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;

 49:   if (ksp->pc_side == PC_SYMMETRIC) {
 50:     SETERRQ(PETSC_ERR_SUP,"no symmetric preconditioning for KSPGMRES");
 51:   } else if (ksp->pc_side == PC_RIGHT) {
 52:     SETERRQ(PETSC_ERR_SUP, "no right preconditioning for KSPGMRES use KSPFGMRES");
 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:   if (gmres->q_preallocate) {
 87:     gmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
 88:     KSPGetVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,PETSC_NULL);
 89:     PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
 90:     gmres->mwork_alloc[0] = gmres->vv_allocated;
 91:     gmres->nwork_alloc    = 1;
 92:     for (k=0; k<gmres->vv_allocated; k++) {
 93:       gmres->vecs[k] = gmres->user_work[0][k];
 94:     }
 95:   } else {
 96:     gmres->vv_allocated    = 5;
 97:     KSPGetVecs(ksp,5,&gmres->user_work[0],0,PETSC_NULL);
 98:     PetscLogObjectParents(ksp,5,gmres->user_work[0]);
 99:     gmres->mwork_alloc[0]  = 5;
100:     gmres->nwork_alloc     = 1;
101:     for (k=0; k<gmres->vv_allocated; k++) {
102:       gmres->vecs[k] = gmres->user_work[0][k];
103:     }
104:   }
105:   return(0);
106: }

108: /*
109:     Run gmres, possibly with restart.  Return residual history if requested.
110:     input parameters:

112: .        gmres  - structure containing parameters and work areas

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

136:   VecNormalize(VEC_VV(0),&res_norm);
137:   res     = res_norm;
138:   *GRS(0) = res_norm;

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

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

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

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

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

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

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

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

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

209:   if (itcount) *itcount    = it;


212:   /*
213:     Down here we have to solve for the "best" coefficients of the Krylov
214:     columns, add the solution values together, and possibly unwind the
215:     preconditioning from the solution
216:    */
217:   /* Form the solution (or the solution so far) */
218:   BuildGmresSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

220:   return(0);
221: }

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

233:   if (ksp->calc_sings && !gmres->Rsvd) {
234:     SETERRQ(PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
235:   }
236:   if (ksp->normtype != KSP_NORM_PRECONDITIONED) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Currently can use GMRES with only preconditioned residual (right preconditioning not coded)");

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:       if (!ksp->reason) 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->sol_temp       = 0;
287:   gmres->vv_allocated   = 0;
288:   gmres->vecs_allocated = 0;
289:   gmres->sol_temp       = 0;
290:   return(0);
291: }

295: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
296: {

300:   KSPDestroy_GMRES_Internal(ksp);
301:   PetscFree(ksp->data);
302:   /* clear composed functions */
303:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C","",PETSC_NULL);
304:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C","",PETSC_NULL);
305:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C","",PETSC_NULL);
306:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C","",PETSC_NULL);
307:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C","",PETSC_NULL);
308:   return(0);
309: }
310: /*
311:     BuildGmresSoln - create the solution from the starting vector and the
312:     current iterates.

314:     Input parameters:
315:         nrs - work area of size it + 1.
316:         vs  - index of initial guess
317:         vdest - index of result.  Note that vs may == vdest (replace
318:                 guess with the solution).

320:      This is an internal routine that knows about the GMRES internals.
321:  */
324: static PetscErrorCode BuildGmresSoln(PetscScalar* nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
325: {
326:   PetscScalar    tt;
328:   PetscInt       ii,k,j;
329:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);

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

334:   /* If it is < 0, no gmres steps have been performed */
335:   if (it < 0) {
336:     if (vdest != vs) {
337:       VecCopy(vs,vdest);
338:     }
339:     return(0);
340:   }
341:   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)));
342:   if (*HH(it,it) != 0.0) {
343:     nrs[it] = *GRS(it) / *HH(it,it);
344:   } else {
345:     nrs[it] = 0.0;
346:   }
347:   for (ii=1; ii<=it; ii++) {
348:     k   = it - ii;
349:     tt  = *GRS(k);
350:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
351:     nrs[k]   = tt / *HH(k,k);
352:   }

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

358:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
359:   /* add solution to previous solution */
360:   if (vdest != vs) {
361:     VecCopy(vs,vdest);
362:   }
363:   VecAXPY(vdest,1.0,VEC_TEMP);
364:   return(0);
365: }
366: /*
367:    Do the scalar work for the orthogonalization.  Return new residual.
368:  */
371: static PetscErrorCode GMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
372: {
373:   PetscScalar *hh,*cc,*ss,tt;
374:   PetscInt    j;
375:   KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);

378:   hh  = HH(0,it);
379:   cc  = CC(0);
380:   ss  = SS(0);

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

395:   /*
396:     compute the new plane rotation, and apply it to:
397:      1) the right-hand-side of the Hessenberg system
398:      2) the new column of the Hessenberg matrix
399:     thus obtaining the updated value of the residual
400:   */
401:   if (!hapend) {
402: #if defined(PETSC_USE_COMPLEX)
403:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
404: #else
405:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
406: #endif
407:     if (tt == 0.0) {
408:       ksp->reason = KSP_DIVERGED_NULL;
409:       return(0);
410:     }
411:     *cc       = *hh / tt;
412:     *ss       = *(hh+1) / tt;
413:     *GRS(it+1) = - (*ss * *GRS(it));
414: #if defined(PETSC_USE_COMPLEX)
415:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
416:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
417: #else
418:     *GRS(it)   = *cc * *GRS(it);
419:     *hh       = *cc * *hh + *ss * *(hh+1);
420: #endif
421:     *res      = PetscAbsScalar(*GRS(it+1));
422:   } else {
423:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
424:             another rotation matrix (so RH doesn't change).  The new residual is 
425:             always the new sine term times the residual from last time (GRS(it)), 
426:             but now the new sine rotation would be zero...so the residual should
427:             be zero...so we will multiply "zero" by the last residual.  This might
428:             not be exactly what we want to do here -could just return "zero". */
429: 
430:     *res = 0.0;
431:   }
432:   return(0);
433: }
434: /*
435:    This routine allocates more work vectors, starting from VEC_VV(it).
436:  */
439: static PetscErrorCode GMRESGetNewVectors(KSP ksp,PetscInt it)
440: {
441:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
443:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

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

454:   gmres->vv_allocated += nalloc;
455:   KSPGetVecs(ksp,nalloc,&gmres->user_work[nwork],0,PETSC_NULL);
456:   PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
457:   gmres->mwork_alloc[nwork] = nalloc;
458:   for (k=0; k<nalloc; k++) {
459:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
460:   }
461:   gmres->nwork_alloc++;
462:   return(0);
463: }

467: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec  ptr,Vec *result)
468: {
469:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

473:   if (!ptr) {
474:     if (!gmres->sol_temp) {
475:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
476:       PetscLogObjectParent(ksp,gmres->sol_temp);
477:     }
478:     ptr = gmres->sol_temp;
479:   }
480:   if (!gmres->nrs) {
481:     /* allocate the work area */
482:     PetscMalloc(gmres->max_k*sizeof(PetscScalar),&gmres->nrs);
483:     PetscLogObjectMemory(ksp,gmres->max_k*sizeof(PetscScalar));
484:   }

486:   BuildGmresSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
487:   *result = ptr;
488:   return(0);
489: }

493: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
494: {
495:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
496:   const char     *cstr;
498:   PetscTruth     iascii,isstring;

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

535: /*@C
536:    KSPGMRESMonitorKrylov - Calls VecView() for each direction in the 
537:    GMRES accumulated Krylov space.

539:    Collective on KSP

541:    Input Parameters:
542: +  ksp - the KSP context
543: .  its - iteration number
544: .  fgnorm - 2-norm of residual (or gradient)
545: -  a viewers object created with PetscViewersCreate()

547:    Level: intermediate

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

551: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
552: @*/
553: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
554: {
555:   PetscViewers   viewers = (PetscViewers)dummy;
556:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
558:   Vec            x;
559:   PetscViewer    viewer;

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

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

568:   return(0);
569: }

573: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp)
574: {
576:   PetscInt       restart;
577:   PetscReal      haptol;
578:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
579:   PetscTruth     flg;

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

605: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
606: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);


612: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
613: {
614:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

617:   if (tol < 0.0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
618:   gmres->haptol = tol;
619:   return(0);
620: }

626: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
627: {
628:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

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

649: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
650: {
653:   ((KSP_GMRES *)ksp->data)->orthog = fcn;
654:   return(0);
655: }

661: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
662: {
663:   KSP_GMRES *gmres;

666:   gmres = (KSP_GMRES *)ksp->data;
667:   gmres->q_preallocate = 1;
668:   return(0);
669: }

675: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
676: {
677:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

680:   gmres->cgstype = type;
681:   return(0);
682: }

687: /*@
688:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
689:          in the classical Gram Schmidt orthogonalization.
690:    of the preconditioned problem.

692:    Collective on KSP

694:    Input Parameters:
695: +  ksp - the Krylov space context
696: -  type - the type of refinement

698:   Options Database:
699: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

701:    Level: intermediate

703: .keywords: KSP, GMRES, iterative refinement

705: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization()
706: @*/
707: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
708: {
709:   PetscErrorCode ierr,(*f)(KSP,KSPGMRESCGSRefinementType);

713:   PetscObjectQueryFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",(void (**)(void))&f);
714:   if (f) {
715:     (*f)(ksp,type);
716:   }
717:   return(0);
718: }

722: /*@
723:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

725:    Collective on KSP

727:    Input Parameters:
728: +  ksp - the Krylov space context
729: -  restart - integer restart value

731:   Options Database:
732: .  -ksp_gmres_restart <positive integer>

734:     Note: The default value is 30.

736:    Level: intermediate

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

740: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors()
741: @*/
742: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
743: {

747:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
748:   return(0);
749: }

753: /*@
754:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

756:    Collective on KSP

758:    Input Parameters:
759: +  ksp - the Krylov space context
760: -  tol - the tolerance

762:   Options Database:
763: .  -ksp_gmres_haptol <positive real value>

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

769:    Level: intermediate

771: .keywords: KSP, GMRES, tolerance

773: .seealso: KSPSetTolerances()
774: @*/
775: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
776: {

780:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
781:   return(0);
782: }

784: /*MC
785:      KSPGMRES - Implements the Generalized Minimal Residual method.  
786:                 (Saad and Schultz, 1986) with restart


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

800:    Level: beginner


803: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
804:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
805:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
806:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESMonitorKrylov()

808: M*/

813: PetscErrorCode  KSPCreate_GMRES(KSP ksp)
814: {
815:   KSP_GMRES      *gmres;

819:   PetscNewLog(ksp,KSP_GMRES,&gmres);
820:   ksp->data                              = (void*)gmres;


823:   ksp->normtype                          = KSP_NORM_PRECONDITIONED;
824:   ksp->pc_side                           = PC_LEFT;

826:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
827:   ksp->ops->setup                        = KSPSetUp_GMRES;
828:   ksp->ops->solve                        = KSPSolve_GMRES;
829:   ksp->ops->destroy                      = KSPDestroy_GMRES;
830:   ksp->ops->view                         = KSPView_GMRES;
831:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
832:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
833:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

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

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