Actual source code: dgmres.c

petsc-3.7.1 2016-05-15
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  1: /*
  2:  This file implements the deflated GMRES.

  4:  */

  6: #include <../src/ksp/ksp/impls/gmres/dgmres/dgmresimpl.h>       /*I  "petscksp.h"  I*/

  8: PetscLogEvent KSP_DGMRESComputeDeflationData, KSP_DGMRESApplyDeflation;

 10: #define GMRES_DELTA_DIRECTIONS 10
 11: #define GMRES_DEFAULT_MAXK     30
 12: static PetscErrorCode    KSPDGMRESGetNewVectors(KSP,PetscInt);
 13: static PetscErrorCode    KSPDGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
 14: static PetscErrorCode    KSPDGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

 18: PetscErrorCode  KSPDGMRESSetEigen(KSP ksp,PetscInt nb_eig)
 19: {

 23:   PetscTryMethod((ksp),"KSPDGMRESSetEigen_C",(KSP,PetscInt),(ksp,nb_eig));
 24:   return(0);
 25: }
 28: PetscErrorCode  KSPDGMRESSetMaxEigen(KSP ksp,PetscInt max_neig)
 29: {

 33:   PetscTryMethod((ksp),"KSPDGMRESSetMaxEigen_C",(KSP,PetscInt),(ksp,max_neig));
 34:   return(0);
 35: }
 38: PetscErrorCode  KSPDGMRESForce(KSP ksp,PetscBool force)
 39: {

 43:   PetscTryMethod((ksp),"KSPDGMRESForce_C",(KSP,PetscBool),(ksp,force));
 44:   return(0);
 45: }
 48: PetscErrorCode  KSPDGMRESSetRatio(KSP ksp,PetscReal ratio)
 49: {

 53:   PetscTryMethod((ksp),"KSPDGMRESSetRatio_C",(KSP,PetscReal),(ksp,ratio));
 54:   return(0);
 55: }
 58: PetscErrorCode  KSPDGMRESComputeSchurForm(KSP ksp,PetscInt *neig)
 59: {

 63:   PetscUseMethod((ksp),"KSPDGMRESComputeSchurForm_C",(KSP, PetscInt*),(ksp, neig));
 64:   return(0);
 65: }
 68: PetscErrorCode  KSPDGMRESComputeDeflationData(KSP ksp)
 69: {

 73:   PetscUseMethod((ksp),"KSPDGMRESComputeDeflationData_C",(KSP),(ksp));
 74:   return(0);
 75: }
 78: PetscErrorCode  KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
 79: {

 83:   PetscUseMethod((ksp),"KSPDGMRESApplyDeflation_C",(KSP, Vec, Vec),(ksp, x, y));
 84:   return(0);
 85: }

 89: PetscErrorCode  KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
 90: {

 94:   PetscUseMethod((ksp), "KSPDGMRESImproveEig_C",(KSP, PetscInt),(ksp, neig));
 95:   return(0);
 96: }

100: PetscErrorCode  KSPSetUp_DGMRES(KSP ksp)
101: {
103:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
104:   PetscInt       neig    = dgmres->neig+EIG_OFFSET;
105:   PetscInt       max_k   = dgmres->max_k+1;

108:   KSPSetUp_GMRES(ksp);
109:   if (!dgmres->neig) return(0);

111:   /* Allocate workspace for the Schur vectors*/
112:   PetscMalloc1(neig*max_k, &SR);
113:   dgmres->wr    = NULL;
114:   dgmres->wi    = NULL;
115:   dgmres->perm  = NULL;
116:   dgmres->modul = NULL;
117:   dgmres->Q     = NULL;
118:   dgmres->Z     = NULL;

120:   UU   = NULL;
121:   XX   = NULL;
122:   MX   = NULL;
123:   AUU  = NULL;
124:   XMX  = NULL;
125:   XMU  = NULL;
126:   UMX  = NULL;
127:   AUAU = NULL;
128:   TT   = NULL;
129:   TTF  = NULL;
130:   INVP = NULL;
131:   X1   = NULL;
132:   X2   = NULL;
133:   MU   = NULL;
134:   return(0);
135: }

137: /*
138:  Run GMRES, possibly with restart.  Return residual history if requested.
139:  input parameters:

141:  .       gmres  - structure containing parameters and work areas

143:  output parameters:
144:  .        nres    - residuals (from preconditioned system) at each step.
145:  If restarting, consider passing nres+it.  If null,
146:  ignored
147:  .        itcount - number of iterations used.  nres[0] to nres[itcount]
148:  are defined.  If null, ignored.

150:  Notes:
151:  On entry, the value in vector VEC_VV(0) should be the initial residual
152:  (this allows shortcuts where the initial preconditioned residual is 0).
153:  */
156: PetscErrorCode KSPDGMRESCycle(PetscInt *itcount,KSP ksp)
157: {
158:   KSP_DGMRES     *dgmres = (KSP_DGMRES*)(ksp->data);
159:   PetscReal      res_norm,res,hapbnd,tt;
161:   PetscInt       it     = 0;
162:   PetscInt       max_k  = dgmres->max_k;
163:   PetscBool      hapend = PETSC_FALSE;
164:   PetscReal      res_old;
165:   PetscInt       test = 0;

168:   VecNormalize(VEC_VV(0),&res_norm);
169:   KSPCheckNorm(ksp,res_norm);
170:   res     = res_norm;
171:   *GRS(0) = res_norm;

173:   /* check for the convergence */
174:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
175:   ksp->rnorm = res;
176:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
177:   dgmres->it = (it - 1);
178:   KSPLogResidualHistory(ksp,res);
179:   KSPMonitor(ksp,ksp->its,res);
180:   if (!res) {
181:     if (itcount) *itcount = 0;
182:     ksp->reason = KSP_CONVERGED_ATOL;
183:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
184:     return(0);
185:   }
186:   /* record the residual norm to test if deflation is needed */
187:   res_old = res;

189:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
190:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
191:     if (it) {
192:       KSPLogResidualHistory(ksp,res);
193:       KSPMonitor(ksp,ksp->its,res);
194:     }
195:     dgmres->it = (it - 1);
196:     if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) {
197:       KSPDGMRESGetNewVectors(ksp,it+1);
198:     }
199:     if (dgmres->r > 0) {
200:       if (ksp->pc_side == PC_LEFT) {
201:         /* Apply the first preconditioner */
202:         KSP_PCApplyBAorAB(ksp,VEC_VV(it), VEC_TEMP,VEC_TEMP_MATOP);
203:         /* Then apply Deflation as a preconditioner */
204:         KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1+it));
205:       } else if (ksp->pc_side == PC_RIGHT) {
206:         KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP);
207:         KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1+it), VEC_TEMP_MATOP);
208:       }
209:     } else {
210:       KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
211:     }
212:     dgmres->matvecs += 1;
213:     /* update hessenberg matrix and do Gram-Schmidt */
214:     (*dgmres->orthog)(ksp,it);

216:     /* vv(i+1) . vv(i+1) */
217:     VecNormalize(VEC_VV(it+1),&tt);
218:     /* save the magnitude */
219:     *HH(it+1,it)  = tt;
220:     *HES(it+1,it) = tt;

222:     /* check for the happy breakdown */
223:     hapbnd = PetscAbsScalar(tt / *GRS(it));
224:     if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
225:     if (tt < hapbnd) {
226:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
227:       hapend = PETSC_TRUE;
228:     }
229:     KSPDGMRESUpdateHessenberg(ksp,it,hapend,&res);

231:     it++;
232:     dgmres->it = (it-1);     /* For converged */
233:     ksp->its++;
234:     ksp->rnorm = res;
235:     if (ksp->reason) break;

237:     (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);

239:     /* Catch error in happy breakdown and signal convergence and break from loop */
240:     if (hapend) {
241:       if (!ksp->reason) {
242:         if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res);
243:         else {
244:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
245:           break;
246:         }
247:       }
248:     }
249:   }

251:   /* Monitor if we know that we will not return for a restart */
252:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
253:     KSPLogResidualHistory(ksp,res);
254:     KSPMonitor(ksp,ksp->its,res);
255:   }
256:   if (itcount) *itcount = it;

258:   /*
259:    Down here we have to solve for the "best" coefficients of the Krylov
260:    columns, add the solution values together, and possibly unwind the
261:    preconditioning from the solution
262:    */
263:   /* Form the solution (or the solution so far) */
264:   KSPDGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

266:   /* Compute data for the deflation to be used during the next restart */
267:   if (!ksp->reason && ksp->its < ksp->max_it) {
268:     test = max_k *PetscLogReal(ksp->rtol/res) /PetscLogReal(res/res_old);
269:     /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed  */
270:     if ((test > dgmres->smv*(ksp->max_it-ksp->its)) || dgmres->force) {
271:        KSPDGMRESComputeDeflationData(ksp);
272:     }
273:   }
274:   return(0);
275: }

279: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
280: {
282:   PetscInt       i,its,itcount;
283:   KSP_DGMRES     *dgmres    = (KSP_DGMRES*) ksp->data;
284:   PetscBool      guess_zero = ksp->guess_zero;

287:   if (ksp->calc_sings && !dgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

289:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
290:   ksp->its        = 0;
291:   dgmres->matvecs = 0;
292:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

294:   itcount     = 0;
295:   ksp->reason = KSP_CONVERGED_ITERATING;
296:   while (!ksp->reason) {
297:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
298:     if (ksp->pc_side == PC_LEFT) {
299:       dgmres->matvecs += 1;
300:       if (dgmres->r > 0) {
301:         KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP);
302:         VecCopy(VEC_TEMP, VEC_VV(0));
303:       }
304:     }

306:     KSPDGMRESCycle(&its,ksp);
307:     itcount += its;
308:     if (itcount >= ksp->max_it) {
309:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
310:       break;
311:     }
312:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
313:   }
314:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */

316:   for (i = 0; i < dgmres->r; i++) {
317:     VecViewFromOptions(UU[i],(PetscObject)ksp,"-ksp_dgmres_view_deflation_vecs");
318:   }
319:   return(0);
320: }

324: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
325: {
327:   KSP_DGMRES     *dgmres  = (KSP_DGMRES*) ksp->data;
328:   PetscInt       neig1    = dgmres->neig+EIG_OFFSET;
329:   PetscInt       max_neig = dgmres->max_neig;

332:   if (dgmres->r) {
333:     VecDestroyVecs(max_neig, &UU);
334:     VecDestroyVecs(max_neig, &MU);
335:     if (XX) {
336:       VecDestroyVecs(neig1, &XX);
337:       VecDestroyVecs(neig1, &MX);
338:     }

340:     PetscFree(TT);
341:     PetscFree(TTF);
342:     PetscFree(INVP);

344:     PetscFree(XMX);
345:     PetscFree(UMX);
346:     PetscFree(XMU);
347:     PetscFree(X1);
348:     PetscFree(X2);
349:     PetscFree(dgmres->work);
350:     PetscFree(dgmres->iwork);
351:     PetscFree(dgmres->wr);
352:     PetscFree(dgmres->wi);
353:     PetscFree(dgmres->modul);
354:     PetscFree(dgmres->Q);
355:     PetscFree(ORTH);
356:     PetscFree(AUAU);
357:     PetscFree(AUU);
358:     PetscFree(SR2);
359:   }
360:   PetscFree(SR);
361:   KSPDestroy_GMRES(ksp);
362:   return(0);
363: }
364: /*
365:  KSPDGMRESBuildSoln - create the solution from the starting vector and the
366:  current iterates.

368:  Input parameters:
369:  nrs - work area of size it + 1.
370:  vs  - index of initial guess
371:  vdest - index of result.  Note that vs may == vdest (replace
372:  guess with the solution).

374:  This is an internal routine that knows about the GMRES internals.
375:  */
378: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
379: {
380:   PetscScalar    tt;
382:   PetscInt       ii,k,j;
383:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) (ksp->data);

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

388:   /* If it is < 0, no gmres steps have been performed */
389:   if (it < 0) {
390:     VecCopy(vs,vdest);     /* VecCopy() is smart, exists immediately if vguess == vdest */
391:     return(0);
392:   }
393:   if (*HH(it,it) == 0.0) SETERRQ2(PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED,"Likely your matrix is the zero operator. HH(it,it) is identically zero; it = %D GRS(it) = %g",it,(double)PetscAbsScalar(*GRS(it)));
394:   if (*HH(it,it) != 0.0) nrs[it] = *GRS(it) / *HH(it,it);
395:   else nrs[it] = 0.0;

397:   for (ii=1; ii<=it; ii++) {
398:     k  = it - ii;
399:     tt = *GRS(k);
400:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
401:     if (*HH(k,k) == 0.0) SETERRQ2(PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED,"Likely your matrix is singular. HH(k,k) is identically zero; it = %D k = %D",it,k);
402:     nrs[k] = tt / *HH(k,k);
403:   }

405:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
406:   VecSet(VEC_TEMP,0.0);
407:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));

409:   /* Apply deflation */
410:   if (ksp->pc_side==PC_RIGHT && dgmres->r > 0) {
411:     KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP);
412:     VecCopy(VEC_TEMP_MATOP, VEC_TEMP);
413:   }
414:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

416:   /* add solution to previous solution */
417:   if (vdest != vs) {
418:     VecCopy(vs,vdest);
419:   }
420:   VecAXPY(vdest,1.0,VEC_TEMP);
421:   return(0);
422: }
423: /*
424:  Do the scalar work for the orthogonalization.  Return new residual norm.
425:  */
428: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
429: {
430:   PetscScalar *hh,*cc,*ss,tt;
431:   PetscInt    j;
432:   KSP_DGMRES  *dgmres = (KSP_DGMRES*) (ksp->data);

435:   hh = HH(0,it);
436:   cc = CC(0);
437:   ss = SS(0);

439:   /* Apply all the previously computed plane rotations to the new column
440:    of the Hessenberg matrix */
441:   for (j=1; j<=it; j++) {
442:     tt  = *hh;
443:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
444:     hh++;
445:     *hh = *cc++ * *hh -(*ss++ * tt);
446:   }

448:   /*
449:    compute the new plane rotation, and apply it to:
450:    1) the right-hand-side of the Hessenberg system
451:    2) the new column of the Hessenberg matrix
452:    thus obtaining the updated value of the residual
453:    */
454:   if (!hapend) {
455:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
456:     if (tt == 0.0) {
457:       ksp->reason = KSP_DIVERGED_NULL;
458:       return(0);
459:     }
460:     *cc        = *hh / tt;
461:     *ss        = *(hh+1) / tt;
462:     *GRS(it+1) = -(*ss * *GRS(it));
463:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
464:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
465:     *res       = PetscAbsScalar(*GRS(it+1));
466:   } else {
467:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
468:      another rotation matrix (so RH doesn't change).  The new residual is
469:      always the new sine term times the residual from last time (GRS(it)),
470:      but now the new sine rotation would be zero...so the residual should
471:      be zero...so we will multiply "zero" by the last residual.  This might
472:      not be exactly what we want to do here -could just return "zero". */

474:     *res = 0.0;
475:   }
476:   return(0);
477: }
478: /*
479:  This routine allocates more work vectors, starting from VEC_VV(it).
480:  */
483: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp,PetscInt it)
484: {
485:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
487:   PetscInt       nwork = dgmres->nwork_alloc,k,nalloc;

490:   nalloc = PetscMin(ksp->max_it,dgmres->delta_allocate);
491:   /* Adjust the number to allocate to make sure that we don't exceed the
492:    number of available slots */
493:   if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) {
494:     nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
495:   }
496:   if (!nalloc) return(0);

498:   dgmres->vv_allocated += nalloc;

500:   KSPCreateVecs(ksp,nalloc,&dgmres->user_work[nwork],0,NULL);
501:   PetscLogObjectParents(ksp,nalloc,dgmres->user_work[nwork]);

503:   dgmres->mwork_alloc[nwork] = nalloc;
504:   for (k=0; k<nalloc; k++) {
505:     dgmres->vecs[it+VEC_OFFSET+k] = dgmres->user_work[nwork][k];
506:   }
507:   dgmres->nwork_alloc++;
508:   return(0);
509: }

513: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp,Vec ptr,Vec *result)
514: {
515:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;

519:   if (!ptr) {
520:     if (!dgmres->sol_temp) {
521:       VecDuplicate(ksp->vec_sol,&dgmres->sol_temp);
522:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)dgmres->sol_temp);
523:     }
524:     ptr = dgmres->sol_temp;
525:   }
526:   if (!dgmres->nrs) {
527:     /* allocate the work area */
528:     PetscMalloc1(dgmres->max_k,&dgmres->nrs);
529:     PetscLogObjectMemory((PetscObject)ksp,dgmres->max_k*sizeof(PetscScalar));
530:   }

532:   KSPDGMRESBuildSoln(dgmres->nrs,ksp->vec_sol,ptr,ksp,dgmres->it);
533:   if (result) *result = ptr;
534:   return(0);
535: }

539: PetscErrorCode KSPView_DGMRES(KSP ksp,PetscViewer viewer)
540: {
541:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
543:   PetscBool      iascii,isharmonic;

546:   KSPView_GMRES(ksp,viewer);
547:   PetscObjectTypeCompare((PetscObject) viewer,PETSCVIEWERASCII,&iascii);
548:   if (iascii) {
549:     if (dgmres->force) PetscViewerASCIIPrintf(viewer, "   DGMRES: Adaptive strategy is used: FALSE\n");
550:     else PetscViewerASCIIPrintf(viewer, "   DGMRES: Adaptive strategy is used: TRUE\n");
551:     PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &isharmonic);
552:     if (isharmonic) {
553:       PetscViewerASCIIPrintf(viewer, "  DGMRES: Frequency of extracted eigenvalues = %D using Harmonic Ritz values \n", dgmres->neig);
554:     } else {
555:       PetscViewerASCIIPrintf(viewer, "  DGMRES: Frequency of extracted eigenvalues = %D using Ritz values \n", dgmres->neig);
556:     }
557:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Total number of extracted eigenvalues = %D\n", dgmres->r);
558:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Maximum number of eigenvalues set to be extracted = %D\n", dgmres->max_neig);
559:     PetscViewerASCIIPrintf(viewer, "  DGMRES: relaxation parameter for the adaptive strategy(smv)  = %g\n", dgmres->smv);
560:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Number of matvecs : %D\n", dgmres->matvecs);
561:   }
562:   return(0);
563: }

565: /* New DGMRES functions */

569: static PetscErrorCode  KSPDGMRESSetEigen_DGMRES(KSP ksp,PetscInt neig)
570: {
571:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

574:   if (neig< 0 && neig >dgmres->max_k) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The value of neig must be positive and less than the restart value ");
575:   dgmres->neig=neig;
576:   return(0);
577: }

581: static PetscErrorCode  KSPDGMRESSetMaxEigen_DGMRES(KSP ksp,PetscInt max_neig)
582: {
583:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

586:   if (max_neig < 0 && max_neig >dgmres->max_k) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The value of max_neig must be positive and less than the restart value ");
587:   dgmres->max_neig=max_neig;
588:   return(0);
589: }

593: static PetscErrorCode  KSPDGMRESSetRatio_DGMRES(KSP ksp,PetscReal ratio)
594: {
595:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

598:   if (ratio <= 0) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The relaxation parameter value must be positive");
599:   dgmres->smv=ratio;
600:   return(0);
601: }

605: static PetscErrorCode  KSPDGMRESForce_DGMRES(KSP ksp,PetscBool force)
606: {
607:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

610:   dgmres->force = force;
611:   return(0);
612: }

614: extern PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP);

618: PetscErrorCode KSPSetFromOptions_DGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
619: {
621:   PetscInt       neig;
622:   PetscInt       max_neig;
623:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
624:   PetscBool      flg;

627:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
628:   PetscOptionsHead(PetscOptionsObject,"KSP DGMRES Options");
629:   PetscOptionsInt("-ksp_dgmres_eigen","Number of smallest eigenvalues to extract at each restart","KSPDGMRESSetEigen",dgmres->neig, &neig, &flg);
630:   if (flg) {
631:     KSPDGMRESSetEigen(ksp, neig);
632:   }
633:   PetscOptionsInt("-ksp_dgmres_max_eigen","Maximum Number of smallest eigenvalues to extract ","KSPDGMRESSetMaxEigen",dgmres->max_neig, &max_neig, &flg);
634:   if (flg) {
635:     KSPDGMRESSetMaxEigen(ksp, max_neig);
636:   }
637:   PetscOptionsReal("-ksp_dgmres_ratio","Relaxation parameter for the smaller number of matrix-vectors product allowed","KSPDGMRESSetRatio",dgmres->smv,&dgmres->smv,NULL);
638:   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);
639:   PetscOptionsBool("-ksp_dgmres_force","Sets DGMRES always at restart active, i.e do not use the adaptive strategy","KSPDGMRESForce",dgmres->force,&dgmres->force,NULL);
640:   PetscOptionsTail();
641:   return(0);
642: }

646: static PetscErrorCode  KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
647: {
648:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
650:   PetscInt       i,j, k;
651:   PetscBLASInt   nr, bmax;
652:   PetscInt       r = dgmres->r;
653:   PetscInt       neig;          /* number of eigenvalues to extract at each restart */
654:   PetscInt       neig1    = dgmres->neig + EIG_OFFSET;  /* max number of eig that can be extracted at each restart */
655:   PetscInt       max_neig = dgmres->max_neig;  /* Max number of eigenvalues to extract during the iterative process */
656:   PetscInt       N        = dgmres->max_k+1;
657:   PetscInt       n        = dgmres->it+1;
658:   PetscReal      alpha;

661:   PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
662:   if (dgmres->neig == 0 || (max_neig < (r+neig1) && !dgmres->improve)) {
663:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
664:     return(0);
665:   }

667:    KSPDGMRESComputeSchurForm(ksp, &neig);
668:   /* Form the extended Schur vectors X=VV*Sr */
669:   if (!XX) {
670:     VecDuplicateVecs(VEC_VV(0), neig1, &XX);
671:   }
672:   for (j = 0; j<neig; j++) {
673:     VecZeroEntries(XX[j]);
674:     VecMAXPY(XX[j], n, &SR[j*N], &VEC_VV(0));
675:   }

677:   /* Orthogonalize X against U */
678:   if (!ORTH) {
679:     PetscMalloc1(max_neig, &ORTH);
680:   }
681:   if (r > 0) {
682:     /* modified Gram-Schmidt */
683:     for (j = 0; j<neig; j++) {
684:       for (i=0; i<r; i++) {
685:         /* First, compute U'*X[j] */
686:         VecDot(XX[j], UU[i], &alpha);
687:         /* Then, compute X(j)=X(j)-U*U'*X(j) */
688:         VecAXPY(XX[j], -alpha, UU[i]);
689:       }
690:     }
691:   }
692:   /* Compute MX = M^{-1}*A*X */
693:   if (!MX) {
694:     VecDuplicateVecs(VEC_VV(0), neig1, &MX);
695:   }
696:   for (j = 0; j<neig; j++) {
697:     KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP);
698:   }
699:   dgmres->matvecs += neig;

701:   if ((r+neig1) > max_neig && dgmres->improve) {    /* Improve the approximate eigenvectors in X by solving a new generalized eigenvalue -- Quite expensive to do this actually */
702:     KSPDGMRESImproveEig(ksp, neig);
703:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
704:     return(0);   /* We return here since data for M have been improved in  KSPDGMRESImproveEig()*/
705:   }

707:   /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
708:   if (!XMX) {
709:     PetscMalloc1(neig1*neig1, &XMX);
710:   }
711:   for (j = 0; j < neig; j++) {
712:     VecMDot(MX[j], neig, XX, &(XMX[j*neig1]));
713:   }

715:   if (r > 0) {
716:     /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
717:     if (!UMX) {
718:       PetscMalloc1(max_neig*neig1, &UMX);
719:     }
720:     for (j = 0; j < neig; j++) {
721:       VecMDot(MX[j], r, UU, &(UMX[j*max_neig]));
722:     }
723:     /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
724:     if (!XMU) {
725:       PetscMalloc1(max_neig*neig1, &XMU);
726:     }
727:     for (j = 0; j<r; j++) {
728:       VecMDot(MU[j], neig, XX, &(XMU[j*neig1]));
729:     }
730:   }

732:   /* Form the new matrix T = [T UMX; XMU XMX]; */
733:   if (!TT) {
734:     PetscMalloc1(max_neig*max_neig, &TT);
735:   }
736:   if (r > 0) {
737:     /* Add XMU to T */
738:     for (j = 0; j < r; j++) {
739:       PetscMemcpy(&(TT[max_neig*j+r]), &(XMU[neig1*j]), neig*sizeof(PetscReal));
740:     }
741:     /* Add [UMX; XMX] to T */
742:     for (j = 0; j < neig; j++) {
743:       k = r+j;
744:       PetscMemcpy(&(TT[max_neig*k]), &(UMX[max_neig*j]), r*sizeof(PetscReal));
745:       PetscMemcpy(&(TT[max_neig*k + r]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
746:     }
747:   } else { /* Add XMX to T */
748:     for (j = 0; j < neig; j++) {
749:       PetscMemcpy(&(TT[max_neig*j]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
750:     }
751:   }

753:   dgmres->r += neig;
754:   r          = dgmres->r;
755:   PetscBLASIntCast(r,&nr);
756:   /*LU Factorize T with Lapack xgetrf routine */

758:   PetscBLASIntCast(max_neig,&bmax);
759:   if (!TTF) {
760:     PetscMalloc1(bmax*bmax, &TTF);
761:   }
762:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
763:   if (!INVP) {
764:     PetscMalloc1(bmax, &INVP);
765:   }
766: #if defined(PETSC_MISSING_LAPACK_GETRF)
767:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
768: #else
769:   {
770:     PetscBLASInt info;
771:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
772:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
773:   }
774: #endif

776:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
777:   if (!UU) {
778:     VecDuplicateVecs(VEC_VV(0), max_neig, &UU);
779:     VecDuplicateVecs(VEC_VV(0), max_neig, &MU);
780:   }
781:   for (j=0; j<neig; j++) {
782:     VecCopy(XX[j], UU[r-neig+j]);
783:     VecCopy(MX[j], MU[r-neig+j]);
784:   }
785:   PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
786:   return(0);
787: }

791: static PetscErrorCode  KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
792: {
793:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
795:   PetscInt       N = dgmres->max_k + 1, n=dgmres->it+1;
796:   PetscBLASInt   bn, bN;
797:   PetscReal      *A;
798:   PetscBLASInt   ihi;
799:   PetscBLASInt   ldA;          /* leading dimension of A */
800:   PetscBLASInt   ldQ;          /* leading dimension of Q */
801:   PetscReal      *Q;           /*  orthogonal matrix of  (left) schur vectors */
802:   PetscReal      *work;        /* working vector */
803:   PetscBLASInt   lwork;        /* size of the working vector */
804:   PetscInt       *perm;        /* Permutation vector to sort eigenvalues */
805:   PetscInt       i, j;
806:   PetscBLASInt   NbrEig;       /* Number of eigenvalues really extracted */
807:   PetscReal      *wr, *wi, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
808:   PetscBLASInt   *select;
809:   PetscBLASInt   *iwork;
810:   PetscBLASInt   liwork;
811:   PetscScalar    *Ht;           /* Transpose of the Hessenberg matrix */
812:   PetscScalar    *t;            /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
813:   PetscBLASInt   *ipiv;         /* Permutation vector to be used in LAPACK */
814:   PetscBool      flag;            /* determine whether to use Ritz vectors or harmonic Ritz vectors */

817:   PetscBLASIntCast(n,&bn);
818:   PetscBLASIntCast(N,&bN);
819:   ihi  = ldQ = bn;
820:   ldA  = bN;
821:   PetscBLASIntCast(5*N,&lwork);

823: #if defined(PETSC_USE_COMPLEX)
824:   SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "NO SUPPORT FOR COMPLEX VALUES AT THIS TIME");
825: #endif

827:   PetscMalloc1(ldA*ldA, &A);
828:   PetscMalloc1(ldQ*n, &Q);
829:   PetscMalloc1(lwork, &work);
830:   if (!dgmres->wr) {
831:     PetscMalloc1(n, &dgmres->wr);
832:     PetscMalloc1(n, &dgmres->wi);
833:   }
834:   wr   = dgmres->wr;
835:   wi   = dgmres->wi;
836:   PetscMalloc1(n,&modul);
837:   PetscMalloc1(n,&perm);
838:   /* copy the Hessenberg matrix to work space */
839:   PetscMemcpy(A, dgmres->hes_origin, ldA*ldA*sizeof(PetscReal));
840:   PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag);
841:   if (flag) {
842:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
843:     /* Transpose the Hessenberg matrix */
844:     PetscMalloc1(bn*bn, &Ht);
845:     for (i = 0; i < bn; i++) {
846:       for (j = 0; j < bn; j++) {
847:         Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
848:       }
849:     }

851:     /* Solve the system H^T*t = h_{m+1,m}e_m */
852:     PetscCalloc1(bn, &t);
853:     t[bn-1] = dgmres->hes_origin[(bn -1) * ldA + bn]; /* Pick the last element H(m+1,m) */
854:     PetscMalloc1(bn, &ipiv);
855:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
856: #if   defined(PETSC_MISSING_LAPACK_GESV)
857:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GESV - Lapack routine is unavailable.");
858: #else
859:     {
860:       PetscBLASInt info;
861:       PetscBLASInt nrhs = 1;
862:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
863:       if (info) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB, "Error while calling the Lapack routine DGESV");
864:     }
865: #endif
866:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
867:     for (i = 0; i < bn; i++) A[(bn-1)*bn+i] += t[i];
868:     PetscFree(t);
869:     PetscFree(Ht);
870:   }
871:   /* Compute eigenvalues with the Schur form */
872: #if defined(PETSC_MISSING_LAPACK_HSEQR)
873:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable.");
874: #else
875:   {
876:     PetscBLASInt info;
877:     PetscBLASInt ilo = 1;
878:     PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
879:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XHSEQR %d",(int) info);
880:   }
881: #endif
882:   PetscFree(work);

884:   /* sort the eigenvalues */
885:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
886:   for (i=0; i<n; i++) perm[i] = i;

888:   PetscSortRealWithPermutation(n, modul, perm);
889:   /* save the complex modulus of the largest eigenvalue in magnitude */
890:   if (dgmres->lambdaN < modul[perm[n-1]]) dgmres->lambdaN=modul[perm[n-1]];
891:   /* count the number of extracted eigenvalues (with complex conjugates) */
892:   NbrEig = 0;
893:   while (NbrEig < dgmres->neig) {
894:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
895:     else NbrEig += 1;
896:   }
897:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

899:   PetscCalloc1(n, &select);

901:   if (!dgmres->GreatestEig) {
902:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
903:   } else {
904:     for (j = 0; j < NbrEig; j++) select[perm[n-j-1]] = 1;
905:   }
906:   /* call Lapack dtrsen */
907:   lwork  =  PetscMax(1, 4 * NbrEig *(bn-NbrEig));
908:   liwork = PetscMax(1, 2 * NbrEig *(bn-NbrEig));
909:   PetscMalloc1(lwork, &work);
910:   PetscMalloc1(liwork, &iwork);
911: #if defined(PETSC_MISSING_LAPACK_TRSEN)
912:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable.");
913: #else
914:   {
915:     PetscBLASInt info;
916:     PetscReal    CondEig;         /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
917:     PetscReal    CondSub;         /* estimated reciprocal condition number of the specified invariant subspace. */
918:     PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
919:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
920:   }
921: #endif
922:   PetscFree(select);

924:   /* Extract the Schur vectors */
925:   for (j = 0; j < NbrEig; j++) {
926:     PetscMemcpy(&SR[j*N], &(Q[j*ldQ]), n*sizeof(PetscReal));
927:   }
928:   *neig = NbrEig;
929:   PetscFree(A);
930:   PetscFree(work);
931:   PetscFree(perm);
932:   PetscFree(work);
933:   PetscFree(iwork);
934:   PetscFree(modul);
935:   PetscFree(Q);
936:   return(0);
937: }

941: static PetscErrorCode  KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
942: {
943:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
944:   PetscInt       i, r     = dgmres->r;
946:   PetscReal      alpha    = 1.0;
947:   PetscInt       max_neig = dgmres->max_neig;
948:   PetscBLASInt   br,bmax;
949:   PetscReal      lambda = dgmres->lambdaN;

952:   PetscBLASIntCast(r,&br);
953:   PetscBLASIntCast(max_neig,&bmax);
954:   PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
955:   if (!r) {
956:     VecCopy(x,y);
957:     return(0);
958:   }
959:   /* Compute U'*x */
960:   if (!X1) {
961:     PetscMalloc1(bmax, &X1);
962:     PetscMalloc1(bmax, &X2);
963:   }
964:   VecMDot(x, r, UU, X1);

966:   /* Solve T*X1=X2 for X1*/
967:   PetscMemcpy(X2, X1, br*sizeof(PetscReal));
968: #if defined(PETSC_MISSING_LAPACK_GETRS)
969:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable.");
970: #else
971:   {
972:     PetscBLASInt info;
973:     PetscBLASInt nrhs = 1;
974:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
975:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRS %d", (int) info);
976:   }
977: #endif
978:   /* Iterative refinement -- is it really necessary ?? */
979:   if (!WORK) {
980:     PetscMalloc1(3*bmax, &WORK);
981:     PetscMalloc1(bmax, &IWORK);
982:   }
983: #if defined(PETSC_MISSING_LAPACK_GERFS)
984:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GERFS - Lapack routine is unavailable.");
985: #else
986:   {
987:     PetscBLASInt info;
988:     PetscReal    berr, ferr;
989:     PetscBLASInt nrhs = 1;
990:     PetscStackCallBLAS("LAPACKgerfs",LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax,X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
991:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGERFS %d", (int) info);
992:   }
993: #endif

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

997:   /* Compute X2=U*X2 */
998:   VecZeroEntries(y);
999:   VecMAXPY(y, r, X2, UU);
1000:   VecAXPY(y, alpha, x);

1002:   PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
1003:   return(0);
1004: }

1008: static PetscErrorCode  KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
1009: {
1010:   KSP_DGMRES   *dgmres = (KSP_DGMRES*) ksp->data;
1011:   PetscInt     j,r_old, r = dgmres->r;
1012:   PetscBLASInt i     = 0;
1013:   PetscInt     neig1 = dgmres->neig + EIG_OFFSET;
1014:   PetscInt     bmax  = dgmres->max_neig;
1015:   PetscInt     aug   = r + neig;         /* actual size of the augmented invariant basis */
1016:   PetscInt     aug1  = bmax+neig1;       /* maximum size of the augmented invariant basis */
1017:   PetscBLASInt ldA;            /* leading dimension of AUAU and AUU*/
1018:   PetscBLASInt N;              /* size of AUAU */
1019:   PetscReal    *Q;             /*  orthogonal matrix of  (left) schur vectors */
1020:   PetscReal    *Z;             /*  orthogonal matrix of  (right) schur vectors */
1021:   PetscReal    *work;          /* working vector */
1022:   PetscBLASInt lwork;          /* size of the working vector */
1023:   PetscInt     *perm;          /* Permutation vector to sort eigenvalues */
1024:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
1025:   PetscInt     ierr;
1026:   PetscBLASInt NbrEig = 0,nr,bm;
1027:   PetscBLASInt *select;
1028:   PetscBLASInt liwork, *iwork;

1031:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
1032:   if (!AUU) {
1033:     PetscMalloc1(aug1*aug1, &AUU);
1034:     PetscMalloc1(aug1*aug1, &AUAU);
1035:   }
1036:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
1037:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
1038:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
1039:   for (j=0; j < r; j++) {
1040:     VecMDot(UU[j], r, MU, &AUU[j*aug1]);
1041:   }
1042:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
1043:   for (j = 0; j < neig; j++) {
1044:     VecMDot(XX[j], r, MU, &AUU[(r+j) *aug1]);
1045:   }
1046:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
1047:   for (j = 0; j < r; j++) {
1048:     VecMDot(UU[j], neig, MX, &AUU[j*aug1+r]);
1049:   }
1050:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
1051:   for (j = 0; j < neig; j++) {
1052:     VecMDot(XX[j], neig, MX, &AUU[(r+j) *aug1 + r]);
1053:   }

1055:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
1056:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
1057:   for (j=0; j < r; j++) {
1058:     VecMDot(MU[j], r, MU, &AUAU[j*aug1]);
1059:   }
1060:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
1061:   for (j = 0; j < neig; j++) {
1062:     VecMDot(MX[j], r, MU, &AUAU[(r+j) *aug1]);
1063:   }
1064:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
1065:   for (j = 0; j < r; j++) {
1066:     VecMDot(MU[j], neig, MX, &AUAU[j*aug1+r]);
1067:   }
1068:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
1069:   for (j = 0; j < neig; j++) {
1070:     VecMDot(MX[j], neig, MX, &AUAU[(r+j) *aug1 + r]);
1071:   }

1073:   /* Computation of the eigenvectors */
1074:   PetscBLASIntCast(aug1,&ldA);
1075:   PetscBLASIntCast(aug,&N);
1076:   lwork = 8 * N + 20; /* sizeof the working space */
1077:   PetscMalloc1(N, &wr);
1078:   PetscMalloc1(N, &wi);
1079:   PetscMalloc1(N, &beta);
1080:   PetscMalloc1(N, &modul);
1081:   PetscMalloc1(N, &perm);
1082:   PetscMalloc1(N*N, &Q);
1083:   PetscMalloc1(N*N, &Z);
1084:   PetscMalloc1(lwork, &work);
1085: #if defined(PETSC_MISSING_LAPACK_GGES)
1086:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
1087: #else
1088:   {
1089:     PetscBLASInt info;
1090:     PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
1091:     if (info) SETERRQ1 (PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGGES %d", (int) info);
1092:   }
1093: #endif
1094:   for (i=0; i<N; i++) {
1095:     if (beta[i] !=0.0) {
1096:       wr[i] /=beta[i];
1097:       wi[i] /=beta[i];
1098:     }
1099:   }
1100:   /* sort the eigenvalues */
1101:   for (i=0; i<N; i++) modul[i]=PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
1102:   for (i=0; i<N; i++) perm[i] = i;
1103:   PetscSortRealWithPermutation(N, modul, perm);
1104:   /* Save the norm of the largest eigenvalue */
1105:   if (dgmres->lambdaN < modul[perm[N-1]]) dgmres->lambdaN = modul[perm[N-1]];
1106:   /* Allocate space to extract the first r schur vectors   */
1107:   if (!SR2) {
1108:     PetscMalloc1(aug1*bmax, &SR2);
1109:   }
1110:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
1111:   while (NbrEig < bmax) {
1112:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
1113:     else NbrEig += 2;
1114:   }
1115:   if (NbrEig > bmax) NbrEig = bmax - 1;
1116:   r_old     = r; /* previous size of r */
1117:   dgmres->r = r = NbrEig;

1119:   /* Select the eigenvalues to reorder */
1120:   PetscCalloc1(N, &select);
1121:   if (!dgmres->GreatestEig) {
1122:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
1123:   } else {
1124:     for (j = 0; j < NbrEig; j++) select[perm[N-j-1]] = 1;
1125:   }
1126:   /* Reorder and extract the new <r> schur vectors */
1127:   lwork  = PetscMax(4 * N + 16,  2 * NbrEig *(N - NbrEig));
1128:   liwork = PetscMax(N + 6,  2 * NbrEig *(N - NbrEig));
1129:   PetscFree(work);
1130:   PetscMalloc1(lwork, &work);
1131:   PetscMalloc1(liwork, &iwork);
1132: #if defined(PETSC_MISSING_LAPACK_TGSEN)
1133:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable.");
1134: #else
1135:   {
1136:     PetscBLASInt info;
1137:     PetscReal    Dif[2];
1138:     PetscBLASInt ijob  = 2;
1139:     PetscBLASInt wantQ = 1, wantZ = 1;
1140:     PetscStackCallBLAS("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));
1141:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
1142:   }
1143: #endif
1144:   PetscFree(select);

1146:   for (j=0; j<r; j++) {
1147:     PetscMemcpy(&SR2[j*aug1], &(Z[j*N]), N*sizeof(PetscReal));
1148:   }

1150:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
1151:    -- save it temporarily in MU */
1152:   for (j = 0; j < r; j++) {
1153:     VecZeroEntries(MU[j]);
1154:     VecMAXPY(MU[j], r_old, &SR2[j*aug1], UU);
1155:     VecMAXPY(MU[j], neig, &SR2[j*aug1+r_old], XX);
1156:   }
1157:   /* Form T = U'*MU*U */
1158:   for (j = 0; j < r; j++) {
1159:     VecCopy(MU[j], UU[j]);
1160:     KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP);
1161:   }
1162:   dgmres->matvecs += r;
1163:   for (j = 0; j < r; j++) {
1164:     VecMDot(MU[j], r, UU, &TT[j*bmax]);
1165:   }
1166:   /* Factorize T */
1167:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
1168:   PetscBLASIntCast(r,&nr);
1169:   PetscBLASIntCast(bmax,&bm);
1170: #if defined(PETSC_MISSING_LAPACK_GETRF)
1171:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
1172: #else
1173:   {
1174:     PetscBLASInt info;
1175:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
1176:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
1177:   }
1178: #endif
1179:   /* Free Memory */
1180:   PetscFree(wr);
1181:   PetscFree(wi);
1182:   PetscFree(beta);
1183:   PetscFree(modul);
1184:   PetscFree(perm);
1185:   PetscFree(Q);
1186:   PetscFree(Z);
1187:   PetscFree(work);
1188:   PetscFree(iwork);
1189:   return(0);
1190: }

1192: /* end new DGMRES functions */

1194: /*MC
1195:      KSPDGMRES - Implements the deflated GMRES as defined in [1,2].
1196:                  In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the
1197:                  stagnation occurs.

1199:    Options Database Keys:
1200:    GMRES Options (inherited):
1201: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
1202: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
1203: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
1204:                              vectors are allocated as needed)
1205: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
1206: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
1207: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
1208:                                    stability of the classical Gram-Schmidt  orthogonalization.
1209: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

1211:    DGMRES Options Database Keys:
1212: +   -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
1213: .   -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative
1214:                                        process
1215: .   -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
1216: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
1217:                                                    parsed by PetscOptionsGetViewer().  If neig > 1, viewerspec should
1218:                                                    end with ":append".  No vectors will be viewed if the adaptive
1219:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
1220:                                                    be given.
1221:                                                    The deflation vectors span a subspace that may be a good
1222:                                                    approximation of the subspace of smallest eigenvectors of the
1223:                                                    preconditioned operator, so this option can aid in understanding
1224:                                                    the performance of a preconditioner.

1226:  Level: beginner

1228:  Notes: Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

1230:  References:
1231: +  1. - J. Erhel, K. Burrage and B. Pohl,  Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).
1232: -  2. - D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, 
1233:    In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

1235:  Contributed by: Desire NUENTSA WAKAM,INRIA

1237:  .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
1238:  KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
1239:  KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
1240:  KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

1242:  M*/

1246: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
1247: {
1248:   KSP_DGMRES     *dgmres;

1252:   PetscNewLog(ksp,&dgmres);
1253:   ksp->data = (void*) dgmres;

1255:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
1256:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

1258:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
1259:   ksp->ops->setup                        = KSPSetUp_DGMRES;
1260:   ksp->ops->solve                        = KSPSolve_DGMRES;
1261:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
1262:   ksp->ops->view                         = KSPView_DGMRES;
1263:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
1264:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
1265:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

1267:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
1268:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
1269:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
1270:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
1271:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
1272:   /* -- New functions defined in DGMRES -- */
1273:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C",KSPDGMRESSetEigen_DGMRES);
1274:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C",KSPDGMRESSetMaxEigen_DGMRES);
1275:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C",KSPDGMRESSetRatio_DGMRES);
1276:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C",KSPDGMRESForce_DGMRES);
1277:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C",KSPDGMRESComputeSchurForm_DGMRES);
1278:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C",KSPDGMRESComputeDeflationData_DGMRES);
1279:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C",KSPDGMRESApplyDeflation_DGMRES);
1280:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES);

1282:   PetscLogEventRegister("DGMRESComputeDefl", KSP_CLASSID, &KSP_DGMRESComputeDeflationData);
1283:   PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation);

1285:   dgmres->haptol         = 1.0e-30;
1286:   dgmres->q_preallocate  = 0;
1287:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
1288:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
1289:   dgmres->nrs            = 0;
1290:   dgmres->sol_temp       = 0;
1291:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
1292:   dgmres->Rsvd           = 0;
1293:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
1294:   dgmres->orthogwork     = 0;

1296:   /* Default values for the deflation */
1297:   dgmres->r           = 0;
1298:   dgmres->neig        = DGMRES_DEFAULT_EIG;
1299:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG-1;
1300:   dgmres->lambdaN     = 0.0;
1301:   dgmres->smv         = SMV;
1302:   dgmres->matvecs     = 0;
1303:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
1304:   dgmres->HasSchur    = PETSC_FALSE;
1305:   return(0);
1306: }