed");
512: return 0;
513: }
515: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
516: {
517: AppCtx *user;
518: PetscInt its,i;
520: MatShellGetContext(J_shell,&user);
522: if (Y == user->ytrue) {
523: /* First solve is done with true solution to set up problem */
524: KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
525: } else {
526: KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
527: }
529: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
530: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
531: KSPGetIterationNumber(user->solver,&its);
532: user->ksp_its = user->ksp_its + its;
534: for (i=1; i<user->nt; i++) {
535: VecAXPY(user->yi[i],1.0,user->yiwork[i-1]);
536: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
537: KSPGetIterationNumber(user->solver,&its);
538: user->ksp_its = user->ksp_its + its;
539: }
540: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
541: return 0;
542: }
544: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
545: {
546: AppCtx *user;
547: PetscInt its,i;
549: MatShellGetContext(J_shell,&user);
551: Scatter_i(X,user->yi,user->yi_scatter,user->nt);
553: i = user->nt - 1;
554: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
556: KSPGetIterationNumber(user->solver,&its);
557: user->ksp_its = user->ksp_its + its;
559: for (i=user->nt-2; i>=0; i--) {
560: VecAXPY(user->yi[i],1.0,user->yiwork[i+1]);
561: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
563: KSPGetIterationNumber(user->solver,&its);
564: user->ksp_its = user->ksp_its + its;
566: }
568: Gather_i(Y,user->yiwork,user->yi_scatter,user->nt);
569: return 0;
570: }
572: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
573: {
574: AppCtx *user;
576: MatShellGetContext(J_shell,&user);
578: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
579: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
580: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
581: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
582: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
583: return 0;
584: }
586: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
587: {
588: AppCtx *user;
590: MatShellGetContext(J_shell,&user);
591: VecCopy(user->js_diag,X);
592: return 0;
594: }
596: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
597: {
598: /* con = Ay - q, A = [B 0 0 ... 0;
599: -I B 0 ... 0;
600: 0 -I B ... 0;
601: ... ;
602: 0 ... -I B]
603: B = ht * Div * Sigma * Grad + eye */
604: PetscInt i;
605: AppCtx *user = (AppCtx*)ptr;
607: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
608: Scatter_i(user->y,user->yi,user->yi_scatter,user->nt);
609: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
610: for (i=1; i<user->nt; i++) {
611: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
612: VecAXPY(user->yiwork[i],-1.0,user->yi[i-1]);
613: }
614: Gather_i(C,user->yiwork,user->yi_scatter,user->nt);
615: VecAXPY(C,-1.0,user->q);
616: return 0;
617: }
619: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
620: {
621: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
622: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
623: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
624: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
625: return 0;
626: }
628: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
629: {
630: PetscInt i;
632: for (i=0; i<nt; i++) {
633: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
634: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
635: }
636: return 0;
637: }
639: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
640: {
641: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
642: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
643: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
644: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
645: return 0;
646: }
648: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
649: {
650: PetscInt i;
652: for (i=0; i<nt; i++) {
653: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
654: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
655: }
656: return 0;
657: }
659: PetscErrorCode ParabolicInitialize(AppCtx *user)
660: {
661: PetscInt m,n,i,j,k,linear_index,istart,iend,iblock,lo,hi,lo2,hi2;
662: Vec XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork,yi,di,bc;
663: PetscReal *x, *y, *z;
664: PetscReal h,stime;
665: PetscScalar hinv,neg_hinv,half = 0.5,sqrt_beta;
666: PetscInt im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
667: PetscReal xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
668: PetscScalar v,vx,vy,vz;
669: IS is_from_y,is_to_yi,is_from_d,is_to_di;
670: /* Data locations */
671: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160,
672: 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774,
673: 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997, 0.5198, 0.8326,
674: 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728,
675: 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273,
676: 0.5724, 0.4331, 0.5136, 0.3547, 0.4413, 0.2602, 0.5698, 0.7278,
677: 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594,
678: 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
680: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256,
681: 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792,
682: 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437, 0.5938, 0.6137,
683: 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985,
684: 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288,
685: 0.5761, 0.1129, 0.3841, 0.6150, 0.6904, 0.6686, 0.1361, 0.4601,
686: 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480,
687: 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
689: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295,
690: 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819,
691: 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236, 0.8800, 0.2939,
692: 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712,
693: 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078,
694: 0.1987, 0.2297, 0.4321, 0.8115, 0.4915, 0.7764, 0.4657, 0.4627,
695: 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313,
696: 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
698: PetscMalloc1(user->mx,&x);
699: PetscMalloc1(user->mx,&y);
700: PetscMalloc1(user->mx,&z);
701: user->jformed = PETSC_FALSE;
702: user->dsg_formed = PETSC_FALSE;
704: n = user->mx * user->mx * user->mx;
705: m = 3 * user->mx * user->mx * (user->mx-1);
706: sqrt_beta = PetscSqrtScalar(user->beta);
708: user->ksp_its = 0;
709: user->ksp_its_initial = 0;
711: stime = (PetscReal)user->nt/user->ns;
712: PetscMalloc1(user->ns,&user->sample_times);
713: for (i=0; i<user->ns; i++) {
714: user->sample_times[i] = (PetscInt)(stime*((PetscReal)i+1.0)-0.5);
715: }
717: VecCreate(PETSC_COMM_WORLD,&XX);
718: VecCreate(PETSC_COMM_WORLD,&user->q);
719: VecSetSizes(XX,PETSC_DECIDE,n);
720: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
721: VecSetFromOptions(XX);
722: VecSetFromOptions(user->q);
724: VecDuplicate(XX,&YY);
725: VecDuplicate(XX,&ZZ);
726: VecDuplicate(XX,&XXwork);
727: VecDuplicate(XX,&YYwork);
728: VecDuplicate(XX,&ZZwork);
729: VecDuplicate(XX,&UTwork);
730: VecDuplicate(XX,&user->utrue);
731: VecDuplicate(XX,&bc);
733: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
734: h = 1.0/user->mx;
735: hinv = user->mx;
736: neg_hinv = -hinv;
738: VecGetOwnershipRange(XX,&istart,&iend);
739: for (linear_index=istart; linear_index<iend; linear_index++) {
740: i = linear_index % user->mx;
741: j = ((linear_index-i)/user->mx) % user->mx;
742: k = ((linear_index-i)/user->mx-j) / user->mx;
743: vx = h*(i+0.5);
744: vy = h*(j+0.5);
745: vz = h*(k+0.5);
746: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
747: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
748: VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
749: if ((vx<0.6) && (vx>0.4) && (vy<0.6) && (vy>0.4) && (vy<0.6) && (vz<0.6) && (vz>0.4)) {
750: v = 1000.0;
751: VecSetValues(bc,1,&linear_index,&v,INSERT_VALUES);
752: }
753: }
755: VecAssemblyBegin(XX);
756: VecAssemblyEnd(XX);
757: VecAssemblyBegin(YY);
758: VecAssemblyEnd(YY);
759: VecAssemblyBegin(ZZ);
760: VecAssemblyEnd(ZZ);
761: VecAssemblyBegin(bc);
762: VecAssemblyEnd(bc);
764: /* Compute true parameter function
765: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
766: VecCopy(XX,XXwork);
767: VecCopy(YY,YYwork);
768: VecCopy(ZZ,ZZwork);
770: VecShift(XXwork,-0.5);
771: VecShift(YYwork,-0.5);
772: VecShift(ZZwork,-0.5);
774: VecPointwiseMult(XXwork,XXwork,XXwork);
775: VecPointwiseMult(YYwork,YYwork,YYwork);
776: VecPointwiseMult(ZZwork,ZZwork,ZZwork);
778: VecCopy(XXwork,user->utrue);
779: VecAXPY(user->utrue,1.0,YYwork);
780: VecAXPY(user->utrue,1.0,ZZwork);
781: VecScale(user->utrue,-10.0);
782: VecExp(user->utrue);
783: VecShift(user->utrue,0.5);
785: VecDestroy(&XX);
786: VecDestroy(&YY);
787: VecDestroy(&ZZ);
788: VecDestroy(&XXwork);
789: VecDestroy(&YYwork);
790: VecDestroy(&ZZwork);
791: VecDestroy(&UTwork);
793: /* Initial guess and reference model */
794: VecDuplicate(user->utrue,&user->ur);
795: VecSet(user->ur,0.0);
797: /* Generate Grad matrix */
798: MatCreate(PETSC_COMM_WORLD,&user->Grad);
799: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,m,n);
800: MatSetFromOptions(user->Grad);
801: MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
802: MatSeqAIJSetPreallocation(user->Grad,2,NULL);
803: MatGetOwnershipRange(user->Grad,&istart,&iend);
805: for (i=istart; i<iend; i++) {
806: if (i<m/3) {
807: iblock = i / (user->mx-1);
808: j = iblock*user->mx + (i % (user->mx-1));
809: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
810: j = j+1;
811: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
812: }
813: if (i>=m/3 && i<2*m/3) {
814: iblock = (i-m/3) / (user->mx*(user->mx-1));
815: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
816: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
817: j = j + user->mx;
818: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
819: }
820: if (i>=2*m/3) {
821: j = i-2*m/3;
822: MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
823: j = j + user->mx*user->mx;
824: MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
825: }
826: }
828: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
829: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
831: /* Generate arithmetic averaging matrix Av */
832: MatCreate(PETSC_COMM_WORLD,&user->Av);
833: MatSetSizes(user->Av,PETSC_DECIDE,PETSC_DECIDE,m,n);
834: MatSetFromOptions(user->Av);
835: MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
836: MatSeqAIJSetPreallocation(user->Av,2,NULL);
837: MatGetOwnershipRange(user->Av,&istart,&iend);
839: for (i=istart; i<iend; i++) {
840: if (i<m/3) {
841: iblock = i / (user->mx-1);
842: j = iblock*user->mx + (i % (user->mx-1));
843: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
844: j = j+1;
845: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
846: }
847: if (i>=m/3 && i<2*m/3) {
848: iblock = (i-m/3) / (user->mx*(user->mx-1));
849: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
850: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
851: j = j + user->mx;
852: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
853: }
854: if (i>=2*m/3) {
855: j = i-2*m/3;
856: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
857: j = j + user->mx*user->mx;
858: MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
859: }
860: }
862: MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
863: MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);
865: /* Generate transpose of averaging matrix Av */
866: MatTranspose(user->Av,MAT_INITIAL_MATRIX,&user->AvT);
868: MatCreate(PETSC_COMM_WORLD,&user->L);
869: MatSetSizes(user->L,PETSC_DECIDE,PETSC_DECIDE,m+n,n);
870: MatSetFromOptions(user->L);
871: MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
872: MatSeqAIJSetPreallocation(user->L,2,NULL);
873: MatGetOwnershipRange(user->L,&istart,&iend);
875: for (i=istart; i<iend; i++) {
876: if (i<m/3) {
877: iblock = i / (user->mx-1);
878: j = iblock*user->mx + (i % (user->mx-1));
879: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
880: j = j+1;
881: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
882: }
883: if (i>=m/3 && i<2*m/3) {
884: iblock = (i-m/3) / (user->mx*(user->mx-1));
885: j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
886: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
887: j = j + user->mx;
888: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
889: }
890: if (i>=2*m/3 && i<m) {
891: j = i-2*m/3;
892: MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
893: j = j + user->mx*user->mx;
894: MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
895: }
896: if (i>=m) {
897: j = i - m;
898: MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
899: }
900: }
902: MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
903: MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
905: MatScale(user->L,PetscPowScalar(h,1.5));
907: /* Generate Div matrix */
908: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
910: /* Build work vectors and matrices */
911: VecCreate(PETSC_COMM_WORLD,&user->S);
912: VecSetSizes(user->S, PETSC_DECIDE, user->mx*user->mx*(user->mx-1)*3);
913: VecSetFromOptions(user->S);
915: VecCreate(PETSC_COMM_WORLD,&user->lwork);
916: VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
917: VecSetFromOptions(user->lwork);
919: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
920: MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);
922: VecCreate(PETSC_COMM_WORLD,&user->d);
923: VecSetSizes(user->d,PETSC_DECIDE,user->ndata*user->nt);
924: VecSetFromOptions(user->d);
926: VecDuplicate(user->S,&user->Swork);
927: VecDuplicate(user->S,&user->Av_u);
928: VecDuplicate(user->S,&user->Twork);
929: VecDuplicate(user->S,&user->Rwork);
930: VecDuplicate(user->y,&user->ywork);
931: VecDuplicate(user->u,&user->uwork);
932: VecDuplicate(user->u,&user->js_diag);
933: VecDuplicate(user->c,&user->cwork);
934: VecDuplicate(user->d,&user->dwork);
936: /* Create matrix-free shell user->Js for computing A*x */
937: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->Js);
938: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
939: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
940: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
941: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
943: /* Diagonal blocks of user->Js */
944: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlock);
945: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
946: /* Blocks are symmetric */
947: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMult);
949: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
950: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
951: This is an SSOR preconditioner for user->JsBlock. */
952: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsBlockPrec);
953: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
954: /* JsBlockPrec is symmetric */
955: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMult);
956: MatSetOption(user->JsBlockPrec,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
958: /* Create a matrix-free shell user->Jd for computing B*x */
959: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m,user,&user->Jd);
960: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
961: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
963: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
964: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m*user->nt,user->m*user->nt,user,&user->JsInv);
965: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
966: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
968: /* Solver options and tolerances */
969: KSPCreate(PETSC_COMM_WORLD,&user->solver);
970: KSPSetType(user->solver,KSPCG);
971: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
972: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE);
973: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
974: KSPSetFromOptions(user->solver);
975: KSPGetPC(user->solver,&user->prec);
976: PCSetType(user->prec,PCSHELL);
978: PCShellSetApply(user->prec,StateMatBlockPrecMult);
979: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMult);
980: PCShellSetContext(user->prec,user);
982: /* Create scatter from y to y_1,y_2,...,y_nt */
983: PetscMalloc1(user->nt*user->m,&user->yi_scatter);
984: VecCreate(PETSC_COMM_WORLD,&yi);
985: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx*user->mx);
986: VecSetFromOptions(yi);
987: VecDuplicateVecs(yi,user->nt,&user->yi);
988: VecDuplicateVecs(yi,user->nt,&user->yiwork);
990: VecGetOwnershipRange(user->y,&lo2,&hi2);
991: istart = 0;
992: for (i=0; i<user->nt; i++) {
993: VecGetOwnershipRange(user->yi[i],&lo,&hi);
994: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
995: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
996: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
997: istart = istart + hi-lo;
998: ISDestroy(&is_to_yi);
999: ISDestroy(&is_from_y);
1000: }
1001: VecDestroy(&yi);
1003: /* Create scatter from d to d_1,d_2,...,d_ns */
1004: PetscMalloc1(user->ns*user->ndata,&user->di_scatter);
1005: VecCreate(PETSC_COMM_WORLD,&di);
1006: VecSetSizes(di,PETSC_DECIDE,user->ndata);
1007: VecSetFromOptions(di);
1008: VecDuplicateVecs(di,user->ns,&user->di);
1009: VecGetOwnershipRange(user->d,&lo2,&hi2);
1010: istart = 0;
1011: for (i=0; i<user->ns; i++) {
1012: VecGetOwnershipRange(user->di[i],&lo,&hi);
1013: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_di);
1014: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
1015: VecScatterCreate(user->d,is_from_d,user->di[i],is_to_di,&user->di_scatter[i]);
1016: istart = istart + hi-lo;
1017: ISDestroy(&is_to_di);
1018: ISDestroy(&is_from_d);
1019: }
1020: VecDestroy(&di);
1022: /* Assemble RHS of forward problem */
1023: VecCopy(bc,user->yiwork[0]);
1024: for (i=1; i<user->nt; i++) {
1025: VecSet(user->yiwork[i],0.0);
1026: }
1027: Gather_i(user->q,user->yiwork,user->yi_scatter,user->nt);
1028: VecDestroy(&bc);
1030: /* Compute true state function yt given ut */
1031: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1032: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1033: VecSetFromOptions(user->ytrue);
1035: /* First compute Av_u = Av*exp(-u) */
1036: VecSet(user->uwork,0);
1037: VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
1038: VecExp(user->uwork);
1039: MatMult(user->Av,user->uwork,user->Av_u);
1041: /* Symbolic DSG = Div * Grad */
1042: MatProductCreate(user->Div,user->Grad,NULL,&user->DSG);
1043: MatProductSetType(user->DSG,MATPRODUCT_AB);
1044: MatProductSetAlgorithm(user->DSG,"default");
1045: MatProductSetFill(user->DSG,PETSC_DEFAULT);
1046: MatProductSetFromOptions(user->DSG);
1047: MatProductSymbolic(user->DSG);
1049: user->dsg_formed = PETSC_TRUE;
1051: /* Next form DSG = Div*Grad */
1052: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1053: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1054: if (user->dsg_formed) {
1055: MatProductNumeric(user->DSG);
1056: } else {
1057: MatMatMult(user->Div,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&user->DSG);
1058: user->dsg_formed = PETSC_TRUE;
1059: }
1060: /* B = speye(nx^3) + ht*DSG; */
1061: MatScale(user->DSG,user->ht);
1062: MatShift(user->DSG,1.0);
1064: /* Now solve for ytrue */
1065: StateMatInvMult(user->Js,user->q,user->ytrue);
1067: /* Initial guess y0 for state given u0 */
1069: /* First compute Av_u = Av*exp(-u) */
1070: VecSet(user->uwork,0);
1071: VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
1072: VecExp(user->uwork);
1073: MatMult(user->Av,user->uwork,user->Av_u);
1075: /* Next form DSG = Div*S*Grad */
1076: MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
1077: MatDiagonalScale(user->Divwork,NULL,user->Av_u);
1078: if (user->dsg_formed) {
1079: MatProductNumeric(user->DSG);
1080: } else {
1081: MatMatMult(user->Div,user->Grad,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&user->DSG);
1083: user->dsg_formed = PETSC_TRUE;
1084: }
1085: /* B = speye(nx^3) + ht*DSG; */
1086: MatScale(user->DSG,user->ht);
1087: MatShift(user->DSG,1.0);
1089: /* Now solve for y */
1090: StateMatInvMult(user->Js,user->q,user->y);
1092: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1093: MatCreate(PETSC_COMM_WORLD,&user->Qblock);
1094: MatSetSizes(user->Qblock,PETSC_DECIDE,PETSC_DECIDE,user->ndata,n);
1095: MatSetFromOptions(user->Qblock);
1096: MatMPIAIJSetPreallocation(user->Qblock,8,NULL,8,NULL);
1097: MatSeqAIJSetPreallocation(user->Qblock,8,NULL);
1099: for (i=0; i<user->mx; i++) {
1100: x[i] = h*(i+0.5);
1101: y[i] = h*(i+0.5);
1102: z[i] = h*(i+0.5);
1103: }
1105: MatGetOwnershipRange(user->Qblock,&istart,&iend);
1106: nx = user->mx; ny = user->mx; nz = user->mx;
1107: for (i=istart; i<iend; i++) {
1108: xri = xr[i];
1109: im = 0;
1110: xim = x[im];
1111: while (xri>xim && im<nx) {
1112: im = im+1;
1113: xim = x[im];
1114: }
1115: indx1 = im-1;
1116: indx2 = im;
1117: dx1 = xri - x[indx1];
1118: dx2 = x[indx2] - xri;
1120: yri = yr[i];
1121: im = 0;
1122: yim = y[im];
1123: while (yri>yim && im<ny) {
1124: im = im+1;
1125: yim = y[im];
1126: }
1127: indy1 = im-1;
1128: indy2 = im;
1129: dy1 = yri - y[indy1];
1130: dy2 = y[indy2] - yri;
1132: zri = zr[i];
1133: im = 0;
1134: zim = z[im];
1135: while (zri>zim && im<nz) {
1136: im = im+1;
1137: zim = z[im];
1138: }
1139: indz1 = im-1;
1140: indz2 = im;
1141: dz1 = zri - z[indz1];
1142: dz2 = z[indz2] - zri;
1144: Dx = x[indx2] - x[indx1];
1145: Dy = y[indy2] - y[indy1];
1146: Dz = z[indz2] - z[indz1];
1148: j = indx1 + indy1*nx + indz1*nx*ny;
1149: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1150: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1152: j = indx1 + indy1*nx + indz2*nx*ny;
1153: v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1154: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1156: j = indx1 + indy2*nx + indz1*nx*ny;
1157: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1158: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1160: j = indx1 + indy2*nx + indz2*nx*ny;
1161: v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1162: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1164: j = indx2 + indy1*nx + indz1*nx*ny;
1165: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
1166: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1168: j = indx2 + indy1*nx + indz2*nx*ny;
1169: v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
1170: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1172: j = indx2 + indy2*nx + indz1*nx*ny;
1173: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
1174: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1176: j = indx2 + indy2*nx + indz2*nx*ny;
1177: v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
1178: MatSetValues(user->Qblock,1,&i,1,&j,&v,INSERT_VALUES);
1179: }
1180: MatAssemblyBegin(user->Qblock,MAT_FINAL_ASSEMBLY);
1181: MatAssemblyEnd(user->Qblock,MAT_FINAL_ASSEMBLY);
1183: MatTranspose(user->Qblock,MAT_INITIAL_MATRIX,&user->QblockT);
1184: MatTranspose(user->L,MAT_INITIAL_MATRIX,&user->LT);
1186: /* Add noise to the measurement data */
1187: VecSet(user->ywork,1.0);
1188: VecAYPX(user->ywork,user->noise,user->ytrue);
1189: Scatter_i(user->ywork,user->yiwork,user->yi_scatter,user->nt);
1190: for (j=0; j<user->ns; j++) {
1191: i = user->sample_times[j];
1192: MatMult(user->Qblock,user->yiwork[i],user->di[j]);
1193: }
1194: Gather_i(user->d,user->di,user->di_scatter,user->ns);
1196: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1197: KSPSetFromOptions(user->solver);
1198: PetscFree(x);
1199: PetscFree(y);
1200: PetscFree(z);
1201: return 0;
1202: }
1204: PetscErrorCode ParabolicDestroy(AppCtx *user)
1205: {
1206: PetscInt i;
1208: MatDestroy(&user->Qblock);
1209: MatDestroy(&user->QblockT);
1210: MatDestroy(&user->Div);
1211: MatDestroy(&user->Divwork);
1212: MatDestroy(&user->Grad);
1213: MatDestroy(&user->Av);
1214: MatDestroy(&user->Avwork);
1215: MatDestroy(&user->AvT);
1216: MatDestroy(&user->DSG);
1217: MatDestroy(&user->L);
1218: MatDestroy(&user->LT);
1219: KSPDestroy(&user->solver);
1220: MatDestroy(&user->Js);
1221: MatDestroy(&user->Jd);
1222: MatDestroy(&user->JsInv);
1223: MatDestroy(&user->JsBlock);
1224: MatDestroy(&user->JsBlockPrec);
1225: VecDestroy(&user->u);
1226: VecDestroy(&user->uwork);
1227: VecDestroy(&user->utrue);
1228: VecDestroy(&user->y);
1229: VecDestroy(&user->ywork);
1230: VecDestroy(&user->ytrue);
1231: VecDestroyVecs(user->nt,&user->yi);
1232: VecDestroyVecs(user->nt,&user->yiwork);
1233: VecDestroyVecs(user->ns,&user->di);
1234: PetscFree(user->yi);
1235: PetscFree(user->yiwork);
1236: PetscFree(user->di);
1237: VecDestroy(&user->c);
1238: VecDestroy(&user->cwork);
1239: VecDestroy(&user->ur);
1240: VecDestroy(&user->q);
1241: VecDestroy(&user->d);
1242: VecDestroy(&user->dwork);
1243: VecDestroy(&user->lwork);
1244: VecDestroy(&user->S);
1245: VecDestroy(&user->Swork);
1246: VecDestroy(&user->Av_u);
1247: VecDestroy(&user->Twork);
1248: VecDestroy(&user->Rwork);
1249: VecDestroy(&user->js_diag);
1250: ISDestroy(&user->s_is);
1251: ISDestroy(&user->d_is);
1252: VecScatterDestroy(&user->state_scatter);
1253: VecScatterDestroy(&user->design_scatter);
1254: for (i=0; i<user->nt; i++) {
1255: VecScatterDestroy(&user->yi_scatter[i]);
1256: }
1257: for (i=0; i<user->ns; i++) {
1258: VecScatterDestroy(&user->di_scatter[i]);
1259: }
1260: PetscFree(user->yi_scatter);
1261: PetscFree(user->di_scatter);
1262: PetscFree(user->sample_times);
1263: return 0;
1264: }
1266: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1267: {
1268: Vec X;
1269: PetscReal unorm,ynorm;
1270: AppCtx *user = (AppCtx*)ptr;
1272: TaoGetSolution(tao,&X);
1273: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1274: VecAXPY(user->ywork,-1.0,user->ytrue);
1275: VecAXPY(user->uwork,-1.0,user->utrue);
1276: VecNorm(user->uwork,NORM_2,&unorm);
1277: VecNorm(user->ywork,NORM_2,&ynorm);
1278: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1279: return 0;
1280: }
1282: /*TEST
1284: build:
1285: requires: !complex
1287: test:
1288: args: -tao_cmonitor -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1289: requires: !single
1291: TEST*/