Actual source code: gmres.c

petsc-3.3-p7 2013-05-11
  2: /*
  3:     This file implements GMRES (a Generalized Minimal Residual) method.  
  4:     Reference:  Saad and Schultz, 1986.


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

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

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

 31: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>       /*I  "petscksp.h"  I*/
 32: #define GMRES_DELTA_DIRECTIONS 10
 33: #define GMRES_DEFAULT_MAXK     30
 34: static PetscErrorCode    KSPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool ,PetscReal*);
 35: static PetscErrorCode    KSPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

 39: PetscErrorCode    KSPSetUp_GMRES(KSP ksp)
 40: {
 41:   PetscInt       hh,hes,rs,cc;
 43:   PetscInt       max_k,k;
 44:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

 47:   max_k         = gmres->max_k;  /* restart size */
 48:   hh            = (max_k + 2) * (max_k + 1);
 49:   hes           = (max_k + 1) * (max_k + 1);
 50:   rs            = (max_k + 2);
 51:   cc            = (max_k + 1);

 53:   PetscMalloc5(hh,PetscScalar,&gmres->hh_origin,hes,PetscScalar,&gmres->hes_origin,rs,PetscScalar,&gmres->rs_origin,cc,PetscScalar,&gmres->cc_origin,cc,PetscScalar,& gmres->ss_origin);
 54:   PetscMemzero(gmres->hh_origin,hh*sizeof(PetscScalar));
 55:   PetscMemzero(gmres->hes_origin,hes*sizeof(PetscScalar));
 56:   PetscMemzero(gmres->rs_origin,rs*sizeof(PetscScalar));
 57:   PetscMemzero(gmres->cc_origin,cc*sizeof(PetscScalar));
 58:   PetscMemzero(gmres->ss_origin,cc*sizeof(PetscScalar));
 59:   PetscLogObjectMemory(ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));

 61:   if (ksp->calc_sings) {
 62:     /* Allocate workspace to hold Hessenberg matrix needed by lapack */
 63:     PetscMalloc((max_k + 3)*(max_k + 9)*sizeof(PetscScalar),&gmres->Rsvd);
 64:     PetscLogObjectMemory(ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
 65:     PetscMalloc(6*(max_k+2)*sizeof(PetscReal),&gmres->Dsvd);
 66:     PetscLogObjectMemory(ksp,6*(max_k+2)*sizeof(PetscReal));
 67:   }

 69:   /* Allocate array to hold pointers to user vectors.  Note that we need
 70:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
 71:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
 72:   PetscMalloc((gmres->vecs_allocated)*sizeof(Vec),&gmres->vecs);
 73:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(Vec*),&gmres->user_work);
 74:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(PetscInt),&gmres->mwork_alloc);
 75:   PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));

 77:   if (gmres->q_preallocate) {
 78:     gmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
 79:     KSPGetVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,PETSC_NULL);
 80:     PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
 81:     gmres->mwork_alloc[0] = gmres->vv_allocated;
 82:     gmres->nwork_alloc    = 1;
 83:     for (k=0; k<gmres->vv_allocated; k++) {
 84:       gmres->vecs[k] = gmres->user_work[0][k];
 85:     }
 86:   } else {
 87:     gmres->vv_allocated    = 5;
 88:     KSPGetVecs(ksp,5,&gmres->user_work[0],0,PETSC_NULL);
 89:     PetscLogObjectParents(ksp,5,gmres->user_work[0]);
 90:     gmres->mwork_alloc[0]  = 5;
 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:   }
 96:   return(0);
 97: }

 99: /*
100:     Run gmres, possibly with restart.  Return residual history if requested.
101:     input parameters:

103: .        gmres  - structure containing parameters and work areas

105:     output parameters:
106: .        nres    - residuals (from preconditioned system) at each step.
107:                   If restarting, consider passing nres+it.  If null, 
108:                   ignored
109: .        itcount - number of iterations used.  nres[0] to nres[itcount]
110:                   are defined.  If null, ignored.
111:                   
112:     Notes:
113:     On entry, the value in vector VEC_VV(0) should be the initial residual
114:     (this allows shortcuts where the initial preconditioned residual is 0).
115:  */
118: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
119: {
120:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);
121:   PetscReal      res_norm,res,hapbnd,tt;
123:   PetscInt       it = 0, max_k = gmres->max_k;
124:   PetscBool      hapend = PETSC_FALSE;

127:   VecNormalize(VEC_VV(0),&res_norm);
128:   res     = res_norm;
129:   *GRS(0) = res_norm;

131:   /* check for the convergence */
132:   PetscObjectTakeAccess(ksp);
133:   ksp->rnorm = res;
134:   PetscObjectGrantAccess(ksp);
135:   gmres->it = (it - 1);
136:   KSPLogResidualHistory(ksp,res);
137:   KSPMonitor(ksp,ksp->its,res);
138:   if (!res) {
139:     if (itcount) *itcount = 0;
140:     ksp->reason = KSP_CONVERGED_ATOL;
141:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
142:     return(0);
143:   }

145:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
146:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
147:     if (it) {
148:       KSPLogResidualHistory(ksp,res);
149:       KSPMonitor(ksp,ksp->its,res);
150:     }
151:     gmres->it = (it - 1);
152:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
153:       KSPGMRESGetNewVectors(ksp,it+1);
154:     }
155:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

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

160:     /* vv(i+1) . vv(i+1) */
161:     VecNormalize(VEC_VV(it+1),&tt);

163:     /* save the magnitude */
164:     *HH(it+1,it)    = tt;
165:     *HES(it+1,it)   = tt;

167:     /* check for the happy breakdown */
168:     hapbnd  = PetscAbsScalar(tt / *GRS(it));
169:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
170:     if (tt < hapbnd) {
171:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
172:       hapend = PETSC_TRUE;
173:     }
174:     KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);

176:     it++;
177:     gmres->it  = (it-1);  /* For converged */
178:     ksp->its++;
179:     ksp->rnorm = res;
180:     if (ksp->reason) break;

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

184:     /* Catch error in happy breakdown and signal convergence and break from loop */
185:     if (hapend) {
186:       if (!ksp->reason) SETERRQ1(((PetscObject)ksp)->comm,PETSC_ERR_PLIB,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res);
187:       break;
188:     }
189:   }

191:   /* Monitor if we know that we will not return for a restart */
192:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
193:     KSPLogResidualHistory(ksp,res);
194:     KSPMonitor(ksp,ksp->its,res);
195:   }

197:   if (itcount) *itcount    = it;


200:   /*
201:     Down here we have to solve for the "best" coefficients of the Krylov
202:     columns, add the solution values together, and possibly unwind the
203:     preconditioning from the solution
204:    */
205:   /* Form the solution (or the solution so far) */
206:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

208:   return(0);
209: }

213: PetscErrorCode KSPSolve_GMRES(KSP ksp)
214: {
216:   PetscInt       its,itcount;
217:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
218:   PetscBool      guess_zero = ksp->guess_zero;

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

223:   PetscObjectTakeAccess(ksp);
224:   ksp->its = 0;
225:   PetscObjectGrantAccess(ksp);

227:   itcount     = 0;
228:   ksp->reason = KSP_CONVERGED_ITERATING;
229:   while (!ksp->reason) {
230:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
231:     KSPGMRESCycle(&its,ksp);
232:     itcount += its;
233:     if (itcount >= ksp->max_it) {
234:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
235:       break;
236:     }
237:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
238:   }
239:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
240:   return(0);
241: }

245: PetscErrorCode KSPReset_GMRES(KSP ksp)
246: {
247:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
249:   PetscInt       i;

252:   /* Free the Hessenberg matrices */
253:   PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);

255:   /* free work vectors */
256:   PetscFree(gmres->vecs);
257:   for (i=0; i<gmres->nwork_alloc; i++) {
258:     VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
259:   }
260:   gmres->nwork_alloc = 0;
261:   PetscFree(gmres->user_work);
262:   PetscFree(gmres->mwork_alloc);
263:   PetscFree(gmres->nrs);
264:   VecDestroy(&gmres->sol_temp);
265:   PetscFree(gmres->Rsvd);
266:   PetscFree(gmres->Dsvd);
267:   PetscFree(gmres->orthogwork);
268:   gmres->sol_temp       = 0;
269:   gmres->vv_allocated   = 0;
270:   gmres->vecs_allocated = 0;
271:   gmres->sol_temp       = 0;
272:   return(0);
273: }

277: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
278: {

282:   KSPReset_GMRES(ksp);
283:   PetscFree(ksp->data);
284:   /* clear composed functions */
285:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C","",PETSC_NULL);
286:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C","",PETSC_NULL);
287:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C","",PETSC_NULL);
288:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C","",PETSC_NULL);
289:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetRestart_C","",PETSC_NULL);
290:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C","",PETSC_NULL);
291:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C","",PETSC_NULL);
292:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C","",PETSC_NULL);
293:   return(0);
294: }
295: /*
296:     KSPGMRESBuildSoln - create the solution from the starting vector and the
297:     current iterates.

299:     Input parameters:
300:         nrs - work area of size it + 1.
301:         vs  - index of initial guess
302:         vdest - index of result.  Note that vs may == vdest (replace
303:                 guess with the solution).

305:      This is an internal routine that knows about the GMRES internals.
306:  */
309: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar* nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
310: {
311:   PetscScalar    tt;
313:   PetscInt       ii,k,j;
314:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);

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

319:   /* If it is < 0, no gmres steps have been performed */
320:   if (it < 0) {
321:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
322:     return(0);
323:   }
324:   if (*HH(it,it) != 0.0) {
325:     nrs[it] = *GRS(it) / *HH(it,it);
326:   } else {
327:     ksp->reason = KSP_DIVERGED_BREAKDOWN;
328:     PetscInfo2(ksp,"Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %D GRS(it) = %G",it,PetscAbsScalar(*GRS(it)));
329:     return(0);
330:   }
331:   for (ii=1; ii<=it; ii++) {
332:     k   = it - ii;
333:     tt  = *GRS(k);
334:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
335:     if (*HH(k,k) == 0.0) {
336:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
337:       PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D",k);
338:       return(0);
339:     }
340:     nrs[k]   = tt / *HH(k,k);
341:   }

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

347:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
348:   /* add solution to previous solution */
349:   if (vdest != vs) {
350:     VecCopy(vs,vdest);
351:   }
352:   VecAXPY(vdest,1.0,VEC_TEMP);
353:   return(0);
354: }
355: /*
356:    Do the scalar work for the orthogonalization.  Return new residual norm.
357:  */
360: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool  hapend,PetscReal *res)
361: {
362:   PetscScalar *hh,*cc,*ss,tt;
363:   PetscInt    j;
364:   KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);

367:   hh  = HH(0,it);
368:   cc  = CC(0);
369:   ss  = SS(0);

371:   /* Apply all the previously computed plane rotations to the new column
372:      of the Hessenberg matrix */
373:   for (j=1; j<=it; j++) {
374:     tt  = *hh;
375: #if defined(PETSC_USE_COMPLEX)
376:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
377: #else
378:     *hh = *cc * tt + *ss * *(hh+1);
379: #endif
380:     hh++;
381:     *hh = *cc++ * *hh - (*ss++ * tt);
382:   }

384:   /*
385:     compute the new plane rotation, and apply it to:
386:      1) the right-hand-side of the Hessenberg system
387:      2) the new column of the Hessenberg matrix
388:     thus obtaining the updated value of the residual
389:   */
390:   if (!hapend) {
391: #if defined(PETSC_USE_COMPLEX)
392:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
393: #else
394:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
395: #endif
396:     if (tt == 0.0) {
397:       ksp->reason = KSP_DIVERGED_NULL;
398:       return(0);
399:     }
400:     *cc       = *hh / tt;
401:     *ss       = *(hh+1) / tt;
402:     *GRS(it+1) = - (*ss * *GRS(it));
403: #if defined(PETSC_USE_COMPLEX)
404:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
405:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
406: #else
407:     *GRS(it)   = *cc * *GRS(it);
408:     *hh       = *cc * *hh + *ss * *(hh+1);
409: #endif
410:     *res      = PetscAbsScalar(*GRS(it+1));
411:   } else {
412:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
413:             another rotation matrix (so RH doesn't change).  The new residual is 
414:             always the new sine term times the residual from last time (GRS(it)), 
415:             but now the new sine rotation would be zero...so the residual should
416:             be zero...so we will multiply "zero" by the last residual.  This might
417:             not be exactly what we want to do here -could just return "zero". */
418: 
419:     *res = 0.0;
420:   }
421:   return(0);
422: }
423: /*
424:    This routine allocates more work vectors, starting from VEC_VV(it).
425:  */
428: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
429: {
430:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
432:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

435:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
436:   /* Adjust the number to allocate to make sure that we don't exceed the
437:     number of available slots */
438:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated){
439:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
440:   }
441:   if (!nalloc) return(0);

443:   gmres->vv_allocated += nalloc;
444:   KSPGetVecs(ksp,nalloc,&gmres->user_work[nwork],0,PETSC_NULL);
445:   PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
446:   gmres->mwork_alloc[nwork] = nalloc;
447:   for (k=0; k<nalloc; k++) {
448:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
449:   }
450:   gmres->nwork_alloc++;
451:   return(0);
452: }

456: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec  ptr,Vec *result)
457: {
458:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

462:   if (!ptr) {
463:     if (!gmres->sol_temp) {
464:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
465:       PetscLogObjectParent(ksp,gmres->sol_temp);
466:     }
467:     ptr = gmres->sol_temp;
468:   }
469:   if (!gmres->nrs) {
470:     /* allocate the work area */
471:     PetscMalloc(gmres->max_k*sizeof(PetscScalar),&gmres->nrs);
472:     PetscLogObjectMemory(ksp,gmres->max_k*sizeof(PetscScalar));
473:   }

475:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
476:   if (result) *result = ptr;
477:   return(0);
478: }

482: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
483: {
484:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
485:   const char     *cstr;
487:   PetscBool      iascii,isstring;

490:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
491:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
492:   if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
493:     switch (gmres->cgstype) {
494:       case (KSP_GMRES_CGS_REFINE_NEVER):
495:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
496:         break;
497:       case (KSP_GMRES_CGS_REFINE_ALWAYS):
498:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
499:         break;
500:       case (KSP_GMRES_CGS_REFINE_IFNEEDED):
501:         cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
502:         break;
503:       default:
504:         SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
505:     }
506:   } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
507:     cstr = "Modified Gram-Schmidt Orthogonalization";
508:   } else {
509:     cstr = "unknown orthogonalization";
510:   }
511:   if (iascii) {
512:     PetscViewerASCIIPrintf(viewer,"  GMRES: restart=%D, using %s\n",gmres->max_k,cstr);
513:     PetscViewerASCIIPrintf(viewer,"  GMRES: happy breakdown tolerance %G\n",gmres->haptol);
514:   } else if (isstring) {
515:     PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
516:   } else {
517:     SETERRQ1(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"Viewer type %s not supported for KSP GMRES",((PetscObject)viewer)->type_name);
518:   }
519:   return(0);
520: }

524: /*@C
525:    KSPGMRESMonitorKrylov - Calls VecView() for each direction in the 
526:    GMRES accumulated Krylov space.

528:    Collective on KSP

530:    Input Parameters:
531: +  ksp - the KSP context
532: .  its - iteration number
533: .  fgnorm - 2-norm of residual (or gradient)
534: -  a viewers object created with PetscViewersCreate()

536:    Level: intermediate

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

540: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
541: @*/
542: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
543: {
544:   PetscViewers   viewers = (PetscViewers)dummy;
545:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
547:   Vec            x;
548:   PetscViewer    viewer;
549:   PetscBool      flg;

552:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
553:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
554:   if (!flg) {
555:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
556:     PetscViewerDrawSetInfo(viewer,PETSC_NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
557:   }

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

562:   return(0);
563: }

567: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp)
568: {
570:   PetscInt       restart;
571:   PetscReal      haptol;
572:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
573:   PetscBool      flg;

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

601: extern PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
602: extern PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);


605: EXTERN_C_BEGIN
608: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
609: {
610:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

613:   if (tol < 0.0) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
614:   gmres->haptol = tol;
615:   return(0);
616: }
617: EXTERN_C_END

619: EXTERN_C_BEGIN
622: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
623: {
624:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

627:   *max_k = gmres->max_k;
628:   return(0);
629: }
630: EXTERN_C_END

632: EXTERN_C_BEGIN
635: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
636: {
637:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

641:   if (max_k < 1) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
642:   if (!ksp->setupstage) {
643:     gmres->max_k = max_k;
644:   } else if (gmres->max_k != max_k) {
645:      gmres->max_k = max_k;
646:      ksp->setupstage = KSP_SETUP_NEW;
647:      /* free the data structures, then create them again */
648:      KSPReset_GMRES(ksp);
649:   }
650:   return(0);
651: }
652: EXTERN_C_END

654: EXTERN_C_BEGIN
657: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
658: {
660:   ((KSP_GMRES *)ksp->data)->orthog = fcn;
661:   return(0);
662: }
663: EXTERN_C_END

665: EXTERN_C_BEGIN
668: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
669: {
671:   *fcn = ((KSP_GMRES *)ksp->data)->orthog;
672:   return(0);
673: }
674: EXTERN_C_END

676: EXTERN_C_BEGIN
679: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
680: {
681:   KSP_GMRES *gmres;

684:   gmres = (KSP_GMRES *)ksp->data;
685:   gmres->q_preallocate = 1;
686:   return(0);
687: }
688: EXTERN_C_END

690: EXTERN_C_BEGIN
693: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
694: {
695:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

698:   gmres->cgstype = type;
699:   return(0);
700: }
701: EXTERN_C_END

703: EXTERN_C_BEGIN
706: PetscErrorCode  KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
707: {
708:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

711:   *type = gmres->cgstype;
712:   return(0);
713: }
714: EXTERN_C_END

718: /*@
719:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
720:          in the classical Gram Schmidt orthogonalization.

722:    Logically Collective on KSP

724:    Input Parameters:
725: +  ksp - the Krylov space context
726: -  type - the type of refinement

728:   Options Database:
729: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

731:    Level: intermediate

733: .keywords: KSP, GMRES, iterative refinement

735: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
736:           KSPGMRESGetOrthogonalization()
737: @*/
738: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
739: {

745:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
746:   return(0);
747: }

751: /*@
752:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
753:          in the classical Gram Schmidt orthogonalization.

755:    Not Collective

757:    Input Parameter:
758: .  ksp - the Krylov space context

760:    Output Parameter:
761: .  type - the type of refinement

763:   Options Database:
764: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

766:    Level: intermediate

768: .keywords: KSP, GMRES, iterative refinement

770: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
771:           KSPGMRESGetOrthogonalization()
772: @*/
773: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
774: {

779:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType *),(ksp,type));
780:   return(0);
781: }


786: /*@
787:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

789:    Logically Collective on KSP

791:    Input Parameters:
792: +  ksp - the Krylov space context
793: -  restart - integer restart value

795:   Options Database:
796: .  -ksp_gmres_restart <positive integer>

798:     Note: The default value is 30.

800:    Level: intermediate

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

804: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
805: @*/
806: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
807: {


813:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
814:   return(0);
815: }

819: /*@
820:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

822:    Not Collective

824:    Input Parameter:
825: .  ksp - the Krylov space context

827:    Output Parameter:
828: .   restart - integer restart value

830:     Note: The default value is 30.

832:    Level: intermediate

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

836: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
837: @*/
838: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
839: {

843:   PetscTryMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
844:   return(0);
845: }

849: /*@
850:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

852:    Logically Collective on KSP

854:    Input Parameters:
855: +  ksp - the Krylov space context
856: -  tol - the tolerance

858:   Options Database:
859: .  -ksp_gmres_haptol <positive real value>

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

865:    Level: intermediate

867: .keywords: KSP, GMRES, tolerance

869: .seealso: KSPSetTolerances()
870: @*/
871: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
872: {

877:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
878:   return(0);
879: }

881: /*MC
882:      KSPGMRES - Implements the Generalized Minimal Residual method.  
883:                 (Saad and Schultz, 1986) with restart


886:    Options Database Keys:
887: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
888: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
889: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of 
890:                              vectors are allocated as needed)
891: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
892: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
893: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the 
894:                                    stability of the classical Gram-Schmidt  orthogonalization.
895: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

897:    Level: beginner

899:    Notes: Left and right preconditioning are supported, but not symmetric preconditioning.

901:    References:
902:      GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS. YOUCEF SAAD AND MARTIN H. SCHULTZ,
903:           SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986, pp. 856--869.

905: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
906:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
907:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
908:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

910: M*/

912: EXTERN_C_BEGIN
915: PetscErrorCode  KSPCreate_GMRES(KSP ksp)
916: {
917:   KSP_GMRES      *gmres;

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

924:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
925:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,1);

927:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
928:   ksp->ops->setup                        = KSPSetUp_GMRES;
929:   ksp->ops->solve                        = KSPSolve_GMRES;
930:   ksp->ops->reset                        = KSPReset_GMRES;
931:   ksp->ops->destroy                      = KSPDestroy_GMRES;
932:   ksp->ops->view                         = KSPView_GMRES;
933:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
934:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
935:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

937:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
938:                                     "KSPGMRESSetPreAllocateVectors_GMRES",
939:                                      KSPGMRESSetPreAllocateVectors_GMRES);
940:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
941:                                     "KSPGMRESSetOrthogonalization_GMRES",
942:                                      KSPGMRESSetOrthogonalization_GMRES);
943:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",
944:                                     "KSPGMRESGetOrthogonalization_GMRES",
945:                                      KSPGMRESGetOrthogonalization_GMRES);
946:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
947:                                     "KSPGMRESSetRestart_GMRES",
948:                                      KSPGMRESSetRestart_GMRES);
949:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetRestart_C",
950:                                     "KSPGMRESGetRestart_GMRES",
951:                                      KSPGMRESGetRestart_GMRES);
952:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C",
953:                                     "KSPGMRESSetHapTol_GMRES",
954:                                      KSPGMRESSetHapTol_GMRES);
955:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
956:                                     "KSPGMRESSetCGSRefinementType_GMRES",
957:                                      KSPGMRESSetCGSRefinementType_GMRES);
958:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",
959:                                     "KSPGMRESGetCGSRefinementType_GMRES",
960:                                      KSPGMRESGetCGSRefinementType_GMRES);

962:   gmres->haptol              = 1.0e-30;
963:   gmres->q_preallocate       = 0;
964:   gmres->delta_allocate      = GMRES_DELTA_DIRECTIONS;
965:   gmres->orthog              = KSPGMRESClassicalGramSchmidtOrthogonalization;
966:   gmres->nrs                 = 0;
967:   gmres->sol_temp            = 0;
968:   gmres->max_k               = GMRES_DEFAULT_MAXK;
969:   gmres->Rsvd                = 0;
970:   gmres->cgstype             = KSP_GMRES_CGS_REFINE_NEVER;
971:   gmres->orthogwork          = 0;
972:   return(0);
973: }
974: EXTERN_C_END