Actual source code: elliptic.c

  1: #include <petsc/private/taoimpl.h>

  3: typedef struct {
  4:   PetscInt n; /* Number of total variables */
  5:   PetscInt m; /* Number of constraints */
  6:   PetscInt nstate;
  7:   PetscInt ndesign;
  8:   PetscInt mx;    /* grid points in each direction */
  9:   PetscInt ns;    /* Number of data samples (1<=ns<=8)
 10:                   Currently only ns=1 is supported */
 11:   PetscInt ndata; /* Number of data points per sample */
 12:   IS       s_is;
 13:   IS       d_is;

 15:   VecScatter  state_scatter;
 16:   VecScatter  design_scatter;
 17:   VecScatter *yi_scatter, *di_scatter;
 18:   Vec         suby, subq, subd;
 19:   Mat         Js, Jd, JsPrec, JsInv, JsBlock;

 21:   PetscReal  alpha; /* Regularization parameter */
 22:   PetscReal  beta;  /* Weight attributed to ||u||^2 in regularization functional */
 23:   PetscReal  noise; /* Amount of noise to add to data */
 24:   PetscReal *ones;
 25:   Mat        Q;
 26:   Mat        MQ;
 27:   Mat        L;

 29:   Mat Grad;
 30:   Mat Av, Avwork;
 31:   Mat Div, Divwork;
 32:   Mat DSG;
 33:   Mat Diag, Ones;

 35:   Vec q;
 36:   Vec ur; /* reference */

 38:   Vec d;
 39:   Vec dwork;

 41:   Vec x; /* super vec of y,u */

 43:   Vec y; /* state variables */
 44:   Vec ywork;

 46:   Vec ytrue;

 48:   Vec u; /* design variables */
 49:   Vec uwork;

 51:   Vec utrue;

 53:   Vec js_diag;

 55:   Vec c; /* constraint vector */
 56:   Vec cwork;

 58:   Vec lwork;
 59:   Vec S;
 60:   Vec Swork, Twork, Sdiag, Ywork;
 61:   Vec Av_u;

 63:   KSP solver;
 64:   PC  prec;

 66:   PetscReal     tola, tolb, tolc, told;
 67:   PetscInt      ksp_its;
 68:   PetscInt      ksp_its_initial;
 69:   PetscLogStage stages[10];
 70:   PetscBool     use_ptap;
 71:   PetscBool     use_lrc;
 72: } AppCtx;

 74: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
 75: PetscErrorCode FormGradient(Tao, Vec, Vec, void *);
 76: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
 77: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void *);
 78: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void *);
 79: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
 80: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void *);
 81: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
 82: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
 83: PetscErrorCode EllipticInitialize(AppCtx *);
 84: PetscErrorCode EllipticDestroy(AppCtx *);
 85: PetscErrorCode EllipticMonitor(Tao, void *);

 87: PetscErrorCode StateBlockMatMult(Mat, Vec, Vec);
 88: PetscErrorCode StateMatMult(Mat, Vec, Vec);

 90: PetscErrorCode StateInvMatMult(Mat, Vec, Vec);
 91: PetscErrorCode DesignMatMult(Mat, Vec, Vec);
 92: PetscErrorCode DesignMatMultTranspose(Mat, Vec, Vec);

 94: PetscErrorCode QMatMult(Mat, Vec, Vec);
 95: PetscErrorCode QMatMultTranspose(Mat, Vec, Vec);

 97: static char help[] = "";

 99: int main(int argc, char **argv)
100: {
101:   Vec      x0;
102:   Tao      tao;
103:   AppCtx   user;
104:   PetscInt ntests = 1;
105:   PetscInt i;

107:   PetscFunctionBeginUser;
108:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
109:   user.mx = 8;
110:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "elliptic example", NULL);
111:   PetscCall(PetscOptionsInt("-mx", "Number of grid points in each direction", "", user.mx, &user.mx, NULL));
112:   user.ns = 6;
113:   PetscCall(PetscOptionsInt("-ns", "Number of data samples (1<=ns<=8)", "", user.ns, &user.ns, NULL));
114:   user.ndata = 64;
115:   PetscCall(PetscOptionsInt("-ndata", "Numbers of data points per sample", "", user.ndata, &user.ndata, NULL));
116:   user.alpha = 0.1;
117:   PetscCall(PetscOptionsReal("-alpha", "Regularization parameter", "", user.alpha, &user.alpha, NULL));
118:   user.beta = 0.00001;
119:   PetscCall(PetscOptionsReal("-beta", "Weight attributed to ||u||^2 in regularization functional", "", user.beta, &user.beta, NULL));
120:   user.noise = 0.01;
121:   PetscCall(PetscOptionsReal("-noise", "Amount of noise to add to data", "", user.noise, &user.noise, NULL));

123:   user.use_ptap = PETSC_FALSE;
124:   PetscCall(PetscOptionsBool("-use_ptap", "Use ptap matrix for DSG", "", user.use_ptap, &user.use_ptap, NULL));
125:   user.use_lrc = PETSC_FALSE;
126:   PetscCall(PetscOptionsBool("-use_lrc", "Use lrc matrix for Js", "", user.use_lrc, &user.use_lrc, NULL));
127:   PetscCall(PetscOptionsInt("-ntests", "Number of times to repeat TaoSolve", "", ntests, &ntests, NULL));
128:   PetscOptionsEnd();

130:   user.m       = user.ns * user.mx * user.mx * user.mx; /* number of constraints */
131:   user.nstate  = user.m;
132:   user.ndesign = user.mx * user.mx * user.mx;
133:   user.n       = user.nstate + user.ndesign; /* number of variables */

135:   /* Create TAO solver and set desired solution method */
136:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
137:   PetscCall(TaoSetType(tao, TAOLCL));

139:   /* Set up initial vectors and matrices */
140:   PetscCall(EllipticInitialize(&user));

142:   PetscCall(Gather(user.x, user.y, user.state_scatter, user.u, user.design_scatter));
143:   PetscCall(VecDuplicate(user.x, &x0));
144:   PetscCall(VecCopy(user.x, x0));

146:   /* Set solution vector with an initial guess */
147:   PetscCall(TaoSetSolution(tao, user.x));
148:   PetscCall(TaoSetObjective(tao, FormFunction, &user));
149:   PetscCall(TaoSetGradient(tao, NULL, FormGradient, &user));
150:   PetscCall(TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user));

152:   PetscCall(TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, &user));
153:   PetscCall(TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user));

155:   PetscCall(TaoSetStateDesignIS(tao, user.s_is, user.d_is));
156:   PetscCall(TaoSetFromOptions(tao));

158:   /* SOLVE THE APPLICATION */
159:   PetscCall(PetscLogStageRegister("Trials", &user.stages[1]));
160:   PetscCall(PetscLogStagePush(user.stages[1]));
161:   for (i = 0; i < ntests; i++) {
162:     PetscCall(TaoSolve(tao));
163:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP Iterations = %" PetscInt_FMT "\n", user.ksp_its));
164:     PetscCall(VecCopy(x0, user.x));
165:   }
166:   PetscCall(PetscLogStagePop());
167:   PetscCall(PetscBarrier((PetscObject)user.x));
168:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations within initialization: "));
169:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its_initial));

171:   PetscCall(TaoDestroy(&tao));
172:   PetscCall(VecDestroy(&x0));
173:   PetscCall(EllipticDestroy(&user));
174:   PetscCall(PetscFinalize());
175:   return 0;
176: }
177: /* ------------------------------------------------------------------- */
178: /*
179:    dwork = Qy - d
180:    lwork = L*(u-ur)
181:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
182: */
183: PetscErrorCode FormFunction(Tao tao, Vec X, PetscReal *f, void *ptr)
184: {
185:   PetscReal d1 = 0, d2 = 0;
186:   AppCtx   *user = (AppCtx *)ptr;

188:   PetscFunctionBegin;
189:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
190:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
191:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
192:   PetscCall(VecDot(user->dwork, user->dwork, &d1));
193:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
194:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
195:   PetscCall(VecDot(user->lwork, user->lwork, &d2));
196:   *f = 0.5 * (d1 + user->alpha * d2);
197:   PetscFunctionReturn(PETSC_SUCCESS);
198: }

200: /* ------------------------------------------------------------------- */
201: /*
202:     state: g_s = Q' *(Qy - d)
203:     design: g_d = alpha*L'*L*(u-ur)
204: */
205: PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
206: {
207:   AppCtx *user = (AppCtx *)ptr;

209:   PetscFunctionBegin;
210:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
211:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
212:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
213:   PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));
214:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
215:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
216:   PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
217:   PetscCall(VecScale(user->uwork, user->alpha));
218:   PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
219:   PetscFunctionReturn(PETSC_SUCCESS);
220: }

222: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
223: {
224:   PetscReal d1, d2;
225:   AppCtx   *user = (AppCtx *)ptr;

227:   PetscFunctionBegin;
228:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
229:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
230:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
231:   PetscCall(VecDot(user->dwork, user->dwork, &d1));
232:   PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));

234:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
235:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
236:   PetscCall(VecDot(user->lwork, user->lwork, &d2));
237:   PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
238:   PetscCall(VecScale(user->uwork, user->alpha));
239:   *f = 0.5 * (d1 + user->alpha * d2);
240:   PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
241:   PetscFunctionReturn(PETSC_SUCCESS);
242: }

244: /* ------------------------------------------------------------------- */
245: /* A
246: MatShell object
247: */
248: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
249: {
250:   AppCtx *user = (AppCtx *)ptr;

252:   PetscFunctionBegin;
253:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
254:   /* DSG = Div * (1/Av_u) * Grad */
255:   PetscCall(VecSet(user->uwork, 0));
256:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
257:   PetscCall(VecExp(user->uwork));
258:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
259:   PetscCall(VecCopy(user->Av_u, user->Swork));
260:   PetscCall(VecReciprocal(user->Swork));
261:   if (user->use_ptap) {
262:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
263:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
264:   } else {
265:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
266:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
267:     PetscCall(MatProductNumeric(user->DSG));
268:   }
269:   PetscFunctionReturn(PETSC_SUCCESS);
270: }
271: /* ------------------------------------------------------------------- */
272: /* B */
273: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
274: {
275:   AppCtx *user = (AppCtx *)ptr;

277:   PetscFunctionBegin;
278:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
279:   PetscFunctionReturn(PETSC_SUCCESS);
280: }

282: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
283: {
284:   PetscReal sum;
285:   AppCtx   *user;

287:   PetscFunctionBegin;
288:   PetscCall(MatShellGetContext(J_shell, &user));
289:   PetscCall(MatMult(user->DSG, X, Y));
290:   PetscCall(VecSum(X, &sum));
291:   sum /= user->ndesign;
292:   PetscCall(VecShift(Y, sum));
293:   PetscFunctionReturn(PETSC_SUCCESS);
294: }

296: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
297: {
298:   PetscInt i;
299:   AppCtx  *user;

301:   PetscFunctionBegin;
302:   PetscCall(MatShellGetContext(J_shell, &user));
303:   if (user->ns == 1) {
304:     PetscCall(MatMult(user->JsBlock, X, Y));
305:   } else {
306:     for (i = 0; i < user->ns; i++) {
307:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
308:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
309:       PetscCall(MatMult(user->JsBlock, user->subq, user->suby));
310:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
311:     }
312:   }
313:   PetscFunctionReturn(PETSC_SUCCESS);
314: }

316: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
317: {
318:   PetscInt its, i;
319:   AppCtx  *user;

321:   PetscFunctionBegin;
322:   PetscCall(MatShellGetContext(J_shell, &user));
323:   PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));
324:   if (Y == user->ytrue) {
325:     /* First solve is done using true solution to set up problem */
326:     PetscCall(KSPSetTolerances(user->solver, 1e-8, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
327:   } else {
328:     PetscCall(KSPSetTolerances(user->solver, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
329:   }
330:   if (user->ns == 1) {
331:     PetscCall(KSPSolve(user->solver, X, Y));
332:     PetscCall(KSPGetIterationNumber(user->solver, &its));
333:     user->ksp_its += its;
334:   } else {
335:     for (i = 0; i < user->ns; i++) {
336:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
337:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
338:       PetscCall(KSPSolve(user->solver, user->subq, user->suby));
339:       PetscCall(KSPGetIterationNumber(user->solver, &its));
340:       user->ksp_its += its;
341:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
342:     }
343:   }
344:   PetscFunctionReturn(PETSC_SUCCESS);
345: }
346: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
347: {
348:   AppCtx  *user;
349:   PetscInt i;

351:   PetscFunctionBegin;
352:   PetscCall(MatShellGetContext(J_shell, &user));
353:   if (user->ns == 1) {
354:     PetscCall(MatMult(user->Q, X, Y));
355:   } else {
356:     for (i = 0; i < user->ns; i++) {
357:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
358:       PetscCall(Scatter(Y, user->subd, user->di_scatter[i], 0, 0));
359:       PetscCall(MatMult(user->Q, user->subq, user->subd));
360:       PetscCall(Gather(Y, user->subd, user->di_scatter[i], 0, 0));
361:     }
362:   }
363:   PetscFunctionReturn(PETSC_SUCCESS);
364: }

366: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
367: {
368:   AppCtx  *user;
369:   PetscInt i;

371:   PetscFunctionBegin;
372:   PetscCall(MatShellGetContext(J_shell, &user));
373:   if (user->ns == 1) {
374:     PetscCall(MatMultTranspose(user->Q, X, Y));
375:   } else {
376:     for (i = 0; i < user->ns; i++) {
377:       PetscCall(Scatter(X, user->subd, user->di_scatter[i], 0, 0));
378:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
379:       PetscCall(MatMultTranspose(user->Q, user->subd, user->suby));
380:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
381:     }
382:   }
383:   PetscFunctionReturn(PETSC_SUCCESS);
384: }

386: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
387: {
388:   PetscInt i;
389:   AppCtx  *user;

391:   PetscFunctionBegin;
392:   PetscCall(MatShellGetContext(J_shell, &user));

394:   /* sdiag(1./v) */
395:   PetscCall(VecSet(user->uwork, 0));
396:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
397:   PetscCall(VecExp(user->uwork));

399:   /* sdiag(1./((Av*(1./v)).^2)) */
400:   PetscCall(MatMult(user->Av, user->uwork, user->Swork));
401:   PetscCall(VecPointwiseMult(user->Swork, user->Swork, user->Swork));
402:   PetscCall(VecReciprocal(user->Swork));

404:   /* (Av * (sdiag(1./v) * b)) */
405:   PetscCall(VecPointwiseMult(user->uwork, user->uwork, X));
406:   PetscCall(MatMult(user->Av, user->uwork, user->Twork));

408:   /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
409:   PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));

411:   if (user->ns == 1) {
412:     /* (sdiag(Grad*y(:,i)) */
413:     PetscCall(MatMult(user->Grad, user->y, user->Twork));

415:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
416:     PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
417:     PetscCall(MatMultTranspose(user->Grad, user->Swork, Y));
418:   } else {
419:     for (i = 0; i < user->ns; i++) {
420:       PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
421:       PetscCall(Scatter(Y, user->subq, user->yi_scatter[i], 0, 0));

423:       PetscCall(MatMult(user->Grad, user->suby, user->Twork));
424:       PetscCall(VecPointwiseMult(user->Twork, user->Twork, user->Swork));
425:       PetscCall(MatMultTranspose(user->Grad, user->Twork, user->subq));
426:       PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
427:       PetscCall(Gather(Y, user->subq, user->yi_scatter[i], 0, 0));
428:     }
429:   }
430:   PetscFunctionReturn(PETSC_SUCCESS);
431: }

433: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
434: {
435:   PetscInt i;
436:   AppCtx  *user;

438:   PetscFunctionBegin;
439:   PetscCall(MatShellGetContext(J_shell, &user));
440:   PetscCall(VecZeroEntries(Y));

442:   /* Sdiag = 1./((Av*(1./v)).^2) */
443:   PetscCall(VecSet(user->uwork, 0));
444:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
445:   PetscCall(VecExp(user->uwork));
446:   PetscCall(MatMult(user->Av, user->uwork, user->Swork));
447:   PetscCall(VecPointwiseMult(user->Sdiag, user->Swork, user->Swork));
448:   PetscCall(VecReciprocal(user->Sdiag));

450:   for (i = 0; i < user->ns; i++) {
451:     PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
452:     PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));

454:     /* Swork = (Div' * b(:,i)) */
455:     PetscCall(MatMult(user->Grad, user->subq, user->Swork));

457:     /* Twork = Grad*y(:,i) */
458:     PetscCall(MatMult(user->Grad, user->suby, user->Twork));

460:     /* Twork = sdiag(Twork) * Swork */
461:     PetscCall(VecPointwiseMult(user->Twork, user->Swork, user->Twork));

463:     /* Swork = pointwisemult(Sdiag,Twork) */
464:     PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Sdiag));

466:     /* Ywork = Av' * Swork */
467:     PetscCall(MatMultTranspose(user->Av, user->Swork, user->Ywork));

469:     /* Ywork = pointwisemult(uwork,Ywork) */
470:     PetscCall(VecPointwiseMult(user->Ywork, user->uwork, user->Ywork));
471:     PetscCall(VecAXPY(Y, 1.0, user->Ywork));
472:     PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
473:   }
474:   PetscFunctionReturn(PETSC_SUCCESS);
475: }

477: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
478: {
479:   /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
480:   PetscReal sum;
481:   PetscInt  i;
482:   AppCtx   *user = (AppCtx *)ptr;

484:   PetscFunctionBegin;
485:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
486:   if (user->ns == 1) {
487:     PetscCall(MatMult(user->Grad, user->y, user->Swork));
488:     PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
489:     PetscCall(MatMultTranspose(user->Grad, user->Swork, C));
490:     PetscCall(VecSum(user->y, &sum));
491:     sum /= user->ndesign;
492:     PetscCall(VecShift(C, sum));
493:   } else {
494:     for (i = 0; i < user->ns; i++) {
495:       PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
496:       PetscCall(Scatter(C, user->subq, user->yi_scatter[i], 0, 0));
497:       PetscCall(MatMult(user->Grad, user->suby, user->Swork));
498:       PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
499:       PetscCall(MatMultTranspose(user->Grad, user->Swork, user->subq));

501:       PetscCall(VecSum(user->suby, &sum));
502:       sum /= user->ndesign;
503:       PetscCall(VecShift(user->subq, sum));

505:       PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
506:       PetscCall(Gather(C, user->subq, user->yi_scatter[i], 0, 0));
507:     }
508:   }
509:   PetscCall(VecAXPY(C, -1.0, user->q));
510:   PetscFunctionReturn(PETSC_SUCCESS);
511: }

513: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
514: {
515:   PetscFunctionBegin;
516:   PetscCall(VecScatterBegin(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
517:   PetscCall(VecScatterEnd(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
518:   if (sub2) {
519:     PetscCall(VecScatterBegin(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
520:     PetscCall(VecScatterEnd(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
521:   }
522:   PetscFunctionReturn(PETSC_SUCCESS);
523: }

525: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
526: {
527:   PetscFunctionBegin;
528:   PetscCall(VecScatterBegin(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
529:   PetscCall(VecScatterEnd(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
530:   if (sub2) {
531:     PetscCall(VecScatterBegin(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
532:     PetscCall(VecScatterEnd(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
533:   }
534:   PetscFunctionReturn(PETSC_SUCCESS);
535: }

537: PetscErrorCode EllipticInitialize(AppCtx *user)
538: {
539:   PetscInt        m, n, i, j, k, l, linear_index, is, js, ks, ls, istart, iend, iblock;
540:   Vec             XX, YY, ZZ, XXwork, YYwork, ZZwork, UTwork;
541:   PetscReal      *x, *y, *z;
542:   PetscReal       h, meanut;
543:   PetscScalar     hinv, neg_hinv, half = 0.5, sqrt_beta;
544:   PetscInt        im, indx1, indx2, indy1, indy2, indz1, indz2, nx, ny, nz;
545:   IS              is_alldesign, is_allstate;
546:   IS              is_from_d;
547:   IS              is_from_y;
548:   PetscInt        lo, hi, hi2, lo2, ysubnlocal, dsubnlocal;
549:   const PetscInt *ranges, *subranges;
550:   PetscMPIInt     size;
551:   PetscReal       xri, yri, zri, xim, yim, zim, dx1, dx2, dy1, dy2, dz1, dz2, Dx, Dy, Dz;
552:   PetscScalar     v, vx, vy, vz;
553:   PetscInt        offset, subindex, subvec, nrank, kk;

555:   PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160, 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774, 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997,
556:                         0.5198, 0.8326, 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728, 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273, 0.5724, 0.4331, 0.5136, 0.3547,
557:                         0.4413, 0.2602, 0.5698, 0.7278, 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594, 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};

559:   PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256, 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792, 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437,
560:                         0.5938, 0.6137, 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985, 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288, 0.5761, 0.1129, 0.3841, 0.6150,
561:                         0.6904, 0.6686, 0.1361, 0.4601, 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480, 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};

563:   PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295, 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819, 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236,
564:                         0.8800, 0.2939, 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712, 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078, 0.1987, 0.2297, 0.4321, 0.8115,
565:                         0.4915, 0.7764, 0.4657, 0.4627, 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313, 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};

567:   PetscFunctionBegin;
568:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
569:   PetscCall(PetscLogStageRegister("Elliptic Setup", &user->stages[0]));
570:   PetscCall(PetscLogStagePush(user->stages[0]));

572:   /* Create u,y,c,x */
573:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->u));
574:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->y));
575:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->c));
576:   PetscCall(VecSetSizes(user->u, PETSC_DECIDE, user->ndesign));
577:   PetscCall(VecSetFromOptions(user->u));
578:   PetscCall(VecGetLocalSize(user->u, &ysubnlocal));
579:   PetscCall(VecSetSizes(user->y, ysubnlocal * user->ns, user->nstate));
580:   PetscCall(VecSetSizes(user->c, ysubnlocal * user->ns, user->m));
581:   PetscCall(VecSetFromOptions(user->y));
582:   PetscCall(VecSetFromOptions(user->c));

584:   /*
585:      *******************************
586:      Create scatters for x <-> y,u
587:      *******************************

589:      If the state vector y and design vector u are partitioned as
590:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
591:      then the solution vector x is organized as
592:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
593:      The index sets user->s_is and user->d_is correspond to the indices of the
594:      state and design variables owned by the current processor.
595:   */
596:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->x));

598:   PetscCall(VecGetOwnershipRange(user->y, &lo, &hi));
599:   PetscCall(VecGetOwnershipRange(user->u, &lo2, &hi2));

601:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_allstate));
602:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo + lo2, 1, &user->s_is));
603:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, lo2, 1, &is_alldesign));
604:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, hi + lo2, 1, &user->d_is));

606:   PetscCall(VecSetSizes(user->x, hi - lo + hi2 - lo2, user->n));
607:   PetscCall(VecSetFromOptions(user->x));

609:   PetscCall(VecScatterCreate(user->x, user->s_is, user->y, is_allstate, &user->state_scatter));
610:   PetscCall(VecScatterCreate(user->x, user->d_is, user->u, is_alldesign, &user->design_scatter));
611:   PetscCall(ISDestroy(&is_alldesign));
612:   PetscCall(ISDestroy(&is_allstate));
613:   /*
614:      *******************************
615:      Create scatter from y to y_1,y_2,...,y_ns
616:      *******************************
617:   */
618:   PetscCall(PetscMalloc1(user->ns, &user->yi_scatter));
619:   PetscCall(VecDuplicate(user->u, &user->suby));
620:   PetscCall(VecDuplicate(user->u, &user->subq));

622:   PetscCall(VecGetOwnershipRange(user->y, &lo2, &hi2));
623:   istart = 0;
624:   for (i = 0; i < user->ns; i++) {
625:     PetscCall(VecGetOwnershipRange(user->suby, &lo, &hi));
626:     PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_y));
627:     PetscCall(VecScatterCreate(user->y, is_from_y, user->suby, NULL, &user->yi_scatter[i]));
628:     istart = istart + hi - lo;
629:     PetscCall(ISDestroy(&is_from_y));
630:   }
631:   /*
632:      *******************************
633:      Create scatter from d to d_1,d_2,...,d_ns
634:      *******************************
635:   */
636:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->subd));
637:   PetscCall(VecSetSizes(user->subd, PETSC_DECIDE, user->ndata));
638:   PetscCall(VecSetFromOptions(user->subd));
639:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->d));
640:   PetscCall(VecGetLocalSize(user->subd, &dsubnlocal));
641:   PetscCall(VecSetSizes(user->d, dsubnlocal * user->ns, user->ndata * user->ns));
642:   PetscCall(VecSetFromOptions(user->d));
643:   PetscCall(PetscMalloc1(user->ns, &user->di_scatter));

645:   PetscCall(VecGetOwnershipRange(user->d, &lo2, &hi2));
646:   istart = 0;
647:   for (i = 0; i < user->ns; i++) {
648:     PetscCall(VecGetOwnershipRange(user->subd, &lo, &hi));
649:     PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_d));
650:     PetscCall(VecScatterCreate(user->d, is_from_d, user->subd, NULL, &user->di_scatter[i]));
651:     istart = istart + hi - lo;
652:     PetscCall(ISDestroy(&is_from_d));
653:   }

655:   PetscCall(PetscMalloc1(user->mx, &x));
656:   PetscCall(PetscMalloc1(user->mx, &y));
657:   PetscCall(PetscMalloc1(user->mx, &z));

659:   user->ksp_its         = 0;
660:   user->ksp_its_initial = 0;

662:   n         = user->mx * user->mx * user->mx;
663:   m         = 3 * user->mx * user->mx * (user->mx - 1);
664:   sqrt_beta = PetscSqrtScalar(user->beta);

666:   PetscCall(VecCreate(PETSC_COMM_WORLD, &XX));
667:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->q));
668:   PetscCall(VecSetSizes(XX, ysubnlocal, n));
669:   PetscCall(VecSetSizes(user->q, ysubnlocal * user->ns, user->m));
670:   PetscCall(VecSetFromOptions(XX));
671:   PetscCall(VecSetFromOptions(user->q));

673:   PetscCall(VecDuplicate(XX, &YY));
674:   PetscCall(VecDuplicate(XX, &ZZ));
675:   PetscCall(VecDuplicate(XX, &XXwork));
676:   PetscCall(VecDuplicate(XX, &YYwork));
677:   PetscCall(VecDuplicate(XX, &ZZwork));
678:   PetscCall(VecDuplicate(XX, &UTwork));
679:   PetscCall(VecDuplicate(XX, &user->utrue));

681:   /* map for striding q */
682:   PetscCall(VecGetOwnershipRanges(user->q, &ranges));
683:   PetscCall(VecGetOwnershipRanges(user->u, &subranges));

685:   PetscCall(VecGetOwnershipRange(user->q, &lo2, &hi2));
686:   PetscCall(VecGetOwnershipRange(user->u, &lo, &hi));
687:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
688:   h        = 1.0 / user->mx;
689:   hinv     = user->mx;
690:   neg_hinv = -hinv;

692:   PetscCall(VecGetOwnershipRange(XX, &istart, &iend));
693:   for (linear_index = istart; linear_index < iend; linear_index++) {
694:     i  = linear_index % user->mx;
695:     j  = ((linear_index - i) / user->mx) % user->mx;
696:     k  = ((linear_index - i) / user->mx - j) / user->mx;
697:     vx = h * (i + 0.5);
698:     vy = h * (j + 0.5);
699:     vz = h * (k + 0.5);
700:     PetscCall(VecSetValues(XX, 1, &linear_index, &vx, INSERT_VALUES));
701:     PetscCall(VecSetValues(YY, 1, &linear_index, &vy, INSERT_VALUES));
702:     PetscCall(VecSetValues(ZZ, 1, &linear_index, &vz, INSERT_VALUES));
703:     for (is = 0; is < 2; is++) {
704:       for (js = 0; js < 2; js++) {
705:         for (ks = 0; ks < 2; ks++) {
706:           ls = is * 4 + js * 2 + ks;
707:           if (ls < user->ns) {
708:             l = ls * n + linear_index;
709:             /* remap */
710:             subindex = l % n;
711:             subvec   = l / n;
712:             nrank    = 0;
713:             while (subindex >= subranges[nrank + 1]) nrank++;
714:             offset = subindex - subranges[nrank];
715:             istart = 0;
716:             for (kk = 0; kk < nrank; kk++) istart += user->ns * (subranges[kk + 1] - subranges[kk]);
717:             istart += (subranges[nrank + 1] - subranges[nrank]) * subvec;
718:             l = istart + offset;
719:             v = 100 * PetscSinScalar(2 * PETSC_PI * (vx + 0.25 * is)) * PetscSinScalar(2 * PETSC_PI * (vy + 0.25 * js)) * PetscSinScalar(2 * PETSC_PI * (vz + 0.25 * ks));
720:             PetscCall(VecSetValues(user->q, 1, &l, &v, INSERT_VALUES));
721:           }
722:         }
723:       }
724:     }
725:   }

727:   PetscCall(VecAssemblyBegin(XX));
728:   PetscCall(VecAssemblyEnd(XX));
729:   PetscCall(VecAssemblyBegin(YY));
730:   PetscCall(VecAssemblyEnd(YY));
731:   PetscCall(VecAssemblyBegin(ZZ));
732:   PetscCall(VecAssemblyEnd(ZZ));
733:   PetscCall(VecAssemblyBegin(user->q));
734:   PetscCall(VecAssemblyEnd(user->q));

736:   /* Compute true parameter function
737:      ut = exp(-((x-0.25)^2+(y-0.25)^2+(z-0.25)^2)/0.05) - exp((x-0.75)^2-(y-0.75)^2-(z-0.75))^2/0.05) */
738:   PetscCall(VecCopy(XX, XXwork));
739:   PetscCall(VecCopy(YY, YYwork));
740:   PetscCall(VecCopy(ZZ, ZZwork));

742:   PetscCall(VecShift(XXwork, -0.25));
743:   PetscCall(VecShift(YYwork, -0.25));
744:   PetscCall(VecShift(ZZwork, -0.25));

746:   PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
747:   PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
748:   PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));

750:   PetscCall(VecCopy(XXwork, UTwork));
751:   PetscCall(VecAXPY(UTwork, 1.0, YYwork));
752:   PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
753:   PetscCall(VecScale(UTwork, -20.0));
754:   PetscCall(VecExp(UTwork));
755:   PetscCall(VecCopy(UTwork, user->utrue));

757:   PetscCall(VecCopy(XX, XXwork));
758:   PetscCall(VecCopy(YY, YYwork));
759:   PetscCall(VecCopy(ZZ, ZZwork));

761:   PetscCall(VecShift(XXwork, -0.75));
762:   PetscCall(VecShift(YYwork, -0.75));
763:   PetscCall(VecShift(ZZwork, -0.75));

765:   PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
766:   PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
767:   PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));

769:   PetscCall(VecCopy(XXwork, UTwork));
770:   PetscCall(VecAXPY(UTwork, 1.0, YYwork));
771:   PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
772:   PetscCall(VecScale(UTwork, -20.0));
773:   PetscCall(VecExp(UTwork));

775:   PetscCall(VecAXPY(user->utrue, -1.0, UTwork));

777:   PetscCall(VecDestroy(&XX));
778:   PetscCall(VecDestroy(&YY));
779:   PetscCall(VecDestroy(&ZZ));
780:   PetscCall(VecDestroy(&XXwork));
781:   PetscCall(VecDestroy(&YYwork));
782:   PetscCall(VecDestroy(&ZZwork));
783:   PetscCall(VecDestroy(&UTwork));

785:   /* Initial guess and reference model */
786:   PetscCall(VecDuplicate(user->utrue, &user->ur));
787:   PetscCall(VecSum(user->utrue, &meanut));
788:   meanut = meanut / n;
789:   PetscCall(VecSet(user->ur, meanut));
790:   PetscCall(VecCopy(user->ur, user->u));

792:   /* Generate Grad matrix */
793:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Grad));
794:   PetscCall(MatSetSizes(user->Grad, PETSC_DECIDE, ysubnlocal, m, n));
795:   PetscCall(MatSetFromOptions(user->Grad));
796:   PetscCall(MatMPIAIJSetPreallocation(user->Grad, 2, NULL, 2, NULL));
797:   PetscCall(MatSeqAIJSetPreallocation(user->Grad, 2, NULL));
798:   PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));

800:   for (i = istart; i < iend; i++) {
801:     if (i < m / 3) {
802:       iblock = i / (user->mx - 1);
803:       j      = iblock * user->mx + (i % (user->mx - 1));
804:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
805:       j = j + 1;
806:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
807:     }
808:     if (i >= m / 3 && i < 2 * m / 3) {
809:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
810:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
811:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
812:       j = j + user->mx;
813:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
814:     }
815:     if (i >= 2 * m / 3) {
816:       j = i - 2 * m / 3;
817:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
818:       j = j + user->mx * user->mx;
819:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
820:     }
821:   }

823:   PetscCall(MatAssemblyBegin(user->Grad, MAT_FINAL_ASSEMBLY));
824:   PetscCall(MatAssemblyEnd(user->Grad, MAT_FINAL_ASSEMBLY));

826:   /* Generate arithmetic averaging matrix Av */
827:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Av));
828:   PetscCall(MatSetSizes(user->Av, PETSC_DECIDE, ysubnlocal, m, n));
829:   PetscCall(MatSetFromOptions(user->Av));
830:   PetscCall(MatMPIAIJSetPreallocation(user->Av, 2, NULL, 2, NULL));
831:   PetscCall(MatSeqAIJSetPreallocation(user->Av, 2, NULL));
832:   PetscCall(MatGetOwnershipRange(user->Av, &istart, &iend));

834:   for (i = istart; i < iend; i++) {
835:     if (i < m / 3) {
836:       iblock = i / (user->mx - 1);
837:       j      = iblock * user->mx + (i % (user->mx - 1));
838:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
839:       j = j + 1;
840:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
841:     }
842:     if (i >= m / 3 && i < 2 * m / 3) {
843:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
844:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
845:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
846:       j = j + user->mx;
847:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
848:     }
849:     if (i >= 2 * m / 3) {
850:       j = i - 2 * m / 3;
851:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
852:       j = j + user->mx * user->mx;
853:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
854:     }
855:   }

857:   PetscCall(MatAssemblyBegin(user->Av, MAT_FINAL_ASSEMBLY));
858:   PetscCall(MatAssemblyEnd(user->Av, MAT_FINAL_ASSEMBLY));

860:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->L));
861:   PetscCall(MatSetSizes(user->L, PETSC_DECIDE, ysubnlocal, m + n, n));
862:   PetscCall(MatSetFromOptions(user->L));
863:   PetscCall(MatMPIAIJSetPreallocation(user->L, 2, NULL, 2, NULL));
864:   PetscCall(MatSeqAIJSetPreallocation(user->L, 2, NULL));
865:   PetscCall(MatGetOwnershipRange(user->L, &istart, &iend));

867:   for (i = istart; i < iend; i++) {
868:     if (i < m / 3) {
869:       iblock = i / (user->mx - 1);
870:       j      = iblock * user->mx + (i % (user->mx - 1));
871:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
872:       j = j + 1;
873:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
874:     }
875:     if (i >= m / 3 && i < 2 * m / 3) {
876:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
877:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
878:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
879:       j = j + user->mx;
880:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
881:     }
882:     if (i >= 2 * m / 3 && i < m) {
883:       j = i - 2 * m / 3;
884:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
885:       j = j + user->mx * user->mx;
886:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
887:     }
888:     if (i >= m) {
889:       j = i - m;
890:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &sqrt_beta, INSERT_VALUES));
891:     }
892:   }
893:   PetscCall(MatAssemblyBegin(user->L, MAT_FINAL_ASSEMBLY));
894:   PetscCall(MatAssemblyEnd(user->L, MAT_FINAL_ASSEMBLY));
895:   PetscCall(MatScale(user->L, PetscPowScalar(h, 1.5)));

897:   /* Generate Div matrix */
898:   if (!user->use_ptap) {
899:     /* Generate Div matrix */
900:     PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Div));
901:     PetscCall(MatSetSizes(user->Div, ysubnlocal, PETSC_DECIDE, n, m));
902:     PetscCall(MatSetFromOptions(user->Div));
903:     PetscCall(MatMPIAIJSetPreallocation(user->Div, 4, NULL, 4, NULL));
904:     PetscCall(MatSeqAIJSetPreallocation(user->Div, 6, NULL));
905:     PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));

907:     for (i = istart; i < iend; i++) {
908:       if (i < m / 3) {
909:         iblock = i / (user->mx - 1);
910:         j      = iblock * user->mx + (i % (user->mx - 1));
911:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
912:         j = j + 1;
913:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
914:       }
915:       if (i >= m / 3 && i < 2 * m / 3) {
916:         iblock = (i - m / 3) / (user->mx * (user->mx - 1));
917:         j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
918:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
919:         j = j + user->mx;
920:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
921:       }
922:       if (i >= 2 * m / 3) {
923:         j = i - 2 * m / 3;
924:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
925:         j = j + user->mx * user->mx;
926:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
927:       }
928:     }

930:     PetscCall(MatAssemblyBegin(user->Div, MAT_FINAL_ASSEMBLY));
931:     PetscCall(MatAssemblyEnd(user->Div, MAT_FINAL_ASSEMBLY));
932:     PetscCall(MatDuplicate(user->Div, MAT_SHARE_NONZERO_PATTERN, &user->Divwork));
933:   } else {
934:     PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Diag));
935:     PetscCall(MatSetSizes(user->Diag, PETSC_DECIDE, PETSC_DECIDE, m, m));
936:     PetscCall(MatSetFromOptions(user->Diag));
937:     PetscCall(MatMPIAIJSetPreallocation(user->Diag, 1, NULL, 0, NULL));
938:     PetscCall(MatSeqAIJSetPreallocation(user->Diag, 1, NULL));
939:   }

941:   /* Build work vectors and matrices */
942:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->S));
943:   PetscCall(VecSetSizes(user->S, PETSC_DECIDE, m));
944:   PetscCall(VecSetFromOptions(user->S));

946:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->lwork));
947:   PetscCall(VecSetSizes(user->lwork, PETSC_DECIDE, m + user->mx * user->mx * user->mx));
948:   PetscCall(VecSetFromOptions(user->lwork));

950:   PetscCall(MatDuplicate(user->Av, MAT_SHARE_NONZERO_PATTERN, &user->Avwork));

952:   PetscCall(VecDuplicate(user->S, &user->Swork));
953:   PetscCall(VecDuplicate(user->S, &user->Sdiag));
954:   PetscCall(VecDuplicate(user->S, &user->Av_u));
955:   PetscCall(VecDuplicate(user->S, &user->Twork));
956:   PetscCall(VecDuplicate(user->y, &user->ywork));
957:   PetscCall(VecDuplicate(user->u, &user->Ywork));
958:   PetscCall(VecDuplicate(user->u, &user->uwork));
959:   PetscCall(VecDuplicate(user->u, &user->js_diag));
960:   PetscCall(VecDuplicate(user->c, &user->cwork));
961:   PetscCall(VecDuplicate(user->d, &user->dwork));

963:   /* Create a matrix-free shell user->Jd for computing B*x */
964:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal, user->nstate, user->ndesign, user, &user->Jd));
965:   PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT, (void (*)(void))DesignMatMult));
966:   PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT_TRANSPOSE, (void (*)(void))DesignMatMultTranspose));

968:   /* Compute true state function ytrue given utrue */
969:   PetscCall(VecDuplicate(user->y, &user->ytrue));

971:   /* First compute Av_u = Av*exp(-u) */
972:   PetscCall(VecSet(user->uwork, 0));
973:   PetscCall(VecAXPY(user->uwork, -1.0, user->utrue)); /* Note: user->utrue */
974:   PetscCall(VecExp(user->uwork));
975:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));

977:   /* Next form DSG = Div*S*Grad */
978:   PetscCall(VecCopy(user->Av_u, user->Swork));
979:   PetscCall(VecReciprocal(user->Swork));
980:   if (user->use_ptap) {
981:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
982:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
983:   } else {
984:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
985:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));

987:     PetscCall(MatMatMult(user->Divwork, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
988:   }

990:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
991:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

993:   if (user->use_lrc == PETSC_TRUE) {
994:     v = PetscSqrtReal(1.0 / user->ndesign);
995:     PetscCall(PetscMalloc1(user->ndesign, &user->ones));

997:     for (i = 0; i < user->ndesign; i++) user->ones[i] = v;
998:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, ysubnlocal, PETSC_DECIDE, user->ndesign, 1, user->ones, &user->Ones));
999:     PetscCall(MatCreateLRC(user->DSG, user->Ones, NULL, user->Ones, &user->JsBlock));
1000:     PetscCall(MatSetUp(user->JsBlock));
1001:   } else {
1002:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
1003:     PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal, ysubnlocal, user->ndesign, user->ndesign, user, &user->JsBlock));
1004:     PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT, (void (*)(void))StateBlockMatMult));
1005:     PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT_TRANSPOSE, (void (*)(void))StateBlockMatMult));
1006:   }
1007:   PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRIC, PETSC_TRUE));
1008:   PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1009:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->Js));
1010:   PetscCall(MatShellSetOperation(user->Js, MATOP_MULT, (void (*)(void))StateMatMult));
1011:   PetscCall(MatShellSetOperation(user->Js, MATOP_MULT_TRANSPOSE, (void (*)(void))StateMatMult));
1012:   PetscCall(MatSetOption(user->Js, MAT_SYMMETRIC, PETSC_TRUE));
1013:   PetscCall(MatSetOption(user->Js, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

1015:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->JsInv));
1016:   PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT, (void (*)(void))StateInvMatMult));
1017:   PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT_TRANSPOSE, (void (*)(void))StateInvMatMult));
1018:   PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRIC, PETSC_TRUE));
1019:   PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

1021:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
1022:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
1023:   /* Now solve for ytrue */
1024:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &user->solver));
1025:   PetscCall(KSPSetFromOptions(user->solver));

1027:   PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));

1029:   PetscCall(MatMult(user->JsInv, user->q, user->ytrue));
1030:   /* First compute Av_u = Av*exp(-u) */
1031:   PetscCall(VecSet(user->uwork, 0));
1032:   PetscCall(VecAXPY(user->uwork, -1.0, user->u)); /* Note: user->u */
1033:   PetscCall(VecExp(user->uwork));
1034:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));

1036:   /* Next update DSG = Div*S*Grad  with user->u */
1037:   PetscCall(VecCopy(user->Av_u, user->Swork));
1038:   PetscCall(VecReciprocal(user->Swork));
1039:   if (user->use_ptap) {
1040:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
1041:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
1042:   } else {
1043:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
1044:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
1045:     PetscCall(MatProductNumeric(user->DSG));
1046:   }

1048:   /* Now solve for y */

1050:   PetscCall(MatMult(user->JsInv, user->q, user->y));

1052:   user->ksp_its_initial = user->ksp_its;
1053:   user->ksp_its         = 0;
1054:   /* Construct projection matrix Q (blocks) */
1055:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Q));
1056:   PetscCall(MatSetSizes(user->Q, dsubnlocal, ysubnlocal, user->ndata, user->ndesign));
1057:   PetscCall(MatSetFromOptions(user->Q));
1058:   PetscCall(MatMPIAIJSetPreallocation(user->Q, 8, NULL, 8, NULL));
1059:   PetscCall(MatSeqAIJSetPreallocation(user->Q, 8, NULL));

1061:   for (i = 0; i < user->mx; i++) {
1062:     x[i] = h * (i + 0.5);
1063:     y[i] = h * (i + 0.5);
1064:     z[i] = h * (i + 0.5);
1065:   }
1066:   PetscCall(MatGetOwnershipRange(user->Q, &istart, &iend));

1068:   nx = user->mx;
1069:   ny = user->mx;
1070:   nz = user->mx;
1071:   for (i = istart; i < iend; i++) {
1072:     xri = xr[i];
1073:     im  = 0;
1074:     xim = x[im];
1075:     while (xri > xim && im < nx) {
1076:       im  = im + 1;
1077:       xim = x[im];
1078:     }
1079:     indx1 = im - 1;
1080:     indx2 = im;
1081:     dx1   = xri - x[indx1];
1082:     dx2   = x[indx2] - xri;

1084:     yri = yr[i];
1085:     im  = 0;
1086:     yim = y[im];
1087:     while (yri > yim && im < ny) {
1088:       im  = im + 1;
1089:       yim = y[im];
1090:     }
1091:     indy1 = im - 1;
1092:     indy2 = im;
1093:     dy1   = yri - y[indy1];
1094:     dy2   = y[indy2] - yri;

1096:     zri = zr[i];
1097:     im  = 0;
1098:     zim = z[im];
1099:     while (zri > zim && im < nz) {
1100:       im  = im + 1;
1101:       zim = z[im];
1102:     }
1103:     indz1 = im - 1;
1104:     indz2 = im;
1105:     dz1   = zri - z[indz1];
1106:     dz2   = z[indz2] - zri;

1108:     Dx = x[indx2] - x[indx1];
1109:     Dy = y[indy2] - y[indy1];
1110:     Dz = z[indz2] - z[indz1];

1112:     j = indx1 + indy1 * nx + indz1 * nx * ny;
1113:     v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1114:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1116:     j = indx1 + indy1 * nx + indz2 * nx * ny;
1117:     v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1118:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1120:     j = indx1 + indy2 * nx + indz1 * nx * ny;
1121:     v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1122:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1124:     j = indx1 + indy2 * nx + indz2 * nx * ny;
1125:     v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1126:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1128:     j = indx2 + indy1 * nx + indz1 * nx * ny;
1129:     v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
1130:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1132:     j = indx2 + indy1 * nx + indz2 * nx * ny;
1133:     v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
1134:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1136:     j = indx2 + indy2 * nx + indz1 * nx * ny;
1137:     v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
1138:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

1140:     j = indx2 + indy2 * nx + indz2 * nx * ny;
1141:     v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
1142:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
1143:   }

1145:   PetscCall(MatAssemblyBegin(user->Q, MAT_FINAL_ASSEMBLY));
1146:   PetscCall(MatAssemblyEnd(user->Q, MAT_FINAL_ASSEMBLY));
1147:   /* Create MQ (composed of blocks of Q */
1148:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, dsubnlocal * user->ns, PETSC_DECIDE, user->ndata * user->ns, user->nstate, user, &user->MQ));
1149:   PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT, (void (*)(void))QMatMult));
1150:   PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT_TRANSPOSE, (void (*)(void))QMatMultTranspose));

1152:   /* Add noise to the measurement data */
1153:   PetscCall(VecSet(user->ywork, 1.0));
1154:   PetscCall(VecAYPX(user->ywork, user->noise, user->ytrue));
1155:   PetscCall(MatMult(user->MQ, user->ywork, user->d));

1157:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1158:   PetscCall(PetscFree(x));
1159:   PetscCall(PetscFree(y));
1160:   PetscCall(PetscFree(z));
1161:   PetscCall(PetscLogStagePop());
1162:   PetscFunctionReturn(PETSC_SUCCESS);
1163: }

1165: PetscErrorCode EllipticDestroy(AppCtx *user)
1166: {
1167:   PetscInt i;

1169:   PetscFunctionBegin;
1170:   PetscCall(MatDestroy(&user->DSG));
1171:   PetscCall(KSPDestroy(&user->solver));
1172:   PetscCall(MatDestroy(&user->Q));
1173:   PetscCall(MatDestroy(&user->MQ));
1174:   if (!user->use_ptap) {
1175:     PetscCall(MatDestroy(&user->Div));
1176:     PetscCall(MatDestroy(&user->Divwork));
1177:   } else {
1178:     PetscCall(MatDestroy(&user->Diag));
1179:   }
1180:   if (user->use_lrc) PetscCall(MatDestroy(&user->Ones));

1182:   PetscCall(MatDestroy(&user->Grad));
1183:   PetscCall(MatDestroy(&user->Av));
1184:   PetscCall(MatDestroy(&user->Avwork));
1185:   PetscCall(MatDestroy(&user->L));
1186:   PetscCall(MatDestroy(&user->Js));
1187:   PetscCall(MatDestroy(&user->Jd));
1188:   PetscCall(MatDestroy(&user->JsBlock));
1189:   PetscCall(MatDestroy(&user->JsInv));

1191:   PetscCall(VecDestroy(&user->x));
1192:   PetscCall(VecDestroy(&user->u));
1193:   PetscCall(VecDestroy(&user->uwork));
1194:   PetscCall(VecDestroy(&user->utrue));
1195:   PetscCall(VecDestroy(&user->y));
1196:   PetscCall(VecDestroy(&user->ywork));
1197:   PetscCall(VecDestroy(&user->ytrue));
1198:   PetscCall(VecDestroy(&user->c));
1199:   PetscCall(VecDestroy(&user->cwork));
1200:   PetscCall(VecDestroy(&user->ur));
1201:   PetscCall(VecDestroy(&user->q));
1202:   PetscCall(VecDestroy(&user->d));
1203:   PetscCall(VecDestroy(&user->dwork));
1204:   PetscCall(VecDestroy(&user->lwork));
1205:   PetscCall(VecDestroy(&user->S));
1206:   PetscCall(VecDestroy(&user->Swork));
1207:   PetscCall(VecDestroy(&user->Sdiag));
1208:   PetscCall(VecDestroy(&user->Ywork));
1209:   PetscCall(VecDestroy(&user->Twork));
1210:   PetscCall(VecDestroy(&user->Av_u));
1211:   PetscCall(VecDestroy(&user->js_diag));
1212:   PetscCall(ISDestroy(&user->s_is));
1213:   PetscCall(ISDestroy(&user->d_is));
1214:   PetscCall(VecDestroy(&user->suby));
1215:   PetscCall(VecDestroy(&user->subd));
1216:   PetscCall(VecDestroy(&user->subq));
1217:   PetscCall(VecScatterDestroy(&user->state_scatter));
1218:   PetscCall(VecScatterDestroy(&user->design_scatter));
1219:   for (i = 0; i < user->ns; i++) {
1220:     PetscCall(VecScatterDestroy(&user->yi_scatter[i]));
1221:     PetscCall(VecScatterDestroy(&user->di_scatter[i]));
1222:   }
1223:   PetscCall(PetscFree(user->yi_scatter));
1224:   PetscCall(PetscFree(user->di_scatter));
1225:   if (user->use_lrc) {
1226:     PetscCall(PetscFree(user->ones));
1227:     PetscCall(MatDestroy(&user->Ones));
1228:   }
1229:   PetscFunctionReturn(PETSC_SUCCESS);
1230: }

1232: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
1233: {
1234:   Vec       X;
1235:   PetscReal unorm, ynorm;
1236:   AppCtx   *user = (AppCtx *)ptr;

1238:   PetscFunctionBegin;
1239:   PetscCall(TaoGetSolution(tao, &X));
1240:   PetscCall(Scatter(X, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
1241:   PetscCall(VecAXPY(user->ywork, -1.0, user->ytrue));
1242:   PetscCall(VecAXPY(user->uwork, -1.0, user->utrue));
1243:   PetscCall(VecNorm(user->uwork, NORM_2, &unorm));
1244:   PetscCall(VecNorm(user->ywork, NORM_2, &ynorm));
1245:   PetscCall(PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n", (double)unorm, (double)ynorm));
1246:   PetscFunctionReturn(PETSC_SUCCESS);
1247: }

1249: /*TEST

1251:    build:
1252:       requires: !complex

1254:    test:
1255:       args: -tao_monitor_constraint_norm -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
1256:       requires: !single

1258:    test:
1259:       suffix: 2
1260:       args: -tao_monitor_constraint_norm -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
1261:       requires: !single

1263: TEST*/