Actual source code: parabolic.c
1: #include <petsc/private/taoimpl.h>
3: typedef struct {
4: PetscInt n; /* Number of variables */
5: PetscInt m; /* Number of constraints per time step */
6: PetscInt mx; /* grid points in each direction */
7: PetscInt nt; /* Number of time steps; as of now, must be divisible by 8 */
8: PetscInt ndata; /* Number of data points per sample */
9: PetscInt ns; /* Number of samples */
10: PetscInt *sample_times; /* Times of samples */
11: IS s_is;
12: IS d_is;
14: VecScatter state_scatter;
15: VecScatter design_scatter;
16: VecScatter *yi_scatter;
17: VecScatter *di_scatter;
19: Mat Js, Jd, JsBlockPrec, JsInv, JsBlock;
20: PetscBool jformed, dsg_formed;
22: PetscReal alpha; /* Regularization parameter */
23: PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
24: PetscReal noise; /* Amount of noise to add to data */
25: PetscReal ht; /* Time step */
27: Mat Qblock, QblockT;
28: Mat L, LT;
29: Mat Div, Divwork;
30: Mat Grad;
31: Mat Av, Avwork, AvT;
32: Mat DSG;
33: Vec q;
34: Vec ur; /* reference */
36: Vec d;
37: Vec dwork;
38: Vec *di;
40: Vec y; /* state variables */
41: Vec ywork;
43: Vec ytrue;
44: Vec *yi, *yiwork;
46: Vec u; /* design variables */
47: Vec uwork;
49: Vec utrue;
50: Vec js_diag;
51: Vec c; /* constraint vector */
52: Vec cwork;
54: Vec lwork;
55: Vec S;
56: Vec Rwork, Swork, Twork;
57: Vec Av_u;
59: KSP solver;
60: PC prec;
62: PetscInt ksp_its;
63: PetscInt ksp_its_initial;
64: } AppCtx;
66: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
67: PetscErrorCode FormGradient(Tao, Vec, Vec, void *);
68: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
69: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void *);
70: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void *);
71: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
72: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void *);
73: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
74: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
75: PetscErrorCode ParabolicInitialize(AppCtx *user);
76: PetscErrorCode ParabolicDestroy(AppCtx *user);
77: PetscErrorCode ParabolicMonitor(Tao, void *);
79: PetscErrorCode StateMatMult(Mat, Vec, Vec);
80: PetscErrorCode StateMatBlockMult(Mat, Vec, Vec);
81: PetscErrorCode StateMatMultTranspose(Mat, Vec, Vec);
82: PetscErrorCode StateMatGetDiagonal(Mat, Vec);
83: PetscErrorCode StateMatDuplicate(Mat, MatDuplicateOption, Mat *);
84: PetscErrorCode StateMatInvMult(Mat, Vec, Vec);
85: PetscErrorCode StateMatInvTransposeMult(Mat, Vec, Vec);
86: PetscErrorCode StateMatBlockPrecMult(PC, Vec, Vec);
88: PetscErrorCode DesignMatMult(Mat, Vec, Vec);
89: PetscErrorCode DesignMatMultTranspose(Mat, Vec, Vec);
91: PetscErrorCode Gather_i(Vec, Vec *, VecScatter *, PetscInt);
92: PetscErrorCode Scatter_i(Vec, Vec *, VecScatter *, PetscInt);
94: static char help[] = "";
96: int main(int argc, char **argv)
97: {
98: Vec x, x0;
99: Tao tao;
100: AppCtx user;
101: IS is_allstate, is_alldesign;
102: PetscInt lo, hi, hi2, lo2, ksp_old;
103: PetscInt ntests = 1;
104: PetscInt i;
105: PetscLogStage stages[1];
107: PetscFunctionBeginUser;
108: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
109: user.mx = 8;
110: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "parabolic example", NULL);
111: PetscCall(PetscOptionsInt("-mx", "Number of grid points in each direction", "", user.mx, &user.mx, NULL));
112: user.nt = 8;
113: PetscCall(PetscOptionsInt("-nt", "Number of time steps", "", user.nt, &user.nt, NULL));
114: user.ndata = 64;
115: PetscCall(PetscOptionsInt("-ndata", "Numbers of data points per sample", "", user.ndata, &user.ndata, NULL));
116: user.ns = 8;
117: PetscCall(PetscOptionsInt("-ns", "Number of samples", "", user.ns, &user.ns, NULL));
118: user.alpha = 1.0;
119: PetscCall(PetscOptionsReal("-alpha", "Regularization parameter", "", user.alpha, &user.alpha, NULL));
120: user.beta = 0.01;
121: PetscCall(PetscOptionsReal("-beta", "Weight attributed to ||u||^2 in regularization functional", "", user.beta, &user.beta, NULL));
122: user.noise = 0.01;
123: PetscCall(PetscOptionsReal("-noise", "Amount of noise to add to data", "", user.noise, &user.noise, NULL));
124: PetscCall(PetscOptionsInt("-ntests", "Number of times to repeat TaoSolve", "", ntests, &ntests, NULL));
125: PetscOptionsEnd();
127: user.m = user.mx * user.mx * user.mx; /* number of constraints per time step */
128: user.n = user.m * (user.nt + 1); /* number of variables */
129: user.ht = (PetscReal)1 / user.nt;
131: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.u));
132: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.y));
133: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.c));
134: PetscCall(VecSetSizes(user.u, PETSC_DECIDE, user.n - user.m * user.nt));
135: PetscCall(VecSetSizes(user.y, PETSC_DECIDE, user.m * user.nt));
136: PetscCall(VecSetSizes(user.c, PETSC_DECIDE, user.m * user.nt));
137: PetscCall(VecSetFromOptions(user.u));
138: PetscCall(VecSetFromOptions(user.y));
139: PetscCall(VecSetFromOptions(user.c));
141: /* Create scatters for reduced spaces.
142: If the state vector y and design vector u are partitioned as
143: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
144: then the solution vector x is organized as
145: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
146: The index sets user.s_is and user.d_is correspond to the indices of the
147: state and design variables owned by the current processor.
148: */
149: PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
151: PetscCall(VecGetOwnershipRange(user.y, &lo, &hi));
152: PetscCall(VecGetOwnershipRange(user.u, &lo2, &hi2));
154: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_allstate));
155: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo + lo2, 1, &user.s_is));
157: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, lo2, 1, &is_alldesign));
158: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, hi + lo2, 1, &user.d_is));
160: PetscCall(VecSetSizes(x, hi - lo + hi2 - lo2, user.n));
161: PetscCall(VecSetFromOptions(x));
163: PetscCall(VecScatterCreate(x, user.s_is, user.y, is_allstate, &user.state_scatter));
164: PetscCall(VecScatterCreate(x, user.d_is, user.u, is_alldesign, &user.design_scatter));
165: PetscCall(ISDestroy(&is_alldesign));
166: PetscCall(ISDestroy(&is_allstate));
168: /* Create TAO solver and set desired solution method */
169: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
170: PetscCall(TaoSetType(tao, TAOLCL));
172: /* Set up initial vectors and matrices */
173: PetscCall(ParabolicInitialize(&user));
175: PetscCall(Gather(x, user.y, user.state_scatter, user.u, user.design_scatter));
176: PetscCall(VecDuplicate(x, &x0));
177: PetscCall(VecCopy(x, x0));
179: /* Set solution vector with an initial guess */
180: PetscCall(TaoSetSolution(tao, x));
181: PetscCall(TaoSetObjective(tao, FormFunction, &user));
182: PetscCall(TaoSetGradient(tao, NULL, FormGradient, &user));
183: PetscCall(TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user));
185: PetscCall(TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, &user));
186: PetscCall(TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user));
188: PetscCall(TaoSetFromOptions(tao));
189: PetscCall(TaoSetStateDesignIS(tao, user.s_is, user.d_is));
191: /* SOLVE THE APPLICATION */
192: PetscCall(PetscLogStageRegister("Trials", &stages[0]));
193: PetscCall(PetscLogStagePush(stages[0]));
194: user.ksp_its_initial = user.ksp_its;
195: ksp_old = user.ksp_its;
196: for (i = 0; i < ntests; i++) {
197: PetscCall(TaoSolve(tao));
198: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP Iterations = %" PetscInt_FMT "\n", user.ksp_its - ksp_old));
199: PetscCall(VecCopy(x0, x));
200: PetscCall(TaoSetSolution(tao, x));
201: }
202: PetscCall(PetscLogStagePop());
203: PetscCall(PetscBarrier((PetscObject)x));
204: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations within initialization: "));
205: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its_initial));
206: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Total KSP iterations over %" PetscInt_FMT " trial(s): ", ntests));
207: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its));
208: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations per trial: "));
209: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", (user.ksp_its - user.ksp_its_initial) / ntests));
211: PetscCall(TaoDestroy(&tao));
212: PetscCall(VecDestroy(&x));
213: PetscCall(VecDestroy(&x0));
214: PetscCall(ParabolicDestroy(&user));
216: PetscCall(PetscFinalize());
217: return 0;
218: }
219: /* ------------------------------------------------------------------- */
220: /*
221: dwork = Qy - d
222: lwork = L*(u-ur)
223: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
224: */
225: PetscErrorCode FormFunction(Tao tao, Vec X, PetscReal *f, void *ptr)
226: {
227: PetscReal d1 = 0, d2 = 0;
228: PetscInt i, j;
229: AppCtx *user = (AppCtx *)ptr;
231: PetscFunctionBegin;
232: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
233: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
234: for (j = 0; j < user->ns; j++) {
235: i = user->sample_times[j];
236: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
237: }
238: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
239: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
240: PetscCall(VecDot(user->dwork, user->dwork, &d1));
242: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
243: PetscCall(MatMult(user->L, user->uwork, user->lwork));
244: PetscCall(VecDot(user->lwork, user->lwork, &d2));
246: *f = 0.5 * (d1 + user->alpha * d2);
247: PetscFunctionReturn(PETSC_SUCCESS);
248: }
250: /* ------------------------------------------------------------------- */
251: /*
252: state: g_s = Q' *(Qy - d)
253: design: g_d = alpha*L'*L*(u-ur)
254: */
255: PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
256: {
257: PetscInt i;
258: AppCtx *user = (AppCtx *)ptr;
260: PetscFunctionBegin;
261: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
262: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
263: for (PetscInt j = 0; j < user->ns; j++) {
264: i = user->sample_times[j];
265: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
266: }
267: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
268: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
269: PetscCall(Scatter_i(user->dwork, user->di, user->di_scatter, user->ns));
270: PetscCall(VecSet(user->ywork, 0.0));
271: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
272: for (PetscInt j = 0; j < user->ns; j++) {
273: i = user->sample_times[j];
274: PetscCall(MatMult(user->QblockT, user->di[j], user->yiwork[i]));
275: }
276: PetscCall(Gather_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
278: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
279: PetscCall(MatMult(user->L, user->uwork, user->lwork));
280: PetscCall(MatMult(user->LT, user->lwork, user->uwork));
281: PetscCall(VecScale(user->uwork, user->alpha));
282: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
283: PetscFunctionReturn(PETSC_SUCCESS);
284: }
286: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
287: {
288: PetscReal d1, d2;
289: PetscInt i;
290: AppCtx *user = (AppCtx *)ptr;
292: PetscFunctionBegin;
293: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
294: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
295: for (PetscInt j = 0; j < user->ns; j++) {
296: i = user->sample_times[j];
297: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
298: }
299: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
300: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
301: PetscCall(VecDot(user->dwork, user->dwork, &d1));
302: PetscCall(Scatter_i(user->dwork, user->di, user->di_scatter, user->ns));
303: PetscCall(VecSet(user->ywork, 0.0));
304: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
305: for (PetscInt j = 0; j < user->ns; j++) {
306: i = user->sample_times[j];
307: PetscCall(MatMult(user->QblockT, user->di[j], user->yiwork[i]));
308: }
309: PetscCall(Gather_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
311: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
312: PetscCall(MatMult(user->L, user->uwork, user->lwork));
313: PetscCall(VecDot(user->lwork, user->lwork, &d2));
314: PetscCall(MatMult(user->LT, user->lwork, user->uwork));
315: PetscCall(VecScale(user->uwork, user->alpha));
316: *f = 0.5 * (d1 + user->alpha * d2);
318: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
319: PetscFunctionReturn(PETSC_SUCCESS);
320: }
322: /* ------------------------------------------------------------------- */
323: /* A
324: MatShell object
325: */
326: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
327: {
328: AppCtx *user = (AppCtx *)ptr;
330: PetscFunctionBegin;
331: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
332: PetscCall(VecSet(user->uwork, 0));
333: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
334: PetscCall(VecExp(user->uwork));
335: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
336: PetscCall(VecCopy(user->Av_u, user->Swork));
337: PetscCall(VecReciprocal(user->Swork));
338: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
339: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
340: if (user->dsg_formed) {
341: PetscCall(MatProductNumeric(user->DSG));
342: } else {
343: PetscCall(MatMatMult(user->Divwork, user->Grad, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &user->DSG));
344: user->dsg_formed = PETSC_TRUE;
345: }
347: /* B = speye(nx^3) + ht*DSG; */
348: PetscCall(MatScale(user->DSG, user->ht));
349: PetscCall(MatShift(user->DSG, 1.0));
350: PetscFunctionReturn(PETSC_SUCCESS);
351: }
353: /* ------------------------------------------------------------------- */
354: /* B */
355: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
356: {
357: AppCtx *user = (AppCtx *)ptr;
359: PetscFunctionBegin;
360: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
361: PetscFunctionReturn(PETSC_SUCCESS);
362: }
364: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
365: {
366: PetscInt i;
367: AppCtx *user;
369: PetscFunctionBegin;
370: PetscCall(MatShellGetContext(J_shell, &user));
371: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
372: PetscCall(MatMult(user->JsBlock, user->yi[0], user->yiwork[0]));
373: for (i = 1; i < user->nt; i++) {
374: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
375: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i - 1]));
376: }
377: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
378: PetscFunctionReturn(PETSC_SUCCESS);
379: }
381: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
382: {
383: PetscInt i;
384: AppCtx *user;
386: PetscFunctionBegin;
387: PetscCall(MatShellGetContext(J_shell, &user));
388: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
389: for (i = 0; i < user->nt - 1; i++) {
390: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
391: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i + 1]));
392: }
393: i = user->nt - 1;
394: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
395: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
396: PetscFunctionReturn(PETSC_SUCCESS);
397: }
399: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
400: {
401: AppCtx *user;
403: PetscFunctionBegin;
404: PetscCall(MatShellGetContext(J_shell, &user));
405: PetscCall(MatMult(user->Grad, X, user->Swork));
406: PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
407: PetscCall(MatMult(user->Div, user->Swork, Y));
408: PetscCall(VecAYPX(Y, user->ht, X));
409: PetscFunctionReturn(PETSC_SUCCESS);
410: }
412: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
413: {
414: PetscInt i;
415: AppCtx *user;
417: PetscFunctionBegin;
418: PetscCall(MatShellGetContext(J_shell, &user));
420: /* sdiag(1./v) */
421: PetscCall(VecSet(user->uwork, 0));
422: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
423: PetscCall(VecExp(user->uwork));
425: /* sdiag(1./((Av*(1./v)).^2)) */
426: PetscCall(MatMult(user->Av, user->uwork, user->Swork));
427: PetscCall(VecPointwiseMult(user->Swork, user->Swork, user->Swork));
428: PetscCall(VecReciprocal(user->Swork));
430: /* (Av * (sdiag(1./v) * b)) */
431: PetscCall(VecPointwiseMult(user->uwork, user->uwork, X));
432: PetscCall(MatMult(user->Av, user->uwork, user->Twork));
434: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
435: PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
437: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
438: for (i = 0; i < user->nt; i++) {
439: /* (sdiag(Grad*y(:,i)) */
440: PetscCall(MatMult(user->Grad, user->yi[i], user->Twork));
442: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
443: PetscCall(VecPointwiseMult(user->Twork, user->Twork, user->Swork));
444: PetscCall(MatMult(user->Div, user->Twork, user->yiwork[i]));
445: PetscCall(VecScale(user->yiwork[i], user->ht));
446: }
447: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
448: PetscFunctionReturn(PETSC_SUCCESS);
449: }
451: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
452: {
453: PetscInt i;
454: AppCtx *user;
456: PetscFunctionBegin;
457: PetscCall(MatShellGetContext(J_shell, &user));
459: /* sdiag(1./((Av*(1./v)).^2)) */
460: PetscCall(VecSet(user->uwork, 0));
461: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
462: PetscCall(VecExp(user->uwork));
463: PetscCall(MatMult(user->Av, user->uwork, user->Rwork));
464: PetscCall(VecPointwiseMult(user->Rwork, user->Rwork, user->Rwork));
465: PetscCall(VecReciprocal(user->Rwork));
467: PetscCall(VecSet(Y, 0.0));
468: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
469: PetscCall(Scatter_i(X, user->yiwork, user->yi_scatter, user->nt));
470: for (i = 0; i < user->nt; i++) {
471: /* (Div' * b(:,i)) */
472: PetscCall(MatMult(user->Grad, user->yiwork[i], user->Swork));
474: /* sdiag(Grad*y(:,i)) */
475: PetscCall(MatMult(user->Grad, user->yi[i], user->Twork));
477: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
478: PetscCall(VecPointwiseMult(user->Twork, user->Swork, user->Twork));
480: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
481: PetscCall(VecPointwiseMult(user->Twork, user->Rwork, user->Twork));
483: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
484: PetscCall(MatMult(user->AvT, user->Twork, user->yiwork[i]));
486: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
487: PetscCall(VecPointwiseMult(user->yiwork[i], user->uwork, user->yiwork[i]));
488: PetscCall(VecAXPY(Y, user->ht, user->yiwork[i]));
489: }
490: PetscFunctionReturn(PETSC_SUCCESS);
491: }
493: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
494: {
495: AppCtx *user;
497: PetscFunctionBegin;
498: PetscCall(PCShellGetContext(PC_shell, &user));
500: PetscCheck(user->dsg_formed, PETSC_COMM_SELF, PETSC_ERR_SUP, "DSG not formed");
501: PetscCall(MatSOR(user->DSG, X, 1.0, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP), 0.0, 1, 1, Y));
502: PetscFunctionReturn(PETSC_SUCCESS);
503: }
505: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
506: {
507: AppCtx *user;
508: PetscInt its, i;
510: PetscFunctionBegin;
511: PetscCall(MatShellGetContext(J_shell, &user));
513: if (Y == user->ytrue) {
514: /* First solve is done with true solution to set up problem */
515: PetscCall(KSPSetTolerances(user->solver, 1e-8, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
516: } else {
517: PetscCall(KSPSetTolerances(user->solver, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
518: }
520: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
521: PetscCall(KSPSolve(user->solver, user->yi[0], user->yiwork[0]));
522: PetscCall(KSPGetIterationNumber(user->solver, &its));
523: user->ksp_its = user->ksp_its + its;
525: for (i = 1; i < user->nt; i++) {
526: PetscCall(VecAXPY(user->yi[i], 1.0, user->yiwork[i - 1]));
527: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
528: PetscCall(KSPGetIterationNumber(user->solver, &its));
529: user->ksp_its = user->ksp_its + its;
530: }
531: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
532: PetscFunctionReturn(PETSC_SUCCESS);
533: }
535: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
536: {
537: AppCtx *user;
538: PetscInt its, i;
540: PetscFunctionBegin;
541: PetscCall(MatShellGetContext(J_shell, &user));
543: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
545: i = user->nt - 1;
546: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
548: PetscCall(KSPGetIterationNumber(user->solver, &its));
549: user->ksp_its = user->ksp_its + its;
551: for (i = user->nt - 2; i >= 0; i--) {
552: PetscCall(VecAXPY(user->yi[i], 1.0, user->yiwork[i + 1]));
553: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
555: PetscCall(KSPGetIterationNumber(user->solver, &its));
556: user->ksp_its = user->ksp_its + its;
557: }
559: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
560: PetscFunctionReturn(PETSC_SUCCESS);
561: }
563: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
564: {
565: AppCtx *user;
567: PetscFunctionBegin;
568: PetscCall(MatShellGetContext(J_shell, &user));
570: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, new_shell));
571: PetscCall(MatShellSetOperation(*new_shell, MATOP_MULT, (PetscErrorCodeFn *)StateMatMult));
572: PetscCall(MatShellSetOperation(*new_shell, MATOP_DUPLICATE, (PetscErrorCodeFn *)StateMatDuplicate));
573: PetscCall(MatShellSetOperation(*new_shell, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatMultTranspose));
574: PetscCall(MatShellSetOperation(*new_shell, MATOP_GET_DIAGONAL, (PetscErrorCodeFn *)StateMatGetDiagonal));
575: PetscFunctionReturn(PETSC_SUCCESS);
576: }
578: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
579: {
580: AppCtx *user;
582: PetscFunctionBegin;
583: PetscCall(MatShellGetContext(J_shell, &user));
584: PetscCall(VecCopy(user->js_diag, X));
585: PetscFunctionReturn(PETSC_SUCCESS);
586: }
588: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
589: {
590: /* con = Ay - q, A = [B 0 0 ... 0;
591: -I B 0 ... 0;
592: 0 -I B ... 0;
593: ... ;
594: 0 ... -I B]
595: B = ht * Div * Sigma * Grad + eye */
596: PetscInt i;
597: AppCtx *user = (AppCtx *)ptr;
599: PetscFunctionBegin;
600: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
601: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
602: PetscCall(MatMult(user->JsBlock, user->yi[0], user->yiwork[0]));
603: for (i = 1; i < user->nt; i++) {
604: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
605: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i - 1]));
606: }
607: PetscCall(Gather_i(C, user->yiwork, user->yi_scatter, user->nt));
608: PetscCall(VecAXPY(C, -1.0, user->q));
609: PetscFunctionReturn(PETSC_SUCCESS);
610: }
612: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
613: {
614: PetscFunctionBegin;
615: PetscCall(VecScatterBegin(s_scat, x, state, INSERT_VALUES, SCATTER_FORWARD));
616: PetscCall(VecScatterEnd(s_scat, x, state, INSERT_VALUES, SCATTER_FORWARD));
617: PetscCall(VecScatterBegin(d_scat, x, design, INSERT_VALUES, SCATTER_FORWARD));
618: PetscCall(VecScatterEnd(d_scat, x, design, INSERT_VALUES, SCATTER_FORWARD));
619: PetscFunctionReturn(PETSC_SUCCESS);
620: }
622: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
623: {
624: PetscInt i;
626: PetscFunctionBegin;
627: for (i = 0; i < nt; i++) {
628: PetscCall(VecScatterBegin(scat[i], y, yi[i], INSERT_VALUES, SCATTER_FORWARD));
629: PetscCall(VecScatterEnd(scat[i], y, yi[i], INSERT_VALUES, SCATTER_FORWARD));
630: }
631: PetscFunctionReturn(PETSC_SUCCESS);
632: }
634: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
635: {
636: PetscFunctionBegin;
637: PetscCall(VecScatterBegin(s_scat, state, x, INSERT_VALUES, SCATTER_REVERSE));
638: PetscCall(VecScatterEnd(s_scat, state, x, INSERT_VALUES, SCATTER_REVERSE));
639: PetscCall(VecScatterBegin(d_scat, design, x, INSERT_VALUES, SCATTER_REVERSE));
640: PetscCall(VecScatterEnd(d_scat, design, x, INSERT_VALUES, SCATTER_REVERSE));
641: PetscFunctionReturn(PETSC_SUCCESS);
642: }
644: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
645: {
646: PetscInt i;
648: PetscFunctionBegin;
649: for (i = 0; i < nt; i++) {
650: PetscCall(VecScatterBegin(scat[i], yi[i], y, INSERT_VALUES, SCATTER_REVERSE));
651: PetscCall(VecScatterEnd(scat[i], yi[i], y, INSERT_VALUES, SCATTER_REVERSE));
652: }
653: PetscFunctionReturn(PETSC_SUCCESS);
654: }
656: PetscErrorCode ParabolicInitialize(AppCtx *user)
657: {
658: PetscInt m, n, i, j, k, linear_index, istart, iend, iblock, lo, hi, lo2, hi2;
659: Vec XX, YY, ZZ, XXwork, YYwork, ZZwork, UTwork, yi, di, bc;
660: PetscReal *x, *y, *z;
661: PetscReal h, stime;
662: PetscScalar hinv, neg_hinv, half = 0.5, sqrt_beta;
663: PetscInt im, indx1, indx2, indy1, indy2, indz1, indz2, nx, ny, nz;
664: PetscReal xri, yri, zri, xim, yim, zim, dx1, dx2, dy1, dy2, dz1, dz2, Dx, Dy, Dz;
665: PetscScalar v, vx, vy, vz;
666: IS is_from_y, is_to_yi, is_from_d, is_to_di;
667: /* Data locations */
668: 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,
669: 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,
670: 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};
672: 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,
673: 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,
674: 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};
676: 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,
677: 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,
678: 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};
680: PetscFunctionBegin;
681: PetscCall(PetscMalloc1(user->mx, &x));
682: PetscCall(PetscMalloc1(user->mx, &y));
683: PetscCall(PetscMalloc1(user->mx, &z));
684: user->jformed = PETSC_FALSE;
685: user->dsg_formed = PETSC_FALSE;
687: n = user->mx * user->mx * user->mx;
688: m = 3 * user->mx * user->mx * (user->mx - 1);
689: sqrt_beta = PetscSqrtScalar(user->beta);
691: user->ksp_its = 0;
692: user->ksp_its_initial = 0;
694: stime = (PetscReal)user->nt / user->ns;
695: PetscCall(PetscMalloc1(user->ns, &user->sample_times));
696: for (i = 0; i < user->ns; i++) user->sample_times[i] = (PetscInt)(stime * ((PetscReal)i + 1.0) - 0.5);
698: PetscCall(VecCreate(PETSC_COMM_WORLD, &XX));
699: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->q));
700: PetscCall(VecSetSizes(XX, PETSC_DECIDE, n));
701: PetscCall(VecSetSizes(user->q, PETSC_DECIDE, n * user->nt));
702: PetscCall(VecSetFromOptions(XX));
703: PetscCall(VecSetFromOptions(user->q));
705: PetscCall(VecDuplicate(XX, &YY));
706: PetscCall(VecDuplicate(XX, &ZZ));
707: PetscCall(VecDuplicate(XX, &XXwork));
708: PetscCall(VecDuplicate(XX, &YYwork));
709: PetscCall(VecDuplicate(XX, &ZZwork));
710: PetscCall(VecDuplicate(XX, &UTwork));
711: PetscCall(VecDuplicate(XX, &user->utrue));
712: PetscCall(VecDuplicate(XX, &bc));
714: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
715: h = 1.0 / user->mx;
716: hinv = user->mx;
717: neg_hinv = -hinv;
719: PetscCall(VecGetOwnershipRange(XX, &istart, &iend));
720: for (linear_index = istart; linear_index < iend; linear_index++) {
721: i = linear_index % user->mx;
722: j = ((linear_index - i) / user->mx) % user->mx;
723: k = ((linear_index - i) / user->mx - j) / user->mx;
724: vx = h * (i + 0.5);
725: vy = h * (j + 0.5);
726: vz = h * (k + 0.5);
727: PetscCall(VecSetValues(XX, 1, &linear_index, &vx, INSERT_VALUES));
728: PetscCall(VecSetValues(YY, 1, &linear_index, &vy, INSERT_VALUES));
729: PetscCall(VecSetValues(ZZ, 1, &linear_index, &vz, INSERT_VALUES));
730: if ((vx < 0.6) && (vx > 0.4) && (vy < 0.6) && (vy > 0.4) && (vy < 0.6) && (vz < 0.6) && (vz > 0.4)) {
731: v = 1000.0;
732: PetscCall(VecSetValues(bc, 1, &linear_index, &v, INSERT_VALUES));
733: }
734: }
736: PetscCall(VecAssemblyBegin(XX));
737: PetscCall(VecAssemblyEnd(XX));
738: PetscCall(VecAssemblyBegin(YY));
739: PetscCall(VecAssemblyEnd(YY));
740: PetscCall(VecAssemblyBegin(ZZ));
741: PetscCall(VecAssemblyEnd(ZZ));
742: PetscCall(VecAssemblyBegin(bc));
743: PetscCall(VecAssemblyEnd(bc));
745: /* Compute true parameter function
746: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
747: PetscCall(VecCopy(XX, XXwork));
748: PetscCall(VecCopy(YY, YYwork));
749: PetscCall(VecCopy(ZZ, ZZwork));
751: PetscCall(VecShift(XXwork, -0.5));
752: PetscCall(VecShift(YYwork, -0.5));
753: PetscCall(VecShift(ZZwork, -0.5));
755: PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
756: PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
757: PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));
759: PetscCall(VecCopy(XXwork, user->utrue));
760: PetscCall(VecAXPY(user->utrue, 1.0, YYwork));
761: PetscCall(VecAXPY(user->utrue, 1.0, ZZwork));
762: PetscCall(VecScale(user->utrue, -10.0));
763: PetscCall(VecExp(user->utrue));
764: PetscCall(VecShift(user->utrue, 0.5));
766: PetscCall(VecDestroy(&XX));
767: PetscCall(VecDestroy(&YY));
768: PetscCall(VecDestroy(&ZZ));
769: PetscCall(VecDestroy(&XXwork));
770: PetscCall(VecDestroy(&YYwork));
771: PetscCall(VecDestroy(&ZZwork));
772: PetscCall(VecDestroy(&UTwork));
774: /* Initial guess and reference model */
775: PetscCall(VecDuplicate(user->utrue, &user->ur));
777: /* Generate Grad matrix */
778: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Grad));
779: PetscCall(MatSetSizes(user->Grad, PETSC_DECIDE, PETSC_DECIDE, m, n));
780: PetscCall(MatSetFromOptions(user->Grad));
781: PetscCall(MatMPIAIJSetPreallocation(user->Grad, 2, NULL, 2, NULL));
782: PetscCall(MatSeqAIJSetPreallocation(user->Grad, 2, NULL));
783: PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));
785: for (i = istart; i < iend; i++) {
786: if (i < m / 3) {
787: iblock = i / (user->mx - 1);
788: j = iblock * user->mx + (i % (user->mx - 1));
789: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
790: j = j + 1;
791: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
792: }
793: if (i >= m / 3 && i < 2 * m / 3) {
794: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
795: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
796: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
797: j = j + user->mx;
798: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
799: }
800: if (i >= 2 * m / 3) {
801: j = i - 2 * m / 3;
802: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
803: j = j + user->mx * user->mx;
804: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
805: }
806: }
808: PetscCall(MatAssemblyBegin(user->Grad, MAT_FINAL_ASSEMBLY));
809: PetscCall(MatAssemblyEnd(user->Grad, MAT_FINAL_ASSEMBLY));
811: /* Generate arithmetic averaging matrix Av */
812: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Av));
813: PetscCall(MatSetSizes(user->Av, PETSC_DECIDE, PETSC_DECIDE, m, n));
814: PetscCall(MatSetFromOptions(user->Av));
815: PetscCall(MatMPIAIJSetPreallocation(user->Av, 2, NULL, 2, NULL));
816: PetscCall(MatSeqAIJSetPreallocation(user->Av, 2, NULL));
817: PetscCall(MatGetOwnershipRange(user->Av, &istart, &iend));
819: for (i = istart; i < iend; i++) {
820: if (i < m / 3) {
821: iblock = i / (user->mx - 1);
822: j = iblock * user->mx + (i % (user->mx - 1));
823: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
824: j = j + 1;
825: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
826: }
827: if (i >= m / 3 && i < 2 * m / 3) {
828: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
829: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
830: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
831: j = j + user->mx;
832: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
833: }
834: if (i >= 2 * m / 3) {
835: j = i - 2 * m / 3;
836: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
837: j = j + user->mx * user->mx;
838: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
839: }
840: }
842: PetscCall(MatAssemblyBegin(user->Av, MAT_FINAL_ASSEMBLY));
843: PetscCall(MatAssemblyEnd(user->Av, MAT_FINAL_ASSEMBLY));
845: /* Generate transpose of averaging matrix Av */
846: PetscCall(MatTranspose(user->Av, MAT_INITIAL_MATRIX, &user->AvT));
848: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->L));
849: PetscCall(MatSetSizes(user->L, PETSC_DECIDE, PETSC_DECIDE, m + n, n));
850: PetscCall(MatSetFromOptions(user->L));
851: PetscCall(MatMPIAIJSetPreallocation(user->L, 2, NULL, 2, NULL));
852: PetscCall(MatSeqAIJSetPreallocation(user->L, 2, NULL));
853: PetscCall(MatGetOwnershipRange(user->L, &istart, &iend));
855: for (i = istart; i < iend; i++) {
856: if (i < m / 3) {
857: iblock = i / (user->mx - 1);
858: j = iblock * user->mx + (i % (user->mx - 1));
859: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
860: j = j + 1;
861: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
862: }
863: if (i >= m / 3 && i < 2 * m / 3) {
864: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
865: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
866: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
867: j = j + user->mx;
868: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
869: }
870: if (i >= 2 * m / 3 && i < m) {
871: j = i - 2 * m / 3;
872: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
873: j = j + user->mx * user->mx;
874: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
875: }
876: if (i >= m) {
877: j = i - m;
878: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &sqrt_beta, INSERT_VALUES));
879: }
880: }
882: PetscCall(MatAssemblyBegin(user->L, MAT_FINAL_ASSEMBLY));
883: PetscCall(MatAssemblyEnd(user->L, MAT_FINAL_ASSEMBLY));
885: PetscCall(MatScale(user->L, PetscPowScalar(h, 1.5)));
887: /* Generate Div matrix */
888: PetscCall(MatTranspose(user->Grad, MAT_INITIAL_MATRIX, &user->Div));
890: /* Build work vectors and matrices */
891: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->S));
892: PetscCall(VecSetSizes(user->S, PETSC_DECIDE, user->mx * user->mx * (user->mx - 1) * 3));
893: PetscCall(VecSetFromOptions(user->S));
895: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->lwork));
896: PetscCall(VecSetSizes(user->lwork, PETSC_DECIDE, m + user->mx * user->mx * user->mx));
897: PetscCall(VecSetFromOptions(user->lwork));
899: PetscCall(MatDuplicate(user->Div, MAT_SHARE_NONZERO_PATTERN, &user->Divwork));
900: PetscCall(MatDuplicate(user->Av, MAT_SHARE_NONZERO_PATTERN, &user->Avwork));
902: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->d));
903: PetscCall(VecSetSizes(user->d, PETSC_DECIDE, user->ndata * user->nt));
904: PetscCall(VecSetFromOptions(user->d));
906: PetscCall(VecDuplicate(user->S, &user->Swork));
907: PetscCall(VecDuplicate(user->S, &user->Av_u));
908: PetscCall(VecDuplicate(user->S, &user->Twork));
909: PetscCall(VecDuplicate(user->S, &user->Rwork));
910: PetscCall(VecDuplicate(user->y, &user->ywork));
911: PetscCall(VecDuplicate(user->u, &user->uwork));
912: PetscCall(VecDuplicate(user->u, &user->js_diag));
913: PetscCall(VecDuplicate(user->c, &user->cwork));
914: PetscCall(VecDuplicate(user->d, &user->dwork));
916: /* Create matrix-free shell user->Js for computing A*x */
917: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m * user->nt, user, &user->Js));
918: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT, (PetscErrorCodeFn *)StateMatMult));
919: PetscCall(MatShellSetOperation(user->Js, MATOP_DUPLICATE, (PetscErrorCodeFn *)StateMatDuplicate));
920: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatMultTranspose));
921: PetscCall(MatShellSetOperation(user->Js, MATOP_GET_DIAGONAL, (PetscErrorCodeFn *)StateMatGetDiagonal));
923: /* Diagonal blocks of user->Js */
924: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, &user->JsBlock));
925: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT, (PetscErrorCodeFn *)StateMatBlockMult));
926: /* Blocks are symmetric */
927: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatBlockMult));
929: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
930: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
931: This is an SSOR preconditioner for user->JsBlock. */
932: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, &user->JsBlockPrec));
933: PetscCall(MatShellSetOperation(user->JsBlockPrec, MATOP_MULT, (PetscErrorCodeFn *)StateMatBlockPrecMult));
934: /* JsBlockPrec is symmetric */
935: PetscCall(MatShellSetOperation(user->JsBlockPrec, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatBlockPrecMult));
936: PetscCall(MatSetOption(user->JsBlockPrec, MAT_SYMMETRIC, PETSC_TRUE));
937: PetscCall(MatSetOption(user->JsBlockPrec, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
939: /* Create a matrix-free shell user->Jd for computing B*x */
940: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m, user, &user->Jd));
941: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT, (PetscErrorCodeFn *)DesignMatMult));
942: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)DesignMatMultTranspose));
944: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
945: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m * user->nt, user, &user->JsInv));
946: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT, (PetscErrorCodeFn *)StateMatInvMult));
947: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatInvTransposeMult));
949: /* Solver options and tolerances */
950: PetscCall(KSPCreate(PETSC_COMM_WORLD, &user->solver));
951: PetscCall(KSPSetType(user->solver, KSPCG));
952: PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->JsBlockPrec));
953: PetscCall(KSPSetInitialGuessNonzero(user->solver, PETSC_FALSE));
954: PetscCall(KSPSetTolerances(user->solver, 1e-4, 1e-20, 1e3, 500));
955: PetscCall(KSPSetFromOptions(user->solver));
956: PetscCall(KSPGetPC(user->solver, &user->prec));
957: PetscCall(PCSetType(user->prec, PCSHELL));
959: PetscCall(PCShellSetApply(user->prec, StateMatBlockPrecMult));
960: PetscCall(PCShellSetApplyTranspose(user->prec, StateMatBlockPrecMult));
961: PetscCall(PCShellSetContext(user->prec, user));
963: /* Create scatter from y to y_1,y_2,...,y_nt */
964: PetscCall(PetscMalloc1(user->nt * user->m, &user->yi_scatter));
965: PetscCall(VecCreate(PETSC_COMM_WORLD, &yi));
966: PetscCall(VecSetSizes(yi, PETSC_DECIDE, user->mx * user->mx * user->mx));
967: PetscCall(VecSetFromOptions(yi));
968: PetscCall(VecDuplicateVecs(yi, user->nt, &user->yi));
969: PetscCall(VecDuplicateVecs(yi, user->nt, &user->yiwork));
971: PetscCall(VecGetOwnershipRange(user->y, &lo2, &hi2));
972: istart = 0;
973: for (i = 0; i < user->nt; i++) {
974: PetscCall(VecGetOwnershipRange(user->yi[i], &lo, &hi));
975: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_to_yi));
976: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_y));
977: PetscCall(VecScatterCreate(user->y, is_from_y, user->yi[i], is_to_yi, &user->yi_scatter[i]));
978: istart = istart + hi - lo;
979: PetscCall(ISDestroy(&is_to_yi));
980: PetscCall(ISDestroy(&is_from_y));
981: }
982: PetscCall(VecDestroy(&yi));
984: /* Create scatter from d to d_1,d_2,...,d_ns */
985: PetscCall(PetscMalloc1(user->ns * user->ndata, &user->di_scatter));
986: PetscCall(VecCreate(PETSC_COMM_WORLD, &di));
987: PetscCall(VecSetSizes(di, PETSC_DECIDE, user->ndata));
988: PetscCall(VecSetFromOptions(di));
989: PetscCall(VecDuplicateVecs(di, user->ns, &user->di));
990: PetscCall(VecGetOwnershipRange(user->d, &lo2, &hi2));
991: istart = 0;
992: for (i = 0; i < user->ns; i++) {
993: PetscCall(VecGetOwnershipRange(user->di[i], &lo, &hi));
994: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_to_di));
995: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_d));
996: PetscCall(VecScatterCreate(user->d, is_from_d, user->di[i], is_to_di, &user->di_scatter[i]));
997: istart = istart + hi - lo;
998: PetscCall(ISDestroy(&is_to_di));
999: PetscCall(ISDestroy(&is_from_d));
1000: }
1001: PetscCall(VecDestroy(&di));
1003: /* Assemble RHS of forward problem */
1004: PetscCall(VecCopy(bc, user->yiwork[0]));
1005: for (i = 1; i < user->nt; i++) PetscCall(VecSet(user->yiwork[i], 0.0));
1006: PetscCall(Gather_i(user->q, user->yiwork, user->yi_scatter, user->nt));
1007: PetscCall(VecDestroy(&bc));
1009: /* Compute true state function yt given ut */
1010: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->ytrue));
1011: PetscCall(VecSetSizes(user->ytrue, PETSC_DECIDE, n * user->nt));
1012: PetscCall(VecSetFromOptions(user->ytrue));
1014: /* First compute Av_u = Av*exp(-u) */
1015: PetscCall(VecSet(user->uwork, 0));
1016: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue)); /* Note: user->utrue */
1017: PetscCall(VecExp(user->uwork));
1018: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
1020: /* Symbolic DSG = Div * Grad */
1021: PetscCall(MatProductCreate(user->Div, user->Grad, NULL, &user->DSG));
1022: PetscCall(MatProductSetType(user->DSG, MATPRODUCT_AB));
1023: PetscCall(MatProductSetAlgorithm(user->DSG, "default"));
1024: PetscCall(MatProductSetFill(user->DSG, PETSC_DETERMINE));
1025: PetscCall(MatProductSetFromOptions(user->DSG));
1026: PetscCall(MatProductSymbolic(user->DSG));
1028: user->dsg_formed = PETSC_TRUE;
1030: /* Next form DSG = Div*Grad */
1031: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1032: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1033: if (user->dsg_formed) {
1034: PetscCall(MatProductNumeric(user->DSG));
1035: } else {
1036: PetscCall(MatMatMult(user->Div, user->Grad, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &user->DSG));
1037: user->dsg_formed = PETSC_TRUE;
1038: }
1039: /* B = speye(nx^3) + ht*DSG; */
1040: PetscCall(MatScale(user->DSG, user->ht));
1041: PetscCall(MatShift(user->DSG, 1.0));
1043: /* Now solve for ytrue */
1044: PetscCall(StateMatInvMult(user->Js, user->q, user->ytrue));
1046: /* Initial guess y0 for state given u0 */
1048: /* First compute Av_u = Av*exp(-u) */
1049: PetscCall(VecSet(user->uwork, 0));
1050: PetscCall(VecAXPY(user->uwork, -1.0, user->u)); /* Note: user->u */
1051: PetscCall(VecExp(user->uwork));
1052: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
1054: /* Next form DSG = Div*S*Grad */
1055: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1056: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1057: if (user->dsg_formed) {
1058: PetscCall(MatProductNumeric(user->DSG));
1059: } else {
1060: PetscCall(MatMatMult(user->Div, user->Grad, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &user->DSG));
1062: user->dsg_formed = PETSC_TRUE;
1063: }
1064: /* B = speye(nx^3) + ht*DSG; */
1065: PetscCall(MatScale(user->DSG, user->ht));
1066: PetscCall(MatShift(user->DSG, 1.0));
1068: /* Now solve for y */
1069: PetscCall(StateMatInvMult(user->Js, user->q, user->y));
1071: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1072: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Qblock));
1073: PetscCall(MatSetSizes(user->Qblock, PETSC_DECIDE, PETSC_DECIDE, user->ndata, n));
1074: PetscCall(MatSetFromOptions(user->Qblock));
1075: PetscCall(MatMPIAIJSetPreallocation(user->Qblock, 8, NULL, 8, NULL));
1076: PetscCall(MatSeqAIJSetPreallocation(user->Qblock, 8, NULL));
1078: for (i = 0; i < user->mx; i++) {
1079: x[i] = h * (i + 0.5);
1080: y[i] = h * (i + 0.5);
1081: z[i] = h * (i + 0.5);
1082: }
1084: PetscCall(MatGetOwnershipRange(user->Qblock, &istart, &iend));
1085: nx = user->mx;
1086: ny = user->mx;
1087: nz = user->mx;
1088: for (i = istart; i < iend; i++) {
1089: xri = xr[i];
1090: im = 0;
1091: xim = x[im];
1092: while (xri > xim && im < nx) {
1093: im = im + 1;
1094: xim = x[im];
1095: }
1096: indx1 = im - 1;
1097: indx2 = im;
1098: dx1 = xri - x[indx1];
1099: dx2 = x[indx2] - xri;
1101: yri = yr[i];
1102: im = 0;
1103: yim = y[im];
1104: while (yri > yim && im < ny) {
1105: im = im + 1;
1106: yim = y[im];
1107: }
1108: indy1 = im - 1;
1109: indy2 = im;
1110: dy1 = yri - y[indy1];
1111: dy2 = y[indy2] - yri;
1113: zri = zr[i];
1114: im = 0;
1115: zim = z[im];
1116: while (zri > zim && im < nz) {
1117: im = im + 1;
1118: zim = z[im];
1119: }
1120: indz1 = im - 1;
1121: indz2 = im;
1122: dz1 = zri - z[indz1];
1123: dz2 = z[indz2] - zri;
1125: Dx = x[indx2] - x[indx1];
1126: Dy = y[indy2] - y[indy1];
1127: Dz = z[indz2] - z[indz1];
1129: j = indx1 + indy1 * nx + indz1 * nx * ny;
1130: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1131: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1133: j = indx1 + indy1 * nx + indz2 * nx * ny;
1134: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1135: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1137: j = indx1 + indy2 * nx + indz1 * nx * ny;
1138: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1139: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1141: j = indx1 + indy2 * nx + indz2 * nx * ny;
1142: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1143: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1145: j = indx2 + indy1 * nx + indz1 * nx * ny;
1146: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1147: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1149: j = indx2 + indy1 * nx + indz2 * nx * ny;
1150: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1151: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1153: j = indx2 + indy2 * nx + indz1 * nx * ny;
1154: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1155: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1157: j = indx2 + indy2 * nx + indz2 * nx * ny;
1158: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1159: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1160: }
1161: PetscCall(MatAssemblyBegin(user->Qblock, MAT_FINAL_ASSEMBLY));
1162: PetscCall(MatAssemblyEnd(user->Qblock, MAT_FINAL_ASSEMBLY));
1164: PetscCall(MatTranspose(user->Qblock, MAT_INITIAL_MATRIX, &user->QblockT));
1165: PetscCall(MatTranspose(user->L, MAT_INITIAL_MATRIX, &user->LT));
1167: /* Add noise to the measurement data */
1168: PetscCall(VecSet(user->ywork, 1.0));
1169: PetscCall(VecAYPX(user->ywork, user->noise, user->ytrue));
1170: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
1171: for (j = 0; j < user->ns; j++) {
1172: i = user->sample_times[j];
1173: PetscCall(MatMult(user->Qblock, user->yiwork[i], user->di[j]));
1174: }
1175: PetscCall(Gather_i(user->d, user->di, user->di_scatter, user->ns));
1177: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1178: PetscCall(KSPSetFromOptions(user->solver));
1179: PetscCall(PetscFree(x));
1180: PetscCall(PetscFree(y));
1181: PetscCall(PetscFree(z));
1182: PetscFunctionReturn(PETSC_SUCCESS);
1183: }
1185: PetscErrorCode ParabolicDestroy(AppCtx *user)
1186: {
1187: PetscFunctionBegin;
1188: PetscCall(MatDestroy(&user->Qblock));
1189: PetscCall(MatDestroy(&user->QblockT));
1190: PetscCall(MatDestroy(&user->Div));
1191: PetscCall(MatDestroy(&user->Divwork));
1192: PetscCall(MatDestroy(&user->Grad));
1193: PetscCall(MatDestroy(&user->Av));
1194: PetscCall(MatDestroy(&user->Avwork));
1195: PetscCall(MatDestroy(&user->AvT));
1196: PetscCall(MatDestroy(&user->DSG));
1197: PetscCall(MatDestroy(&user->L));
1198: PetscCall(MatDestroy(&user->LT));
1199: PetscCall(KSPDestroy(&user->solver));
1200: PetscCall(MatDestroy(&user->Js));
1201: PetscCall(MatDestroy(&user->Jd));
1202: PetscCall(MatDestroy(&user->JsInv));
1203: PetscCall(MatDestroy(&user->JsBlock));
1204: PetscCall(MatDestroy(&user->JsBlockPrec));
1205: PetscCall(VecDestroy(&user->u));
1206: PetscCall(VecDestroy(&user->uwork));
1207: PetscCall(VecDestroy(&user->utrue));
1208: PetscCall(VecDestroy(&user->y));
1209: PetscCall(VecDestroy(&user->ywork));
1210: PetscCall(VecDestroy(&user->ytrue));
1211: PetscCall(VecDestroyVecs(user->nt, &user->yi));
1212: PetscCall(VecDestroyVecs(user->nt, &user->yiwork));
1213: PetscCall(VecDestroyVecs(user->ns, &user->di));
1214: PetscCall(PetscFree(user->yi));
1215: PetscCall(PetscFree(user->yiwork));
1216: PetscCall(PetscFree(user->di));
1217: PetscCall(VecDestroy(&user->c));
1218: PetscCall(VecDestroy(&user->cwork));
1219: PetscCall(VecDestroy(&user->ur));
1220: PetscCall(VecDestroy(&user->q));
1221: PetscCall(VecDestroy(&user->d));
1222: PetscCall(VecDestroy(&user->dwork));
1223: PetscCall(VecDestroy(&user->lwork));
1224: PetscCall(VecDestroy(&user->S));
1225: PetscCall(VecDestroy(&user->Swork));
1226: PetscCall(VecDestroy(&user->Av_u));
1227: PetscCall(VecDestroy(&user->Twork));
1228: PetscCall(VecDestroy(&user->Rwork));
1229: PetscCall(VecDestroy(&user->js_diag));
1230: PetscCall(ISDestroy(&user->s_is));
1231: PetscCall(ISDestroy(&user->d_is));
1232: PetscCall(VecScatterDestroy(&user->state_scatter));
1233: PetscCall(VecScatterDestroy(&user->design_scatter));
1234: for (PetscInt i = 0; i < user->nt; i++) PetscCall(VecScatterDestroy(&user->yi_scatter[i]));
1235: for (PetscInt i = 0; i < user->ns; i++) PetscCall(VecScatterDestroy(&user->di_scatter[i]));
1236: PetscCall(PetscFree(user->yi_scatter));
1237: PetscCall(PetscFree(user->di_scatter));
1238: PetscCall(PetscFree(user->sample_times));
1239: PetscFunctionReturn(PETSC_SUCCESS);
1240: }
1242: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1243: {
1244: Vec X;
1245: PetscReal unorm, ynorm;
1246: AppCtx *user = (AppCtx *)ptr;
1248: PetscFunctionBegin;
1249: PetscCall(TaoGetSolution(tao, &X));
1250: PetscCall(Scatter(X, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
1251: PetscCall(VecAXPY(user->ywork, -1.0, user->ytrue));
1252: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue));
1253: PetscCall(VecNorm(user->uwork, NORM_2, &unorm));
1254: PetscCall(VecNorm(user->ywork, NORM_2, &ynorm));
1255: PetscCall(PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n", (double)unorm, (double)ynorm));
1256: PetscFunctionReturn(PETSC_SUCCESS);
1257: }
1259: /*TEST
1261: build:
1262: requires: !complex
1264: test:
1265: args: -tao_monitor_constraint_norm -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1266: requires: !single
1268: TEST*/