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: #if defined(PETSC_USE_LOG)
106: PetscLogStage stages[1];
107: #endif
109: PetscFunctionBeginUser;
110: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
111: user.mx = 8;
112: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "parabolic example", NULL);
113: PetscCall(PetscOptionsInt("-mx", "Number of grid points in each direction", "", user.mx, &user.mx, NULL));
114: user.nt = 8;
115: PetscCall(PetscOptionsInt("-nt", "Number of time steps", "", user.nt, &user.nt, NULL));
116: user.ndata = 64;
117: PetscCall(PetscOptionsInt("-ndata", "Numbers of data points per sample", "", user.ndata, &user.ndata, NULL));
118: user.ns = 8;
119: PetscCall(PetscOptionsInt("-ns", "Number of samples", "", user.ns, &user.ns, NULL));
120: user.alpha = 1.0;
121: PetscCall(PetscOptionsReal("-alpha", "Regularization parameter", "", user.alpha, &user.alpha, NULL));
122: user.beta = 0.01;
123: PetscCall(PetscOptionsReal("-beta", "Weight attributed to ||u||^2 in regularization functional", "", user.beta, &user.beta, NULL));
124: user.noise = 0.01;
125: PetscCall(PetscOptionsReal("-noise", "Amount of noise to add to data", "", user.noise, &user.noise, NULL));
126: PetscCall(PetscOptionsInt("-ntests", "Number of times to repeat TaoSolve", "", ntests, &ntests, NULL));
127: PetscOptionsEnd();
129: user.m = user.mx * user.mx * user.mx; /* number of constraints per time step */
130: user.n = user.m * (user.nt + 1); /* number of variables */
131: user.ht = (PetscReal)1 / user.nt;
133: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.u));
134: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.y));
135: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.c));
136: PetscCall(VecSetSizes(user.u, PETSC_DECIDE, user.n - user.m * user.nt));
137: PetscCall(VecSetSizes(user.y, PETSC_DECIDE, user.m * user.nt));
138: PetscCall(VecSetSizes(user.c, PETSC_DECIDE, user.m * user.nt));
139: PetscCall(VecSetFromOptions(user.u));
140: PetscCall(VecSetFromOptions(user.y));
141: PetscCall(VecSetFromOptions(user.c));
143: /* Create scatters for reduced spaces.
144: If the state vector y and design vector u are partitioned as
145: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
146: then the solution vector x is organized as
147: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
148: The index sets user.s_is and user.d_is correspond to the indices of the
149: state and design variables owned by the current processor.
150: */
151: PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
153: PetscCall(VecGetOwnershipRange(user.y, &lo, &hi));
154: PetscCall(VecGetOwnershipRange(user.u, &lo2, &hi2));
156: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_allstate));
157: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo + lo2, 1, &user.s_is));
159: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, lo2, 1, &is_alldesign));
160: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, hi + lo2, 1, &user.d_is));
162: PetscCall(VecSetSizes(x, hi - lo + hi2 - lo2, user.n));
163: PetscCall(VecSetFromOptions(x));
165: PetscCall(VecScatterCreate(x, user.s_is, user.y, is_allstate, &user.state_scatter));
166: PetscCall(VecScatterCreate(x, user.d_is, user.u, is_alldesign, &user.design_scatter));
167: PetscCall(ISDestroy(&is_alldesign));
168: PetscCall(ISDestroy(&is_allstate));
170: /* Create TAO solver and set desired solution method */
171: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
172: PetscCall(TaoSetType(tao, TAOLCL));
174: /* Set up initial vectors and matrices */
175: PetscCall(ParabolicInitialize(&user));
177: PetscCall(Gather(x, user.y, user.state_scatter, user.u, user.design_scatter));
178: PetscCall(VecDuplicate(x, &x0));
179: PetscCall(VecCopy(x, x0));
181: /* Set solution vector with an initial guess */
182: PetscCall(TaoSetSolution(tao, x));
183: PetscCall(TaoSetObjective(tao, FormFunction, &user));
184: PetscCall(TaoSetGradient(tao, NULL, FormGradient, &user));
185: PetscCall(TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user));
187: PetscCall(TaoSetJacobianStateRoutine(tao, user.Js, user.JsBlockPrec, user.JsInv, FormJacobianState, &user));
188: PetscCall(TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user));
190: PetscCall(TaoSetFromOptions(tao));
191: PetscCall(TaoSetStateDesignIS(tao, user.s_is, user.d_is));
193: /* SOLVE THE APPLICATION */
194: PetscCall(PetscLogStageRegister("Trials", &stages[0]));
195: PetscCall(PetscLogStagePush(stages[0]));
196: user.ksp_its_initial = user.ksp_its;
197: ksp_old = user.ksp_its;
198: for (i = 0; i < ntests; i++) {
199: PetscCall(TaoSolve(tao));
200: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP Iterations = %" PetscInt_FMT "\n", user.ksp_its - ksp_old));
201: PetscCall(VecCopy(x0, x));
202: PetscCall(TaoSetSolution(tao, x));
203: }
204: PetscCall(PetscLogStagePop());
205: PetscCall(PetscBarrier((PetscObject)x));
206: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations within initialization: "));
207: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its_initial));
208: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Total KSP iterations over %" PetscInt_FMT " trial(s): ", ntests));
209: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its));
210: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations per trial: "));
211: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", (user.ksp_its - user.ksp_its_initial) / ntests));
213: PetscCall(TaoDestroy(&tao));
214: PetscCall(VecDestroy(&x));
215: PetscCall(VecDestroy(&x0));
216: PetscCall(ParabolicDestroy(&user));
218: PetscCall(PetscFinalize());
219: return 0;
220: }
221: /* ------------------------------------------------------------------- */
222: /*
223: dwork = Qy - d
224: lwork = L*(u-ur)
225: f = 1/2 * (dwork.dork + alpha*lwork.lwork)
226: */
227: PetscErrorCode FormFunction(Tao tao, Vec X, PetscReal *f, void *ptr)
228: {
229: PetscReal d1 = 0, d2 = 0;
230: PetscInt i, j;
231: AppCtx *user = (AppCtx *)ptr;
233: PetscFunctionBegin;
234: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
235: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
236: for (j = 0; j < user->ns; j++) {
237: i = user->sample_times[j];
238: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
239: }
240: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
241: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
242: PetscCall(VecDot(user->dwork, user->dwork, &d1));
244: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
245: PetscCall(MatMult(user->L, user->uwork, user->lwork));
246: PetscCall(VecDot(user->lwork, user->lwork, &d2));
248: *f = 0.5 * (d1 + user->alpha * d2);
249: PetscFunctionReturn(PETSC_SUCCESS);
250: }
252: /* ------------------------------------------------------------------- */
253: /*
254: state: g_s = Q' *(Qy - d)
255: design: g_d = alpha*L'*L*(u-ur)
256: */
257: PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
258: {
259: PetscInt i, j;
260: AppCtx *user = (AppCtx *)ptr;
262: PetscFunctionBegin;
263: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
264: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
265: for (j = 0; j < user->ns; j++) {
266: i = user->sample_times[j];
267: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
268: }
269: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
270: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
271: PetscCall(Scatter_i(user->dwork, user->di, user->di_scatter, user->ns));
272: PetscCall(VecSet(user->ywork, 0.0));
273: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
274: for (j = 0; j < user->ns; j++) {
275: i = user->sample_times[j];
276: PetscCall(MatMult(user->QblockT, user->di[j], user->yiwork[i]));
277: }
278: PetscCall(Gather_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
280: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
281: PetscCall(MatMult(user->L, user->uwork, user->lwork));
282: PetscCall(MatMult(user->LT, user->lwork, user->uwork));
283: PetscCall(VecScale(user->uwork, user->alpha));
284: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
285: PetscFunctionReturn(PETSC_SUCCESS);
286: }
288: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
289: {
290: PetscReal d1, d2;
291: PetscInt i, j;
292: AppCtx *user = (AppCtx *)ptr;
294: PetscFunctionBegin;
295: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
296: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
297: for (j = 0; j < user->ns; j++) {
298: i = user->sample_times[j];
299: PetscCall(MatMult(user->Qblock, user->yi[i], user->di[j]));
300: }
301: PetscCall(Gather_i(user->dwork, user->di, user->di_scatter, user->ns));
302: PetscCall(VecAXPY(user->dwork, -1.0, user->d));
303: PetscCall(VecDot(user->dwork, user->dwork, &d1));
304: PetscCall(Scatter_i(user->dwork, user->di, user->di_scatter, user->ns));
305: PetscCall(VecSet(user->ywork, 0.0));
306: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
307: for (j = 0; j < user->ns; j++) {
308: i = user->sample_times[j];
309: PetscCall(MatMult(user->QblockT, user->di[j], user->yiwork[i]));
310: }
311: PetscCall(Gather_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
313: PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
314: PetscCall(MatMult(user->L, user->uwork, user->lwork));
315: PetscCall(VecDot(user->lwork, user->lwork, &d2));
316: PetscCall(MatMult(user->LT, user->lwork, user->uwork));
317: PetscCall(VecScale(user->uwork, user->alpha));
318: *f = 0.5 * (d1 + user->alpha * d2);
320: PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
321: PetscFunctionReturn(PETSC_SUCCESS);
322: }
324: /* ------------------------------------------------------------------- */
325: /* A
326: MatShell object
327: */
328: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
329: {
330: AppCtx *user = (AppCtx *)ptr;
332: PetscFunctionBegin;
333: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
334: PetscCall(VecSet(user->uwork, 0));
335: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
336: PetscCall(VecExp(user->uwork));
337: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
338: PetscCall(VecCopy(user->Av_u, user->Swork));
339: PetscCall(VecReciprocal(user->Swork));
340: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
341: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
342: if (user->dsg_formed) {
343: PetscCall(MatProductNumeric(user->DSG));
344: } else {
345: PetscCall(MatMatMult(user->Divwork, user->Grad, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &user->DSG));
346: user->dsg_formed = PETSC_TRUE;
347: }
349: /* B = speye(nx^3) + ht*DSG; */
350: PetscCall(MatScale(user->DSG, user->ht));
351: PetscCall(MatShift(user->DSG, 1.0));
352: PetscFunctionReturn(PETSC_SUCCESS);
353: }
355: /* ------------------------------------------------------------------- */
356: /* B */
357: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
358: {
359: AppCtx *user = (AppCtx *)ptr;
361: PetscFunctionBegin;
362: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
363: PetscFunctionReturn(PETSC_SUCCESS);
364: }
366: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
367: {
368: PetscInt i;
369: AppCtx *user;
371: PetscFunctionBegin;
372: PetscCall(MatShellGetContext(J_shell, &user));
373: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
374: PetscCall(MatMult(user->JsBlock, user->yi[0], user->yiwork[0]));
375: for (i = 1; i < user->nt; i++) {
376: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
377: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i - 1]));
378: }
379: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
380: PetscFunctionReturn(PETSC_SUCCESS);
381: }
383: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
384: {
385: PetscInt i;
386: AppCtx *user;
388: PetscFunctionBegin;
389: PetscCall(MatShellGetContext(J_shell, &user));
390: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
391: for (i = 0; i < user->nt - 1; i++) {
392: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
393: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i + 1]));
394: }
395: i = user->nt - 1;
396: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
397: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
398: PetscFunctionReturn(PETSC_SUCCESS);
399: }
401: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
402: {
403: AppCtx *user;
405: PetscFunctionBegin;
406: PetscCall(MatShellGetContext(J_shell, &user));
407: PetscCall(MatMult(user->Grad, X, user->Swork));
408: PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
409: PetscCall(MatMult(user->Div, user->Swork, Y));
410: PetscCall(VecAYPX(Y, user->ht, X));
411: PetscFunctionReturn(PETSC_SUCCESS);
412: }
414: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
415: {
416: PetscInt i;
417: AppCtx *user;
419: PetscFunctionBegin;
420: PetscCall(MatShellGetContext(J_shell, &user));
422: /* sdiag(1./v) */
423: PetscCall(VecSet(user->uwork, 0));
424: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
425: PetscCall(VecExp(user->uwork));
427: /* sdiag(1./((Av*(1./v)).^2)) */
428: PetscCall(MatMult(user->Av, user->uwork, user->Swork));
429: PetscCall(VecPointwiseMult(user->Swork, user->Swork, user->Swork));
430: PetscCall(VecReciprocal(user->Swork));
432: /* (Av * (sdiag(1./v) * b)) */
433: PetscCall(VecPointwiseMult(user->uwork, user->uwork, X));
434: PetscCall(MatMult(user->Av, user->uwork, user->Twork));
436: /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
437: PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
439: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
440: for (i = 0; i < user->nt; i++) {
441: /* (sdiag(Grad*y(:,i)) */
442: PetscCall(MatMult(user->Grad, user->yi[i], user->Twork));
444: /* ht * Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
445: PetscCall(VecPointwiseMult(user->Twork, user->Twork, user->Swork));
446: PetscCall(MatMult(user->Div, user->Twork, user->yiwork[i]));
447: PetscCall(VecScale(user->yiwork[i], user->ht));
448: }
449: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
451: PetscFunctionReturn(PETSC_SUCCESS);
452: }
454: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
455: {
456: PetscInt i;
457: AppCtx *user;
459: PetscFunctionBegin;
460: PetscCall(MatShellGetContext(J_shell, &user));
462: /* sdiag(1./((Av*(1./v)).^2)) */
463: PetscCall(VecSet(user->uwork, 0));
464: PetscCall(VecAXPY(user->uwork, -1.0, user->u));
465: PetscCall(VecExp(user->uwork));
466: PetscCall(MatMult(user->Av, user->uwork, user->Rwork));
467: PetscCall(VecPointwiseMult(user->Rwork, user->Rwork, user->Rwork));
468: PetscCall(VecReciprocal(user->Rwork));
470: PetscCall(VecSet(Y, 0.0));
471: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
472: PetscCall(Scatter_i(X, user->yiwork, user->yi_scatter, user->nt));
473: for (i = 0; i < user->nt; i++) {
474: /* (Div' * b(:,i)) */
475: PetscCall(MatMult(user->Grad, user->yiwork[i], user->Swork));
477: /* sdiag(Grad*y(:,i)) */
478: PetscCall(MatMult(user->Grad, user->yi[i], user->Twork));
480: /* (sdiag(Grad*y(:,i)) * (Div' * b(:,i))) */
481: PetscCall(VecPointwiseMult(user->Twork, user->Swork, user->Twork));
483: /* (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i)))) */
484: PetscCall(VecPointwiseMult(user->Twork, user->Rwork, user->Twork));
486: /* (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
487: PetscCall(MatMult(user->AvT, user->Twork, user->yiwork[i]));
489: /* sdiag(1./v) * (Av' * (sdiag(1./((Av*(1./v)).^2)) * (sdiag(Grad*y(:,i)) * (Div' * b(:,i))))) */
490: PetscCall(VecPointwiseMult(user->yiwork[i], user->uwork, user->yiwork[i]));
491: PetscCall(VecAXPY(Y, user->ht, user->yiwork[i]));
492: }
493: PetscFunctionReturn(PETSC_SUCCESS);
494: }
496: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
497: {
498: AppCtx *user;
500: PetscFunctionBegin;
501: PetscCall(PCShellGetContext(PC_shell, &user));
503: if (user->dsg_formed) {
504: PetscCall(MatSOR(user->DSG, X, 1.0, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP), 0.0, 1, 1, Y));
505: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "DSG not formed");
506: PetscFunctionReturn(PETSC_SUCCESS);
507: }
509: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
510: {
511: AppCtx *user;
512: PetscInt its, i;
514: PetscFunctionBegin;
515: PetscCall(MatShellGetContext(J_shell, &user));
517: if (Y == user->ytrue) {
518: /* First solve is done with true solution to set up problem */
519: PetscCall(KSPSetTolerances(user->solver, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
520: } else {
521: PetscCall(KSPSetTolerances(user->solver, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
522: }
524: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
525: PetscCall(KSPSolve(user->solver, user->yi[0], user->yiwork[0]));
526: PetscCall(KSPGetIterationNumber(user->solver, &its));
527: user->ksp_its = user->ksp_its + its;
529: for (i = 1; i < user->nt; i++) {
530: PetscCall(VecAXPY(user->yi[i], 1.0, user->yiwork[i - 1]));
531: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
532: PetscCall(KSPGetIterationNumber(user->solver, &its));
533: user->ksp_its = user->ksp_its + its;
534: }
535: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
536: PetscFunctionReturn(PETSC_SUCCESS);
537: }
539: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
540: {
541: AppCtx *user;
542: PetscInt its, i;
544: PetscFunctionBegin;
545: PetscCall(MatShellGetContext(J_shell, &user));
547: PetscCall(Scatter_i(X, user->yi, user->yi_scatter, user->nt));
549: i = user->nt - 1;
550: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
552: PetscCall(KSPGetIterationNumber(user->solver, &its));
553: user->ksp_its = user->ksp_its + its;
555: for (i = user->nt - 2; i >= 0; i--) {
556: PetscCall(VecAXPY(user->yi[i], 1.0, user->yiwork[i + 1]));
557: PetscCall(KSPSolve(user->solver, user->yi[i], user->yiwork[i]));
559: PetscCall(KSPGetIterationNumber(user->solver, &its));
560: user->ksp_its = user->ksp_its + its;
561: }
563: PetscCall(Gather_i(Y, user->yiwork, user->yi_scatter, user->nt));
564: PetscFunctionReturn(PETSC_SUCCESS);
565: }
567: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
568: {
569: AppCtx *user;
571: PetscFunctionBegin;
572: PetscCall(MatShellGetContext(J_shell, &user));
574: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, new_shell));
575: PetscCall(MatShellSetOperation(*new_shell, MATOP_MULT, (void (*)(void))StateMatMult));
576: PetscCall(MatShellSetOperation(*new_shell, MATOP_DUPLICATE, (void (*)(void))StateMatDuplicate));
577: PetscCall(MatShellSetOperation(*new_shell, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatMultTranspose));
578: PetscCall(MatShellSetOperation(*new_shell, MATOP_GET_DIAGONAL, (void (*)(void))StateMatGetDiagonal));
579: PetscFunctionReturn(PETSC_SUCCESS);
580: }
582: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
583: {
584: AppCtx *user;
586: PetscFunctionBegin;
587: PetscCall(MatShellGetContext(J_shell, &user));
588: PetscCall(VecCopy(user->js_diag, X));
589: PetscFunctionReturn(PETSC_SUCCESS);
590: }
592: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
593: {
594: /* con = Ay - q, A = [B 0 0 ... 0;
595: -I B 0 ... 0;
596: 0 -I B ... 0;
597: ... ;
598: 0 ... -I B]
599: B = ht * Div * Sigma * Grad + eye */
600: PetscInt i;
601: AppCtx *user = (AppCtx *)ptr;
603: PetscFunctionBegin;
604: PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
605: PetscCall(Scatter_i(user->y, user->yi, user->yi_scatter, user->nt));
606: PetscCall(MatMult(user->JsBlock, user->yi[0], user->yiwork[0]));
607: for (i = 1; i < user->nt; i++) {
608: PetscCall(MatMult(user->JsBlock, user->yi[i], user->yiwork[i]));
609: PetscCall(VecAXPY(user->yiwork[i], -1.0, user->yi[i - 1]));
610: }
611: PetscCall(Gather_i(C, user->yiwork, user->yi_scatter, user->nt));
612: PetscCall(VecAXPY(C, -1.0, user->q));
613: PetscFunctionReturn(PETSC_SUCCESS);
614: }
616: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
617: {
618: PetscFunctionBegin;
619: PetscCall(VecScatterBegin(s_scat, x, state, INSERT_VALUES, SCATTER_FORWARD));
620: PetscCall(VecScatterEnd(s_scat, x, state, INSERT_VALUES, SCATTER_FORWARD));
621: PetscCall(VecScatterBegin(d_scat, x, design, INSERT_VALUES, SCATTER_FORWARD));
622: PetscCall(VecScatterEnd(d_scat, x, design, INSERT_VALUES, SCATTER_FORWARD));
623: PetscFunctionReturn(PETSC_SUCCESS);
624: }
626: PetscErrorCode Scatter_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
627: {
628: PetscInt i;
630: PetscFunctionBegin;
631: for (i = 0; i < nt; i++) {
632: PetscCall(VecScatterBegin(scat[i], y, yi[i], INSERT_VALUES, SCATTER_FORWARD));
633: PetscCall(VecScatterEnd(scat[i], y, yi[i], INSERT_VALUES, SCATTER_FORWARD));
634: }
635: PetscFunctionReturn(PETSC_SUCCESS);
636: }
638: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
639: {
640: PetscFunctionBegin;
641: PetscCall(VecScatterBegin(s_scat, state, x, INSERT_VALUES, SCATTER_REVERSE));
642: PetscCall(VecScatterEnd(s_scat, state, x, INSERT_VALUES, SCATTER_REVERSE));
643: PetscCall(VecScatterBegin(d_scat, design, x, INSERT_VALUES, SCATTER_REVERSE));
644: PetscCall(VecScatterEnd(d_scat, design, x, INSERT_VALUES, SCATTER_REVERSE));
645: PetscFunctionReturn(PETSC_SUCCESS);
646: }
648: PetscErrorCode Gather_i(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
649: {
650: PetscInt i;
652: PetscFunctionBegin;
653: for (i = 0; i < nt; i++) {
654: PetscCall(VecScatterBegin(scat[i], yi[i], y, INSERT_VALUES, SCATTER_REVERSE));
655: PetscCall(VecScatterEnd(scat[i], yi[i], y, INSERT_VALUES, SCATTER_REVERSE));
656: }
657: PetscFunctionReturn(PETSC_SUCCESS);
658: }
660: PetscErrorCode ParabolicInitialize(AppCtx *user)
661: {
662: PetscInt m, n, i, j, k, linear_index, istart, iend, iblock, lo, hi, lo2, hi2;
663: Vec XX, YY, ZZ, XXwork, YYwork, ZZwork, UTwork, yi, di, bc;
664: PetscReal *x, *y, *z;
665: PetscReal h, stime;
666: PetscScalar hinv, neg_hinv, half = 0.5, sqrt_beta;
667: PetscInt im, indx1, indx2, indy1, indy2, indz1, indz2, nx, ny, nz;
668: PetscReal xri, yri, zri, xim, yim, zim, dx1, dx2, dy1, dy2, dz1, dz2, Dx, Dy, Dz;
669: PetscScalar v, vx, vy, vz;
670: IS is_from_y, is_to_yi, is_from_d, is_to_di;
671: /* Data locations */
672: 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,
673: 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,
674: 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};
676: 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,
677: 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,
678: 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};
680: 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,
681: 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,
682: 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};
684: PetscFunctionBegin;
685: PetscCall(PetscMalloc1(user->mx, &x));
686: PetscCall(PetscMalloc1(user->mx, &y));
687: PetscCall(PetscMalloc1(user->mx, &z));
688: user->jformed = PETSC_FALSE;
689: user->dsg_formed = PETSC_FALSE;
691: n = user->mx * user->mx * user->mx;
692: m = 3 * user->mx * user->mx * (user->mx - 1);
693: sqrt_beta = PetscSqrtScalar(user->beta);
695: user->ksp_its = 0;
696: user->ksp_its_initial = 0;
698: stime = (PetscReal)user->nt / user->ns;
699: PetscCall(PetscMalloc1(user->ns, &user->sample_times));
700: for (i = 0; i < user->ns; i++) user->sample_times[i] = (PetscInt)(stime * ((PetscReal)i + 1.0) - 0.5);
702: PetscCall(VecCreate(PETSC_COMM_WORLD, &XX));
703: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->q));
704: PetscCall(VecSetSizes(XX, PETSC_DECIDE, n));
705: PetscCall(VecSetSizes(user->q, PETSC_DECIDE, n * user->nt));
706: PetscCall(VecSetFromOptions(XX));
707: PetscCall(VecSetFromOptions(user->q));
709: PetscCall(VecDuplicate(XX, &YY));
710: PetscCall(VecDuplicate(XX, &ZZ));
711: PetscCall(VecDuplicate(XX, &XXwork));
712: PetscCall(VecDuplicate(XX, &YYwork));
713: PetscCall(VecDuplicate(XX, &ZZwork));
714: PetscCall(VecDuplicate(XX, &UTwork));
715: PetscCall(VecDuplicate(XX, &user->utrue));
716: PetscCall(VecDuplicate(XX, &bc));
718: /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
719: h = 1.0 / user->mx;
720: hinv = user->mx;
721: neg_hinv = -hinv;
723: PetscCall(VecGetOwnershipRange(XX, &istart, &iend));
724: for (linear_index = istart; linear_index < iend; linear_index++) {
725: i = linear_index % user->mx;
726: j = ((linear_index - i) / user->mx) % user->mx;
727: k = ((linear_index - i) / user->mx - j) / user->mx;
728: vx = h * (i + 0.5);
729: vy = h * (j + 0.5);
730: vz = h * (k + 0.5);
731: PetscCall(VecSetValues(XX, 1, &linear_index, &vx, INSERT_VALUES));
732: PetscCall(VecSetValues(YY, 1, &linear_index, &vy, INSERT_VALUES));
733: PetscCall(VecSetValues(ZZ, 1, &linear_index, &vz, INSERT_VALUES));
734: if ((vx < 0.6) && (vx > 0.4) && (vy < 0.6) && (vy > 0.4) && (vy < 0.6) && (vz < 0.6) && (vz > 0.4)) {
735: v = 1000.0;
736: PetscCall(VecSetValues(bc, 1, &linear_index, &v, INSERT_VALUES));
737: }
738: }
740: PetscCall(VecAssemblyBegin(XX));
741: PetscCall(VecAssemblyEnd(XX));
742: PetscCall(VecAssemblyBegin(YY));
743: PetscCall(VecAssemblyEnd(YY));
744: PetscCall(VecAssemblyBegin(ZZ));
745: PetscCall(VecAssemblyEnd(ZZ));
746: PetscCall(VecAssemblyBegin(bc));
747: PetscCall(VecAssemblyEnd(bc));
749: /* Compute true parameter function
750: ut = 0.5 + exp(-10*((x-0.5)^2+(y-0.5)^2+(z-0.5)^2)) */
751: PetscCall(VecCopy(XX, XXwork));
752: PetscCall(VecCopy(YY, YYwork));
753: PetscCall(VecCopy(ZZ, ZZwork));
755: PetscCall(VecShift(XXwork, -0.5));
756: PetscCall(VecShift(YYwork, -0.5));
757: PetscCall(VecShift(ZZwork, -0.5));
759: PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
760: PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
761: PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));
763: PetscCall(VecCopy(XXwork, user->utrue));
764: PetscCall(VecAXPY(user->utrue, 1.0, YYwork));
765: PetscCall(VecAXPY(user->utrue, 1.0, ZZwork));
766: PetscCall(VecScale(user->utrue, -10.0));
767: PetscCall(VecExp(user->utrue));
768: PetscCall(VecShift(user->utrue, 0.5));
770: PetscCall(VecDestroy(&XX));
771: PetscCall(VecDestroy(&YY));
772: PetscCall(VecDestroy(&ZZ));
773: PetscCall(VecDestroy(&XXwork));
774: PetscCall(VecDestroy(&YYwork));
775: PetscCall(VecDestroy(&ZZwork));
776: PetscCall(VecDestroy(&UTwork));
778: /* Initial guess and reference model */
779: PetscCall(VecDuplicate(user->utrue, &user->ur));
780: PetscCall(VecSet(user->ur, 0.0));
782: /* Generate Grad matrix */
783: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Grad));
784: PetscCall(MatSetSizes(user->Grad, PETSC_DECIDE, PETSC_DECIDE, m, n));
785: PetscCall(MatSetFromOptions(user->Grad));
786: PetscCall(MatMPIAIJSetPreallocation(user->Grad, 2, NULL, 2, NULL));
787: PetscCall(MatSeqAIJSetPreallocation(user->Grad, 2, NULL));
788: PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));
790: for (i = istart; i < iend; i++) {
791: if (i < m / 3) {
792: iblock = i / (user->mx - 1);
793: j = iblock * user->mx + (i % (user->mx - 1));
794: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
795: j = j + 1;
796: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
797: }
798: if (i >= m / 3 && i < 2 * m / 3) {
799: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
800: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
801: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
802: j = j + user->mx;
803: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
804: }
805: if (i >= 2 * m / 3) {
806: j = i - 2 * m / 3;
807: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
808: j = j + user->mx * user->mx;
809: PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
810: }
811: }
813: PetscCall(MatAssemblyBegin(user->Grad, MAT_FINAL_ASSEMBLY));
814: PetscCall(MatAssemblyEnd(user->Grad, MAT_FINAL_ASSEMBLY));
816: /* Generate arithmetic averaging matrix Av */
817: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Av));
818: PetscCall(MatSetSizes(user->Av, PETSC_DECIDE, PETSC_DECIDE, m, n));
819: PetscCall(MatSetFromOptions(user->Av));
820: PetscCall(MatMPIAIJSetPreallocation(user->Av, 2, NULL, 2, NULL));
821: PetscCall(MatSeqAIJSetPreallocation(user->Av, 2, NULL));
822: PetscCall(MatGetOwnershipRange(user->Av, &istart, &iend));
824: for (i = istart; i < iend; i++) {
825: if (i < m / 3) {
826: iblock = i / (user->mx - 1);
827: j = iblock * user->mx + (i % (user->mx - 1));
828: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
829: j = j + 1;
830: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
831: }
832: if (i >= m / 3 && i < 2 * m / 3) {
833: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
834: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
835: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
836: j = j + user->mx;
837: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
838: }
839: if (i >= 2 * m / 3) {
840: j = i - 2 * m / 3;
841: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
842: j = j + user->mx * user->mx;
843: PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
844: }
845: }
847: PetscCall(MatAssemblyBegin(user->Av, MAT_FINAL_ASSEMBLY));
848: PetscCall(MatAssemblyEnd(user->Av, MAT_FINAL_ASSEMBLY));
850: /* Generate transpose of averaging matrix Av */
851: PetscCall(MatTranspose(user->Av, MAT_INITIAL_MATRIX, &user->AvT));
853: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->L));
854: PetscCall(MatSetSizes(user->L, PETSC_DECIDE, PETSC_DECIDE, m + n, n));
855: PetscCall(MatSetFromOptions(user->L));
856: PetscCall(MatMPIAIJSetPreallocation(user->L, 2, NULL, 2, NULL));
857: PetscCall(MatSeqAIJSetPreallocation(user->L, 2, NULL));
858: PetscCall(MatGetOwnershipRange(user->L, &istart, &iend));
860: for (i = istart; i < iend; i++) {
861: if (i < m / 3) {
862: iblock = i / (user->mx - 1);
863: j = iblock * user->mx + (i % (user->mx - 1));
864: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
865: j = j + 1;
866: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
867: }
868: if (i >= m / 3 && i < 2 * m / 3) {
869: iblock = (i - m / 3) / (user->mx * (user->mx - 1));
870: j = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
871: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
872: j = j + user->mx;
873: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
874: }
875: if (i >= 2 * m / 3 && i < m) {
876: j = i - 2 * m / 3;
877: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
878: j = j + user->mx * user->mx;
879: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
880: }
881: if (i >= m) {
882: j = i - m;
883: PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &sqrt_beta, INSERT_VALUES));
884: }
885: }
887: PetscCall(MatAssemblyBegin(user->L, MAT_FINAL_ASSEMBLY));
888: PetscCall(MatAssemblyEnd(user->L, MAT_FINAL_ASSEMBLY));
890: PetscCall(MatScale(user->L, PetscPowScalar(h, 1.5)));
892: /* Generate Div matrix */
893: PetscCall(MatTranspose(user->Grad, MAT_INITIAL_MATRIX, &user->Div));
895: /* Build work vectors and matrices */
896: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->S));
897: PetscCall(VecSetSizes(user->S, PETSC_DECIDE, user->mx * user->mx * (user->mx - 1) * 3));
898: PetscCall(VecSetFromOptions(user->S));
900: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->lwork));
901: PetscCall(VecSetSizes(user->lwork, PETSC_DECIDE, m + user->mx * user->mx * user->mx));
902: PetscCall(VecSetFromOptions(user->lwork));
904: PetscCall(MatDuplicate(user->Div, MAT_SHARE_NONZERO_PATTERN, &user->Divwork));
905: PetscCall(MatDuplicate(user->Av, MAT_SHARE_NONZERO_PATTERN, &user->Avwork));
907: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->d));
908: PetscCall(VecSetSizes(user->d, PETSC_DECIDE, user->ndata * user->nt));
909: PetscCall(VecSetFromOptions(user->d));
911: PetscCall(VecDuplicate(user->S, &user->Swork));
912: PetscCall(VecDuplicate(user->S, &user->Av_u));
913: PetscCall(VecDuplicate(user->S, &user->Twork));
914: PetscCall(VecDuplicate(user->S, &user->Rwork));
915: PetscCall(VecDuplicate(user->y, &user->ywork));
916: PetscCall(VecDuplicate(user->u, &user->uwork));
917: PetscCall(VecDuplicate(user->u, &user->js_diag));
918: PetscCall(VecDuplicate(user->c, &user->cwork));
919: PetscCall(VecDuplicate(user->d, &user->dwork));
921: /* Create matrix-free shell user->Js for computing A*x */
922: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m * user->nt, user, &user->Js));
923: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT, (void (*)(void))StateMatMult));
924: PetscCall(MatShellSetOperation(user->Js, MATOP_DUPLICATE, (void (*)(void))StateMatDuplicate));
925: PetscCall(MatShellSetOperation(user->Js, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatMultTranspose));
926: PetscCall(MatShellSetOperation(user->Js, MATOP_GET_DIAGONAL, (void (*)(void))StateMatGetDiagonal));
928: /* Diagonal blocks of user->Js */
929: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, &user->JsBlock));
930: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT, (void (*)(void))StateMatBlockMult));
931: /* Blocks are symmetric */
932: PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatBlockMult));
934: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
935: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
936: This is an SSOR preconditioner for user->JsBlock. */
937: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m, user->m, user, &user->JsBlockPrec));
938: PetscCall(MatShellSetOperation(user->JsBlockPrec, MATOP_MULT, (void (*)(void))StateMatBlockPrecMult));
939: /* JsBlockPrec is symmetric */
940: PetscCall(MatShellSetOperation(user->JsBlockPrec, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatBlockPrecMult));
941: PetscCall(MatSetOption(user->JsBlockPrec, MAT_SYMMETRIC, PETSC_TRUE));
942: PetscCall(MatSetOption(user->JsBlockPrec, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
944: /* Create a matrix-free shell user->Jd for computing B*x */
945: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m, user, &user->Jd));
946: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT, (void (*)(void))DesignMatMult));
947: PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT_TRANSPOSE, (void (*)(void))DesignMatMultTranspose));
949: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
950: PetscCall(MatCreateShell(PETSC_COMM_WORLD, PETSC_DETERMINE, PETSC_DETERMINE, user->m * user->nt, user->m * user->nt, user, &user->JsInv));
951: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT, (void (*)(void))StateMatInvMult));
952: PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatInvTransposeMult));
954: /* Solver options and tolerances */
955: PetscCall(KSPCreate(PETSC_COMM_WORLD, &user->solver));
956: PetscCall(KSPSetType(user->solver, KSPCG));
957: PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->JsBlockPrec));
958: PetscCall(KSPSetInitialGuessNonzero(user->solver, PETSC_FALSE));
959: PetscCall(KSPSetTolerances(user->solver, 1e-4, 1e-20, 1e3, 500));
960: PetscCall(KSPSetFromOptions(user->solver));
961: PetscCall(KSPGetPC(user->solver, &user->prec));
962: PetscCall(PCSetType(user->prec, PCSHELL));
964: PetscCall(PCShellSetApply(user->prec, StateMatBlockPrecMult));
965: PetscCall(PCShellSetApplyTranspose(user->prec, StateMatBlockPrecMult));
966: PetscCall(PCShellSetContext(user->prec, user));
968: /* Create scatter from y to y_1,y_2,...,y_nt */
969: PetscCall(PetscMalloc1(user->nt * user->m, &user->yi_scatter));
970: PetscCall(VecCreate(PETSC_COMM_WORLD, &yi));
971: PetscCall(VecSetSizes(yi, PETSC_DECIDE, user->mx * user->mx * user->mx));
972: PetscCall(VecSetFromOptions(yi));
973: PetscCall(VecDuplicateVecs(yi, user->nt, &user->yi));
974: PetscCall(VecDuplicateVecs(yi, user->nt, &user->yiwork));
976: PetscCall(VecGetOwnershipRange(user->y, &lo2, &hi2));
977: istart = 0;
978: for (i = 0; i < user->nt; i++) {
979: PetscCall(VecGetOwnershipRange(user->yi[i], &lo, &hi));
980: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_to_yi));
981: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_y));
982: PetscCall(VecScatterCreate(user->y, is_from_y, user->yi[i], is_to_yi, &user->yi_scatter[i]));
983: istart = istart + hi - lo;
984: PetscCall(ISDestroy(&is_to_yi));
985: PetscCall(ISDestroy(&is_from_y));
986: }
987: PetscCall(VecDestroy(&yi));
989: /* Create scatter from d to d_1,d_2,...,d_ns */
990: PetscCall(PetscMalloc1(user->ns * user->ndata, &user->di_scatter));
991: PetscCall(VecCreate(PETSC_COMM_WORLD, &di));
992: PetscCall(VecSetSizes(di, PETSC_DECIDE, user->ndata));
993: PetscCall(VecSetFromOptions(di));
994: PetscCall(VecDuplicateVecs(di, user->ns, &user->di));
995: PetscCall(VecGetOwnershipRange(user->d, &lo2, &hi2));
996: istart = 0;
997: for (i = 0; i < user->ns; i++) {
998: PetscCall(VecGetOwnershipRange(user->di[i], &lo, &hi));
999: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_to_di));
1000: PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_d));
1001: PetscCall(VecScatterCreate(user->d, is_from_d, user->di[i], is_to_di, &user->di_scatter[i]));
1002: istart = istart + hi - lo;
1003: PetscCall(ISDestroy(&is_to_di));
1004: PetscCall(ISDestroy(&is_from_d));
1005: }
1006: PetscCall(VecDestroy(&di));
1008: /* Assemble RHS of forward problem */
1009: PetscCall(VecCopy(bc, user->yiwork[0]));
1010: for (i = 1; i < user->nt; i++) PetscCall(VecSet(user->yiwork[i], 0.0));
1011: PetscCall(Gather_i(user->q, user->yiwork, user->yi_scatter, user->nt));
1012: PetscCall(VecDestroy(&bc));
1014: /* Compute true state function yt given ut */
1015: PetscCall(VecCreate(PETSC_COMM_WORLD, &user->ytrue));
1016: PetscCall(VecSetSizes(user->ytrue, PETSC_DECIDE, n * user->nt));
1017: PetscCall(VecSetFromOptions(user->ytrue));
1019: /* First compute Av_u = Av*exp(-u) */
1020: PetscCall(VecSet(user->uwork, 0));
1021: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue)); /* Note: user->utrue */
1022: PetscCall(VecExp(user->uwork));
1023: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
1025: /* Symbolic DSG = Div * Grad */
1026: PetscCall(MatProductCreate(user->Div, user->Grad, NULL, &user->DSG));
1027: PetscCall(MatProductSetType(user->DSG, MATPRODUCT_AB));
1028: PetscCall(MatProductSetAlgorithm(user->DSG, "default"));
1029: PetscCall(MatProductSetFill(user->DSG, PETSC_DEFAULT));
1030: PetscCall(MatProductSetFromOptions(user->DSG));
1031: PetscCall(MatProductSymbolic(user->DSG));
1033: user->dsg_formed = PETSC_TRUE;
1035: /* Next form DSG = Div*Grad */
1036: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1037: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1038: if (user->dsg_formed) {
1039: PetscCall(MatProductNumeric(user->DSG));
1040: } else {
1041: PetscCall(MatMatMult(user->Div, user->Grad, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &user->DSG));
1042: user->dsg_formed = PETSC_TRUE;
1043: }
1044: /* B = speye(nx^3) + ht*DSG; */
1045: PetscCall(MatScale(user->DSG, user->ht));
1046: PetscCall(MatShift(user->DSG, 1.0));
1048: /* Now solve for ytrue */
1049: PetscCall(StateMatInvMult(user->Js, user->q, user->ytrue));
1051: /* Initial guess y0 for state given u0 */
1053: /* First compute Av_u = Av*exp(-u) */
1054: PetscCall(VecSet(user->uwork, 0));
1055: PetscCall(VecAXPY(user->uwork, -1.0, user->u)); /* Note: user->u */
1056: PetscCall(VecExp(user->uwork));
1057: PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
1059: /* Next form DSG = Div*S*Grad */
1060: PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1061: PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1062: if (user->dsg_formed) {
1063: PetscCall(MatProductNumeric(user->DSG));
1064: } else {
1065: PetscCall(MatMatMult(user->Div, user->Grad, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &user->DSG));
1067: user->dsg_formed = PETSC_TRUE;
1068: }
1069: /* B = speye(nx^3) + ht*DSG; */
1070: PetscCall(MatScale(user->DSG, user->ht));
1071: PetscCall(MatShift(user->DSG, 1.0));
1073: /* Now solve for y */
1074: PetscCall(StateMatInvMult(user->Js, user->q, user->y));
1076: /* Construct projection matrix Q, a block diagonal matrix consisting of nt copies of Qblock along the diagonal */
1077: PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Qblock));
1078: PetscCall(MatSetSizes(user->Qblock, PETSC_DECIDE, PETSC_DECIDE, user->ndata, n));
1079: PetscCall(MatSetFromOptions(user->Qblock));
1080: PetscCall(MatMPIAIJSetPreallocation(user->Qblock, 8, NULL, 8, NULL));
1081: PetscCall(MatSeqAIJSetPreallocation(user->Qblock, 8, NULL));
1083: for (i = 0; i < user->mx; i++) {
1084: x[i] = h * (i + 0.5);
1085: y[i] = h * (i + 0.5);
1086: z[i] = h * (i + 0.5);
1087: }
1089: PetscCall(MatGetOwnershipRange(user->Qblock, &istart, &iend));
1090: nx = user->mx;
1091: ny = user->mx;
1092: nz = user->mx;
1093: for (i = istart; i < iend; i++) {
1094: xri = xr[i];
1095: im = 0;
1096: xim = x[im];
1097: while (xri > xim && im < nx) {
1098: im = im + 1;
1099: xim = x[im];
1100: }
1101: indx1 = im - 1;
1102: indx2 = im;
1103: dx1 = xri - x[indx1];
1104: dx2 = x[indx2] - xri;
1106: yri = yr[i];
1107: im = 0;
1108: yim = y[im];
1109: while (yri > yim && im < ny) {
1110: im = im + 1;
1111: yim = y[im];
1112: }
1113: indy1 = im - 1;
1114: indy2 = im;
1115: dy1 = yri - y[indy1];
1116: dy2 = y[indy2] - yri;
1118: zri = zr[i];
1119: im = 0;
1120: zim = z[im];
1121: while (zri > zim && im < nz) {
1122: im = im + 1;
1123: zim = z[im];
1124: }
1125: indz1 = im - 1;
1126: indz2 = im;
1127: dz1 = zri - z[indz1];
1128: dz2 = z[indz2] - zri;
1130: Dx = x[indx2] - x[indx1];
1131: Dy = y[indy2] - y[indy1];
1132: Dz = z[indz2] - z[indz1];
1134: j = indx1 + indy1 * nx + indz1 * nx * ny;
1135: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1136: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1138: j = indx1 + indy1 * nx + indz2 * nx * ny;
1139: v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1140: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1142: j = indx1 + indy2 * nx + indz1 * nx * ny;
1143: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1144: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1146: j = indx1 + indy2 * nx + indz2 * nx * ny;
1147: v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1148: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1150: j = indx2 + indy1 * nx + indz1 * nx * ny;
1151: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1152: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1154: j = indx2 + indy1 * nx + indz2 * nx * ny;
1155: v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1156: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1158: j = indx2 + indy2 * nx + indz1 * nx * ny;
1159: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1160: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1162: j = indx2 + indy2 * nx + indz2 * nx * ny;
1163: v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1164: PetscCall(MatSetValues(user->Qblock, 1, &i, 1, &j, &v, INSERT_VALUES));
1165: }
1166: PetscCall(MatAssemblyBegin(user->Qblock, MAT_FINAL_ASSEMBLY));
1167: PetscCall(MatAssemblyEnd(user->Qblock, MAT_FINAL_ASSEMBLY));
1169: PetscCall(MatTranspose(user->Qblock, MAT_INITIAL_MATRIX, &user->QblockT));
1170: PetscCall(MatTranspose(user->L, MAT_INITIAL_MATRIX, &user->LT));
1172: /* Add noise to the measurement data */
1173: PetscCall(VecSet(user->ywork, 1.0));
1174: PetscCall(VecAYPX(user->ywork, user->noise, user->ytrue));
1175: PetscCall(Scatter_i(user->ywork, user->yiwork, user->yi_scatter, user->nt));
1176: for (j = 0; j < user->ns; j++) {
1177: i = user->sample_times[j];
1178: PetscCall(MatMult(user->Qblock, user->yiwork[i], user->di[j]));
1179: }
1180: PetscCall(Gather_i(user->d, user->di, user->di_scatter, user->ns));
1182: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1183: PetscCall(KSPSetFromOptions(user->solver));
1184: PetscCall(PetscFree(x));
1185: PetscCall(PetscFree(y));
1186: PetscCall(PetscFree(z));
1187: PetscFunctionReturn(PETSC_SUCCESS);
1188: }
1190: PetscErrorCode ParabolicDestroy(AppCtx *user)
1191: {
1192: PetscInt i;
1194: PetscFunctionBegin;
1195: PetscCall(MatDestroy(&user->Qblock));
1196: PetscCall(MatDestroy(&user->QblockT));
1197: PetscCall(MatDestroy(&user->Div));
1198: PetscCall(MatDestroy(&user->Divwork));
1199: PetscCall(MatDestroy(&user->Grad));
1200: PetscCall(MatDestroy(&user->Av));
1201: PetscCall(MatDestroy(&user->Avwork));
1202: PetscCall(MatDestroy(&user->AvT));
1203: PetscCall(MatDestroy(&user->DSG));
1204: PetscCall(MatDestroy(&user->L));
1205: PetscCall(MatDestroy(&user->LT));
1206: PetscCall(KSPDestroy(&user->solver));
1207: PetscCall(MatDestroy(&user->Js));
1208: PetscCall(MatDestroy(&user->Jd));
1209: PetscCall(MatDestroy(&user->JsInv));
1210: PetscCall(MatDestroy(&user->JsBlock));
1211: PetscCall(MatDestroy(&user->JsBlockPrec));
1212: PetscCall(VecDestroy(&user->u));
1213: PetscCall(VecDestroy(&user->uwork));
1214: PetscCall(VecDestroy(&user->utrue));
1215: PetscCall(VecDestroy(&user->y));
1216: PetscCall(VecDestroy(&user->ywork));
1217: PetscCall(VecDestroy(&user->ytrue));
1218: PetscCall(VecDestroyVecs(user->nt, &user->yi));
1219: PetscCall(VecDestroyVecs(user->nt, &user->yiwork));
1220: PetscCall(VecDestroyVecs(user->ns, &user->di));
1221: PetscCall(PetscFree(user->yi));
1222: PetscCall(PetscFree(user->yiwork));
1223: PetscCall(PetscFree(user->di));
1224: PetscCall(VecDestroy(&user->c));
1225: PetscCall(VecDestroy(&user->cwork));
1226: PetscCall(VecDestroy(&user->ur));
1227: PetscCall(VecDestroy(&user->q));
1228: PetscCall(VecDestroy(&user->d));
1229: PetscCall(VecDestroy(&user->dwork));
1230: PetscCall(VecDestroy(&user->lwork));
1231: PetscCall(VecDestroy(&user->S));
1232: PetscCall(VecDestroy(&user->Swork));
1233: PetscCall(VecDestroy(&user->Av_u));
1234: PetscCall(VecDestroy(&user->Twork));
1235: PetscCall(VecDestroy(&user->Rwork));
1236: PetscCall(VecDestroy(&user->js_diag));
1237: PetscCall(ISDestroy(&user->s_is));
1238: PetscCall(ISDestroy(&user->d_is));
1239: PetscCall(VecScatterDestroy(&user->state_scatter));
1240: PetscCall(VecScatterDestroy(&user->design_scatter));
1241: for (i = 0; i < user->nt; i++) PetscCall(VecScatterDestroy(&user->yi_scatter[i]));
1242: for (i = 0; i < user->ns; i++) PetscCall(VecScatterDestroy(&user->di_scatter[i]));
1243: PetscCall(PetscFree(user->yi_scatter));
1244: PetscCall(PetscFree(user->di_scatter));
1245: PetscCall(PetscFree(user->sample_times));
1246: PetscFunctionReturn(PETSC_SUCCESS);
1247: }
1249: PetscErrorCode ParabolicMonitor(Tao tao, void *ptr)
1250: {
1251: Vec X;
1252: PetscReal unorm, ynorm;
1253: AppCtx *user = (AppCtx *)ptr;
1255: PetscFunctionBegin;
1256: PetscCall(TaoGetSolution(tao, &X));
1257: PetscCall(Scatter(X, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
1258: PetscCall(VecAXPY(user->ywork, -1.0, user->ytrue));
1259: PetscCall(VecAXPY(user->uwork, -1.0, user->utrue));
1260: PetscCall(VecNorm(user->uwork, NORM_2, &unorm));
1261: PetscCall(VecNorm(user->ywork, NORM_2, &ynorm));
1262: PetscCall(PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n", (double)unorm, (double)ynorm));
1263: PetscFunctionReturn(PETSC_SUCCESS);
1264: }
1266: /*TEST
1268: build:
1269: requires: !complex
1271: test:
1272: args: -tao_cmonitor -tao_type lcl -ns 1 -tao_gatol 1.e-4 -ksp_max_it 30
1273: requires: !single
1275: TEST*/