Actual source code: dgmres.c

petsc-3.13.4 2020-08-01
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  1: /*
  2:  This file implements the deflated GMRES.

  4:  */

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

  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);

 16: PetscErrorCode  KSPDGMRESSetEigen(KSP ksp,PetscInt nb_eig)
 17: {

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

 29:   PetscTryMethod((ksp),"KSPDGMRESSetMaxEigen_C",(KSP,PetscInt),(ksp,max_neig));
 30:   return(0);
 31: }
 32: PetscErrorCode  KSPDGMRESForce(KSP ksp,PetscBool force)
 33: {

 37:   PetscTryMethod((ksp),"KSPDGMRESForce_C",(KSP,PetscBool),(ksp,force));
 38:   return(0);
 39: }
 40: PetscErrorCode  KSPDGMRESSetRatio(KSP ksp,PetscReal ratio)
 41: {

 45:   PetscTryMethod((ksp),"KSPDGMRESSetRatio_C",(KSP,PetscReal),(ksp,ratio));
 46:   return(0);
 47: }
 48: PetscErrorCode  KSPDGMRESComputeSchurForm(KSP ksp,PetscInt *neig)
 49: {

 53:   PetscUseMethod((ksp),"KSPDGMRESComputeSchurForm_C",(KSP, PetscInt*),(ksp, neig));
 54:   return(0);
 55: }
 56: PetscErrorCode  KSPDGMRESComputeDeflationData(KSP ksp,PetscInt *curneigh)
 57: {

 61:   PetscUseMethod((ksp),"KSPDGMRESComputeDeflationData_C",(KSP,PetscInt*),(ksp,curneigh));
 62:   return(0);
 63: }
 64: PetscErrorCode  KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
 65: {

 69:   PetscUseMethod((ksp),"KSPDGMRESApplyDeflation_C",(KSP, Vec, Vec),(ksp, x, y));
 70:   return(0);
 71: }

 73: PetscErrorCode  KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
 74: {

 78:   PetscUseMethod((ksp), "KSPDGMRESImproveEig_C",(KSP, PetscInt),(ksp, neig));
 79:   return(0);
 80: }

 82: PetscErrorCode  KSPSetUp_DGMRES(KSP ksp)
 83: {
 85:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
 86:   PetscInt       neig    = dgmres->neig+EIG_OFFSET;
 87:   PetscInt       max_k   = dgmres->max_k+1;

 90:   KSPSetUp_GMRES(ksp);
 91:   if (!dgmres->neig) return(0);

 93:   /* Allocate workspace for the Schur vectors*/
 94:   PetscMalloc1(neig*max_k, &SR);
 95:   dgmres->wr    = NULL;
 96:   dgmres->wi    = NULL;
 97:   dgmres->perm  = NULL;
 98:   dgmres->modul = NULL;
 99:   dgmres->Q     = NULL;
100:   dgmres->Z     = NULL;

102:   UU   = NULL;
103:   XX   = NULL;
104:   MX   = NULL;
105:   AUU  = NULL;
106:   XMX  = NULL;
107:   XMU  = NULL;
108:   UMX  = NULL;
109:   AUAU = NULL;
110:   TT   = NULL;
111:   TTF  = NULL;
112:   INVP = NULL;
113:   X1   = NULL;
114:   X2   = NULL;
115:   MU   = NULL;
116:   return(0);
117: }

119: /*
120:  Run GMRES, possibly with restart.  Return residual history if requested.
121:  input parameters:

123:  .       gmres  - structure containing parameters and work areas

125:  output parameters:
126:  .        nres    - residuals (from preconditioned system) at each step.
127:  If restarting, consider passing nres+it.  If null,
128:  ignored
129:  .        itcount - number of iterations used.  nres[0] to nres[itcount]
130:  are defined.  If null, ignored.

132:  Notes:
133:  On entry, the value in vector VEC_VV(0) should be the initial residual
134:  (this allows shortcuts where the initial preconditioned residual is 0).
135:  */
136: PetscErrorCode KSPDGMRESCycle(PetscInt *itcount,KSP ksp)
137: {
138:   KSP_DGMRES     *dgmres = (KSP_DGMRES*)(ksp->data);
139:   PetscReal      res_norm,res,hapbnd,tt;
141:   PetscInt       it     = 0;
142:   PetscInt       max_k  = dgmres->max_k;
143:   PetscBool      hapend = PETSC_FALSE;
144:   PetscReal      res_old;
145:   PetscInt       test = 0;

148:   VecNormalize(VEC_VV(0),&res_norm);
149:   KSPCheckNorm(ksp,res_norm);
150:   res     = res_norm;
151:   *GRS(0) = res_norm;

153:   /* check for the convergence */
154:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
155:   ksp->rnorm = res;
156:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
157:   dgmres->it = (it - 1);
158:   KSPLogResidualHistory(ksp,res);
159:   KSPMonitor(ksp,ksp->its,res);
160:   if (!res) {
161:     if (itcount) *itcount = 0;
162:     ksp->reason = KSP_CONVERGED_ATOL;
163:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
164:     return(0);
165:   }
166:   /* record the residual norm to test if deflation is needed */
167:   res_old = res;

169:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
170:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
171:     if (it) {
172:       KSPLogResidualHistory(ksp,res);
173:       KSPMonitor(ksp,ksp->its,res);
174:     }
175:     dgmres->it = (it - 1);
176:     if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) {
177:       KSPDGMRESGetNewVectors(ksp,it+1);
178:     }
179:     if (dgmres->r > 0) {
180:       if (ksp->pc_side == PC_LEFT) {
181:         /* Apply the first preconditioner */
182:         KSP_PCApplyBAorAB(ksp,VEC_VV(it), VEC_TEMP,VEC_TEMP_MATOP);
183:         /* Then apply Deflation as a preconditioner */
184:         KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1+it));
185:       } else if (ksp->pc_side == PC_RIGHT) {
186:         KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP);
187:         KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1+it), VEC_TEMP_MATOP);
188:       }
189:     } else {
190:       KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
191:     }
192:     dgmres->matvecs += 1;
193:     /* update hessenberg matrix and do Gram-Schmidt */
194:     (*dgmres->orthog)(ksp,it);

196:     /* vv(i+1) . vv(i+1) */
197:     VecNormalize(VEC_VV(it+1),&tt);
198:     /* save the magnitude */
199:     *HH(it+1,it)  = tt;
200:     *HES(it+1,it) = tt;

202:     /* check for the happy breakdown */
203:     hapbnd = PetscAbsScalar(tt / *GRS(it));
204:     if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
205:     if (tt < hapbnd) {
206:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
207:       hapend = PETSC_TRUE;
208:     }
209:     KSPDGMRESUpdateHessenberg(ksp,it,hapend,&res);

211:     it++;
212:     dgmres->it = (it-1);     /* For converged */
213:     ksp->its++;
214:     ksp->rnorm = res;
215:     if (ksp->reason) break;

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

219:     /* Catch error in happy breakdown and signal convergence and break from loop */
220:     if (hapend) {
221:       if (!ksp->reason) {
222:         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);
223:         else {
224:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
225:           break;
226:         }
227:       }
228:     }
229:   }

231:   /* Monitor if we know that we will not return for a restart */
232:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
233:     KSPLogResidualHistory(ksp,res);
234:     KSPMonitor(ksp,ksp->its,res);
235:   }
236:   if (itcount) *itcount = it;

238:   /*
239:    Down here we have to solve for the "best" coefficients of the Krylov
240:    columns, add the solution values together, and possibly unwind the
241:    preconditioning from the solution
242:    */
243:   /* Form the solution (or the solution so far) */
244:   KSPDGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

246:   /* Compute data for the deflation to be used during the next restart */
247:   if (!ksp->reason && ksp->its < ksp->max_it) {
248:     test = max_k *PetscLogReal(ksp->rtol/res) /PetscLogReal(res/res_old);
249:     /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed  */
250:     if ((test > dgmres->smv*(ksp->max_it-ksp->its)) || dgmres->force) {
251:        KSPDGMRESComputeDeflationData(ksp,NULL);
252:     }
253:   }
254:   return(0);
255: }

257: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
258: {
260:   PetscInt       i,its,itcount;
261:   KSP_DGMRES     *dgmres    = (KSP_DGMRES*) ksp->data;
262:   PetscBool      guess_zero = ksp->guess_zero;

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

267:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
268:   ksp->its        = 0;
269:   dgmres->matvecs = 0;
270:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

272:   itcount     = 0;
273:   ksp->reason = KSP_CONVERGED_ITERATING;
274:   while (!ksp->reason) {
275:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
276:     if (ksp->pc_side == PC_LEFT) {
277:       dgmres->matvecs += 1;
278:       if (dgmres->r > 0) {
279:         KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP);
280:         VecCopy(VEC_TEMP, VEC_VV(0));
281:       }
282:     }

284:     KSPDGMRESCycle(&its,ksp);
285:     itcount += its;
286:     if (itcount >= ksp->max_it) {
287:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
288:       break;
289:     }
290:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
291:   }
292:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */

294:   for (i = 0; i < dgmres->r; i++) {
295:     VecViewFromOptions(UU[i],(PetscObject)ksp,"-ksp_dgmres_view_deflation_vecs");
296:   }
297:   return(0);
298: }

300: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
301: {
303:   KSP_DGMRES     *dgmres  = (KSP_DGMRES*) ksp->data;
304:   PetscInt       neig1    = dgmres->neig+EIG_OFFSET;
305:   PetscInt       max_neig = dgmres->max_neig;

308:   if (dgmres->r) {
309:     VecDestroyVecs(max_neig, &UU);
310:     VecDestroyVecs(max_neig, &MU);
311:     if (XX) {
312:       VecDestroyVecs(neig1, &XX);
313:       VecDestroyVecs(neig1, &MX);
314:     }

316:     PetscFree(TT);
317:     PetscFree(TTF);
318:     PetscFree(INVP);

320:     PetscFree(XMX);
321:     PetscFree(UMX);
322:     PetscFree(XMU);
323:     PetscFree(X1);
324:     PetscFree(X2);
325:     PetscFree(dgmres->work);
326:     PetscFree(dgmres->iwork);
327:     PetscFree(dgmres->wr);
328:     PetscFree(dgmres->wi);
329:     PetscFree(dgmres->modul);
330:     PetscFree(dgmres->Q);
331:     PetscFree(ORTH);
332:     PetscFree(AUAU);
333:     PetscFree(AUU);
334:     PetscFree(SR2);
335:   }
336:   PetscFree(SR);
337:   KSPDestroy_GMRES(ksp);
338:   return(0);
339: }
340: /*
341:  KSPDGMRESBuildSoln - create the solution from the starting vector and the
342:  current iterates.

344:  Input parameters:
345:  nrs - work area of size it + 1.
346:  vs  - index of initial guess
347:  vdest - index of result.  Note that vs may == vdest (replace
348:  guess with the solution).

350:  This is an internal routine that knows about the GMRES internals.
351:  */
352: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
353: {
354:   PetscScalar    tt;
356:   PetscInt       ii,k,j;
357:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) (ksp->data);

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

362:   /* If it is < 0, no gmres steps have been performed */
363:   if (it < 0) {
364:     VecCopy(vs,vdest);     /* VecCopy() is smart, exists immediately if vguess == vdest */
365:     return(0);
366:   }
367:   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)));
368:   if (*HH(it,it) != 0.0) nrs[it] = *GRS(it) / *HH(it,it);
369:   else nrs[it] = 0.0;

371:   for (ii=1; ii<=it; ii++) {
372:     k  = it - ii;
373:     tt = *GRS(k);
374:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
375:     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);
376:     nrs[k] = tt / *HH(k,k);
377:   }

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

383:   /* Apply deflation */
384:   if (ksp->pc_side==PC_RIGHT && dgmres->r > 0) {
385:     KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP);
386:     VecCopy(VEC_TEMP_MATOP, VEC_TEMP);
387:   }
388:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

390:   /* add solution to previous solution */
391:   if (vdest != vs) {
392:     VecCopy(vs,vdest);
393:   }
394:   VecAXPY(vdest,1.0,VEC_TEMP);
395:   return(0);
396: }
397: /*
398:  Do the scalar work for the orthogonalization.  Return new residual norm.
399:  */
400: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
401: {
402:   PetscScalar *hh,*cc,*ss,tt;
403:   PetscInt    j;
404:   KSP_DGMRES  *dgmres = (KSP_DGMRES*) (ksp->data);

407:   hh = HH(0,it);
408:   cc = CC(0);
409:   ss = SS(0);

411:   /* Apply all the previously computed plane rotations to the new column
412:    of the Hessenberg matrix */
413:   for (j=1; j<=it; j++) {
414:     tt  = *hh;
415:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
416:     hh++;
417:     *hh = *cc++ * *hh -(*ss++ * tt);
418:   }

420:   /*
421:    compute the new plane rotation, and apply it to:
422:    1) the right-hand-side of the Hessenberg system
423:    2) the new column of the Hessenberg matrix
424:    thus obtaining the updated value of the residual
425:    */
426:   if (!hapend) {
427:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
428:     if (tt == 0.0) {
429:       ksp->reason = KSP_DIVERGED_NULL;
430:       return(0);
431:     }
432:     *cc        = *hh / tt;
433:     *ss        = *(hh+1) / tt;
434:     *GRS(it+1) = -(*ss * *GRS(it));
435:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
436:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
437:     *res       = PetscAbsScalar(*GRS(it+1));
438:   } else {
439:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
440:      another rotation matrix (so RH doesn't change).  The new residual is
441:      always the new sine term times the residual from last time (GRS(it)),
442:      but now the new sine rotation would be zero...so the residual should
443:      be zero...so we will multiply "zero" by the last residual.  This might
444:      not be exactly what we want to do here -could just return "zero". */

446:     *res = 0.0;
447:   }
448:   return(0);
449: }
450: /*
451:  This routine allocates more work vectors, starting from VEC_VV(it).
452:  */
453: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp,PetscInt it)
454: {
455:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
457:   PetscInt       nwork = dgmres->nwork_alloc,k,nalloc;

460:   nalloc = PetscMin(ksp->max_it,dgmres->delta_allocate);
461:   /* Adjust the number to allocate to make sure that we don't exceed the
462:    number of available slots */
463:   if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) {
464:     nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
465:   }
466:   if (!nalloc) return(0);

468:   dgmres->vv_allocated += nalloc;

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

473:   dgmres->mwork_alloc[nwork] = nalloc;
474:   for (k=0; k<nalloc; k++) {
475:     dgmres->vecs[it+VEC_OFFSET+k] = dgmres->user_work[nwork][k];
476:   }
477:   dgmres->nwork_alloc++;
478:   return(0);
479: }

481: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp,Vec ptr,Vec *result)
482: {
483:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;

487:   if (!ptr) {
488:     if (!dgmres->sol_temp) {
489:       VecDuplicate(ksp->vec_sol,&dgmres->sol_temp);
490:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)dgmres->sol_temp);
491:     }
492:     ptr = dgmres->sol_temp;
493:   }
494:   if (!dgmres->nrs) {
495:     /* allocate the work area */
496:     PetscMalloc1(dgmres->max_k,&dgmres->nrs);
497:     PetscLogObjectMemory((PetscObject)ksp,dgmres->max_k*sizeof(PetscScalar));
498:   }

500:   KSPDGMRESBuildSoln(dgmres->nrs,ksp->vec_sol,ptr,ksp,dgmres->it);
501:   if (result) *result = ptr;
502:   return(0);
503: }

505: PetscErrorCode KSPView_DGMRES(KSP ksp,PetscViewer viewer)
506: {
507:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
509:   PetscBool      iascii,isharmonic;

512:   KSPView_GMRES(ksp,viewer);
513:   PetscObjectTypeCompare((PetscObject) viewer,PETSCVIEWERASCII,&iascii);
514:   if (iascii) {
515:     if (dgmres->force) PetscViewerASCIIPrintf(viewer, "    Adaptive strategy is used: FALSE\n");
516:     else PetscViewerASCIIPrintf(viewer, "    Adaptive strategy is used: TRUE\n");
517:     PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &isharmonic);
518:     if (isharmonic) {
519:       PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %D using Harmonic Ritz values \n", dgmres->neig);
520:     } else {
521:       PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %D using Ritz values \n", dgmres->neig);
522:     }
523:     PetscViewerASCIIPrintf(viewer, "   Total number of extracted eigenvalues = %D\n", dgmres->r);
524:     PetscViewerASCIIPrintf(viewer, "   Maximum number of eigenvalues set to be extracted = %D\n", dgmres->max_neig);
525:     PetscViewerASCIIPrintf(viewer, "   relaxation parameter for the adaptive strategy(smv)  = %g\n", dgmres->smv);
526:     PetscViewerASCIIPrintf(viewer, "   Number of matvecs : %D\n", dgmres->matvecs);
527:   }
528:   return(0);
529: }

531: /* New DGMRES functions */

533: PetscErrorCode  KSPDGMRESSetEigen_DGMRES(KSP ksp,PetscInt neig)
534: {
535:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

538:   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 ");
539:   dgmres->neig=neig;
540:   return(0);
541: }

543: static PetscErrorCode  KSPDGMRESSetMaxEigen_DGMRES(KSP ksp,PetscInt max_neig)
544: {
545:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

548:   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 ");
549:   dgmres->max_neig=max_neig;
550:   return(0);
551: }

553: static PetscErrorCode  KSPDGMRESSetRatio_DGMRES(KSP ksp,PetscReal ratio)
554: {
555:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

558:   if (ratio <= 0) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The relaxation parameter value must be positive");
559:   dgmres->smv=ratio;
560:   return(0);
561: }

563: static PetscErrorCode  KSPDGMRESForce_DGMRES(KSP ksp,PetscBool force)
564: {
565:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

568:   dgmres->force = force;
569:   return(0);
570: }

572: PetscErrorCode KSPSetFromOptions_DGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
573: {
575:   PetscInt       neig;
576:   PetscInt       max_neig;
577:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
578:   PetscBool      flg;

581:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
582:   PetscOptionsHead(PetscOptionsObject,"KSP DGMRES Options");
583:   PetscOptionsInt("-ksp_dgmres_eigen","Number of smallest eigenvalues to extract at each restart","KSPDGMRESSetEigen",dgmres->neig, &neig, &flg);
584:   if (flg) {
585:     KSPDGMRESSetEigen(ksp, neig);
586:   }
587:   PetscOptionsInt("-ksp_dgmres_max_eigen","Maximum Number of smallest eigenvalues to extract ","KSPDGMRESSetMaxEigen",dgmres->max_neig, &max_neig, &flg);
588:   if (flg) {
589:     KSPDGMRESSetMaxEigen(ksp, max_neig);
590:   }
591:   PetscOptionsReal("-ksp_dgmres_ratio","Relaxation parameter for the smaller number of matrix-vectors product allowed","KSPDGMRESSetRatio",dgmres->smv,&dgmres->smv,NULL);
592:   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);
593:   PetscOptionsBool("-ksp_dgmres_force","Sets DGMRES always at restart active, i.e do not use the adaptive strategy","KSPDGMRESForce",dgmres->force,&dgmres->force,NULL);
594:   PetscOptionsTail();
595:   return(0);
596: }

598: PetscErrorCode  KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
599: {
600:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
602:   PetscInt       i,j, k;
603:   PetscBLASInt   nr, bmax;
604:   PetscInt       r = dgmres->r;
605:   PetscInt       neig;          /* number of eigenvalues to extract at each restart */
606:   PetscInt       neig1    = dgmres->neig + EIG_OFFSET;  /* max number of eig that can be extracted at each restart */
607:   PetscInt       max_neig = dgmres->max_neig;  /* Max number of eigenvalues to extract during the iterative process */
608:   PetscInt       N        = dgmres->max_k+1;
609:   PetscInt       n        = dgmres->it+1;
610:   PetscReal      alpha;

613:   PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
614:   if (dgmres->neig == 0 || (max_neig < (r+neig1) && !dgmres->improve)) {
615:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
616:     return(0);
617:   }

619:    KSPDGMRESComputeSchurForm(ksp, &neig);
620:   /* Form the extended Schur vectors X=VV*Sr */
621:   if (!XX) {
622:     VecDuplicateVecs(VEC_VV(0), neig1, &XX);
623:   }
624:   for (j = 0; j<neig; j++) {
625:     VecZeroEntries(XX[j]);
626:     VecMAXPY(XX[j], n, &SR[j*N], &VEC_VV(0));
627:   }

629:   /* Orthogonalize X against U */
630:   if (!ORTH) {
631:     PetscMalloc1(max_neig, &ORTH);
632:   }
633:   if (r > 0) {
634:     /* modified Gram-Schmidt */
635:     for (j = 0; j<neig; j++) {
636:       for (i=0; i<r; i++) {
637:         /* First, compute U'*X[j] */
638:         VecDot(XX[j], UU[i], &alpha);
639:         /* Then, compute X(j)=X(j)-U*U'*X(j) */
640:         VecAXPY(XX[j], -alpha, UU[i]);
641:       }
642:     }
643:   }
644:   /* Compute MX = M^{-1}*A*X */
645:   if (!MX) {
646:     VecDuplicateVecs(VEC_VV(0), neig1, &MX);
647:   }
648:   for (j = 0; j<neig; j++) {
649:     KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP);
650:   }
651:   dgmres->matvecs += neig;

653:   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 */
654:     KSPDGMRESImproveEig(ksp, neig);
655:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
656:     return(0);   /* We return here since data for M have been improved in  KSPDGMRESImproveEig()*/
657:   }

659:   /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
660:   if (!XMX) {
661:     PetscMalloc1(neig1*neig1, &XMX);
662:   }
663:   for (j = 0; j < neig; j++) {
664:     VecMDot(MX[j], neig, XX, &(XMX[j*neig1]));
665:   }

667:   if (r > 0) {
668:     /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
669:     if (!UMX) {
670:       PetscMalloc1(max_neig*neig1, &UMX);
671:     }
672:     for (j = 0; j < neig; j++) {
673:       VecMDot(MX[j], r, UU, &(UMX[j*max_neig]));
674:     }
675:     /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
676:     if (!XMU) {
677:       PetscMalloc1(max_neig*neig1, &XMU);
678:     }
679:     for (j = 0; j<r; j++) {
680:       VecMDot(MU[j], neig, XX, &(XMU[j*neig1]));
681:     }
682:   }

684:   /* Form the new matrix T = [T UMX; XMU XMX]; */
685:   if (!TT) {
686:     PetscMalloc1(max_neig*max_neig, &TT);
687:   }
688:   if (r > 0) {
689:     /* Add XMU to T */
690:     for (j = 0; j < r; j++) {
691:       PetscArraycpy(&(TT[max_neig*j+r]), &(XMU[neig1*j]), neig);
692:     }
693:     /* Add [UMX; XMX] to T */
694:     for (j = 0; j < neig; j++) {
695:       k = r+j;
696:       PetscArraycpy(&(TT[max_neig*k]), &(UMX[max_neig*j]), r);
697:       PetscArraycpy(&(TT[max_neig*k + r]), &(XMX[neig1*j]), neig);
698:     }
699:   } else { /* Add XMX to T */
700:     for (j = 0; j < neig; j++) {
701:       PetscArraycpy(&(TT[max_neig*j]), &(XMX[neig1*j]), neig);
702:     }
703:   }

705:   dgmres->r += neig;
706:   r          = dgmres->r;
707:   PetscBLASIntCast(r,&nr);
708:   /*LU Factorize T with Lapack xgetrf routine */

710:   PetscBLASIntCast(max_neig,&bmax);
711:   if (!TTF) {
712:     PetscMalloc1(bmax*bmax, &TTF);
713:   }
714:   PetscArraycpy(TTF, TT, bmax*r);
715:   if (!INVP) {
716:     PetscMalloc1(bmax, &INVP);
717:   }
718:   {
719:     PetscBLASInt info;
720:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
721:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
722:   }

724:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
725:   if (!UU) {
726:     VecDuplicateVecs(VEC_VV(0), max_neig, &UU);
727:     VecDuplicateVecs(VEC_VV(0), max_neig, &MU);
728:   }
729:   for (j=0; j<neig; j++) {
730:     VecCopy(XX[j], UU[r-neig+j]);
731:     VecCopy(MX[j], MU[r-neig+j]);
732:   }
733:   PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
734:   return(0);
735: }

737: PetscErrorCode  KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
738: {
739:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
741:   PetscInt       N = dgmres->max_k + 1, n=dgmres->it+1;
742:   PetscBLASInt   bn, bN;
743:   PetscReal      *A;
744:   PetscBLASInt   ihi;
745:   PetscBLASInt   ldA;          /* leading dimension of A */
746:   PetscBLASInt   ldQ;          /* leading dimension of Q */
747:   PetscReal      *Q;           /*  orthogonal matrix of  (left) schur vectors */
748:   PetscReal      *work;        /* working vector */
749:   PetscBLASInt   lwork;        /* size of the working vector */
750:   PetscInt       *perm;        /* Permutation vector to sort eigenvalues */
751:   PetscInt       i, j;
752:   PetscBLASInt   NbrEig;       /* Number of eigenvalues really extracted */
753:   PetscReal      *wr, *wi, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
754:   PetscBLASInt   *select;
755:   PetscBLASInt   *iwork;
756:   PetscBLASInt   liwork;
757:   PetscScalar    *Ht;           /* Transpose of the Hessenberg matrix */
758:   PetscScalar    *t;            /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
759:   PetscBLASInt   *ipiv;         /* Permutation vector to be used in LAPACK */
760:   PetscBool      flag;            /* determine whether to use Ritz vectors or harmonic Ritz vectors */

763:   PetscBLASIntCast(n,&bn);
764:   PetscBLASIntCast(N,&bN);
765:   ihi  = ldQ = bn;
766:   ldA  = bN;
767:   PetscBLASIntCast(5*N,&lwork);

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

773:   PetscMalloc1(ldA*ldA, &A);
774:   PetscMalloc1(ldQ*n, &Q);
775:   PetscMalloc1(lwork, &work);
776:   if (!dgmres->wr) {
777:     PetscMalloc1(n, &dgmres->wr);
778:     PetscMalloc1(n, &dgmres->wi);
779:   }
780:   wr   = dgmres->wr;
781:   wi   = dgmres->wi;
782:   PetscMalloc1(n,&modul);
783:   PetscMalloc1(n,&perm);
784:   /* copy the Hessenberg matrix to work space */
785:   PetscArraycpy(A, dgmres->hes_origin, ldA*ldA);
786:   PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag);
787:   if (flag) {
788:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
789:     /* Transpose the Hessenberg matrix */
790:     PetscMalloc1(bn*bn, &Ht);
791:     for (i = 0; i < bn; i++) {
792:       for (j = 0; j < bn; j++) {
793:         Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
794:       }
795:     }

797:     /* Solve the system H^T*t = h_{m+1,m}e_m */
798:     PetscCalloc1(bn, &t);
799:     t[bn-1] = dgmres->hes_origin[(bn -1) * ldA + bn]; /* Pick the last element H(m+1,m) */
800:     PetscMalloc1(bn, &ipiv);
801:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
802:     {
803:       PetscBLASInt info;
804:       PetscBLASInt nrhs = 1;
805:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
806:       if (info) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB, "Error while calling the Lapack routine DGESV");
807:     }
808:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
809:     for (i = 0; i < bn; i++) A[(bn-1)*bn+i] += t[i];
810:     PetscFree(t);
811:     PetscFree(Ht);
812:   }
813:   /* Compute eigenvalues with the Schur form */
814:   {
815:     PetscBLASInt info=0;
816:     PetscBLASInt ilo = 1;
817:     PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
818:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XHSEQR %d",(int) info);
819:   }
820:   PetscFree(work);

822:   /* sort the eigenvalues */
823:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
824:   for (i=0; i<n; i++) perm[i] = i;

826:   PetscSortRealWithPermutation(n, modul, perm);
827:   /* save the complex modulus of the largest eigenvalue in magnitude */
828:   if (dgmres->lambdaN < modul[perm[n-1]]) dgmres->lambdaN=modul[perm[n-1]];
829:   /* count the number of extracted eigenvalues (with complex conjugates) */
830:   NbrEig = 0;
831:   while (NbrEig < dgmres->neig) {
832:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
833:     else NbrEig += 1;
834:   }
835:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

837:   PetscCalloc1(n, &select);

839:   if (!dgmres->GreatestEig) {
840:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
841:   } else {
842:     for (j = 0; j < NbrEig; j++) select[perm[n-j-1]] = 1;
843:   }
844:   /* call Lapack dtrsen */
845:   lwork  =  PetscMax(1, 4 * NbrEig *(bn-NbrEig));
846:   liwork = PetscMax(1, 2 * NbrEig *(bn-NbrEig));
847:   PetscMalloc1(lwork, &work);
848:   PetscMalloc1(liwork, &iwork);
849:   {
850:     PetscBLASInt info=0;
851:     PetscReal    CondEig;         /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
852:     PetscReal    CondSub;         /* estimated reciprocal condition number of the specified invariant subspace. */
853:     PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
854:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
855:   }
856:   PetscFree(select);

858:   /* Extract the Schur vectors */
859:   for (j = 0; j < NbrEig; j++) {
860:     PetscArraycpy(&SR[j*N], &(Q[j*ldQ]), n);
861:   }
862:   *neig = NbrEig;
863:   PetscFree(A);
864:   PetscFree(work);
865:   PetscFree(perm);
866:   PetscFree(work);
867:   PetscFree(iwork);
868:   PetscFree(modul);
869:   PetscFree(Q);
870:   return(0);
871: }

873: PetscErrorCode  KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
874: {
875:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
876:   PetscInt       i, r     = dgmres->r;
878:   PetscReal      alpha    = 1.0;
879:   PetscInt       max_neig = dgmres->max_neig;
880:   PetscBLASInt   br,bmax;
881:   PetscReal      lambda = dgmres->lambdaN;

884:   PetscBLASIntCast(r,&br);
885:   PetscBLASIntCast(max_neig,&bmax);
886:   PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
887:   if (!r) {
888:     VecCopy(x,y);
889:     return(0);
890:   }
891:   /* Compute U'*x */
892:   if (!X1) {
893:     PetscMalloc1(bmax, &X1);
894:     PetscMalloc1(bmax, &X2);
895:   }
896:   VecMDot(x, r, UU, X1);

898:   /* Solve T*X1=X2 for X1*/
899:   PetscArraycpy(X2, X1, br);
900:   {
901:     PetscBLASInt info;
902:     PetscBLASInt nrhs = 1;
903:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
904:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRS %d", (int) info);
905:   }
906:   /* Iterative refinement -- is it really necessary ?? */
907:   if (!WORK) {
908:     PetscMalloc1(3*bmax, &WORK);
909:     PetscMalloc1(bmax, &IWORK);
910:   }
911:   {
912:     PetscBLASInt info;
913:     PetscReal    berr, ferr;
914:     PetscBLASInt nrhs = 1;
915:     PetscStackCallBLAS("LAPACKgerfs",LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax,X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
916:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGERFS %d", (int) info);
917:   }

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

921:   /* Compute X2=U*X2 */
922:   VecZeroEntries(y);
923:   VecMAXPY(y, r, X2, UU);
924:   VecAXPY(y, alpha, x);

926:   PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
927:   return(0);
928: }

930: static PetscErrorCode  KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
931: {
932:   KSP_DGMRES   *dgmres = (KSP_DGMRES*) ksp->data;
933:   PetscInt     j,r_old, r = dgmres->r;
934:   PetscBLASInt i     = 0;
935:   PetscInt     neig1 = dgmres->neig + EIG_OFFSET;
936:   PetscInt     bmax  = dgmres->max_neig;
937:   PetscInt     aug   = r + neig;         /* actual size of the augmented invariant basis */
938:   PetscInt     aug1  = bmax+neig1;       /* maximum size of the augmented invariant basis */
939:   PetscBLASInt ldA;            /* leading dimension of AUAU and AUU*/
940:   PetscBLASInt N;              /* size of AUAU */
941:   PetscReal    *Q;             /*  orthogonal matrix of  (left) schur vectors */
942:   PetscReal    *Z;             /*  orthogonal matrix of  (right) schur vectors */
943:   PetscReal    *work;          /* working vector */
944:   PetscBLASInt lwork;          /* size of the working vector */
945:   PetscInt     *perm;          /* Permutation vector to sort eigenvalues */
946:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
947:   PetscInt     ierr;
948:   PetscBLASInt NbrEig = 0,nr,bm;
949:   PetscBLASInt *select;
950:   PetscBLASInt liwork, *iwork;

953:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
954:   if (!AUU) {
955:     PetscMalloc1(aug1*aug1, &AUU);
956:     PetscMalloc1(aug1*aug1, &AUAU);
957:   }
958:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
959:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
960:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
961:   for (j=0; j < r; j++) {
962:     VecMDot(UU[j], r, MU, &AUU[j*aug1]);
963:   }
964:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
965:   for (j = 0; j < neig; j++) {
966:     VecMDot(XX[j], r, MU, &AUU[(r+j) *aug1]);
967:   }
968:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
969:   for (j = 0; j < r; j++) {
970:     VecMDot(UU[j], neig, MX, &AUU[j*aug1+r]);
971:   }
972:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
973:   for (j = 0; j < neig; j++) {
974:     VecMDot(XX[j], neig, MX, &AUU[(r+j) *aug1 + r]);
975:   }

977:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
978:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
979:   for (j=0; j < r; j++) {
980:     VecMDot(MU[j], r, MU, &AUAU[j*aug1]);
981:   }
982:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
983:   for (j = 0; j < neig; j++) {
984:     VecMDot(MX[j], r, MU, &AUAU[(r+j) *aug1]);
985:   }
986:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
987:   for (j = 0; j < r; j++) {
988:     VecMDot(MU[j], neig, MX, &AUAU[j*aug1+r]);
989:   }
990:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
991:   for (j = 0; j < neig; j++) {
992:     VecMDot(MX[j], neig, MX, &AUAU[(r+j) *aug1 + r]);
993:   }

995:   /* Computation of the eigenvectors */
996:   PetscBLASIntCast(aug1,&ldA);
997:   PetscBLASIntCast(aug,&N);
998:   lwork = 8 * N + 20; /* sizeof the working space */
999:   PetscMalloc1(N, &wr);
1000:   PetscMalloc1(N, &wi);
1001:   PetscMalloc1(N, &beta);
1002:   PetscMalloc1(N, &modul);
1003:   PetscMalloc1(N, &perm);
1004:   PetscMalloc1(N*N, &Q);
1005:   PetscMalloc1(N*N, &Z);
1006:   PetscMalloc1(lwork, &work);
1007:   {
1008:     PetscBLASInt info=0;
1009:     PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
1010:     if (info) SETERRQ1 (PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGGES %d", (int) info);
1011:   }
1012:   for (i=0; i<N; i++) {
1013:     if (beta[i] !=0.0) {
1014:       wr[i] /=beta[i];
1015:       wi[i] /=beta[i];
1016:     }
1017:   }
1018:   /* sort the eigenvalues */
1019:   for (i=0; i<N; i++) modul[i]=PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
1020:   for (i=0; i<N; i++) perm[i] = i;
1021:   PetscSortRealWithPermutation(N, modul, perm);
1022:   /* Save the norm of the largest eigenvalue */
1023:   if (dgmres->lambdaN < modul[perm[N-1]]) dgmres->lambdaN = modul[perm[N-1]];
1024:   /* Allocate space to extract the first r schur vectors   */
1025:   if (!SR2) {
1026:     PetscMalloc1(aug1*bmax, &SR2);
1027:   }
1028:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
1029:   while (NbrEig < bmax) {
1030:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
1031:     else NbrEig += 2;
1032:   }
1033:   if (NbrEig > bmax) NbrEig = bmax - 1;
1034:   r_old     = r; /* previous size of r */
1035:   dgmres->r = r = NbrEig;

1037:   /* Select the eigenvalues to reorder */
1038:   PetscCalloc1(N, &select);
1039:   if (!dgmres->GreatestEig) {
1040:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
1041:   } else {
1042:     for (j = 0; j < NbrEig; j++) select[perm[N-j-1]] = 1;
1043:   }
1044:   /* Reorder and extract the new <r> schur vectors */
1045:   lwork  = PetscMax(4 * N + 16,  2 * NbrEig *(N - NbrEig));
1046:   liwork = PetscMax(N + 6,  2 * NbrEig *(N - NbrEig));
1047:   PetscFree(work);
1048:   PetscMalloc1(lwork, &work);
1049:   PetscMalloc1(liwork, &iwork);
1050:   {
1051:     PetscBLASInt info=0;
1052:     PetscReal    Dif[2];
1053:     PetscBLASInt ijob  = 2;
1054:     PetscBLASInt wantQ = 1, wantZ = 1;
1055:     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));
1056:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
1057:   }
1058:   PetscFree(select);

1060:   for (j=0; j<r; j++) {
1061:     PetscArraycpy(&SR2[j*aug1], &(Z[j*N]), N);
1062:   }

1064:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
1065:    -- save it temporarily in MU */
1066:   for (j = 0; j < r; j++) {
1067:     VecZeroEntries(MU[j]);
1068:     VecMAXPY(MU[j], r_old, &SR2[j*aug1], UU);
1069:     VecMAXPY(MU[j], neig, &SR2[j*aug1+r_old], XX);
1070:   }
1071:   /* Form T = U'*MU*U */
1072:   for (j = 0; j < r; j++) {
1073:     VecCopy(MU[j], UU[j]);
1074:     KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP);
1075:   }
1076:   dgmres->matvecs += r;
1077:   for (j = 0; j < r; j++) {
1078:     VecMDot(MU[j], r, UU, &TT[j*bmax]);
1079:   }
1080:   /* Factorize T */
1081:   PetscArraycpy(TTF, TT, bmax*r);
1082:   PetscBLASIntCast(r,&nr);
1083:   PetscBLASIntCast(bmax,&bm);
1084:   {
1085:     PetscBLASInt info;
1086:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
1087:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
1088:   }
1089:   /* Free Memory */
1090:   PetscFree(wr);
1091:   PetscFree(wi);
1092:   PetscFree(beta);
1093:   PetscFree(modul);
1094:   PetscFree(perm);
1095:   PetscFree(Q);
1096:   PetscFree(Z);
1097:   PetscFree(work);
1098:   PetscFree(iwork);
1099:   return(0);
1100: }

1102: /* end new DGMRES functions */

1104: /*MC
1105:      KSPDGMRES - Implements the deflated GMRES as defined in [1,2].
1106:                  In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the
1107:                  stagnation occurs.

1109:    Options Database Keys:
1110:    GMRES Options (inherited):
1111: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
1112: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
1113: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
1114:                              vectors are allocated as needed)
1115: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
1116: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
1117: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
1118:                                    stability of the classical Gram-Schmidt  orthogonalization.
1119: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

1121:    DGMRES Options Database Keys:
1122: +   -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
1123: .   -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative
1124:                                        process
1125: .   -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
1126: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
1127:                                                    parsed by PetscOptionsGetViewer().  If neig > 1, viewerspec should
1128:                                                    end with ":append".  No vectors will be viewed if the adaptive
1129:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
1130:                                                    be given.
1131:                                                    The deflation vectors span a subspace that may be a good
1132:                                                    approximation of the subspace of smallest eigenvectors of the
1133:                                                    preconditioned operator, so this option can aid in understanding
1134:                                                    the performance of a preconditioner.

1136:  Level: beginner

1138:  Notes:
1139:     Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

1141:  References:
1142: +  1. - J. Erhel, K. Burrage and B. Pohl,  Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).
1143: -  2. - D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, 
1144:    In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

1146:  Contributed by: Desire NUENTSA WAKAM,INRIA

1148:  .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
1149:  KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
1150:  KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
1151:  KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

1153:  M*/

1155: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
1156: {
1157:   KSP_DGMRES     *dgmres;

1161:   PetscNewLog(ksp,&dgmres);
1162:   ksp->data = (void*) dgmres;

1164:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
1165:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

1167:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
1168:   ksp->ops->setup                        = KSPSetUp_DGMRES;
1169:   ksp->ops->solve                        = KSPSolve_DGMRES;
1170:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
1171:   ksp->ops->view                         = KSPView_DGMRES;
1172:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
1173:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
1174:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

1176:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
1177:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
1178:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
1179:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
1180:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
1181:   /* -- New functions defined in DGMRES -- */
1182:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C",KSPDGMRESSetEigen_DGMRES);
1183:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C",KSPDGMRESSetMaxEigen_DGMRES);
1184:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C",KSPDGMRESSetRatio_DGMRES);
1185:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C",KSPDGMRESForce_DGMRES);
1186:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C",KSPDGMRESComputeSchurForm_DGMRES);
1187:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C",KSPDGMRESComputeDeflationData_DGMRES);
1188:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C",KSPDGMRESApplyDeflation_DGMRES);
1189:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES);

1191:   PetscLogEventRegister("DGMRESCompDefl",  KSP_CLASSID, &KSP_DGMRESComputeDeflationData);
1192:   PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation);

1194:   dgmres->haptol         = 1.0e-30;
1195:   dgmres->q_preallocate  = 0;
1196:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
1197:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
1198:   dgmres->nrs            = 0;
1199:   dgmres->sol_temp       = 0;
1200:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
1201:   dgmres->Rsvd           = 0;
1202:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
1203:   dgmres->orthogwork     = 0;

1205:   /* Default values for the deflation */
1206:   dgmres->r           = 0;
1207:   dgmres->neig        = DGMRES_DEFAULT_EIG;
1208:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG-1;
1209:   dgmres->lambdaN     = 0.0;
1210:   dgmres->smv         = SMV;
1211:   dgmres->matvecs     = 0;
1212:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
1213:   dgmres->HasSchur    = PETSC_FALSE;
1214:   return(0);
1215: }