Actual source code: elliptic.c
1: #include <petsc/private/taoimpl.h>
3: typedef struct {
4: PetscInt n; /* Number of total variables */
5: PetscInt m; /* Number of constraints */
6: PetscInt nstate;
7: PetscInt ndesign;
8: PetscInt mx; /* grid points in each direction */
9: PetscInt ns; /* Number of data samples (1<=ns<=8)
10: Currently only ns=1 is supported */
11: PetscInt ndata; /* Number of data points per sample */
12: IS s_is;
13: IS d_is;
15: VecScatter state_scatter;
16: VecScatter design_scatter;
17: VecScatter *yi_scatter, *di_scatter;
18: Vec suby, subq, subd;
19: Mat Js, Jd, JsPrec, JsInv, JsBlock;
21: PetscReal alpha; /* Regularization parameter */
22: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
23: PetscReal noise; /* Amount of noise to add to data */
24: PetscReal *ones;
25: Mat Q;
26: Mat MQ;
27: Mat L;
29: Mat Grad;
30: Mat Av, Avwork;
31: Mat Div, Divwork;
32: Mat DSG;
33: Mat Diag, Ones;
35: Vec q;
36: Vec ur; /* reference */
38: Vec d;
39: Vec dwork;
41: Vec x; /* super vec of y,u */
43: Vec y; /* state variables */
44: Vec ywork;
46: Vec ytrue;
48: Vec u; /* design variables */
49: Vec uwork;
51: Vec utrue;
53: Vec js_diag;
55: Vec c; /* constraint vector */
56: Vec cwork;
58: Vec lwork;
59: Vec S;
60: Vec Swork, Twork, Sdiag, Ywork;
61: Vec Av_u;
63: KSP solver;
64: PC prec;
66: PetscReal tola, tolb, tolc, told;
67: PetscInt ksp_its;
68: PetscInt ksp_its_initial;
69: PetscLogStage stages[10];
70: PetscBool use_ptap;
71: PetscBool use_lrc;
72: } AppCtx;
74: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
75: PetscErrorCode FormGradient(Tao, Vec, Vec, void *);
76: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
77: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void *);
78: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void *);
79: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
80: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void *);
81: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
82: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
83: PetscErrorCode EllipticInitialize(AppCtx *);
84: PetscErrorCode EllipticDestroy(AppCtx *);
85: PetscErrorCode EllipticMonitor(Tao, void *);
87: PetscErrorCode StateBlockMatMult(Mat, Vec, Vec);
88: PetscErrorCode StateMatMult(Mat, Vec, Vec);
90: PetscErrorCode StateInvMatMult(Mat, Vec, Vec);
91: PetscErrorCode DesignMatMult(Mat, Vec, Vec);
92: PetscErrorCode DesignMatMultTranspose(Mat, Vec, Vec);
94: PetscErrorCode QMatMult(Mat, Vec, Vec);
95: PetscErrorCode QMatMultTranspose(Mat, Vec, Vec);
97: static char help[] = "";
99: int main(int argc, char **argv)
100: {
101: Vec x0;
102: Tao tao;
103: AppCtx user;
104: PetscInt ntests = 1;
105: PetscInt i;
107: PetscFunctionBeginUser;
108: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
109: user.mx = 8;
110: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "elliptic example", NULL);
111: PetscCall(PetscOptionsInt("-mx", "Number of grid points in each direction", "", user.mx, &user.mx, NULL));
112: user.ns = 6;
113: PetscCall(PetscOptionsInt("-ns", "Number of data samples (1<=ns<=8)", "", user.ns, &user.ns, NULL));
114: user.ndata = 64;
115: PetscCall(PetscOptionsInt("-ndata", "Numbers of data points per sample", "", user.ndata, &user.ndata, NULL));
116: user.alpha = 0.1;
117: PetscCall(PetscOptionsReal("-alpha", "Regularization parameter", "", user.alpha, &user.alpha, NULL));
118: user.beta = 0.00001;
119: PetscCall(PetscOptionsReal("-beta", "Weight attributed to ||u||^2 in regularization functional", "", user.beta, &user.beta, NULL));
120: user.noise = 0.01;
121: PetscCall(PetscOptionsReal("-noise", "Amount of noise to add to data", "", user.noise, &user.noise, NULL));
123: user.use_ptap = PETSC_FALSE;
124: PetscCall(PetscOptionsBool("-use_ptap", "Use ptap matrix for DSG", "", user.use_ptap, &user.use_ptap, NULL));
125: user.use_lrc = PETSC_FALSE;
126: PetscCall(PetscOptionsBool("-use_lrc", "Use lrc matrix for Js", "", user.use_lrc, &user.use_lrc, NULL));
127: PetscCall(PetscOptionsInt("-ntests", "Number of times to repeat TaoSolve", "", ntests, &ntests, NULL));
128: PetscOptionsEnd();
130: user.m = user.ns * user.mx * user.mx * user.mx; /* number of constraints */
131: user.nstate = user.m;
132: user.ndesign = user.mx * user.mx * user.mx;
133: user.n = user.nstate + user.ndesign; /* number of variables */
135: /* Create TAO solver and set desired solution method */
136: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
137: PetscCall(TaoSetType(tao, TAOLCL));
139: /* Set up initial vectors and matrices */
140: PetscCall(EllipticInitialize(&user));
142: PetscCall(Gather(user.x, user.y, user.state_scatter, user.u, user.design_scatter));
143: PetscCall(VecDuplicate(user.x, &x0));
144: PetscCall(VecCopy(user.x, x0));
146: /* Set solution vector with an initial guess */
147: PetscCall(TaoSetSolution(tao, user.x));
148: PetscCall(TaoSetObjective(tao, FormFunction, &user));
149: PetscCall(TaoSetGradient(tao, NULL, FormGradient, &user));
150: PetscCall(TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user));
152: PetscCall(TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, &user));
153: PetscCall(TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user));
155: PetscCall(TaoSetStateDesignIS(tao, user.s_is, user.d_is));
156: PetscCall(TaoSetFromOptions(tao));
158: /* SOLVE THE APPLICATION */
159: PetscCall(PetscLogStageRegister("Trials", &user.stages[1]));
160: PetscCall(PetscLogStagePush(user.stages[1]));
161: for (i = 0; i < ntests; i++) {
162: PetscCall(TaoSolve(tao));
163: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP Iterations = %" PetscInt_FMT "\n", user.ksp_its));
164: PetscCall(VecCopy(x0, user.x));
165: }
166: PetscCall(PetscLogStagePop());
167: PetscCall(PetscBarrier((PetscObject)user.x));
168: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations within initialization: "));
169: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its_initial));
171: PetscCall(TaoDestroy(&tao));
172: PetscCall(VecDestroy(&x0));
173: PetscCall(EllipticDestroy(&user));
174: PetscCall(PetscFinalize());
175: return 0;
176: }
177: /* ------------------------------------------------------------------- */
178: /*
179: dwork = Qy - d
180: lwork = L*(u-ur)
181: f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
182: */
183: PetscErrorCode FormFunction(Tao tao, Vec X, PetscReal *f, void *ptr)
184: {
185: PetscReal d1 = 0, d2 = 0;
186: AppCtx *user = (AppCtx *)ptr;
188: PetscFunctionBegin;
189: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
190: PetscCall(MatMult(user->MQ, user->y, user->dwork));
191: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
192: PetscCall(VecDot(user->dwork, user->dwork, &d1));
193: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
194: PetscCall(MatMult(user->L, user->uwork, user->lwork));
195: PetscCall(VecDot(user->lwork, user->lwork, &d2));
196: *f = 0.5 * (d1 + user->alpha * d2);
197: PetscFunctionReturn(PETSC_SUCCESS);
198: }
200: /* ------------------------------------------------------------------- */
201: /*
202: state: g_s = Q' *(Qy - d)
203: design: g_d = alpha*L'*L*(u-ur)
204: */
205: PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
206: {
207: AppCtx *user = (AppCtx *)ptr;
209: PetscFunctionBegin;
210: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
211: PetscCall(MatMult(user->MQ, user->y, user->dwork));
212: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
213: PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));
214: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
215: PetscCall(MatMult(user->L, user->uwork, user->lwork));
216: PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
217: PetscCall(VecScale(user->uwork, user->alpha));
218: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
219: PetscFunctionReturn(PETSC_SUCCESS);
220: }
222: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
223: {
224: PetscReal d1, d2;
225: AppCtx *user = (AppCtx *)ptr;
227: PetscFunctionBegin;
228: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
229: PetscCall(MatMult(user->MQ, user->y, user->dwork));
230: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
231: PetscCall(VecDot(user->dwork, user->dwork, &d1));
232: PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));
234: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
235: PetscCall(MatMult(user->L, user->uwork, user->lwork));
236: PetscCall(VecDot(user->lwork, user->lwork, &d2));
237: PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
238: PetscCall(VecScale(user->uwork, user->alpha));
239: *f = 0.5 * (d1 + user->alpha * d2);
240: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
241: PetscFunctionReturn(PETSC_SUCCESS);
242: }
244: /* ------------------------------------------------------------------- */
245: /* A
246: MatShell object
247: */
248: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
249: {
250: AppCtx *user = (AppCtx *)ptr;
252: PetscFunctionBegin;
253: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
254: /* DSG = Div * (1/Av_u) * Grad */
255: PetscCall(VecSet(user->uwork, 0));
256: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
257: PetscCall(VecExp(user->uwork));
258: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
259: PetscCall(VecCopy(user->Av_u, user->Swork));
260: PetscCall(VecReciprocal(user->Swork));
261: if (user->use_ptap) {
262: PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
263: PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
264: } else {
265: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
266: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
267: PetscCall(MatProductNumeric(user->DSG));
268: }
269: PetscFunctionReturn(PETSC_SUCCESS);
270: }
271: /* ------------------------------------------------------------------- */
272: /* B */
273: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
274: {
275: AppCtx *user = (AppCtx *)ptr;
277: PetscFunctionBegin;
278: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
279: PetscFunctionReturn(PETSC_SUCCESS);
280: }
282: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
283: {
284: PetscReal sum;
285: AppCtx *user;
287: PetscFunctionBegin;
288: PetscCall(MatShellGetContext(J_shell, &user));
289: PetscCall(MatMult(user->DSG, X, Y));
290: PetscCall(VecSum(X, &sum));
291: sum /= user->ndesign;
292: PetscCall(VecShift(Y, sum));
293: PetscFunctionReturn(PETSC_SUCCESS);
294: }
296: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
297: {
298: PetscInt i;
299: AppCtx *user;
301: PetscFunctionBegin;
302: PetscCall(MatShellGetContext(J_shell, &user));
303: if (user->ns == 1) {
304: PetscCall(MatMult(user->JsBlock, X, Y));
305: } else {
306: for (i = 0; i < user->ns; i++) {
307: PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
308: PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
309: PetscCall(MatMult(user->JsBlock, user->subq, user->suby));
310: PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
311: }
312: }
313: PetscFunctionReturn(PETSC_SUCCESS);
314: }
316: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
317: {
318: PetscInt its, i;
319: AppCtx *user;
321: PetscFunctionBegin;
322: PetscCall(MatShellGetContext(J_shell, &user));
323: PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));
324: if (Y == user->ytrue) {
325: /* First solve is done using true solution to set up problem */
326: PetscCall(KSPSetTolerances(user->solver, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
327: } else {
328: PetscCall(KSPSetTolerances(user->solver, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
329: }
330: if (user->ns == 1) {
331: PetscCall(KSPSolve(user->solver, X, Y));
332: PetscCall(KSPGetIterationNumber(user->solver, &its));
333: user->ksp_its += its;
334: } else {
335: for (i = 0; i < user->ns; i++) {
336: PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
337: PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
338: PetscCall(KSPSolve(user->solver, user->subq, user->suby));
339: PetscCall(KSPGetIterationNumber(user->solver, &its));
340: user->ksp_its += its;
341: PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
342: }
343: }
344: PetscFunctionReturn(PETSC_SUCCESS);
345: }
346: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
347: {
348: AppCtx *user;
349: PetscInt i;
351: PetscFunctionBegin;
352: PetscCall(MatShellGetContext(J_shell, &user));
353: if (user->ns == 1) {
354: PetscCall(MatMult(user->Q, X, Y));
355: } else {
356: for (i = 0; i < user->ns; i++) {
357: PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
358: PetscCall(Scatter(Y, user->subd, user->di_scatter[i], 0, 0));
359: PetscCall(MatMult(user->Q, user->subq, user->subd));
360: PetscCall(Gather(Y, user->subd, user->di_scatter[i], 0, 0));
361: }
362: }
363: PetscFunctionReturn(PETSC_SUCCESS);
364: }
366: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
367: {
368: AppCtx *user;
369: PetscInt i;
371: PetscFunctionBegin;
372: PetscCall(MatShellGetContext(J_shell, &user));
373: if (user->ns == 1) {
374: PetscCall(MatMultTranspose(user->Q, X, Y));
375: } else {
376: for (i = 0; i < user->ns; i++) {
377: PetscCall(Scatter(X, user->subd, user->di_scatter[i], 0, 0));
378: PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
379: PetscCall(MatMultTranspose(user->Q, user->subd, user->suby));
380: PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
381: }
382: }
383: PetscFunctionReturn(PETSC_SUCCESS);
384: }
386: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
387: {
388: PetscInt i;
389: AppCtx *user;
391: PetscFunctionBegin;
392: PetscCall(MatShellGetContext(J_shell, &user));
394: /* sdiag(1./v) */
395: PetscCall(VecSet(user->uwork, 0));
396: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
397: PetscCall(VecExp(user->uwork));
399: /* sdiag(1./((Av*(1./v)).^2)) */
400: PetscCall(MatMult(user->Av, user->uwork, user->Swork));
401: PetscCall(VecPointwiseMult(user->Swork, user->Swork, user->Swork));
402: PetscCall(VecReciprocal(user->Swork));
404: /* (Av * (sdiag(1./v) * b)) */
405: PetscCall(VecPointwiseMult(user->uwork, user->uwork, X));
406: PetscCall(MatMult(user->Av, user->uwork, user->Twork));
408: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
409: PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
411: if (user->ns == 1) {
412: /* (sdiag(Grad*y(:,i)) */
413: PetscCall(MatMult(user->Grad, user->y, user->Twork));
415: /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
416: PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
417: PetscCall(MatMultTranspose(user->Grad, user->Swork, Y));
418: } else {
419: for (i = 0; i < user->ns; i++) {
420: PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
421: PetscCall(Scatter(Y, user->subq, user->yi_scatter[i], 0, 0));
423: PetscCall(MatMult(user->Grad, user->suby, user->Twork));
424: PetscCall(VecPointwiseMult(user->Twork, user->Twork, user->Swork));
425: PetscCall(MatMultTranspose(user->Grad, user->Twork, user->subq));
426: PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
427: PetscCall(Gather(Y, user->subq, user->yi_scatter[i], 0, 0));
428: }
429: }
430: PetscFunctionReturn(PETSC_SUCCESS);
431: }
433: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
434: {
435: PetscInt i;
436: AppCtx *user;
438: PetscFunctionBegin;
439: PetscCall(MatShellGetContext(J_shell, &user));
440: PetscCall(VecZeroEntries(Y));
442: /* Sdiag = 1./((Av*(1./v)).^2) */
443: PetscCall(VecSet(user->uwork, 0));
444: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
445: PetscCall(VecExp(user->uwork));
446: PetscCall(MatMult(user->Av, user->uwork, user->Swork));
447: PetscCall(VecPointwiseMult(user->Sdiag, user->Swork, user->Swork));
448: PetscCall(VecReciprocal(user->Sdiag));
450: for (i = 0; i < user->ns; i++) {
451: PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
452: PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
454: /* Swork = (Div' * b(:,i)) */
455: PetscCall(MatMult(user->Grad, user->subq, user->Swork));
457: /* Twork = Grad*y(:,i) */
458: PetscCall(MatMult(user->Grad, user->suby, user->Twork));
460: /* Twork = sdiag(Twork) * Swork */
461: PetscCall(VecPointwiseMult(user->Twork, user->Swork, user->Twork));
463: /* Swork = pointwisemult(Sdiag,Twork) */
464: PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Sdiag));
466: /* Ywork = Av' * Swork */
467: PetscCall(MatMultTranspose(user->Av, user->Swork, user->Ywork));
469: /* Ywork = pointwisemult(uwork,Ywork) */
470: PetscCall(VecPointwiseMult(user->Ywork, user->uwork, user->Ywork));
471: PetscCall(VecAXPY(Y, 1.0, user->Ywork));
472: PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
473: }
474: PetscFunctionReturn(PETSC_SUCCESS);
475: }
477: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
478: {
479: /* C=Ay - q A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
480: PetscReal sum;
481: PetscInt i;
482: AppCtx *user = (AppCtx *)ptr;
484: PetscFunctionBegin;
485: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
486: if (user->ns == 1) {
487: PetscCall(MatMult(user->Grad, user->y, user->Swork));
488: PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
489: PetscCall(MatMultTranspose(user->Grad, user->Swork, C));
490: PetscCall(VecSum(user->y, &sum));
491: sum /= user->ndesign;
492: PetscCall(VecShift(C, sum));
493: } else {
494: for (i = 0; i < user->ns; i++) {
495: PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
496: PetscCall(Scatter(C, user->subq, user->yi_scatter[i], 0, 0));
497: PetscCall(MatMult(user->Grad, user->suby, user->Swork));
498: PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
499: PetscCall(MatMultTranspose(user->Grad, user->Swork, user->subq));
501: PetscCall(VecSum(user->suby, &sum));
502: sum /= user->ndesign;
503: PetscCall(VecShift(user->subq, sum));
505: PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
506: PetscCall(Gather(C, user->subq, user->yi_scatter[i], 0, 0));
507: }
508: }
509: PetscCall(VecAXPY(C, -1.0, user->q));
510: PetscFunctionReturn(PETSC_SUCCESS);
511: }
513: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
514: {
515: PetscFunctionBegin;
516: PetscCall(VecScatterBegin(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
517: PetscCall(VecScatterEnd(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
518: if (sub2) {
519: PetscCall(VecScatterBegin(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
520: PetscCall(VecScatterEnd(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
521: }
522: PetscFunctionReturn(PETSC_SUCCESS);
523: }
525: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
526: {
527: PetscFunctionBegin;
528: PetscCall(VecScatterBegin(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
529: PetscCall(VecScatterEnd(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
530: if (sub2) {
531: PetscCall(VecScatterBegin(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
532: PetscCall(VecScatterEnd(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
533: }
534: PetscFunctionReturn(PETSC_SUCCESS);
535: }
537: PetscErrorCode EllipticInitialize(AppCtx *user)
538: {
539: PetscInt m, n, i, j, k, l, linear_index, is, js, ks, ls, istart, iend, iblock;
540: Vec XX, YY, ZZ, XXwork, YYwork, ZZwork, UTwork;
541: PetscReal *x, *y, *z;
542: PetscReal h, meanut;
543: PetscScalar hinv, neg_hinv, half = 0.5, sqrt_beta;
544: PetscInt im, indx1, indx2, indy1, indy2, indz1, indz2, nx, ny, nz;
545: IS is_alldesign, is_allstate;
546: IS is_from_d;
547: IS is_from_y;
548: PetscInt lo, hi, hi2, lo2, ysubnlocal, dsubnlocal;
549: const PetscInt *ranges, *subranges;
550: PetscMPIInt size;
551: PetscReal xri, yri, zri, xim, yim, zim, dx1, dx2, dy1, dy2, dz1, dz2, Dx, Dy, Dz;
552: PetscScalar v, vx, vy, vz;
553: PetscInt offset, subindex, subvec, nrank, kk;
555: PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160, 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774, 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997,
556: 0.5198, 0.8326, 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728, 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273, 0.5724, 0.4331, 0.5136, 0.3547,
557: 0.4413, 0.2602, 0.5698, 0.7278, 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594, 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};
559: PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256, 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792, 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437,
560: 0.5938, 0.6137, 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985, 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288, 0.5761, 0.1129, 0.3841, 0.6150,
561: 0.6904, 0.6686, 0.1361, 0.4601, 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480, 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};
563: PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295, 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819, 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236,
564: 0.8800, 0.2939, 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712, 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078, 0.1987, 0.2297, 0.4321, 0.8115,
565: 0.4915, 0.7764, 0.4657, 0.4627, 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313, 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};
567: PetscFunctionBegin;
568: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
569: PetscCall(PetscLogStageRegister("Elliptic Setup", &user->stages[0]));
570: PetscCall(PetscLogStagePush(user->stages[0]));
572: /* Create u,y,c,x */
573: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->u));
574: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->y));
575: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->c));
576: PetscCall(VecSetSizes(user->u, PETSC_DECIDE, user->ndesign));
577: PetscCall(VecSetFromOptions(user->u));
578: PetscCall(VecGetLocalSize(user->u, &ysubnlocal));
579: PetscCall(VecSetSizes(user->y, ysubnlocal * user->ns, user->nstate));
580: PetscCall(VecSetSizes(user->c, ysubnlocal * user->ns, user->m));
581: PetscCall(VecSetFromOptions(user->y));
582: PetscCall(VecSetFromOptions(user->c));
584: /*
585: *******************************
586: Create scatters for x <-> y,u
587: *******************************
589: If the state vector y and design vector u are partitioned as
590: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
591: then the solution vector x is organized as
592: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
593: The index sets user->s_is and user->d_is correspond to the indices of the
594: state and design variables owned by the current processor.
595: */
596: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->x));
598: PetscCall(VecGetOwnershipRange(user->y, &lo, &hi));
599: PetscCall(VecGetOwnershipRange(user->u, &lo2, &hi2));
601: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_allstate));
602: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo + lo2, 1, &user->s_is));
603: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, lo2, 1, &is_alldesign));
604: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, hi + lo2, 1, &user->d_is));
606: PetscCall(VecSetSizes(user->x, hi - lo + hi2 - lo2, user->n));
607: PetscCall(VecSetFromOptions(user->x));
609: PetscCall(VecScatterCreate(user->x, user->s_is, user->y, is_allstate, &user->state_scatter));
610: PetscCall(VecScatterCreate(user->x, user->d_is, user->u, is_alldesign, &user->design_scatter));
611: PetscCall(ISDestroy(&is_alldesign));
612: PetscCall(ISDestroy(&is_allstate));
613: /*
614: *******************************
615: Create scatter from y to y_1,y_2,...,y_ns
616: *******************************
617: */
618: PetscCall(PetscMalloc1(user->ns, &user->yi_scatter));
619: PetscCall(VecDuplicate(user->u, &user->suby));
620: PetscCall(VecDuplicate(user->u, &user->subq));
622: PetscCall(VecGetOwnershipRange(user->y, &lo2, &hi2));
623: istart = 0;
624: for (i = 0; i < user->ns; i++) {
625: PetscCall(VecGetOwnershipRange(user->suby, &lo, &hi));
626: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_y));
627: PetscCall(VecScatterCreate(user->y, is_from_y, user->suby, NULL, &user->yi_scatter[i]));
628: istart = istart + hi - lo;
629: PetscCall(ISDestroy(&is_from_y));
630: }
631: /*
632: *******************************
633: Create scatter from d to d_1,d_2,...,d_ns
634: *******************************
635: */
636: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->subd));
637: PetscCall(VecSetSizes(user->subd, PETSC_DECIDE, user->ndata));
638: PetscCall(VecSetFromOptions(user->subd));
639: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->d));
640: PetscCall(VecGetLocalSize(user->subd, &dsubnlocal));
641: PetscCall(VecSetSizes(user->d, dsubnlocal * user->ns, user->ndata * user->ns));
642: PetscCall(VecSetFromOptions(user->d));
643: PetscCall(PetscMalloc1(user->ns, &user->di_scatter));
645: PetscCall(VecGetOwnershipRange(user->d, &lo2, &hi2));
646: istart = 0;
647: for (i = 0; i < user->ns; i++) {
648: PetscCall(VecGetOwnershipRange(user->subd, &lo, &hi));
649: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_d));
650: PetscCall(VecScatterCreate(user->d, is_from_d, user->subd, NULL, &user->di_scatter[i]));
651: istart = istart + hi - lo;
652: PetscCall(ISDestroy(&is_from_d));
653: }
655: PetscCall(PetscMalloc1(user->mx, &x));
656: PetscCall(PetscMalloc1(user->mx, &y));
657: PetscCall(PetscMalloc1(user->mx, &z));
659: user->ksp_its = 0;
660: user->ksp_its_initial = 0;
662: n = user->mx * user->mx * user->mx;
663: m = 3 * user->mx * user->mx * (user->mx - 1);
664: sqrt_beta = PetscSqrtScalar(user->beta);
666: PetscCall(VecCreate(PETSC_COMM_WORLD, &XX));
667: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->q));
668: PetscCall(VecSetSizes(XX, ysubnlocal, n));
669: PetscCall(VecSetSizes(user->q, ysubnlocal * user->ns, user->m));
670: PetscCall(VecSetFromOptions(XX));
671: PetscCall(VecSetFromOptions(user->q));
673: PetscCall(VecDuplicate(XX, &YY));
674: PetscCall(VecDuplicate(XX, &ZZ));
675: PetscCall(VecDuplicate(XX, &XXwork));
676: PetscCall(VecDuplicate(XX, &YYwork));
677: PetscCall(VecDuplicate(XX, &ZZwork));
678: PetscCall(VecDuplicate(XX, &UTwork));
679: PetscCall(VecDuplicate(XX, &user->utrue));
681: /* map for striding q */
682: PetscCall(VecGetOwnershipRanges(user->q, &ranges));
683: PetscCall(VecGetOwnershipRanges(user->u, &subranges));
685: PetscCall(VecGetOwnershipRange(user->q, &lo2, &hi2));
686: PetscCall(VecGetOwnershipRange(user->u, &lo, &hi));
687: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
688: h = 1.0 / user->mx;
689: hinv = user->mx;
690: neg_hinv = -hinv;
692: PetscCall(VecGetOwnershipRange(XX, &istart, &iend));
693: for (linear_index = istart; linear_index < iend; linear_index++) {
694: i = linear_index % user->mx;
695: j = ((linear_index - i) / user->mx) % user->mx;
696: k = ((linear_index - i) / user->mx - j) / user->mx;
697: vx = h * (i + 0.5);
698: vy = h * (j + 0.5);
699: vz = h * (k + 0.5);
700: PetscCall(VecSetValues(XX, 1, &linear_index, &vx, INSERT_VALUES));
701: PetscCall(VecSetValues(YY, 1, &linear_index, &vy, INSERT_VALUES));
702: PetscCall(VecSetValues(ZZ, 1, &linear_index, &vz, INSERT_VALUES));
703: for (is = 0; is < 2; is++) {
704: for (js = 0; js < 2; js++) {
705: for (ks = 0; ks < 2; ks++) {
706: ls = is * 4 + js * 2 + ks;
707: if (ls < user->ns) {
708: l = ls * n + linear_index;
709: /* remap */
710: subindex = l % n;
711: subvec = l / n;
712: nrank = 0;
713: while (subindex >= subranges[nrank + 1]) nrank++;
714: offset = subindex - subranges[nrank];
715: istart = 0;
716: for (kk = 0; kk < nrank; kk++) istart += user->ns * (subranges[kk + 1] - subranges[kk]);
717: istart += (subranges[nrank + 1] - subranges[nrank]) * subvec;
718: l = istart + offset;
719: v = 100 * PetscSinScalar(2 * PETSC_PI * (vx + 0.25 * is)) * PetscSinScalar(2 * PETSC_PI * (vy + 0.25 * js)) * PetscSinScalar(2 * PETSC_PI * (vz + 0.25 * ks));
720: PetscCall(VecSetValues(user->q, 1, &l, &v, INSERT_VALUES));
721: }
722: }
723: }
724: }
725: }
727: PetscCall(VecAssemblyBegin(XX));
728: PetscCall(VecAssemblyEnd(XX));
729: PetscCall(VecAssemblyBegin(YY));
730: PetscCall(VecAssemblyEnd(YY));
731: PetscCall(VecAssemblyBegin(ZZ));
732: PetscCall(VecAssemblyEnd(ZZ));
733: PetscCall(VecAssemblyBegin(user->q));
734: PetscCall(VecAssemblyEnd(user->q));
736: /* Compute true parameter function
737: ut = exp(-((x-0.25)^2+(y-0.25)^2+(z-0.25)^2)/0.05) - exp((x-0.75)^2-(y-0.75)^2-(z-0.75))^2/0.05) */
738: PetscCall(VecCopy(XX, XXwork));
739: PetscCall(VecCopy(YY, YYwork));
740: PetscCall(VecCopy(ZZ, ZZwork));
742: PetscCall(VecShift(XXwork, -0.25));
743: PetscCall(VecShift(YYwork, -0.25));
744: PetscCall(VecShift(ZZwork, -0.25));
746: PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
747: PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
748: PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));
750: PetscCall(VecCopy(XXwork, UTwork));
751: PetscCall(VecAXPY(UTwork, 1.0, YYwork));
752: PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
753: PetscCall(VecScale(UTwork, -20.0));
754: PetscCall(VecExp(UTwork));
755: PetscCall(VecCopy(UTwork, user->utrue));
757: PetscCall(VecCopy(XX, XXwork));
758: PetscCall(VecCopy(YY, YYwork));
759: PetscCall(VecCopy(ZZ, ZZwork));
761: PetscCall(VecShift(XXwork, -0.75));
762: PetscCall(VecShift(YYwork, -0.75));
763: PetscCall(VecShift(ZZwork, -0.75));
765: PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
766: PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
767: PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));
769: PetscCall(VecCopy(XXwork, UTwork));
770: PetscCall(VecAXPY(UTwork, 1.0, YYwork));
771: PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
772: PetscCall(VecScale(UTwork, -20.0));
773: PetscCall(VecExp(UTwork));
775: PetscCall(VecAXPY(user->utrue, -1.0, UTwork));
777: PetscCall(VecDestroy(&XX));
778: PetscCall(VecDestroy(&YY));
779: PetscCall(VecDestroy(&ZZ));
780: PetscCall(VecDestroy(&XXwork));
781: PetscCall(VecDestroy(&YYwork));
782: PetscCall(VecDestroy(&ZZwork));
783: PetscCall(VecDestroy(&UTwork));
785: /* Initial guess and reference model */
786: PetscCall(VecDuplicate(user->utrue, &user->ur));
787: PetscCall(VecSum(user->utrue, &meanut));
788: meanut = meanut / n;
789: PetscCall(VecSet(user->ur, meanut));
790: PetscCall(VecCopy(user->ur, user->u));
792: /* Generate Grad matrix */
793: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Grad));
794: PetscCall(MatSetSizes(user->Grad, PETSC_DECIDE, ysubnlocal, m, n));
795: PetscCall(MatSetFromOptions(user->Grad));
796: PetscCall(MatMPIAIJSetPreallocation(user->Grad, 2, NULL, 2, NULL));
797: PetscCall(MatSeqAIJSetPreallocation(user->Grad, 2, NULL));
798: PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));
800: for (i = istart; i < iend; i++) {
801: if (i < m / 3) {
802: iblock = i / (user->mx - 1);
803: j = iblock * user->mx + (i % (user->mx - 1));
804: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
805: j = j + 1;
806: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
807: }
808: if (i >= m / 3 && i < 2 * m / 3) {
809: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
810: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
811: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
812: j = j + user->mx;
813: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
814: }
815: if (i >= 2 * m / 3) {
816: j = i - 2 * m / 3;
817: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
818: j = j + user->mx * user->mx;
819: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
820: }
821: }
823: PetscCall(MatAssemblyBegin(user->Grad, MAT_FINAL_ASSEMBLY));
824: PetscCall(MatAssemblyEnd(user->Grad, MAT_FINAL_ASSEMBLY));
826: /* Generate arithmetic averaging matrix Av */
827: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Av));
828: PetscCall(MatSetSizes(user->Av, PETSC_DECIDE, ysubnlocal, m, n));
829: PetscCall(MatSetFromOptions(user->Av));
830: PetscCall(MatMPIAIJSetPreallocation(user->Av, 2, NULL, 2, NULL));
831: PetscCall(MatSeqAIJSetPreallocation(user->Av, 2, NULL));
832: PetscCall(MatGetOwnershipRange(user->Av, &istart, &iend));
834: for (i = istart; i < iend; i++) {
835: if (i < m / 3) {
836: iblock = i / (user->mx - 1);
837: j = iblock * user->mx + (i % (user->mx - 1));
838: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
839: j = j + 1;
840: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
841: }
842: if (i >= m / 3 && i < 2 * m / 3) {
843: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
844: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
845: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
846: j = j + user->mx;
847: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
848: }
849: if (i >= 2 * m / 3) {
850: j = i - 2 * m / 3;
851: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
852: j = j + user->mx * user->mx;
853: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
854: }
855: }
857: PetscCall(MatAssemblyBegin(user->Av, MAT_FINAL_ASSEMBLY));
858: PetscCall(MatAssemblyEnd(user->Av, MAT_FINAL_ASSEMBLY));
860: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->L));
861: PetscCall(MatSetSizes(user->L, PETSC_DECIDE, ysubnlocal, m + n, n));
862: PetscCall(MatSetFromOptions(user->L));
863: PetscCall(MatMPIAIJSetPreallocation(user->L, 2, NULL, 2, NULL));
864: PetscCall(MatSeqAIJSetPreallocation(user->L, 2, NULL));
865: PetscCall(MatGetOwnershipRange(user->L, &istart, &iend));
867: for (i = istart; i < iend; i++) {
868: if (i < m / 3) {
869: iblock = i / (user->mx - 1);
870: j = iblock * user->mx + (i % (user->mx - 1));
871: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
872: j = j + 1;
873: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
874: }
875: if (i >= m / 3 && i < 2 * m / 3) {
876: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
877: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
878: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
879: j = j + user->mx;
880: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
881: }
882: if (i >= 2 * m / 3 && i < m) {
883: j = i - 2 * m / 3;
884: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
885: j = j + user->mx * user->mx;
886: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
887: }
888: if (i >= m) {
889: j = i - m;
890: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &sqrt_beta, INSERT_VALUES));
891: }
892: }
893: PetscCall(MatAssemblyBegin(user->L, MAT_FINAL_ASSEMBLY));
894: PetscCall(MatAssemblyEnd(user->L, MAT_FINAL_ASSEMBLY));
895: PetscCall(MatScale(user->L, PetscPowScalar(h, 1.5)));
897: /* Generate Div matrix */
898: if (!user->use_ptap) {
899: /* Generate Div matrix */
900: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Div));
901: PetscCall(MatSetSizes(user->Div, ysubnlocal, PETSC_DECIDE, n, m));
902: PetscCall(MatSetFromOptions(user->Div));
903: PetscCall(MatMPIAIJSetPreallocation(user->Div, 4, NULL, 4, NULL));
904: PetscCall(MatSeqAIJSetPreallocation(user->Div, 6, NULL));
905: PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));
907: for (i = istart; i < iend; i++) {
908: if (i < m / 3) {
909: iblock = i / (user->mx - 1);
910: j = iblock * user->mx + (i % (user->mx - 1));
911: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
912: j = j + 1;
913: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
914: }
915: if (i >= m / 3 && i < 2 * m / 3) {
916: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
917: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
918: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
919: j = j + user->mx;
920: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
921: }
922: if (i >= 2 * m / 3) {
923: j = i - 2 * m / 3;
924: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
925: j = j + user->mx * user->mx;
926: PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
927: }
928: }
930: PetscCall(MatAssemblyBegin(user->Div, MAT_FINAL_ASSEMBLY));
931: PetscCall(MatAssemblyEnd(user->Div, MAT_FINAL_ASSEMBLY));
932: PetscCall(MatDuplicate(user->Div, MAT_SHARE_NONZERO_PATTERN, &user->Divwork));
933: } else {
934: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Diag));
935: PetscCall(MatSetSizes(user->Diag, PETSC_DECIDE, PETSC_DECIDE, m, m));
936: PetscCall(MatSetFromOptions(user->Diag));
937: PetscCall(MatMPIAIJSetPreallocation(user->Diag, 1, NULL, 0, NULL));
938: PetscCall(MatSeqAIJSetPreallocation(user->Diag, 1, NULL));
939: }
941: /* Build work vectors and matrices */
942: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->S));
943: PetscCall(VecSetSizes(user->S, PETSC_DECIDE, m));
944: PetscCall(VecSetFromOptions(user->S));
946: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->lwork));
947: PetscCall(VecSetSizes(user->lwork, PETSC_DECIDE, m + user->mx * user->mx * user->mx));
948: PetscCall(VecSetFromOptions(user->lwork));
950: PetscCall(MatDuplicate(user->Av, MAT_SHARE_NONZERO_PATTERN, &user->Avwork));
952: PetscCall(VecDuplicate(user->S, &user->Swork));
953: PetscCall(VecDuplicate(user->S, &user->Sdiag));
954: PetscCall(VecDuplicate(user->S, &user->Av_u));
955: PetscCall(VecDuplicate(user->S, &user->Twork));
956: PetscCall(VecDuplicate(user->y, &user->ywork));
957: PetscCall(VecDuplicate(user->u, &user->Ywork));
958: PetscCall(VecDuplicate(user->u, &user->uwork));
959: PetscCall(VecDuplicate(user->u, &user->js_diag));
960: PetscCall(VecDuplicate(user->c, &user->cwork));
961: PetscCall(VecDuplicate(user->d, &user->dwork));
963: /* Create a matrix-free shell user->Jd for computing B*x */
964: PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal, user->nstate, user->ndesign, user, &user->Jd));
965: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT, (void (*)(void))DesignMatMult));
966: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT_TRANSPOSE, (void (*)(void))DesignMatMultTranspose));
968: /* Compute true state function ytrue given utrue */
969: PetscCall(VecDuplicate(user->y, &user->ytrue));
971: /* First compute Av_u = Av*exp(-u) */
972: PetscCall(VecSet(user->uwork, 0));
973: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue)); /* Note: user->utrue */
974: PetscCall(VecExp(user->uwork));
975: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
977: /* Next form DSG = Div*S*Grad */
978: PetscCall(VecCopy(user->Av_u, user->Swork));
979: PetscCall(VecReciprocal(user->Swork));
980: if (user->use_ptap) {
981: PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
982: PetscCall(MatPtAP(user->Diag, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
983: } else {
984: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
985: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
987: PetscCall(MatMatMult(user->Divwork, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
988: }
990: PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
991: PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
993: if (user->use_lrc == PETSC_TRUE) {
994: v = PetscSqrtReal(1.0 / user->ndesign);
995: PetscCall(PetscMalloc1(user->ndesign, &user->ones));
997: for (i = 0; i < user->ndesign; i++) user->ones[i] = v;
998: PetscCall(MatCreateDense(PETSC_COMM_WORLD, ysubnlocal, PETSC_DECIDE, user->ndesign, 1, user->ones, &user->Ones));
999: PetscCall(MatCreateLRC(user->DSG, user->Ones, NULL, user->Ones, &user->JsBlock));
1000: PetscCall(MatSetUp(user->JsBlock));
1001: } else {
1002: /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1003: PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal, ysubnlocal, user->ndesign, user->ndesign, user, &user->JsBlock));
1004: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT, (void (*)(void))StateBlockMatMult));
1005: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT_TRANSPOSE, (void (*)(void))StateBlockMatMult));
1006: }
1007: PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRIC, PETSC_TRUE));
1008: PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1009: PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->Js));
1010: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT, (void (*)(void))StateMatMult));
1011: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatMult));
1012: PetscCall(MatSetOption(user->Js, MAT_SYMMETRIC, PETSC_TRUE));
1013: PetscCall(MatSetOption(user->Js, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1015: PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->JsInv));
1016: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT, (void (*)(void))StateInvMatMult));
1017: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT_TRANSPOSE, (void (*)(void))StateInvMatMult));
1018: PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRIC, PETSC_TRUE));
1019: PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1021: PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
1022: PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1023: /* Now solve for ytrue */
1024: PetscCall(KSPCreate(PETSC_COMM_WORLD, &user->solver));
1025: PetscCall(KSPSetFromOptions(user->solver));
1027: PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));
1029: PetscCall(MatMult(user->JsInv, user->q, user->ytrue));
1030: /* First compute Av_u = Av*exp(-u) */
1031: PetscCall(VecSet(user->uwork, 0));
1032: PetscCall(VecAXPY(user->uwork, -1.0, user->u)); /* Note: user->u */
1033: PetscCall(VecExp(user->uwork));
1034: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
1036: /* Next update DSG = Div*S*Grad with user->u */
1037: PetscCall(VecCopy(user->Av_u, user->Swork));
1038: PetscCall(VecReciprocal(user->Swork));
1039: if (user->use_ptap) {
1040: PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
1041: PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
1042: } else {
1043: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1044: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1045: PetscCall(MatProductNumeric(user->DSG));
1046: }
1048: /* Now solve for y */
1050: PetscCall(MatMult(user->JsInv, user->q, user->y));
1052: user->ksp_its_initial = user->ksp_its;
1053: user->ksp_its = 0;
1054: /* Construct projection matrix Q (blocks) */
1055: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Q));
1056: PetscCall(MatSetSizes(user->Q, dsubnlocal, ysubnlocal, user->ndata, user->ndesign));
1057: PetscCall(MatSetFromOptions(user->Q));
1058: PetscCall(MatMPIAIJSetPreallocation(user->Q, 8, NULL, 8, NULL));
1059: PetscCall(MatSeqAIJSetPreallocation(user->Q, 8, NULL));
1061: for (i = 0; i < user->mx; i++) {
1062: x[i] = h * (i + 0.5);
1063: y[i] = h * (i + 0.5);
1064: z[i] = h * (i + 0.5);
1065: }
1066: PetscCall(MatGetOwnershipRange(user->Q, &istart, &iend));
1068: nx = user->mx;
1069: ny = user->mx;
1070: nz = user->mx;
1071: for (i = istart; i < iend; i++) {
1072: xri = xr[i];
1073: im = 0;
1074: xim = x[im];
1075: while (xri > xim && im < nx) {
1076: im = im + 1;
1077: xim = x[im];
1078: }
1079: indx1 = im - 1;
1080: indx2 = im;
1081: dx1 = xri - x[indx1];
1082: dx2 = x[indx2] - xri;
1084: yri = yr[i];
1085: im = 0;
1086: yim = y[im];
1087: while (yri > yim && im < ny) {
1088: im = im + 1;
1089: yim = y[im];
1090: }
1091: indy1 = im - 1;
1092: indy2 = im;
1093: dy1 = yri - y[indy1];
1094: dy2 = y[indy2] - yri;
1096: zri = zr[i];
1097: im = 0;
1098: zim = z[im];
1099: while (zri > zim && im < nz) {
1100: im = im + 1;
1101: zim = z[im];
1102: }
1103: indz1 = im - 1;
1104: indz2 = im;
1105: dz1 = zri - z[indz1];
1106: dz2 = z[indz2] - zri;
1108: Dx = x[indx2] - x[indx1];
1109: Dy = y[indy2] - y[indy1];
1110: Dz = z[indz2] - z[indz1];
1112: j = indx1 + indy1 * nx + indz1 * nx * ny;
1113: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1114: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1116: j = indx1 + indy1 * nx + indz2 * nx * ny;
1117: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1118: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1120: j = indx1 + indy2 * nx + indz1 * nx * ny;
1121: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1122: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1124: j = indx1 + indy2 * nx + indz2 * nx * ny;
1125: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1126: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1128: j = indx2 + indy1 * nx + indz1 * nx * ny;
1129: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1130: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1132: j = indx2 + indy1 * nx + indz2 * nx * ny;
1133: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1134: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1136: j = indx2 + indy2 * nx + indz1 * nx * ny;
1137: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1138: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1140: j = indx2 + indy2 * nx + indz2 * nx * ny;
1141: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1142: PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1143: }
1145: PetscCall(MatAssemblyBegin(user->Q, MAT_FINAL_ASSEMBLY));
1146: PetscCall(MatAssemblyEnd(user->Q, MAT_FINAL_ASSEMBLY));
1147: /* Create MQ (composed of blocks of Q */
1148: PetscCall(MatCreateShell(PETSC_COMM_WORLD, dsubnlocal * user->ns, PETSC_DECIDE, user->ndata * user->ns, user->nstate, user, &user->MQ));
1149: PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT, (void (*)(void))QMatMult));
1150: PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT_TRANSPOSE, (void (*)(void))QMatMultTranspose));
1152: /* Add noise to the measurement data */
1153: PetscCall(VecSet(user->ywork, 1.0));
1154: PetscCall(VecAYPX(user->ywork, user->noise, user->ytrue));
1155: PetscCall(MatMult(user->MQ, user->ywork, user->d));
1157: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1158: PetscCall(PetscFree(x));
1159: PetscCall(PetscFree(y));
1160: PetscCall(PetscFree(z));
1161: PetscCall(PetscLogStagePop());
1162: PetscFunctionReturn(PETSC_SUCCESS);
1163: }
1165: PetscErrorCode EllipticDestroy(AppCtx *user)
1166: {
1167: PetscInt i;
1169: PetscFunctionBegin;
1170: PetscCall(MatDestroy(&user->DSG));
1171: PetscCall(KSPDestroy(&user->solver));
1172: PetscCall(MatDestroy(&user->Q));
1173: PetscCall(MatDestroy(&user->MQ));
1174: if (!user->use_ptap) {
1175: PetscCall(MatDestroy(&user->Div));
1176: PetscCall(MatDestroy(&user->Divwork));
1177: } else {
1178: PetscCall(MatDestroy(&user->Diag));
1179: }
1180: if (user->use_lrc) PetscCall(MatDestroy(&user->Ones));
1182: PetscCall(MatDestroy(&user->Grad));
1183: PetscCall(MatDestroy(&user->Av));
1184: PetscCall(MatDestroy(&user->Avwork));
1185: PetscCall(MatDestroy(&user->L));
1186: PetscCall(MatDestroy(&user->Js));
1187: PetscCall(MatDestroy(&user->Jd));
1188: PetscCall(MatDestroy(&user->JsBlock));
1189: PetscCall(MatDestroy(&user->JsInv));
1191: PetscCall(VecDestroy(&user->x));
1192: PetscCall(VecDestroy(&user->u));
1193: PetscCall(VecDestroy(&user->uwork));
1194: PetscCall(VecDestroy(&user->utrue));
1195: PetscCall(VecDestroy(&user->y));
1196: PetscCall(VecDestroy(&user->ywork));
1197: PetscCall(VecDestroy(&user->ytrue));
1198: PetscCall(VecDestroy(&user->c));
1199: PetscCall(VecDestroy(&user->cwork));
1200: PetscCall(VecDestroy(&user->ur));
1201: PetscCall(VecDestroy(&user->q));
1202: PetscCall(VecDestroy(&user->d));
1203: PetscCall(VecDestroy(&user->dwork));
1204: PetscCall(VecDestroy(&user->lwork));
1205: PetscCall(VecDestroy(&user->S));
1206: PetscCall(VecDestroy(&user->Swork));
1207: PetscCall(VecDestroy(&user->Sdiag));
1208: PetscCall(VecDestroy(&user->Ywork));
1209: PetscCall(VecDestroy(&user->Twork));
1210: PetscCall(VecDestroy(&user->Av_u));
1211: PetscCall(VecDestroy(&user->js_diag));
1212: PetscCall(ISDestroy(&user->s_is));
1213: PetscCall(ISDestroy(&user->d_is));
1214: PetscCall(VecDestroy(&user->suby));
1215: PetscCall(VecDestroy(&user->subd));
1216: PetscCall(VecDestroy(&user->subq));
1217: PetscCall(VecScatterDestroy(&user->state_scatter));
1218: PetscCall(VecScatterDestroy(&user->design_scatter));
1219: for (i = 0; i < user->ns; i++) {
1220: PetscCall(VecScatterDestroy(&user->yi_scatter[i]));
1221: PetscCall(VecScatterDestroy(&user->di_scatter[i]));
1222: }
1223: PetscCall(PetscFree(user->yi_scatter));
1224: PetscCall(PetscFree(user->di_scatter));
1225: if (user->use_lrc) {
1226: PetscCall(PetscFree(user->ones));
1227: PetscCall(MatDestroy(&user->Ones));
1228: }
1229: PetscFunctionReturn(PETSC_SUCCESS);
1230: }
1232: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1233: {
1234: Vec X;
1235: PetscReal unorm, ynorm;
1236: AppCtx *user = (AppCtx *)ptr;
1238: PetscFunctionBegin;
1239: PetscCall(TaoGetSolution(tao, &X));
1240: PetscCall(Scatter(X, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
1241: PetscCall(VecAXPY(user->ywork, -1.0, user->ytrue));
1242: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue));
1243: PetscCall(VecNorm(user->uwork, NORM_2, &unorm));
1244: PetscCall(VecNorm(user->ywork, NORM_2, &ynorm));
1245: PetscCall(PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n", (double)unorm, (double)ynorm));
1246: PetscFunctionReturn(PETSC_SUCCESS);
1247: }
1249: /*TEST
1251: build:
1252: requires: !complex
1254: test:
1255: args: -tao_cmonitor -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
1256: requires: !single
1258: test:
1259: suffix: 2
1260: args: -tao_cmonitor -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
1261: requires: !single
1263: TEST*/