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);

184:     it++;
185:     gmres->it  = (it-1);  /* For converged */
186:     ksp->its++;
187:     ksp->rnorm = res;
188:     if (ksp->reason) break;

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

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

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

207:   if (itcount) *itcount    = it;


210:   /*
211:     Down here we have to solve for the "best" coefficients of the Krylov
212:     columns, add the solution values together, and possibly unwind the
213:     preconditioning from the solution
214:    */
215:   /* Form the solution (or the solution so far) */
216:   BuildGmresSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

218:   return(0);
219: }

223: PetscErrorCode KSPSolve_GMRES(KSP ksp)
224: {
226:   PetscInt       its,itcount;
227:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
228:   PetscTruth     guess_zero = ksp->guess_zero;

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

236:   PetscObjectTakeAccess(ksp);
237:   ksp->its = 0;
238:   PetscObjectGrantAccess(ksp);

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

258: PetscErrorCode KSPDestroy_GMRES_Internal(KSP ksp)
259: {
260:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
262:   PetscInt       i;

265:   /* Free the Hessenberg matrix */
266:   PetscFree(gmres->hh_origin);

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

271:   /* free work vectors */
272:   for (i=0; i<gmres->nwork_alloc; i++) {
273:     VecDestroyVecs(gmres->user_work[i],gmres->mwork_alloc[i]);
274:   }
275:   PetscFree(gmres->user_work);
276:   PetscFree(gmres->mwork_alloc);
277:   PetscFree(gmres->nrs);
278:   if (gmres->sol_temp) {
279:     VecDestroy(gmres->sol_temp);
280:   }
281:   PetscFree(gmres->Rsvd);
282:   PetscFree(gmres->Dsvd);
283:   PetscFree(gmres->orthogwork);
284:   gmres->sol_temp       = 0;
285:   gmres->vv_allocated   = 0;
286:   gmres->vecs_allocated = 0;
287:   gmres->sol_temp       = 0;
288:   return(0);
289: }

293: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
294: {

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

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

318:      This is an internal routine that knows about the GMRES internals.
319:  */
322: static PetscErrorCode BuildGmresSoln(PetscScalar* nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
323: {
324:   PetscScalar    tt;
326:   PetscInt       ii,k,j;
327:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);

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

332:   /* If it is < 0, no gmres steps have been performed */
333:   if (it < 0) {
334:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
335:     return(0);
336:   }
337:   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)));
338:   if (*HH(it,it) != 0.0) {
339:     nrs[it] = *GRS(it) / *HH(it,it);
340:   } else {
341:     nrs[it] = 0.0;
342:   }
343:   for (ii=1; ii<=it; ii++) {
344:     k   = it - ii;
345:     tt  = *GRS(k);
346:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
347:     if (*HH(k,k) == 0.0) SETERRQ2(PETSC_ERR_CONV_FAILED,"HH(k,k) is identically zero; it = %D k = %D",it,k);
348:     nrs[k]   = tt / *HH(k,k);
349:   }

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

355:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
356:   /* add solution to previous solution */
357:   if (vdest != vs) {
358:     VecCopy(vs,vdest);
359:   }
360:   VecAXPY(vdest,1.0,VEC_TEMP);
361:   return(0);
362: }
363: /*
364:    Do the scalar work for the orthogonalization.  Return new residual.
365:  */
368: static PetscErrorCode GMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
369: {
370:   PetscScalar *hh,*cc,*ss,tt;
371:   PetscInt    j;
372:   KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);

375:   hh  = HH(0,it);
376:   cc  = CC(0);
377:   ss  = SS(0);

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

392:   /*
393:     compute the new plane rotation, and apply it to:
394:      1) the right-hand-side of the Hessenberg system
395:      2) the new column of the Hessenberg matrix
396:     thus obtaining the updated value of the residual
397:   */
398:   if (!hapend) {
399: #if defined(PETSC_USE_COMPLEX)
400:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
401: #else
402:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
403: #endif
404:     if (tt == 0.0) {
405:       ksp->reason = KSP_DIVERGED_NULL;
406:       return(0);
407:     }
408:     *cc       = *hh / tt;
409:     *ss       = *(hh+1) / tt;
410:     *GRS(it+1) = - (*ss * *GRS(it));
411: #if defined(PETSC_USE_COMPLEX)
412:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
413:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
414: #else
415:     *GRS(it)   = *cc * *GRS(it);
416:     *hh       = *cc * *hh + *ss * *(hh+1);
417: #endif
418:     *res      = PetscAbsScalar(*GRS(it+1));
419:   } else {
420:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
421:             another rotation matrix (so RH doesn't change).  The new residual is 
422:             always the new sine term times the residual from last time (GRS(it)), 
423:             but now the new sine rotation would be zero...so the residual should
424:             be zero...so we will multiply "zero" by the last residual.  This might
425:             not be exactly what we want to do here -could just return "zero". */
426: 
427:     *res = 0.0;
428:   }
429:   return(0);
430: }
431: /*
432:    This routine allocates more work vectors, starting from VEC_VV(it).
433:  */
436: static PetscErrorCode GMRESGetNewVectors(KSP ksp,PetscInt it)
437: {
438:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
440:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

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

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

464: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec  ptr,Vec *result)
465: {
466:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

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

483:   BuildGmresSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
484:   if (result) *result = ptr;
485:   return(0);
486: }

490: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
491: {
492:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;
493:   const char     *cstr;
495:   PetscTruth     iascii,isstring;

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

532: /*@C
533:    KSPGMRESMonitorKrylov - Calls VecView() for each direction in the 
534:    GMRES accumulated Krylov space.

536:    Collective on KSP

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

544:    Level: intermediate

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

548: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
549: @*/
550: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
551: {
552:   PetscViewers   viewers = (PetscViewers)dummy;
553:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
555:   Vec            x;
556:   PetscViewer    viewer;

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

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

565:   return(0);
566: }

570: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp)
571: {
573:   PetscInt       restart;
574:   PetscReal      haptol;
575:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
576:   PetscTruth     flg;

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

602: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
603: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);


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

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

623: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
624: {
625:   KSP_GMRES      *gmres = (KSP_GMRES *)ksp->data;

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

646: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
647: {
650:   ((KSP_GMRES *)ksp->data)->orthog = fcn;
651:   return(0);
652: }

658: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
659: {
660:   KSP_GMRES *gmres;

663:   gmres = (KSP_GMRES *)ksp->data;
664:   gmres->q_preallocate = 1;
665:   return(0);
666: }

672: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
673: {
674:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

677:   gmres->cgstype = type;
678:   return(0);
679: }

684: /*@
685:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
686:          in the classical Gram Schmidt orthogonalization.
687:    of the preconditioned problem.

689:    Collective on KSP

691:    Input Parameters:
692: +  ksp - the Krylov space context
693: -  type - the type of refinement

695:   Options Database:
696: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

698:    Level: intermediate

700: .keywords: KSP, GMRES, iterative refinement

702: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization()
703: @*/
704: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
705: {
706:   PetscErrorCode ierr,(*f)(KSP,KSPGMRESCGSRefinementType);

710:   PetscObjectQueryFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",(void (**)(void))&f);
711:   if (f) {
712:     (*f)(ksp,type);
713:   }
714:   return(0);
715: }

719: /*@
720:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

722:    Collective on KSP

724:    Input Parameters:
725: +  ksp - the Krylov space context
726: -  restart - integer restart value

728:   Options Database:
729: .  -ksp_gmres_restart <positive integer>

731:     Note: The default value is 30.

733:    Level: intermediate

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

737: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors()
738: @*/
739: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
740: {

744:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
745:   return(0);
746: }

750: /*@
751:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

753:    Collective on KSP

755:    Input Parameters:
756: +  ksp - the Krylov space context
757: -  tol - the tolerance

759:   Options Database:
760: .  -ksp_gmres_haptol <positive real value>

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

766:    Level: intermediate

768: .keywords: KSP, GMRES, tolerance

770: .seealso: KSPSetTolerances()
771: @*/
772: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
773: {

777:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
778:   return(0);
779: }

781: /*MC
782:      KSPGMRES - Implements the Generalized Minimal Residual method.  
783:                 (Saad and Schultz, 1986) with restart


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

797:    Level: beginner

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

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: }