Actual source code: dgmres.c

  1: /*
  2:     Implements deflated GMRES.
  3: */

  5: #include <../src/ksp/ksp/impls/gmres/dgmres/dgmresimpl.h>

  7: PetscLogEvent KSP_DGMRESComputeDeflationData, KSP_DGMRESApplyDeflation;

  9: static PetscErrorCode KSPDGMRESGetNewVectors(KSP, PetscInt);
 10: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
 11: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);

 13: static PetscErrorCode KSPDGMRESSetEigen(KSP ksp, PetscInt nb_eig)
 14: {
 15:   PetscFunctionBegin;
 16:   PetscTryMethod((ksp), "KSPDGMRESSetEigen_C", (KSP, PetscInt), (ksp, nb_eig));
 17:   PetscFunctionReturn(PETSC_SUCCESS);
 18: }
 19: static PetscErrorCode KSPDGMRESSetMaxEigen(KSP ksp, PetscInt max_neig)
 20: {
 21:   PetscFunctionBegin;
 22:   PetscTryMethod((ksp), "KSPDGMRESSetMaxEigen_C", (KSP, PetscInt), (ksp, max_neig));
 23:   PetscFunctionReturn(PETSC_SUCCESS);
 24: }
 25: static PetscErrorCode KSPDGMRESComputeSchurForm(KSP ksp, PetscInt *neig)
 26: {
 27:   PetscFunctionBegin;
 28:   PetscUseMethod((ksp), "KSPDGMRESComputeSchurForm_C", (KSP, PetscInt *), (ksp, neig));
 29:   PetscFunctionReturn(PETSC_SUCCESS);
 30: }
 31: PetscErrorCode KSPDGMRESComputeDeflationData(KSP ksp, PetscInt *curneigh)
 32: {
 33:   PetscFunctionBegin;
 34:   PetscUseMethod((ksp), "KSPDGMRESComputeDeflationData_C", (KSP, PetscInt *), (ksp, curneigh));
 35:   PetscFunctionReturn(PETSC_SUCCESS);
 36: }
 37: static PetscErrorCode KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
 38: {
 39:   PetscFunctionBegin;
 40:   PetscUseMethod((ksp), "KSPDGMRESApplyDeflation_C", (KSP, Vec, Vec), (ksp, x, y));
 41:   PetscFunctionReturn(PETSC_SUCCESS);
 42: }

 44: static PetscErrorCode KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
 45: {
 46:   PetscFunctionBegin;
 47:   PetscUseMethod((ksp), "KSPDGMRESImproveEig_C", (KSP, PetscInt), (ksp, neig));
 48:   PetscFunctionReturn(PETSC_SUCCESS);
 49: }

 51: PetscErrorCode KSPSetUp_DGMRES(KSP ksp)
 52: {
 53:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
 54:   PetscInt    neig   = dgmres->neig + EIG_OFFSET;
 55:   PetscInt    max_k  = dgmres->max_k + 1;

 57:   PetscFunctionBegin;
 58:   PetscCall(KSPSetUp_GMRES(ksp));
 59:   if (!dgmres->neig) PetscFunctionReturn(PETSC_SUCCESS);

 61:   /* Allocate workspace for the Schur vectors*/
 62:   PetscCall(PetscMalloc1(neig * max_k, &SR));
 63:   dgmres->wr    = NULL;
 64:   dgmres->wi    = NULL;
 65:   dgmres->perm  = NULL;
 66:   dgmres->modul = NULL;
 67:   dgmres->Q     = NULL;
 68:   dgmres->Z     = NULL;

 70:   UU   = NULL;
 71:   XX   = NULL;
 72:   MX   = NULL;
 73:   AUU  = NULL;
 74:   XMX  = NULL;
 75:   XMU  = NULL;
 76:   UMX  = NULL;
 77:   AUAU = NULL;
 78:   TT   = NULL;
 79:   TTF  = NULL;
 80:   INVP = NULL;
 81:   X1   = NULL;
 82:   X2   = NULL;
 83:   MU   = NULL;
 84:   PetscFunctionReturn(PETSC_SUCCESS);
 85: }

 87: /*
 88:  Run GMRES, possibly with restart.  Return residual history if requested.
 89:  input parameters:

 91:  .       gmres  - structure containing parameters and work areas

 93:  output parameters:
 94:  .        nres    - residuals (from preconditioned system) at each step.
 95:  If restarting, consider passing nres+it.  If null,
 96:  ignored
 97:  .        itcount - number of iterations used.  nres[0] to nres[itcount]
 98:  are defined.  If null, ignored.

100:  Notes:
101:  On entry, the value in vector VEC_VV(0) should be the initial residual
102:  (this allows shortcuts where the initial preconditioned residual is 0).
103:  */
104: static PetscErrorCode KSPDGMRESCycle(PetscInt *itcount, KSP ksp)
105: {
106:   KSP_DGMRES *dgmres = (KSP_DGMRES *)(ksp->data);
107:   PetscReal   res_norm, res, hapbnd, tt;
108:   PetscInt    it     = 0;
109:   PetscInt    max_k  = dgmres->max_k;
110:   PetscBool   hapend = PETSC_FALSE;
111:   PetscReal   res_old;
112:   PetscInt    test = 0;

114:   PetscFunctionBegin;
115:   PetscCall(VecNormalize(VEC_VV(0), &res_norm));
116:   KSPCheckNorm(ksp, res_norm);
117:   res     = res_norm;
118:   *GRS(0) = res_norm;

120:   /* check for the convergence */
121:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
122:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
123:   else ksp->rnorm = 0.0;
124:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
125:   dgmres->it = (it - 1);
126:   PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
127:   PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
128:   if (!res) {
129:     if (itcount) *itcount = 0;
130:     ksp->reason = KSP_CONVERGED_ATOL;
131:     PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
132:     PetscFunctionReturn(PETSC_SUCCESS);
133:   }
134:   /* record the residual norm to test if deflation is needed */
135:   res_old = res;

137:   PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
138:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
139:     if (it) {
140:       PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
141:       PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
142:     }
143:     dgmres->it = (it - 1);
144:     if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) PetscCall(KSPDGMRESGetNewVectors(ksp, it + 1));
145:     if (dgmres->r > 0) {
146:       if (ksp->pc_side == PC_LEFT) {
147:         /* Apply the first preconditioner */
148:         PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_TEMP, VEC_TEMP_MATOP));
149:         /* Then apply Deflation as a preconditioner */
150:         PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1 + it)));
151:       } else if (ksp->pc_side == PC_RIGHT) {
152:         PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP));
153:         PetscCall(KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1 + it), VEC_TEMP_MATOP));
154:       }
155:     } else {
156:       PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_VV(1 + it), VEC_TEMP_MATOP));
157:     }
158:     dgmres->matvecs += 1;
159:     /* update Hessenberg matrix and do Gram-Schmidt */
160:     PetscCall((*dgmres->orthog)(ksp, it));

162:     /* vv(i+1) . vv(i+1) */
163:     PetscCall(VecNormalize(VEC_VV(it + 1), &tt));
164:     /* save the magnitude */
165:     *HH(it + 1, it)  = tt;
166:     *HES(it + 1, it) = tt;

168:     /* check for the happy breakdown */
169:     hapbnd = PetscAbsScalar(tt / *GRS(it));
170:     if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
171:     if (tt < hapbnd) {
172:       PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt));
173:       hapend = PETSC_TRUE;
174:     }
175:     PetscCall(KSPDGMRESUpdateHessenberg(ksp, it, hapend, &res));

177:     it++;
178:     dgmres->it = (it - 1); /* For converged */
179:     ksp->its++;
180:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
181:     else ksp->rnorm = 0.0;
182:     if (ksp->reason) break;

184:     PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));

186:     /* Catch error in happy breakdown and signal convergence and break from loop */
187:     if (hapend) {
188:       if (!ksp->reason) {
189:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
190:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
191:         break;
192:       }
193:     }
194:   }

196:   /* Monitor if we know that we will not return for a restart */
197:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
198:     PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
199:     PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
200:   }
201:   if (itcount) *itcount = it;

203:   /*
204:    Down here we have to solve for the "best" coefficients of the Krylov
205:    columns, add the solution values together, and possibly unwind the
206:    preconditioning from the solution
207:    */
208:   /* Form the solution (or the solution so far) */
209:   PetscCall(KSPDGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, it - 1));

211:   /* Compute data for the deflation to be used during the next restart */
212:   if (!ksp->reason && ksp->its < ksp->max_it) {
213:     test = max_k * PetscLogReal(ksp->rtol / res) / PetscLogReal(res / res_old);
214:     /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed  */
215:     if ((test > dgmres->smv * (ksp->max_it - ksp->its)) || dgmres->force) PetscCall(KSPDGMRESComputeDeflationData(ksp, NULL));
216:   }
217:   PetscFunctionReturn(PETSC_SUCCESS);
218: }

220: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
221: {
222:   PetscInt    i, its = 0, itcount;
223:   KSP_DGMRES *dgmres     = (KSP_DGMRES *)ksp->data;
224:   PetscBool   guess_zero = ksp->guess_zero;

226:   PetscFunctionBegin;
227:   PetscCheck(!ksp->calc_sings || dgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

229:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
230:   ksp->its        = 0;
231:   dgmres->matvecs = 0;
232:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

234:   itcount = 0;
235:   while (!ksp->reason) {
236:     PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
237:     if (ksp->pc_side == PC_LEFT) {
238:       dgmres->matvecs += 1;
239:       if (dgmres->r > 0) {
240:         PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP));
241:         PetscCall(VecCopy(VEC_TEMP, VEC_VV(0)));
242:       }
243:     }

245:     PetscCall(KSPDGMRESCycle(&its, ksp));
246:     itcount += its;
247:     if (itcount >= ksp->max_it) {
248:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
249:       break;
250:     }
251:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
252:   }
253:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */

255:   for (i = 0; i < dgmres->r; i++) PetscCall(VecViewFromOptions(UU[i], (PetscObject)ksp, "-ksp_dgmres_view_deflation_vecs"));
256:   PetscFunctionReturn(PETSC_SUCCESS);
257: }

259: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
260: {
261:   KSP_DGMRES *dgmres   = (KSP_DGMRES *)ksp->data;
262:   PetscInt    neig1    = dgmres->neig + EIG_OFFSET;
263:   PetscInt    max_neig = dgmres->max_neig;

265:   PetscFunctionBegin;
266:   if (dgmres->r) {
267:     PetscCall(VecDestroyVecs(max_neig, &UU));
268:     PetscCall(VecDestroyVecs(max_neig, &MU));
269:     if (XX) {
270:       PetscCall(VecDestroyVecs(neig1, &XX));
271:       PetscCall(VecDestroyVecs(neig1, &MX));
272:     }
273:     PetscCall(PetscFree(TT));
274:     PetscCall(PetscFree(TTF));
275:     PetscCall(PetscFree(INVP));
276:     PetscCall(PetscFree(XMX));
277:     PetscCall(PetscFree(UMX));
278:     PetscCall(PetscFree(XMU));
279:     PetscCall(PetscFree(X1));
280:     PetscCall(PetscFree(X2));
281:     PetscCall(PetscFree(dgmres->work));
282:     PetscCall(PetscFree(dgmres->iwork));
283:     PetscCall(PetscFree(dgmres->wr));
284:     PetscCall(PetscFree(dgmres->wi));
285:     PetscCall(PetscFree(dgmres->modul));
286:     PetscCall(PetscFree(dgmres->Q));
287:     PetscCall(PetscFree(ORTH));
288:     PetscCall(PetscFree(AUAU));
289:     PetscCall(PetscFree(AUU));
290:     PetscCall(PetscFree(SR2));
291:   }
292:   PetscCall(PetscFree(SR));
293:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C", NULL));
294:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C", NULL));
295:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C", NULL));
296:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C", NULL));
297:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C", NULL));
298:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C", NULL));
299:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C", NULL));
300:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", NULL));
301:   PetscCall(KSPDestroy_GMRES(ksp));
302:   PetscFunctionReturn(PETSC_SUCCESS);
303: }

305: /*
306:  KSPDGMRESBuildSoln - create the solution from the starting vector and the
307:  current iterates.

309:  Input parameters:
310:  nrs - work area of size it + 1.
311:  vs  - index of initial guess
312:  vdest - index of result.  Note that vs may == vdest (replace
313:  guess with the solution).

315:  This is an internal routine that knows about the GMRES internals.
316:  */
317: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs, Vec vs, Vec vdest, KSP ksp, PetscInt it)
318: {
319:   PetscScalar tt;
320:   PetscInt    ii, k, j;
321:   KSP_DGMRES *dgmres = (KSP_DGMRES *)(ksp->data);

323:   /* Solve for solution vector that minimizes the residual */

325:   PetscFunctionBegin;
326:   /* If it is < 0, no gmres steps have been performed */
327:   if (it < 0) {
328:     PetscCall(VecCopy(vs, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
329:     PetscFunctionReturn(PETSC_SUCCESS);
330:   }
331:   PetscCheck(*HH(it, it) != 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Likely your matrix is the zero operator. HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g", it, (double)PetscAbsScalar(*GRS(it)));
332:   if (*HH(it, it) != 0.0) nrs[it] = *GRS(it) / *HH(it, it);
333:   else nrs[it] = 0.0;

335:   for (ii = 1; ii <= it; ii++) {
336:     k  = it - ii;
337:     tt = *GRS(k);
338:     for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
339:     PetscCheck(*HH(k, k) != 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Likely your matrix is singular. HH(k,k) is identically zero; it = %" PetscInt_FMT " k = %" PetscInt_FMT, it, k);
340:     nrs[k] = tt / *HH(k, k);
341:   }

343:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
344:   PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));

346:   /* Apply deflation */
347:   if (ksp->pc_side == PC_RIGHT && dgmres->r > 0) {
348:     PetscCall(KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP));
349:     PetscCall(VecCopy(VEC_TEMP_MATOP, VEC_TEMP));
350:   }
351:   PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));

353:   /* add solution to previous solution */
354:   if (vdest != vs) PetscCall(VecCopy(vs, vdest));
355:   PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
356:   PetscFunctionReturn(PETSC_SUCCESS);
357: }

359: /*
360:  Do the scalar work for the orthogonalization.  Return new residual norm.
361:  */
362: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
363: {
364:   PetscScalar *hh, *cc, *ss, tt;
365:   PetscInt     j;
366:   KSP_DGMRES  *dgmres = (KSP_DGMRES *)(ksp->data);

368:   PetscFunctionBegin;
369:   hh = HH(0, it);
370:   cc = CC(0);
371:   ss = SS(0);

373:   /* Apply all the previously computed plane rotations to the new column
374:    of the Hessenberg matrix */
375:   for (j = 1; j <= it; j++) {
376:     tt  = *hh;
377:     *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
378:     hh++;
379:     *hh = *cc++ * *hh - (*ss++ * tt);
380:   }

382:   /*
383:    compute the new plane rotation, and apply it to:
384:    1) the right-hand-side of the Hessenberg system
385:    2) the new column of the Hessenberg matrix
386:    thus obtaining the updated value of the residual
387:    */
388:   if (!hapend) {
389:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
390:     if (tt == 0.0) {
391:       ksp->reason = KSP_DIVERGED_NULL;
392:       PetscFunctionReturn(PETSC_SUCCESS);
393:     }
394:     *cc          = *hh / tt;
395:     *ss          = *(hh + 1) / tt;
396:     *GRS(it + 1) = -(*ss * *GRS(it));
397:     *GRS(it)     = PetscConj(*cc) * *GRS(it);
398:     *hh          = PetscConj(*cc) * *hh + *ss * *(hh + 1);
399:     *res         = PetscAbsScalar(*GRS(it + 1));
400:   } else {
401:     /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
402:      another rotation matrix (so RH doesn't change).  The new residual is
403:      always the new sine term times the residual from last time (GRS(it)),
404:      but now the new sine rotation would be zero...so the residual should
405:      be zero...so we will multiply "zero" by the last residual.  This might
406:      not be exactly what we want to do here -could just return "zero". */
407:     *res = 0.0;
408:   }
409:   PetscFunctionReturn(PETSC_SUCCESS);
410: }

412: /*
413:   Allocates more work vectors, starting from VEC_VV(it).
414: */
415: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp, PetscInt it)
416: {
417:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
418:   PetscInt    nwork  = dgmres->nwork_alloc, k, nalloc;

420:   PetscFunctionBegin;
421:   nalloc = PetscMin(ksp->max_it, dgmres->delta_allocate);
422:   /* Adjust the number to allocate to make sure that we don't exceed the
423:    number of available slots */
424:   if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
425:   if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);

427:   dgmres->vv_allocated += nalloc;

429:   PetscCall(KSPCreateVecs(ksp, nalloc, &dgmres->user_work[nwork], 0, NULL));

431:   dgmres->mwork_alloc[nwork] = nalloc;
432:   for (k = 0; k < nalloc; k++) dgmres->vecs[it + VEC_OFFSET + k] = dgmres->user_work[nwork][k];
433:   dgmres->nwork_alloc++;
434:   PetscFunctionReturn(PETSC_SUCCESS);
435: }

437: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp, Vec ptr, Vec *result)
438: {
439:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;

441:   PetscFunctionBegin;
442:   if (!ptr) {
443:     if (!dgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &dgmres->sol_temp));
444:     ptr = dgmres->sol_temp;
445:   }
446:   if (!dgmres->nrs) {
447:     /* allocate the work area */
448:     PetscCall(PetscMalloc1(dgmres->max_k, &dgmres->nrs));
449:   }
450:   PetscCall(KSPDGMRESBuildSoln(dgmres->nrs, ksp->vec_sol, ptr, ksp, dgmres->it));
451:   if (result) *result = ptr;
452:   PetscFunctionReturn(PETSC_SUCCESS);
453: }

455: static PetscErrorCode KSPView_DGMRES(KSP ksp, PetscViewer viewer)
456: {
457:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
458:   PetscBool   iascii, isharmonic;

460:   PetscFunctionBegin;
461:   PetscCall(KSPView_GMRES(ksp, viewer));
462:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
463:   if (iascii) {
464:     PetscCall(PetscViewerASCIIPrintf(viewer, "    Adaptive strategy is used: %s\n", PetscBools[dgmres->force]));
465:     PetscCall(PetscOptionsHasName(((PetscObject)ksp)->options, ((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &isharmonic));
466:     if (isharmonic) {
467:       PetscCall(PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %" PetscInt_FMT " using Harmonic Ritz values \n", dgmres->neig));
468:     } else {
469:       PetscCall(PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %" PetscInt_FMT " using Ritz values \n", dgmres->neig));
470:     }
471:     PetscCall(PetscViewerASCIIPrintf(viewer, "   Total number of extracted eigenvalues = %" PetscInt_FMT "\n", dgmres->r));
472:     PetscCall(PetscViewerASCIIPrintf(viewer, "   Maximum number of eigenvalues set to be extracted = %" PetscInt_FMT "\n", dgmres->max_neig));
473:     PetscCall(PetscViewerASCIIPrintf(viewer, "   relaxation parameter for the adaptive strategy(smv)  = %g\n", (double)dgmres->smv));
474:     PetscCall(PetscViewerASCIIPrintf(viewer, "   Number of matvecs : %" PetscInt_FMT "\n", dgmres->matvecs));
475:   }
476:   PetscFunctionReturn(PETSC_SUCCESS);
477: }

479: PetscErrorCode KSPDGMRESSetEigen_DGMRES(KSP ksp, PetscInt neig)
480: {
481:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;

483:   PetscFunctionBegin;
484:   PetscCheck(neig >= 0 && neig <= dgmres->max_k, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The value of neig must be positive and less than the restart value ");
485:   dgmres->neig = neig;
486:   PetscFunctionReturn(PETSC_SUCCESS);
487: }

489: static PetscErrorCode KSPDGMRESSetMaxEigen_DGMRES(KSP ksp, PetscInt max_neig)
490: {
491:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;

493:   PetscFunctionBegin;
494:   PetscCheck(max_neig >= 0 && max_neig <= dgmres->max_k, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The value of max_neig must be positive and less than the restart value ");
495:   dgmres->max_neig = max_neig;
496:   PetscFunctionReturn(PETSC_SUCCESS);
497: }

499: static PetscErrorCode KSPDGMRESSetRatio_DGMRES(KSP ksp, PetscReal ratio)
500: {
501:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;

503:   PetscFunctionBegin;
504:   PetscCheck(ratio > 0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "The relaxation parameter value must be positive");
505:   dgmres->smv = ratio;
506:   PetscFunctionReturn(PETSC_SUCCESS);
507: }

509: static PetscErrorCode KSPDGMRESForce_DGMRES(KSP ksp, PetscBool force)
510: {
511:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;

513:   PetscFunctionBegin;
514:   dgmres->force = force;
515:   PetscFunctionReturn(PETSC_SUCCESS);
516: }

518: PetscErrorCode KSPSetFromOptions_DGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
519: {
520:   PetscInt    neig;
521:   PetscInt    max_neig;
522:   KSP_DGMRES *dgmres = (KSP_DGMRES *)ksp->data;
523:   PetscBool   flg;

525:   PetscFunctionBegin;
526:   PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
527:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP DGMRES Options");
528:   PetscCall(PetscOptionsInt("-ksp_dgmres_eigen", "Number of smallest eigenvalues to extract at each restart", "KSPDGMRESSetEigen", dgmres->neig, &neig, &flg));
529:   if (flg) PetscCall(KSPDGMRESSetEigen(ksp, neig));
530:   PetscCall(PetscOptionsInt("-ksp_dgmres_max_eigen", "Maximum Number of smallest eigenvalues to extract ", "KSPDGMRESSetMaxEigen", dgmres->max_neig, &max_neig, &flg));
531:   if (flg) PetscCall(KSPDGMRESSetMaxEigen(ksp, max_neig));
532:   PetscCall(PetscOptionsReal("-ksp_dgmres_ratio", "Relaxation parameter for the smaller number of matrix-vectors product allowed", "KSPDGMRESSetRatio", dgmres->smv, &dgmres->smv, NULL));
533:   PetscCall(PetscOptionsBool("-ksp_dgmres_improve", "Improve the computation of eigenvalues by solving a new generalized eigenvalue problem (experimental - not stable at this time)", NULL, dgmres->improve, &dgmres->improve, NULL));
534:   PetscCall(PetscOptionsBool("-ksp_dgmres_force", "Sets DGMRES always at restart active, i.e do not use the adaptive strategy", "KSPDGMRESForce", dgmres->force, &dgmres->force, NULL));
535:   PetscOptionsHeadEnd();
536:   PetscFunctionReturn(PETSC_SUCCESS);
537: }

539: PetscErrorCode KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
540: {
541:   KSP_DGMRES  *dgmres = (KSP_DGMRES *)ksp->data;
542:   PetscInt     i, j, k;
543:   PetscBLASInt nr, bmax;
544:   PetscInt     r = dgmres->r;
545:   PetscInt     neig;                                 /* number of eigenvalues to extract at each restart */
546:   PetscInt     neig1    = dgmres->neig + EIG_OFFSET; /* max number of eig that can be extracted at each restart */
547:   PetscInt     max_neig = dgmres->max_neig;          /* Max number of eigenvalues to extract during the iterative process */
548:   PetscInt     N        = dgmres->max_k + 1;
549:   PetscInt     n        = dgmres->it + 1;
550:   PetscReal    alpha;

552:   PetscFunctionBegin;
553:   PetscCall(PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
554:   if (dgmres->neig == 0 || (max_neig < (r + neig1) && !dgmres->improve)) {
555:     PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
556:     PetscFunctionReturn(PETSC_SUCCESS);
557:   }

559:   PetscCall(KSPDGMRESComputeSchurForm(ksp, &neig));
560:   /* Form the extended Schur vectors X=VV*Sr */
561:   if (!XX) PetscCall(VecDuplicateVecs(VEC_VV(0), neig1, &XX));
562:   for (j = 0; j < neig; j++) PetscCall(VecMAXPBY(XX[j], n, &SR[j * N], 0, &VEC_VV(0)));

564:   /* Orthogonalize X against U */
565:   if (!ORTH) PetscCall(PetscMalloc1(max_neig, &ORTH));
566:   if (r > 0) {
567:     /* modified Gram-Schmidt */
568:     for (j = 0; j < neig; j++) {
569:       for (i = 0; i < r; i++) {
570:         /* First, compute U'*X[j] */
571:         PetscCall(VecDot(XX[j], UU[i], &alpha));
572:         /* Then, compute X(j)=X(j)-U*U'*X(j) */
573:         PetscCall(VecAXPY(XX[j], -alpha, UU[i]));
574:       }
575:     }
576:   }
577:   /* Compute MX = M^{-1}*A*X */
578:   if (!MX) PetscCall(VecDuplicateVecs(VEC_VV(0), neig1, &MX));
579:   for (j = 0; j < neig; j++) PetscCall(KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP));
580:   dgmres->matvecs += neig;

582:   if ((r + neig1) > max_neig && dgmres->improve) { /* Improve the approximate eigenvectors in X by solving a new generalized eigenvalue -- expensive to do this */
583:     PetscCall(KSPDGMRESImproveEig(ksp, neig));
584:     PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
585:     PetscFunctionReturn(PETSC_SUCCESS); /* We return here since data for M have been improved in KSPDGMRESImproveEig()*/
586:   }

588:   /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
589:   if (!XMX) PetscCall(PetscMalloc1(neig1 * neig1, &XMX));
590:   for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], neig, XX, &(XMX[j * neig1])));

592:   if (r > 0) {
593:     /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
594:     if (!UMX) PetscCall(PetscMalloc1(max_neig * neig1, &UMX));
595:     for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], r, UU, &(UMX[j * max_neig])));
596:     /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
597:     if (!XMU) PetscCall(PetscMalloc1(max_neig * neig1, &XMU));
598:     for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], neig, XX, &(XMU[j * neig1])));
599:   }

601:   /* Form the new matrix T = [T UMX; XMU XMX]; */
602:   if (!TT) PetscCall(PetscMalloc1(max_neig * max_neig, &TT));
603:   if (r > 0) {
604:     /* Add XMU to T */
605:     for (j = 0; j < r; j++) PetscCall(PetscArraycpy(&(TT[max_neig * j + r]), &(XMU[neig1 * j]), neig));
606:     /* Add [UMX; XMX] to T */
607:     for (j = 0; j < neig; j++) {
608:       k = r + j;
609:       PetscCall(PetscArraycpy(&(TT[max_neig * k]), &(UMX[max_neig * j]), r));
610:       PetscCall(PetscArraycpy(&(TT[max_neig * k + r]), &(XMX[neig1 * j]), neig));
611:     }
612:   } else { /* Add XMX to T */
613:     for (j = 0; j < neig; j++) PetscCall(PetscArraycpy(&(TT[max_neig * j]), &(XMX[neig1 * j]), neig));
614:   }

616:   dgmres->r += neig;
617:   r = dgmres->r;
618:   PetscCall(PetscBLASIntCast(r, &nr));
619:   /*LU Factorize T with Lapack xgetrf routine */

621:   PetscCall(PetscBLASIntCast(max_neig, &bmax));
622:   if (!TTF) PetscCall(PetscMalloc1(bmax * bmax, &TTF));
623:   PetscCall(PetscArraycpy(TTF, TT, bmax * r));
624:   if (!INVP) PetscCall(PetscMalloc1(bmax, &INVP));
625:   {
626:     PetscBLASInt info;
627:     PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
628:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRF INFO=%d", (int)info);
629:   }

631:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
632:   if (!UU) {
633:     PetscCall(VecDuplicateVecs(VEC_VV(0), max_neig, &UU));
634:     PetscCall(VecDuplicateVecs(VEC_VV(0), max_neig, &MU));
635:   }
636:   for (j = 0; j < neig; j++) {
637:     PetscCall(VecCopy(XX[j], UU[r - neig + j]));
638:     PetscCall(VecCopy(MX[j], MU[r - neig + j]));
639:   }
640:   PetscCall(PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0, 0, 0));
641:   PetscFunctionReturn(PETSC_SUCCESS);
642: }

644: PetscErrorCode KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
645: {
646:   KSP_DGMRES   *dgmres = (KSP_DGMRES *)ksp->data;
647:   PetscInt      N = dgmres->max_k + 1, n = dgmres->it + 1;
648:   PetscBLASInt  bn;
649:   PetscReal    *A;
650:   PetscBLASInt  ihi;
651:   PetscBLASInt  ldA = 0; /* leading dimension of A */
652:   PetscBLASInt  ldQ;     /* leading dimension of Q */
653:   PetscReal    *Q;       /*  orthogonal matrix of  (left) Schur vectors */
654:   PetscReal    *work;    /* working vector */
655:   PetscBLASInt  lwork;   /* size of the working vector */
656:   PetscInt     *perm;    /* Permutation vector to sort eigenvalues */
657:   PetscInt      i, j;
658:   PetscBLASInt  NbrEig;          /* Number of eigenvalues really extracted */
659:   PetscReal    *wr, *wi, *modul; /* Real and imaginary part and modulus of the eigenvalues of A */
660:   PetscBLASInt *select;
661:   PetscBLASInt *iwork;
662:   PetscBLASInt  liwork;
663:   PetscScalar  *Ht;   /* Transpose of the Hessenberg matrix */
664:   PetscScalar  *t;    /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
665:   PetscBLASInt *ipiv; /* Permutation vector to be used in LAPACK */
666:   PetscBool     flag; /* determine whether to use Ritz vectors or harmonic Ritz vectors */

668:   PetscFunctionBegin;
669:   PetscCall(PetscBLASIntCast(n, &bn));
670:   PetscCall(PetscBLASIntCast(N, &ldA));
671:   ihi = ldQ = bn;
672:   PetscCall(PetscBLASIntCast(5 * N, &lwork));

674: #if defined(PETSC_USE_COMPLEX)
675:   SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "No support for complex numbers.");
676: #endif

678:   PetscCall(PetscMalloc1(ldA * ldA, &A));
679:   PetscCall(PetscMalloc1(ldQ * n, &Q));
680:   PetscCall(PetscMalloc1(lwork, &work));
681:   if (!dgmres->wr) {
682:     PetscCall(PetscMalloc1(n, &dgmres->wr));
683:     PetscCall(PetscMalloc1(n, &dgmres->wi));
684:   }
685:   wr = dgmres->wr;
686:   wi = dgmres->wi;
687:   PetscCall(PetscMalloc1(n, &modul));
688:   PetscCall(PetscMalloc1(n, &perm));
689:   /* copy the Hessenberg matrix to work space */
690:   PetscCall(PetscArraycpy(A, dgmres->hes_origin, ldA * ldA));
691:   PetscCall(PetscOptionsHasName(((PetscObject)ksp)->options, ((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag));
692:   if (flag) {
693:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
694:     /* Transpose the Hessenberg matrix */
695:     PetscCall(PetscMalloc1(bn * bn, &Ht));
696:     for (i = 0; i < bn; i++) {
697:       for (j = 0; j < bn; j++) Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
698:     }

700:     /* Solve the system H^T*t = h_{m+1,m}e_m */
701:     PetscCall(PetscCalloc1(bn, &t));
702:     t[bn - 1] = dgmres->hes_origin[(bn - 1) * ldA + bn]; /* Pick the last element H(m+1,m) */
703:     PetscCall(PetscMalloc1(bn, &ipiv));
704:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
705:     {
706:       PetscBLASInt info;
707:       PetscBLASInt nrhs = 1;
708:       PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
709:       PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error while calling the Lapack routine DGESV");
710:     }
711:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
712:     for (i = 0; i < bn; i++) A[(bn - 1) * bn + i] += t[i];
713:     PetscCall(PetscFree(t));
714:     PetscCall(PetscFree(Ht));
715:   }
716:   /* Compute eigenvalues with the Schur form */
717:   {
718:     PetscBLASInt info = 0;
719:     PetscBLASInt ilo  = 1;
720:     PetscCallBLAS("LAPACKhseqr", LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
721:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XHSEQR %d", (int)info);
722:   }
723:   PetscCall(PetscFree(work));

725:   /* sort the eigenvalues */
726:   for (i = 0; i < n; i++) modul[i] = PetscSqrtReal(wr[i] * wr[i] + wi[i] * wi[i]);
727:   for (i = 0; i < n; i++) perm[i] = i;

729:   PetscCall(PetscSortRealWithPermutation(n, modul, perm));
730:   /* save the complex modulus of the largest eigenvalue in magnitude */
731:   if (dgmres->lambdaN < modul[perm[n - 1]]) dgmres->lambdaN = modul[perm[n - 1]];
732:   /* count the number of extracted eigenvalues (with complex conjugates) */
733:   NbrEig = 0;
734:   while (NbrEig < dgmres->neig) {
735:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
736:     else NbrEig += 1;
737:   }
738:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

740:   PetscCall(PetscCalloc1(n, &select));

742:   if (!dgmres->GreatestEig) {
743:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
744:   } else {
745:     for (j = 0; j < NbrEig; j++) select[perm[n - j - 1]] = 1;
746:   }
747:   /* call Lapack dtrsen */
748:   lwork  = PetscMax(1, 4 * NbrEig * (bn - NbrEig));
749:   liwork = PetscMax(1, 2 * NbrEig * (bn - NbrEig));
750:   PetscCall(PetscMalloc1(lwork, &work));
751:   PetscCall(PetscMalloc1(liwork, &iwork));
752:   {
753:     PetscBLASInt info = 0;
754:     PetscReal    CondEig; /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
755:     PetscReal    CondSub; /* estimated reciprocal condition number of the specified invariant subspace. */
756:     PetscCallBLAS("LAPACKtrsen", LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
757:     PetscCheck(info != 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Unable to reorder the eigenvalues with the LAPACK routine: ILL-CONDITIONED PROBLEM");
758:   }
759:   PetscCall(PetscFree(select));

761:   /* Extract the Schur vectors */
762:   for (j = 0; j < NbrEig; j++) PetscCall(PetscArraycpy(&SR[j * N], &(Q[j * ldQ]), n));
763:   *neig = NbrEig;
764:   PetscCall(PetscFree(A));
765:   PetscCall(PetscFree(work));
766:   PetscCall(PetscFree(perm));
767:   PetscCall(PetscFree(work));
768:   PetscCall(PetscFree(iwork));
769:   PetscCall(PetscFree(modul));
770:   PetscCall(PetscFree(Q));
771:   PetscFunctionReturn(PETSC_SUCCESS);
772: }

774: PetscErrorCode KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
775: {
776:   KSP_DGMRES  *dgmres = (KSP_DGMRES *)ksp->data;
777:   PetscInt     i, r = dgmres->r;
778:   PetscReal    alpha    = 1.0;
779:   PetscInt     max_neig = dgmres->max_neig;
780:   PetscBLASInt br, bmax;
781:   PetscReal    lambda = dgmres->lambdaN;

783:   PetscFunctionBegin;
784:   PetscCall(PetscBLASIntCast(r, &br));
785:   PetscCall(PetscBLASIntCast(max_neig, &bmax));
786:   PetscCall(PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0));
787:   if (!r) {
788:     PetscCall(VecCopy(x, y));
789:     PetscFunctionReturn(PETSC_SUCCESS);
790:   }
791:   /* Compute U'*x */
792:   if (!X1) {
793:     PetscCall(PetscMalloc1(bmax, &X1));
794:     PetscCall(PetscMalloc1(bmax, &X2));
795:   }
796:   PetscCall(VecMDot(x, r, UU, X1));

798:   /* Solve T*X1=X2 for X1*/
799:   PetscCall(PetscArraycpy(X2, X1, br));
800:   {
801:     PetscBLASInt info;
802:     PetscBLASInt nrhs = 1;
803:     PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
804:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRS %d", (int)info);
805:   }
806:   /* Iterative refinement -- is it really necessary ?? */
807:   if (!WORK) {
808:     PetscCall(PetscMalloc1(3 * bmax, &WORK));
809:     PetscCall(PetscMalloc1(bmax, &IWORK));
810:   }
811:   {
812:     PetscBLASInt info;
813:     PetscReal    berr, ferr;
814:     PetscBLASInt nrhs = 1;
815:     PetscCallBLAS("LAPACKgerfs", LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax, X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
816:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGERFS %d", (int)info);
817:   }

819:   for (i = 0; i < r; i++) X2[i] = X1[i] / lambda - X2[i];

821:   /* Compute X2=U*X2 */
822:   PetscCall(VecMAXPBY(y, r, X2, 0, UU));
823:   PetscCall(VecAXPY(y, alpha, x));

825:   PetscCall(PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0));
826:   PetscFunctionReturn(PETSC_SUCCESS);
827: }

829: static PetscErrorCode KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
830: {
831:   KSP_DGMRES   *dgmres = (KSP_DGMRES *)ksp->data;
832:   PetscInt      j, r_old, r = dgmres->r;
833:   PetscBLASInt  i     = 0;
834:   PetscInt      neig1 = dgmres->neig + EIG_OFFSET;
835:   PetscInt      bmax  = dgmres->max_neig;
836:   PetscInt      aug   = r + neig;       /* actual size of the augmented invariant basis */
837:   PetscInt      aug1  = bmax + neig1;   /* maximum size of the augmented invariant basis */
838:   PetscBLASInt  ldA;                    /* leading dimension of AUAU and AUU*/
839:   PetscBLASInt  N;                      /* size of AUAU */
840:   PetscReal    *Q;                      /*  orthogonal matrix of  (left) schur vectors */
841:   PetscReal    *Z;                      /*  orthogonal matrix of  (right) schur vectors */
842:   PetscReal    *work;                   /* working vector */
843:   PetscBLASInt  lwork;                  /* size of the working vector */
844:   PetscInt     *perm;                   /* Permutation vector to sort eigenvalues */
845:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modulus of the eigenvalues of A*/
846:   PetscBLASInt  NbrEig = 0, nr, bm;
847:   PetscBLASInt *select;
848:   PetscBLASInt  liwork, *iwork;

850:   PetscFunctionBegin;
851:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
852:   if (!AUU) {
853:     PetscCall(PetscMalloc1(aug1 * aug1, &AUU));
854:     PetscCall(PetscMalloc1(aug1 * aug1, &AUAU));
855:   }
856:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
857:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
858:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
859:   for (j = 0; j < r; j++) PetscCall(VecMDot(UU[j], r, MU, &AUU[j * aug1]));
860:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
861:   for (j = 0; j < neig; j++) PetscCall(VecMDot(XX[j], r, MU, &AUU[(r + j) * aug1]));
862:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
863:   for (j = 0; j < r; j++) PetscCall(VecMDot(UU[j], neig, MX, &AUU[j * aug1 + r]));
864:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
865:   for (j = 0; j < neig; j++) PetscCall(VecMDot(XX[j], neig, MX, &AUU[(r + j) * aug1 + r]));

867:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
868:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
869:   for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], r, MU, &AUAU[j * aug1]));
870:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
871:   for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], r, MU, &AUAU[(r + j) * aug1]));
872:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
873:   for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], neig, MX, &AUAU[j * aug1 + r]));
874:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
875:   for (j = 0; j < neig; j++) PetscCall(VecMDot(MX[j], neig, MX, &AUAU[(r + j) * aug1 + r]));

877:   /* Computation of the eigenvectors */
878:   PetscCall(PetscBLASIntCast(aug1, &ldA));
879:   PetscCall(PetscBLASIntCast(aug, &N));
880:   lwork = 8 * N + 20; /* sizeof the working space */
881:   PetscCall(PetscMalloc1(N, &wr));
882:   PetscCall(PetscMalloc1(N, &wi));
883:   PetscCall(PetscMalloc1(N, &beta));
884:   PetscCall(PetscMalloc1(N, &modul));
885:   PetscCall(PetscMalloc1(N, &perm));
886:   PetscCall(PetscMalloc1(N * N, &Q));
887:   PetscCall(PetscMalloc1(N * N, &Z));
888:   PetscCall(PetscMalloc1(lwork, &work));
889:   {
890:     PetscBLASInt info = 0;
891:     PetscCallBLAS("LAPACKgges", LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
892:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGGES %d", (int)info);
893:   }
894:   for (i = 0; i < N; i++) {
895:     if (beta[i] != 0.0) {
896:       wr[i] /= beta[i];
897:       wi[i] /= beta[i];
898:     }
899:   }
900:   /* sort the eigenvalues */
901:   for (i = 0; i < N; i++) modul[i] = PetscSqrtReal(wr[i] * wr[i] + wi[i] * wi[i]);
902:   for (i = 0; i < N; i++) perm[i] = i;
903:   PetscCall(PetscSortRealWithPermutation(N, modul, perm));
904:   /* Save the norm of the largest eigenvalue */
905:   if (dgmres->lambdaN < modul[perm[N - 1]]) dgmres->lambdaN = modul[perm[N - 1]];
906:   /* Allocate space to extract the first r schur vectors   */
907:   if (!SR2) PetscCall(PetscMalloc1(aug1 * bmax, &SR2));
908:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
909:   while (NbrEig < bmax) {
910:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
911:     else NbrEig += 2;
912:   }
913:   if (NbrEig > bmax) NbrEig = bmax - 1;
914:   r_old     = r; /* previous size of r */
915:   dgmres->r = r = NbrEig;

917:   /* Select the eigenvalues to reorder */
918:   PetscCall(PetscCalloc1(N, &select));
919:   if (!dgmres->GreatestEig) {
920:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
921:   } else {
922:     for (j = 0; j < NbrEig; j++) select[perm[N - j - 1]] = 1;
923:   }
924:   /* Reorder and extract the new <r> schur vectors */
925:   lwork  = PetscMax(4 * N + 16, 2 * NbrEig * (N - NbrEig));
926:   liwork = PetscMax(N + 6, 2 * NbrEig * (N - NbrEig));
927:   PetscCall(PetscFree(work));
928:   PetscCall(PetscMalloc1(lwork, &work));
929:   PetscCall(PetscMalloc1(liwork, &iwork));
930:   {
931:     PetscBLASInt info = 0;
932:     PetscReal    Dif[2];
933:     PetscBLASInt ijob  = 2;
934:     PetscBLASInt wantQ = 1, wantZ = 1;
935:     PetscCallBLAS("LAPACKtgsen", LAPACKtgsen_(&ijob, &wantQ, &wantZ, select, &N, AUAU, &ldA, AUU, &ldA, wr, wi, beta, Q, &N, Z, &N, &NbrEig, NULL, NULL, &(Dif[0]), work, &lwork, iwork, &liwork, &info));
936:     PetscCheck(info != 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Unable to reorder the eigenvalues with the LAPACK routine: ill-conditioned problem.");
937:   }
938:   PetscCall(PetscFree(select));

940:   for (j = 0; j < r; j++) PetscCall(PetscArraycpy(&SR2[j * aug1], &(Z[j * N]), N));

942:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
943:    -- save it temporarily in MU */
944:   for (j = 0; j < r; j++) {
945:     PetscCall(VecMAXPBY(MU[j], r_old, &SR2[j * aug1], 0, UU));
946:     PetscCall(VecMAXPY(MU[j], neig, &SR2[j * aug1 + r_old], XX));
947:   }
948:   /* Form T = U'*MU*U */
949:   for (j = 0; j < r; j++) {
950:     PetscCall(VecCopy(MU[j], UU[j]));
951:     PetscCall(KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP));
952:   }
953:   dgmres->matvecs += r;
954:   for (j = 0; j < r; j++) PetscCall(VecMDot(MU[j], r, UU, &TT[j * bmax]));
955:   /* Factorize T */
956:   PetscCall(PetscArraycpy(TTF, TT, bmax * r));
957:   PetscCall(PetscBLASIntCast(r, &nr));
958:   PetscCall(PetscBLASIntCast(bmax, &bm));
959:   {
960:     PetscBLASInt info;
961:     PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
962:     PetscCheck(!info, PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "Error in LAPACK routine XGETRF INFO=%d", (int)info);
963:   }
964:   /* Free Memory */
965:   PetscCall(PetscFree(wr));
966:   PetscCall(PetscFree(wi));
967:   PetscCall(PetscFree(beta));
968:   PetscCall(PetscFree(modul));
969:   PetscCall(PetscFree(perm));
970:   PetscCall(PetscFree(Q));
971:   PetscCall(PetscFree(Z));
972:   PetscCall(PetscFree(work));
973:   PetscCall(PetscFree(iwork));
974:   PetscFunctionReturn(PETSC_SUCCESS);
975: }

977: /*MC
978:    KSPDGMRES - Implements the deflated GMRES as defined in {cite}`erhel1996restarted` and {cite}`wakam2013memory`

980:    Options Database Keys:
981:    GMRES Options (inherited):
982: +   -ksp_gmres_restart <restart>                                                - the number of Krylov directions to orthogonalize against
983: .   -ksp_gmres_haptol <tol>                                                     - sets the tolerance for "happy ending" (exact convergence)
984: .   -ksp_gmres_preallocate                                                      - preallocate all the Krylov search directions initially
985:                                                                                 (otherwise groups of vectors are allocated as needed)
986: .   -ksp_gmres_classicalgramschmidt                                             - use classical (unmodified) Gram-Schmidt to orthogonalize against
987:                                                                                 the Krylov space (fast) (the default)
988: .   -ksp_gmres_modifiedgramschmidt                                              - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
989: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
990:                                                                                 stability of the classical Gram-Schmidt orthogonalization.
991: -   -ksp_gmres_krylov_monitor                                                   - plot the Krylov space generated

993:    DGMRES Options Database Keys:
994: +   -ksp_dgmres_eigen <neig>                     - number of smallest eigenvalues to extract at each restart
995: .   -ksp_dgmres_max_eigen <max_neig>             - maximum number of eigenvalues that can be extracted during the iterative process
996: .   -ksp_dgmres_force                            - use the deflation at each restart; switch off the adaptive strategy.
997: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
998:                                                    parsed by `PetscOptionsGetViewer()`.  If neig > 1, viewerspec should
999:                                                    end with ":append".  No vectors will be viewed if the adaptive
1000:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
1001:                                                    be given.
1002:                                                    The deflation vectors span a subspace that may be a good
1003:                                                    approximation of the subspace of smallest eigenvectors of the
1004:                                                    preconditioned operator, so this option can aid in understanding
1005:                                                    the performance of a preconditioner.

1007:    Level: beginner

1009:    Notes:
1010:    Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not supported

1012:    In this implementation, the adaptive strategy allows switching to deflated GMRES when the stagnation occurs.

1014:    Contributed by:
1015:    Desire NUENTSA WAKAM, INRIA

1017: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`,
1018:            `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
1019:            `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
1020:            `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
1021:  M*/

1023: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
1024: {
1025:   KSP_DGMRES *dgmres;

1027:   PetscFunctionBegin;
1028:   PetscCall(PetscNew(&dgmres));
1029:   ksp->data = (void *)dgmres;

1031:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
1032:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
1033:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

1035:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
1036:   ksp->ops->setup                        = KSPSetUp_DGMRES;
1037:   ksp->ops->solve                        = KSPSolve_DGMRES;
1038:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
1039:   ksp->ops->view                         = KSPView_DGMRES;
1040:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
1041:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
1042:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

1044:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
1045:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
1046:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
1047:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
1048:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
1049:   /* -- New functions defined in DGMRES -- */
1050:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C", KSPDGMRESSetEigen_DGMRES));
1051:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C", KSPDGMRESSetMaxEigen_DGMRES));
1052:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C", KSPDGMRESSetRatio_DGMRES));
1053:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C", KSPDGMRESForce_DGMRES));
1054:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C", KSPDGMRESComputeSchurForm_DGMRES));
1055:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C", KSPDGMRESComputeDeflationData_DGMRES));
1056:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C", KSPDGMRESApplyDeflation_DGMRES));
1057:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES));

1059:   PetscCall(PetscLogEventRegister("DGMRESCompDefl", KSP_CLASSID, &KSP_DGMRESComputeDeflationData));
1060:   PetscCall(PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation));

1062:   dgmres->haptol         = 1.0e-30;
1063:   dgmres->q_preallocate  = 0;
1064:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
1065:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
1066:   dgmres->nrs            = NULL;
1067:   dgmres->sol_temp       = NULL;
1068:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
1069:   dgmres->Rsvd           = NULL;
1070:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
1071:   dgmres->orthogwork     = NULL;

1073:   /* Default values for the deflation */
1074:   dgmres->r           = 0;
1075:   dgmres->neig        = DGMRES_DEFAULT_EIG;
1076:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG - 1;
1077:   dgmres->lambdaN     = 0.0;
1078:   dgmres->smv         = SMV;
1079:   dgmres->matvecs     = 0;
1080:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
1081:   dgmres->HasSchur    = PETSC_FALSE;
1082:   PetscFunctionReturn(PETSC_SUCCESS);
1083: }