Actual source code: gmres.c

  1: #define PETSCKSP_DLL

  3: /*
  4:     This file implements GMRES (a Generalized Minimal Residual) method.  
  5:     Reference:  Saad and Schultz, 1986.


  8:     Some comments on left vs. right preconditioning, and restarts.
  9:     Left and right preconditioning.
 10:     If right preconditioning is chosen, then the problem being solved
 11:     by gmres is actually
 12:        My =  AB^-1 y = f
 13:     so the initial residual is 
 14:           r = f - Mx
 15:     Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
 16:     residual is
 17:           r = f - A x
 18:     The final solution is then
 19:           x = B^-1 y 

 21:     If left preconditioning is chosen, then the problem being solved is
 22:        My = B^-1 A x = B^-1 f,
 23:     and the initial residual is
 24:        r  = B^-1(f - Ax)

 26:     Restarts:  Restarts are basically solves with x0 not equal to zero.
 27:     Note that we can eliminate an extra application of B^-1 between
 28:     restarts as long as we don't require that the solution at the end
 29:     of an unsuccessful gmres iteration always be the solution x.
 30:  */

 32:  #include src/ksp/ksp/impls/gmres/gmresp.h
 33: #define GMRES_DELTA_DIRECTIONS 10
 34: #define GMRES_DEFAULT_MAXK     30
 35: static PetscErrorCode    GMRESGetNewVectors(KSP,PetscInt);
 36: static PetscErrorCode    GMRESUpdateHessenberg(KSP,PetscInt,PetscTruth,PetscReal*);
 37: static PetscErrorCode    BuildGmresSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

 41: PetscErrorCode    KSPSetUp_GMRES(KSP ksp)
 42: {
 43:   PetscInt       size,hh,hes,rs,cc;
 45:   PetscInt       max_k,k;
 46:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
 47:   Vec            vec;
 48:   Mat            pmat;

 51:   if (ksp->pc_side == PC_SYMMETRIC) {
 52:     SETERRQ(PETSC_ERR_SUP,"no symmetric preconditioning for KSPGMRES");
 53:   }

 55:   max_k         = gmres->max_k;  /* restart size */
 56:   hh            = (max_k + 2) * (max_k + 1);
 57:   hes           = (max_k + 1) * (max_k + 1);
 58:   rs            = (max_k + 2);
 59:   cc            = (max_k + 1);
 60:   size          = (hh + hes + rs + 2*cc) * sizeof(PetscScalar);

 62:   PetscMalloc(size,&gmres->hh_origin);
 63:   PetscMemzero(gmres->hh_origin,size);
 64:   PetscLogObjectMemory(ksp,size);
 65:   gmres->hes_origin = gmres->hh_origin + hh;
 66:   gmres->rs_origin  = gmres->hes_origin + hes;
 67:   gmres->cc_origin  = gmres->rs_origin + rs;
 68:   gmres->ss_origin  = gmres->cc_origin + cc;

 70:   if (ksp->calc_sings) {
 71:     /* Allocate workspace to hold Hessenberg matrix needed by lapack */
 72:     size = (max_k + 3)*(max_k + 9)*sizeof(PetscScalar);
 73:     PetscMalloc(size,&gmres->Rsvd);
 74:     PetscMalloc(5*(max_k+2)*sizeof(PetscReal),&gmres->Dsvd);
 75:     PetscLogObjectMemory(ksp,size+5*(max_k+2)*sizeof(PetscReal));
 76:   }

 78:   /* Allocate array to hold pointers to user vectors.  Note that we need
 79:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
 80:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&gmres->vecs);
 81:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k;
 82:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&gmres->user_work);
 83:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(PetscInt),&gmres->mwork_alloc);
 84:   PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(2*sizeof(void*)+sizeof(PetscInt)));

 86:   PCGetOperators(ksp->pc,0,&pmat,0);
 87:   if (!pmat) SETERRQ(PETSC_ERR_ORDER,"You must call KSPSetOperators() or PCSetOperators() before this call");
 88:   MatGetVecs(pmat,&vec,0);
 89:   if (gmres->q_preallocate) {
 90:     gmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
 91:     KSPGetVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,PETSC_NULL);
 92:     PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
 93:     gmres->mwork_alloc[0] = gmres->vv_allocated;
 94:     gmres->nwork_alloc    = 1;
 95:     for (k=0; k<gmres->vv_allocated; k++) {
 96:       gmres->vecs[k] = gmres->user_work[0][k];
 97:     }
 98:   } else {
 99:     gmres->vv_allocated    = 5;
100:     KSPGetVecs(ksp,5,&gmres->user_work[0],0,PETSC_NULL);
101:     PetscLogObjectParents(ksp,5,gmres->user_work[0]);
102:     gmres->mwork_alloc[0]  = 5;
103:     gmres->nwork_alloc     = 1;
104:     for (k=0; k<gmres->vv_allocated; k++) {
105:       gmres->vecs[k] = gmres->user_work[0][k];
106:     }
107:   }
108:   VecDestroy(vec);
109:   return(0);
110: }

112: /*
113:     Run gmres, possibly with restart.  Return residual history if requested.
114:     input parameters:

116: .        gmres  - structure containing parameters and work areas

118:     output parameters:
119: .        nres    - residuals (from preconditioned system) at each step.
120:                   If restarting, consider passing nres+it.  If null, 
121:                   ignored
122: .        itcount - number of iterations used.  nres[0] to nres[itcount]
123:                   are defined.  If null, ignored.
124:                   
125:     Notes:
126:     On entry, the value in vector VEC_VV(0) should be the initial residual
127:     (this allows shortcuts where the initial preconditioned residual is 0).
128:  */
131: PetscErrorCode GMREScycle(PetscInt *itcount,KSP ksp)
132: {
133:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);
134:   PetscReal      res_norm,res,hapbnd,tt;
136:   PetscInt       it = 0, max_k = gmres->max_k;
137:   PetscTruth     hapend = PETSC_FALSE;

140:   VecNormalize(VEC_VV(0),&res_norm);
141:   res     = res_norm;
142:   *GRS(0) = res_norm;

144:   /* check for the convergence */
145:   PetscObjectTakeAccess(ksp);
146:   ksp->rnorm = res;
147:   PetscObjectGrantAccess(ksp);
148:   gmres->it = (it - 1);
149:   KSPLogResidualHistory(ksp,res);
150:   if (!res) {
151:     if (itcount) *itcount = 0;
152:     ksp->reason = KSP_CONVERGED_ATOL;
153:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
154:     return(0);
155:   }

157:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
158:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
159:     KSPLogResidualHistory(ksp,res);
160:     gmres->it = (it - 1);
161:     KSPMonitor(ksp,ksp->its,res);
162:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
163:       GMRESGetNewVectors(ksp,it+1);
164:     }
165:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

167:     /* update hessenberg matrix and do Gram-Schmidt */
168:     (*gmres->orthog)(ksp,it);

170:     /* vv(i+1) . vv(i+1) */
171:     VecNormalize(VEC_VV(it+1),&tt);
172:     /* save the magnitude */
173:     *HH(it+1,it)    = tt;
174:     *HES(it+1,it)   = tt;

176:     /* check for the happy breakdown */
177:     hapbnd  = PetscAbsScalar(tt / *GRS(it));
178:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
179:     if (tt < hapbnd) {
180:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %G tt = %G\n",hapbnd,tt);
181:       hapend = PETSC_TRUE;
182:     }
183:     GMRESUpdateHessenberg(ksp,it,hapend,&res);
184:     if (ksp->reason) break;

186:     it++;
187:     gmres->it  = (it-1);  /* For converged */
188:     PetscObjectTakeAccess(ksp);
189:     ksp->its++;
190:     ksp->rnorm = res;
191:     PetscObjectGrantAccess(ksp);

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

195:     /* Catch error in happy breakdown and signal convergence and break from loop */
196:     if (hapend) {
197:       if (!ksp->reason) {
198:         SETERRQ1(0,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res);
199:       }
200:       break;
201:     }
202:   }

204:   /* Monitor if we know that we will not return for a restart */
205:   if (ksp->reason || ksp->its >= ksp->max_it) {
206:     KSPLogResidualHistory(ksp,res);
207:     KSPMonitor(ksp,ksp->its,res);
208:   }

210:   if (itcount) *itcount    = it;


213:   /*
214:     Down here we have to solve for the "best" coefficients of the Krylov
215:     columns, add the solution values together, and possibly unwind the
216:     preconditioning from the solution
217:    */
218:   /* Form the solution (or the solution so far) */
219:   BuildGmresSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

221:   return(0);
222: }

226: PetscErrorCode KSPSolve_GMRES(KSP ksp)
227: {
229:   PetscInt       its,itcount;
230:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
231:   PetscTruth     guess_zero = ksp->guess_zero;

234:   if (ksp->calc_sings && !gmres->Rsvd) {
235:     SETERRQ(PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
236:   }

238:   PetscObjectTakeAccess(ksp);
239:   ksp->its = 0;
240:   PetscObjectGrantAccess(ksp);

242:   itcount     = 0;
243:   ksp->reason = KSP_CONVERGED_ITERATING;
244:   while (!ksp->reason) {
245:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
246:     GMREScycle(&its,ksp);
247:     itcount += its;
248:     if (itcount >= ksp->max_it) {
249:       ksp->reason = KSP_DIVERGED_ITS;
250:       break;
251:     }
252:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
253:   }
254:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
255:   return(0);
256: }

260: PetscErrorCode KSPDestroy_GMRES_Internal(KSP ksp)
261: {
262:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
264:   PetscInt       i;

267:   /* Free the Hessenberg matrix */
268:   PetscFree(gmres->hh_origin);

270:   /* Free the pointer to user variables */
271:   PetscFree(gmres->vecs);

273:   /* free work vectors */
274:   for (i=0; i<gmres->nwork_alloc; i++) {
275:     VecDestroyVecs(gmres->user_work[i],gmres->mwork_alloc[i]);
276:   }
277:   PetscFree(gmres->user_work);
278:   PetscFree(gmres->mwork_alloc);
279:   PetscFree(gmres->nrs);
280:   if (gmres->sol_temp) {
281:     VecDestroy(gmres->sol_temp);
282:   }
283:   PetscFree(gmres->Rsvd);
284:   PetscFree(gmres->Dsvd);
285:   PetscFree(gmres->orthogwork);
286:   gmres->orthogwork     = 0;
287:   gmres->Dsvd           = 0;
288:   gmres->hh_origin      = 0;
289:   gmres->vecs           = 0;
290:   gmres->user_work      = 0;
291:   gmres->mwork_alloc    = 0;
292:   gmres->nrs            = 0;
293:   gmres->sol_temp       = 0;
294:   gmres->nwork_alloc    = 0;
295:   gmres->vv_allocated   = 0;
296:   gmres->vecs_allocated = 0;
297:   gmres->nrs            = 0;
298:   gmres->sol_temp       = 0;
299:   gmres->Rsvd           = 0;
300:   return(0);
301: }

305: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
306: {
307:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

311:   KSPDestroy_GMRES_Internal(ksp);
312:   PetscFree(gmres);
313:   return(0);
314: }
315: /*
316:     BuildGmresSoln - create the solution from the starting vector and the
317:     current iterates.

319:     Input parameters:
320:         nrs - work area of size it + 1.
321:         vs  - index of initial guess
322:         vdest - index of result.  Note that vs may == vdest (replace
323:                 guess with the solution).

325:      This is an internal routine that knows about the GMRES internals.
326:  */
329: static PetscErrorCode BuildGmresSoln(PetscScalar* nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
330: {
331:   PetscScalar    tt;
333:   PetscInt       ii,k,j;
334:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);

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

339:   /* If it is < 0, no gmres steps have been performed */
340:   if (it < 0) {
341:     if (vdest != vs) {
342:       VecCopy(vs,vdest);
343:     }
344:     return(0);
345:   }
346:   if (*HH(it,it) == 0.0) SETERRQ2(PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %G",it,PetscAbsScalar(*GRS(it)));
347:   if (*HH(it,it) != 0.0) {
348:     nrs[it] = *GRS(it) / *HH(it,it);
349:   } else {
350:     nrs[it] = 0.0;
351:   }
352:   for (ii=1; ii<=it; ii++) {
353:     k   = it - ii;
354:     tt  = *GRS(k);
355:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
356:     nrs[k]   = tt / *HH(k,k);
357:   }

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

363:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
364:   /* add solution to previous solution */
365:   if (vdest != vs) {
366:     VecCopy(vs,vdest);
367:   }
368:   VecAXPY(vdest,1.0,VEC_TEMP);
369:   return(0);
370: }
371: /*
372:    Do the scalar work for the orthogonalization.  Return new residual.
373:  */
376: static PetscErrorCode GMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
377: {
378:   PetscScalar *hh,*cc,*ss,tt;
379:   PetscInt    j;
380:   KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);

383:   hh  = HH(0,it);
384:   cc  = CC(0);
385:   ss  = SS(0);

387:   /* Apply all the previously computed plane rotations to the new column
388:      of the Hessenberg matrix */
389:   for (j=1; j<=it; j++) {
390:     tt  = *hh;
391: #if defined(PETSC_USE_COMPLEX)
392:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
393: #else
394:     *hh = *cc * tt + *ss * *(hh+1);
395: #endif
396:     hh++;
397:     *hh = *cc++ * *hh - (*ss++ * tt);
398:   }

400:   /*
401:     compute the new plane rotation, and apply it to:
402:      1) the right-hand-side of the Hessenberg system
403:      2) the new column of the Hessenberg matrix
404:     thus obtaining the updated value of the residual
405:   */
406:   if (!hapend) {
407: #if defined(PETSC_USE_COMPLEX)
408:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
409: #else
410:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
411: #endif
412:     if (tt == 0.0) {
413:       ksp->reason = KSP_DIVERGED_NULL;
414:       return(0);
415:     }
416:     *cc       = *hh / tt;
417:     *ss       = *(hh+1) / tt;
418:     *GRS(it+1) = - (*ss * *GRS(it));
419: #if defined(PETSC_USE_COMPLEX)
420:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
421:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
422: #else
423:     *GRS(it)   = *cc * *GRS(it);
424:     *hh       = *cc * *hh + *ss * *(hh+1);
425: #endif
426:     *res      = PetscAbsScalar(*GRS(it+1));
427:   } else {
428:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
429:             another rotation matrix (so RH doesn't change).  The new residual is 
430:             always the new sine term times the residual from last time (GRS(it)), 
431:             but now the new sine rotation would be zero...so the residual should
432:             be zero...so we will multiply "zero" by the last residual.  This might
433:             not be exactly what we want to do here -could just return "zero". */
434: 
435:     *res = 0.0;
436:   }
437:   return(0);
438: }
439: /*
440:    This routine allocates more work vectors, starting from VEC_VV(it).
441:  */
444: static PetscErrorCode GMRESGetNewVectors(KSP ksp,PetscInt it)
445: {
446:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
448:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

451:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
452:   /* Adjust the number to allocate to make sure that we don't exceed the
453:     number of available slots */
454:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated){
455:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
456:   }
457:   if (!nalloc) return(0);

459:   gmres->vv_allocated += nalloc;
460:   KSPGetVecs(ksp,nalloc,&gmres->user_work[nwork],0,PETSC_NULL);
461:   PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
462:   gmres->mwork_alloc[nwork] = nalloc;
463:   for (k=0; k<nalloc; k++) {
464:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
465:   }
466:   gmres->nwork_alloc++;
467:   return(0);
468: }

472: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec  ptr,Vec *result)
473: {
474:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

478:   if (!ptr) {
479:     if (!gmres->sol_temp) {
480:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
481:       PetscLogObjectParent(ksp,gmres->sol_temp);
482:     }
483:     ptr = gmres->sol_temp;
484:   }
485:   if (!gmres->nrs) {
486:     /* allocate the work area */
487:     PetscMalloc(gmres->max_k*sizeof(PetscScalar),&gmres->nrs);
488:     PetscLogObjectMemory(ksp,gmres->max_k*sizeof(PetscScalar));
489:   }

491:   BuildGmresSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
492:   *result = ptr;
493:   return(0);
494: }

498: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
499: {
500:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
501:   const char     *cstr;
503:   PetscTruth     iascii,isstring;

506:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
507:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_STRING,&isstring);
508:   if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
509:     switch (gmres->cgstype) {
510:       case (KSP_GMRES_CGS_REFINE_NEVER):
511:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
512:         break;
513:       case (KSP_GMRES_CGS_REFINE_ALWAYS):
514:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
515:         break;
516:       case (KSP_GMRES_CGS_REFINE_IFNEEDED):
517:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
518:         break;
519:       default:
520:         SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
521:     }
522:   } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
523:     cstr = "Modified Gram-Schmidt Orthogonalization";
524:   } else {
525:     cstr = "unknown orthogonalization";
526:   }
527:   if (iascii) {
528:     PetscViewerASCIIPrintf(viewer,"  GMRES: restart=%D, using %s\n",gmres->max_k,cstr);
529:     PetscViewerASCIIPrintf(viewer,"  GMRES: happy breakdown tolerance %G\n",gmres->haptol);
530:   } else if (isstring) {
531:     PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
532:   } else {
533:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP GMRES",((PetscObject)viewer)->type_name);
534:   }
535:   return(0);
536: }

540: /*@C
541:    KSPGMRESKrylovMonitor - Calls VecView() for each direction in the 
542:    GMRES accumulated Krylov space.

544:    Collective on KSP

546:    Input Parameters:
547: +  ksp - the KSP context
548: .  its - iteration number
549: .  fgnorm - 2-norm of residual (or gradient)
550: -  a viewers object created with PetscViewersCreate()

552:    Level: intermediate

554: .keywords: KSP, nonlinear, vector, monitor, view, Krylov space

556: .seealso: KSPSetMonitor(), KSPDefaultMonitor(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
557: @*/
558: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESKrylovMonitor(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
559: {
560:   PetscViewers   viewers = (PetscViewers)dummy;
561:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
563:   Vec            x;
564:   PetscViewer    viewer;

567:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
568:   PetscViewerSetType(viewer,PETSC_VIEWER_DRAW);

570:   x      = VEC_VV(gmres->it+1);
571:   VecView(x,viewer);

573:   return(0);
574: }

578: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp)
579: {
581:   PetscInt       restart;
582:   PetscReal      haptol;
583:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
584:   PetscTruth     flg;

587:   PetscOptionsHead("KSP GMRES Options");
588:     PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
589:     if (flg) { KSPGMRESSetRestart(ksp,restart); }
590:     PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
591:     if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
592:     PetscOptionsName("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",&flg);
593:     if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
594:     PetscOptionsTruthGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
595:     if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
596:     PetscOptionsTruthGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
597:     if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
598:     PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
599:                             KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
600:     PetscOptionsName("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPSetMonitor",&flg);
601:     if (flg) {
602:       PetscViewers viewers;
603:       PetscViewersCreate(ksp->comm,&viewers);
604:       KSPSetMonitor(ksp,KSPGMRESKrylovMonitor,viewers,(PetscErrorCode (*)(void*))PetscViewersDestroy);
605:     }
606:   PetscOptionsTail();
607:   return(0);
608: }

610: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
611: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);


617: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
618: {
619:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

622:   if (tol < 0.0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
623:   gmres->haptol = tol;
624:   return(0);
625: }

631: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
632: {
633:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

637:   if (max_k < 1) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
638:   if (!ksp->setupcalled) {
639:     gmres->max_k = max_k;
640:   } else if (gmres->max_k != max_k) {
641:      gmres->max_k = max_k;
642:      ksp->setupcalled = 0;
643:      /* free the data structures, then create them again */
644:      KSPDestroy_GMRES_Internal(ksp);
645:   }
646:   return(0);
647: }

654: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
655: {
658:   ((KSP_GMRES *)ksp->data)->orthog = fcn;
659:   return(0);
660: }

666: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
667: {
668:   KSP_GMRES *gmres;

671:   gmres = (KSP_GMRES *)ksp->data;
672:   gmres->q_preallocate = 1;
673:   return(0);
674: }

680: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
681: {
682:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

685:   gmres->cgstype = type;
686:   return(0);
687: }

692: /*@
693:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
694:          in the classical Gram Schmidt orthogonalization.
695:    of the preconditioned problem.

697:    Collective on KSP

699:    Input Parameters:
700: +  ksp - the Krylov space context
701: -  type - the type of refinement

703:   Options Database:
704: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

706:    Level: intermediate

708: .keywords: KSP, GMRES, iterative refinement

710: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization()
711: @*/
712: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
713: {
714:   PetscErrorCode ierr,(*f)(KSP,KSPGMRESCGSRefinementType);

718:   PetscObjectQueryFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",(void (**)(void))&f);
719:   if (f) {
720:     (*f)(ksp,type);
721:   }
722:   return(0);
723: }

727: /*@
728:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

730:    Collective on KSP

732:    Input Parameters:
733: +  ksp - the Krylov space context
734: -  restart - integer restart value

736:   Options Database:
737: .  -ksp_gmres_restart <positive integer>

739:     Note: The default value is 30.

741:    Level: intermediate

743: .keywords: KSP, GMRES, restart, iterations

745: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors()
746: @*/
747: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetRestart(KSP ksp, PetscInt restart)
748: {

752:   PetscTryMethod(ksp,KSPGMRESSetRestart_C,(KSP,PetscInt),(ksp,restart));
753:   return(0);
754: }

758: /*@
759:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

761:    Collective on KSP

763:    Input Parameters:
764: +  ksp - the Krylov space context
765: -  tol - the tolerance

767:   Options Database:
768: .  -ksp_gmres_haptol <positive real value>

770:    Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
771:          a certain number of iterations. If you attempt more iterations after this point unstable 
772:          things can happen hence very occasionally you may need to set this value to detect this condition

774:    Level: intermediate

776: .keywords: KSP, GMRES, tolerance

778: .seealso: KSPSetTolerances()
779: @*/
780: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
781: {

785:   PetscTryMethod((ksp),KSPGMRESSetHapTol_C,(KSP,PetscReal),((ksp),(tol)));
786:   return(0);
787: }

789: /*MC
790:      KSPGMRES - Implements the Generalized Minimal Residual method.  
791:                 (Saad and Schultz, 1986) with restart


794:    Options Database Keys:
795: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
796: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
797: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of 
798:                              vectors are allocated as needed)
799: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
800: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
801: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the 
802:                                    stability of the classical Gram-Schmidt  orthogonalization.
803: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

805:    Level: beginner


808: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
809:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
810:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
811:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESKrylovMonitor()

813: M*/

818: PetscErrorCode PETSCKSP_DLLEXPORT KSPCreate_GMRES(KSP ksp)
819: {
820:   KSP_GMRES      *gmres;

824:   PetscNew(KSP_GMRES,&gmres);
825:   PetscLogObjectMemory(ksp,sizeof(KSP_GMRES));
826:   ksp->data                              = (void*)gmres;
827:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;

829:   ksp->ops->setup                        = KSPSetUp_GMRES;
830:   ksp->ops->solve                        = KSPSolve_GMRES;
831:   ksp->ops->destroy                      = KSPDestroy_GMRES;
832:   ksp->ops->view                         = KSPView_GMRES;
833:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
834:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
835:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

837:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
838:                                     "KSPGMRESSetPreAllocateVectors_GMRES",
839:                                      KSPGMRESSetPreAllocateVectors_GMRES);
840:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
841:                                     "KSPGMRESSetOrthogonalization_GMRES",
842:                                      KSPGMRESSetOrthogonalization_GMRES);
843:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
844:                                     "KSPGMRESSetRestart_GMRES",
845:                                      KSPGMRESSetRestart_GMRES);
846:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C",
847:                                     "KSPGMRESSetHapTol_GMRES",
848:                                      KSPGMRESSetHapTol_GMRES);
849:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
850:                                     "KSPGMRESSetCGSRefinementType_GMRES",
851:                                      KSPGMRESSetCGSRefinementType_GMRES);

853:   gmres->haptol              = 1.0e-30;
854:   gmres->q_preallocate       = 0;
855:   gmres->delta_allocate      = GMRES_DELTA_DIRECTIONS;
856:   gmres->orthog              = KSPGMRESClassicalGramSchmidtOrthogonalization;
857:   gmres->nrs                 = 0;
858:   gmres->sol_temp            = 0;
859:   gmres->max_k               = GMRES_DEFAULT_MAXK;
860:   gmres->Rsvd                = 0;
861:   gmres->cgstype             = KSP_GMRES_CGS_REFINE_NEVER;
862:   gmres->orthogwork          = 0;
863:   return(0);
864: }