Actual source code: dgmres.c

petsc-3.8.3 2017-12-09
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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:       PetscMemcpy(&(TT[max_neig*j+r]), &(XMU[neig1*j]), neig*sizeof(PetscReal));
692:     }
693:     /* Add [UMX; XMX] to T */
694:     for (j = 0; j < neig; j++) {
695:       k = r+j;
696:       PetscMemcpy(&(TT[max_neig*k]), &(UMX[max_neig*j]), r*sizeof(PetscReal));
697:       PetscMemcpy(&(TT[max_neig*k + r]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
698:     }
699:   } else { /* Add XMX to T */
700:     for (j = 0; j < neig; j++) {
701:       PetscMemcpy(&(TT[max_neig*j]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
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:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
715:   if (!INVP) {
716:     PetscMalloc1(bmax, &INVP);
717:   }
718: #if defined(PETSC_MISSING_LAPACK_GETRF)
719:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
720: #else
721:   {
722:     PetscBLASInt info;
723:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
724:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
725:   }
726: #endif

728:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
729:   if (!UU) {
730:     VecDuplicateVecs(VEC_VV(0), max_neig, &UU);
731:     VecDuplicateVecs(VEC_VV(0), max_neig, &MU);
732:   }
733:   for (j=0; j<neig; j++) {
734:     VecCopy(XX[j], UU[r-neig+j]);
735:     VecCopy(MX[j], MU[r-neig+j]);
736:   }
737:   PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
738:   return(0);
739: }

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

767:   PetscBLASIntCast(n,&bn);
768:   PetscBLASIntCast(N,&bN);
769:   ihi  = ldQ = bn;
770:   ldA  = bN;
771:   PetscBLASIntCast(5*N,&lwork);

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

777:   PetscMalloc1(ldA*ldA, &A);
778:   PetscMalloc1(ldQ*n, &Q);
779:   PetscMalloc1(lwork, &work);
780:   if (!dgmres->wr) {
781:     PetscMalloc1(n, &dgmres->wr);
782:     PetscMalloc1(n, &dgmres->wi);
783:   }
784:   wr   = dgmres->wr;
785:   wi   = dgmres->wi;
786:   PetscMalloc1(n,&modul);
787:   PetscMalloc1(n,&perm);
788:   /* copy the Hessenberg matrix to work space */
789:   PetscMemcpy(A, dgmres->hes_origin, ldA*ldA*sizeof(PetscReal));
790:   PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag);
791:   if (flag) {
792:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
793:     /* Transpose the Hessenberg matrix */
794:     PetscMalloc1(bn*bn, &Ht);
795:     for (i = 0; i < bn; i++) {
796:       for (j = 0; j < bn; j++) {
797:         Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
798:       }
799:     }

801:     /* Solve the system H^T*t = h_{m+1,m}e_m */
802:     PetscCalloc1(bn, &t);
803:     t[bn-1] = dgmres->hes_origin[(bn -1) * ldA + bn]; /* Pick the last element H(m+1,m) */
804:     PetscMalloc1(bn, &ipiv);
805:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
806: #if   defined(PETSC_MISSING_LAPACK_GESV)
807:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GESV - Lapack routine is unavailable.");
808: #else
809:     {
810:       PetscBLASInt info;
811:       PetscBLASInt nrhs = 1;
812:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
813:       if (info) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB, "Error while calling the Lapack routine DGESV");
814:     }
815: #endif
816:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
817:     for (i = 0; i < bn; i++) A[(bn-1)*bn+i] += t[i];
818:     PetscFree(t);
819:     PetscFree(Ht);
820:   }
821:   /* Compute eigenvalues with the Schur form */
822: #if defined(PETSC_MISSING_LAPACK_HSEQR)
823:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable.");
824: #else
825:   {
826:     PetscBLASInt info;
827:     PetscBLASInt ilo = 1;
828:     PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
829:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XHSEQR %d",(int) info);
830:   }
831: #endif
832:   PetscFree(work);

834:   /* sort the eigenvalues */
835:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
836:   for (i=0; i<n; i++) perm[i] = i;

838:   PetscSortRealWithPermutation(n, modul, perm);
839:   /* save the complex modulus of the largest eigenvalue in magnitude */
840:   if (dgmres->lambdaN < modul[perm[n-1]]) dgmres->lambdaN=modul[perm[n-1]];
841:   /* count the number of extracted eigenvalues (with complex conjugates) */
842:   NbrEig = 0;
843:   while (NbrEig < dgmres->neig) {
844:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
845:     else NbrEig += 1;
846:   }
847:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

849:   PetscCalloc1(n, &select);

851:   if (!dgmres->GreatestEig) {
852:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
853:   } else {
854:     for (j = 0; j < NbrEig; j++) select[perm[n-j-1]] = 1;
855:   }
856:   /* call Lapack dtrsen */
857:   lwork  =  PetscMax(1, 4 * NbrEig *(bn-NbrEig));
858:   liwork = PetscMax(1, 2 * NbrEig *(bn-NbrEig));
859:   PetscMalloc1(lwork, &work);
860:   PetscMalloc1(liwork, &iwork);
861: #if defined(PETSC_MISSING_LAPACK_TRSEN)
862:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable.");
863: #else
864:   {
865:     PetscBLASInt info;
866:     PetscReal    CondEig;         /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
867:     PetscReal    CondSub;         /* estimated reciprocal condition number of the specified invariant subspace. */
868:     PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
869:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
870:   }
871: #endif
872:   PetscFree(select);

874:   /* Extract the Schur vectors */
875:   for (j = 0; j < NbrEig; j++) {
876:     PetscMemcpy(&SR[j*N], &(Q[j*ldQ]), n*sizeof(PetscReal));
877:   }
878:   *neig = NbrEig;
879:   PetscFree(A);
880:   PetscFree(work);
881:   PetscFree(perm);
882:   PetscFree(work);
883:   PetscFree(iwork);
884:   PetscFree(modul);
885:   PetscFree(Q);
886:   return(0);
887: }

889: PetscErrorCode  KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
890: {
891:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
892:   PetscInt       i, r     = dgmres->r;
894:   PetscReal      alpha    = 1.0;
895:   PetscInt       max_neig = dgmres->max_neig;
896:   PetscBLASInt   br,bmax;
897:   PetscReal      lambda = dgmres->lambdaN;

900:   PetscBLASIntCast(r,&br);
901:   PetscBLASIntCast(max_neig,&bmax);
902:   PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
903:   if (!r) {
904:     VecCopy(x,y);
905:     return(0);
906:   }
907:   /* Compute U'*x */
908:   if (!X1) {
909:     PetscMalloc1(bmax, &X1);
910:     PetscMalloc1(bmax, &X2);
911:   }
912:   VecMDot(x, r, UU, X1);

914:   /* Solve T*X1=X2 for X1*/
915:   PetscMemcpy(X2, X1, br*sizeof(PetscReal));
916: #if defined(PETSC_MISSING_LAPACK_GETRS)
917:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable.");
918: #else
919:   {
920:     PetscBLASInt info;
921:     PetscBLASInt nrhs = 1;
922:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
923:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRS %d", (int) info);
924:   }
925: #endif
926:   /* Iterative refinement -- is it really necessary ?? */
927:   if (!WORK) {
928:     PetscMalloc1(3*bmax, &WORK);
929:     PetscMalloc1(bmax, &IWORK);
930:   }
931: #if defined(PETSC_MISSING_LAPACK_GERFS)
932:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GERFS - Lapack routine is unavailable.");
933: #else
934:   {
935:     PetscBLASInt info;
936:     PetscReal    berr, ferr;
937:     PetscBLASInt nrhs = 1;
938:     PetscStackCallBLAS("LAPACKgerfs",LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax,X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
939:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGERFS %d", (int) info);
940:   }
941: #endif

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

945:   /* Compute X2=U*X2 */
946:   VecZeroEntries(y);
947:   VecMAXPY(y, r, X2, UU);
948:   VecAXPY(y, alpha, x);

950:   PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
951:   return(0);
952: }

954: static PetscErrorCode  KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
955: {
956:   KSP_DGMRES   *dgmres = (KSP_DGMRES*) ksp->data;
957:   PetscInt     j,r_old, r = dgmres->r;
958:   PetscBLASInt i     = 0;
959:   PetscInt     neig1 = dgmres->neig + EIG_OFFSET;
960:   PetscInt     bmax  = dgmres->max_neig;
961:   PetscInt     aug   = r + neig;         /* actual size of the augmented invariant basis */
962:   PetscInt     aug1  = bmax+neig1;       /* maximum size of the augmented invariant basis */
963:   PetscBLASInt ldA;            /* leading dimension of AUAU and AUU*/
964:   PetscBLASInt N;              /* size of AUAU */
965:   PetscReal    *Q;             /*  orthogonal matrix of  (left) schur vectors */
966:   PetscReal    *Z;             /*  orthogonal matrix of  (right) schur vectors */
967:   PetscReal    *work;          /* working vector */
968:   PetscBLASInt lwork;          /* size of the working vector */
969:   PetscInt     *perm;          /* Permutation vector to sort eigenvalues */
970:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
971:   PetscInt     ierr;
972:   PetscBLASInt NbrEig = 0,nr,bm;
973:   PetscBLASInt *select;
974:   PetscBLASInt liwork, *iwork;

977:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
978:   if (!AUU) {
979:     PetscMalloc1(aug1*aug1, &AUU);
980:     PetscMalloc1(aug1*aug1, &AUAU);
981:   }
982:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
983:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
984:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
985:   for (j=0; j < r; j++) {
986:     VecMDot(UU[j], r, MU, &AUU[j*aug1]);
987:   }
988:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
989:   for (j = 0; j < neig; j++) {
990:     VecMDot(XX[j], r, MU, &AUU[(r+j) *aug1]);
991:   }
992:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
993:   for (j = 0; j < r; j++) {
994:     VecMDot(UU[j], neig, MX, &AUU[j*aug1+r]);
995:   }
996:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
997:   for (j = 0; j < neig; j++) {
998:     VecMDot(XX[j], neig, MX, &AUU[(r+j) *aug1 + r]);
999:   }

1001:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
1002:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
1003:   for (j=0; j < r; j++) {
1004:     VecMDot(MU[j], r, MU, &AUAU[j*aug1]);
1005:   }
1006:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
1007:   for (j = 0; j < neig; j++) {
1008:     VecMDot(MX[j], r, MU, &AUAU[(r+j) *aug1]);
1009:   }
1010:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
1011:   for (j = 0; j < r; j++) {
1012:     VecMDot(MU[j], neig, MX, &AUAU[j*aug1+r]);
1013:   }
1014:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
1015:   for (j = 0; j < neig; j++) {
1016:     VecMDot(MX[j], neig, MX, &AUAU[(r+j) *aug1 + r]);
1017:   }

1019:   /* Computation of the eigenvectors */
1020:   PetscBLASIntCast(aug1,&ldA);
1021:   PetscBLASIntCast(aug,&N);
1022:   lwork = 8 * N + 20; /* sizeof the working space */
1023:   PetscMalloc1(N, &wr);
1024:   PetscMalloc1(N, &wi);
1025:   PetscMalloc1(N, &beta);
1026:   PetscMalloc1(N, &modul);
1027:   PetscMalloc1(N, &perm);
1028:   PetscMalloc1(N*N, &Q);
1029:   PetscMalloc1(N*N, &Z);
1030:   PetscMalloc1(lwork, &work);
1031: #if defined(PETSC_MISSING_LAPACK_GGES)
1032:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
1033: #else
1034:   {
1035:     PetscBLASInt info;
1036:     PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
1037:     if (info) SETERRQ1 (PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGGES %d", (int) info);
1038:   }
1039: #endif
1040:   for (i=0; i<N; i++) {
1041:     if (beta[i] !=0.0) {
1042:       wr[i] /=beta[i];
1043:       wi[i] /=beta[i];
1044:     }
1045:   }
1046:   /* sort the eigenvalues */
1047:   for (i=0; i<N; i++) modul[i]=PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
1048:   for (i=0; i<N; i++) perm[i] = i;
1049:   PetscSortRealWithPermutation(N, modul, perm);
1050:   /* Save the norm of the largest eigenvalue */
1051:   if (dgmres->lambdaN < modul[perm[N-1]]) dgmres->lambdaN = modul[perm[N-1]];
1052:   /* Allocate space to extract the first r schur vectors   */
1053:   if (!SR2) {
1054:     PetscMalloc1(aug1*bmax, &SR2);
1055:   }
1056:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
1057:   while (NbrEig < bmax) {
1058:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
1059:     else NbrEig += 2;
1060:   }
1061:   if (NbrEig > bmax) NbrEig = bmax - 1;
1062:   r_old     = r; /* previous size of r */
1063:   dgmres->r = r = NbrEig;

1065:   /* Select the eigenvalues to reorder */
1066:   PetscCalloc1(N, &select);
1067:   if (!dgmres->GreatestEig) {
1068:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
1069:   } else {
1070:     for (j = 0; j < NbrEig; j++) select[perm[N-j-1]] = 1;
1071:   }
1072:   /* Reorder and extract the new <r> schur vectors */
1073:   lwork  = PetscMax(4 * N + 16,  2 * NbrEig *(N - NbrEig));
1074:   liwork = PetscMax(N + 6,  2 * NbrEig *(N - NbrEig));
1075:   PetscFree(work);
1076:   PetscMalloc1(lwork, &work);
1077:   PetscMalloc1(liwork, &iwork);
1078: #if defined(PETSC_MISSING_LAPACK_TGSEN)
1079:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable.");
1080: #else
1081:   {
1082:     PetscBLASInt info;
1083:     PetscReal    Dif[2];
1084:     PetscBLASInt ijob  = 2;
1085:     PetscBLASInt wantQ = 1, wantZ = 1;
1086:     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));
1087:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
1088:   }
1089: #endif
1090:   PetscFree(select);

1092:   for (j=0; j<r; j++) {
1093:     PetscMemcpy(&SR2[j*aug1], &(Z[j*N]), N*sizeof(PetscReal));
1094:   }

1096:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
1097:    -- save it temporarily in MU */
1098:   for (j = 0; j < r; j++) {
1099:     VecZeroEntries(MU[j]);
1100:     VecMAXPY(MU[j], r_old, &SR2[j*aug1], UU);
1101:     VecMAXPY(MU[j], neig, &SR2[j*aug1+r_old], XX);
1102:   }
1103:   /* Form T = U'*MU*U */
1104:   for (j = 0; j < r; j++) {
1105:     VecCopy(MU[j], UU[j]);
1106:     KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP);
1107:   }
1108:   dgmres->matvecs += r;
1109:   for (j = 0; j < r; j++) {
1110:     VecMDot(MU[j], r, UU, &TT[j*bmax]);
1111:   }
1112:   /* Factorize T */
1113:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
1114:   PetscBLASIntCast(r,&nr);
1115:   PetscBLASIntCast(bmax,&bm);
1116: #if defined(PETSC_MISSING_LAPACK_GETRF)
1117:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
1118: #else
1119:   {
1120:     PetscBLASInt info;
1121:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
1122:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
1123:   }
1124: #endif
1125:   /* Free Memory */
1126:   PetscFree(wr);
1127:   PetscFree(wi);
1128:   PetscFree(beta);
1129:   PetscFree(modul);
1130:   PetscFree(perm);
1131:   PetscFree(Q);
1132:   PetscFree(Z);
1133:   PetscFree(work);
1134:   PetscFree(iwork);
1135:   return(0);
1136: }

1138: /* end new DGMRES functions */

1140: /*MC
1141:      KSPDGMRES - Implements the deflated GMRES as defined in [1,2].
1142:                  In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the
1143:                  stagnation occurs.

1145:    Options Database Keys:
1146:    GMRES Options (inherited):
1147: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
1148: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
1149: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
1150:                              vectors are allocated as needed)
1151: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
1152: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
1153: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
1154:                                    stability of the classical Gram-Schmidt  orthogonalization.
1155: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

1157:    DGMRES Options Database Keys:
1158: +   -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
1159: .   -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative
1160:                                        process
1161: .   -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
1162: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
1163:                                                    parsed by PetscOptionsGetViewer().  If neig > 1, viewerspec should
1164:                                                    end with ":append".  No vectors will be viewed if the adaptive
1165:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
1166:                                                    be given.
1167:                                                    The deflation vectors span a subspace that may be a good
1168:                                                    approximation of the subspace of smallest eigenvectors of the
1169:                                                    preconditioned operator, so this option can aid in understanding
1170:                                                    the performance of a preconditioner.

1172:  Level: beginner

1174:  Notes: Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

1176:  References:
1177: +  1. - J. Erhel, K. Burrage and B. Pohl,  Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).
1178: -  2. - D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, 
1179:    In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

1181:  Contributed by: Desire NUENTSA WAKAM,INRIA

1183:  .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
1184:  KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
1185:  KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
1186:  KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

1188:  M*/

1190: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
1191: {
1192:   KSP_DGMRES     *dgmres;

1196:   PetscNewLog(ksp,&dgmres);
1197:   ksp->data = (void*) dgmres;

1199:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
1200:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

1202:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
1203:   ksp->ops->setup                        = KSPSetUp_DGMRES;
1204:   ksp->ops->solve                        = KSPSolve_DGMRES;
1205:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
1206:   ksp->ops->view                         = KSPView_DGMRES;
1207:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
1208:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
1209:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

1211:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
1212:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
1213:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
1214:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
1215:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
1216:   /* -- New functions defined in DGMRES -- */
1217:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C",KSPDGMRESSetEigen_DGMRES);
1218:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C",KSPDGMRESSetMaxEigen_DGMRES);
1219:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C",KSPDGMRESSetRatio_DGMRES);
1220:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C",KSPDGMRESForce_DGMRES);
1221:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C",KSPDGMRESComputeSchurForm_DGMRES);
1222:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C",KSPDGMRESComputeDeflationData_DGMRES);
1223:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C",KSPDGMRESApplyDeflation_DGMRES);
1224:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES);

1226:   PetscLogEventRegister("DGMRESComputeDefl", KSP_CLASSID, &KSP_DGMRESComputeDeflationData);
1227:   PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation);

1229:   dgmres->haptol         = 1.0e-30;
1230:   dgmres->q_preallocate  = 0;
1231:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
1232:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
1233:   dgmres->nrs            = 0;
1234:   dgmres->sol_temp       = 0;
1235:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
1236:   dgmres->Rsvd           = 0;
1237:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
1238:   dgmres->orthogwork     = 0;

1240:   /* Default values for the deflation */
1241:   dgmres->r           = 0;
1242:   dgmres->neig        = DGMRES_DEFAULT_EIG;
1243:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG-1;
1244:   dgmres->lambdaN     = 0.0;
1245:   dgmres->smv         = SMV;
1246:   dgmres->matvecs     = 0;
1247:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
1248:   dgmres->HasSchur    = PETSC_FALSE;
1249:   return(0);
1250: }