Actual source code: fgmres.c

  1: /* $Id: fgmres.c,v 1.29 2001/08/07 21:30:49 bsmith Exp $ */

  3: /*
  4:     This file implements FGMRES (a Generalized Minimal Residual) method.  
  5:     Reference:  Saad, 1993.

  7:     Preconditioning:  It the preconditioner is constant then this fgmres
  8:     code is equivalent to RIGHT-PRECONDITIONED GMRES.

 10:     Restarts:  Restarts are basically solves with x0 not equal to zero.
 11:  
 12:        Contributed by Allison Baker

 14: */

 16:  #include src/ksp/ksp/impls/fgmres/fgmresp.h
 17: #define FGMRES_DELTA_DIRECTIONS 10
 18: #define FGMRES_DEFAULT_MAXK     30
 19: static int    FGMRESGetNewVectors(KSP,int);
 20: static int    FGMRESUpdateHessenberg(KSP,int,PetscTruth,PetscReal *);
 21: static int    BuildFgmresSoln(PetscScalar*,Vec,Vec,KSP,int);

 23: extern int KSPView_GMRES(KSP,PetscViewer);
 24: /*

 26:     KSPSetUp_FGMRES - Sets up the workspace needed by fgmres.

 28:     This is called once, usually automatically by KSPSolveQ() or KSPSetUp(),
 29:     but can be called directly by KSPSetUp().

 31: */
 34: int    KSPSetUp_FGMRES(KSP ksp)
 35: {
 36:   unsigned  int size,hh,hes,rs,cc;
 37:   int           ierr,max_k,k;
 38:   KSP_FGMRES    *fgmres = (KSP_FGMRES *)ksp->data;

 41:   if (ksp->pc_side == PC_SYMMETRIC) {
 42:     SETERRQ(2,"no symmetric preconditioning for KSPFGMRES");
 43:   } else if (ksp->pc_side == PC_LEFT) {
 44:     SETERRQ(2,"no left preconditioning for KSPFGMRES");
 45:   }
 46:   max_k         = fgmres->max_k;
 47:   hh            = (max_k + 2) * (max_k + 1);
 48:   hes           = (max_k + 1) * (max_k + 1);
 49:   rs            = (max_k + 2);
 50:   cc            = (max_k + 1);  /* SS and CC are the same size */
 51:   size          = (hh + hes + rs + 2*cc) * sizeof(PetscScalar);

 53:   /* Allocate space and set pointers to beginning */
 54:   PetscMalloc(size,&fgmres->hh_origin);
 55:   PetscMemzero(fgmres->hh_origin,size);
 56:   PetscLogObjectMemory(ksp,size);                      /* HH - modified (by plane 
 57:                                                      rotations) hessenburg */
 58:   fgmres->hes_origin = fgmres->hh_origin + hh;     /* HES - unmodified hessenburg */
 59:   fgmres->rs_origin  = fgmres->hes_origin + hes;   /* RS - the right-hand-side of the 
 60:                                                       Hessenberg system */
 61:   fgmres->cc_origin  = fgmres->rs_origin + rs;     /* CC - cosines for rotations */
 62:   fgmres->ss_origin  = fgmres->cc_origin + cc;     /* SS - sines for rotations */

 64:   if (ksp->calc_sings) {
 65:     /* Allocate workspace to hold Hessenberg matrix needed by Eispack */
 66:     size = (max_k + 3)*(max_k + 9)*sizeof(PetscScalar);
 67:     PetscMalloc(size,&fgmres->Rsvd);
 68:     PetscMalloc(5*(max_k+2)*sizeof(PetscReal),&fgmres->Dsvd);
 69:     PetscLogObjectMemory(ksp,size+5*(max_k+2)*sizeof(PetscReal));
 70:   }

 72:   /* Allocate array to hold pointers to user vectors.  Note that we need
 73:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
 74:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void *),&fgmres->vecs);
 75:   fgmres->vecs_allocated = VEC_OFFSET + 2 + max_k;
 76:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void *),&fgmres->user_work);
 77:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(int),&fgmres->mwork_alloc);
 78:   PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(2*sizeof(void *)+sizeof(int)));

 80:   /* New for FGMRES - Allocate array to hold pointers to preconditioned 
 81:      vectors - same sizes as user vectors above */
 82:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void *),&fgmres->prevecs);
 83:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void *),&fgmres->prevecs_user_work);
 84:   PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(2*sizeof(void *)));


 87:   /* if q_preallocate = 0 then only allocate one "chunck" of space (for 
 88:      5 vectors) - additional will then be allocated from FGMREScycle() 
 89:      as needed.  Otherwise, allocate all of the space that could be needed */
 90:   if (fgmres->q_preallocate) {
 91:     fgmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
 92:   } else {
 93:     fgmres->vv_allocated    = 5;
 94:   }

 96:   /* space for work vectors */
 97:   VecDuplicateVecs(VEC_RHS,fgmres->vv_allocated,&fgmres->user_work[0]);
 98:   PetscLogObjectParents(ksp,fgmres->vv_allocated,fgmres->user_work[0]);
 99:   for (k=0; k < fgmres->vv_allocated; k++) {
100:     fgmres->vecs[k] = fgmres->user_work[0][k];
101:   }

103:   /* space for preconditioned vectors */
104:   VecDuplicateVecs(VEC_RHS,fgmres->vv_allocated,&fgmres->prevecs_user_work[0]);
105:   PetscLogObjectParents(ksp,fgmres->vv_allocated,fgmres->prevecs_user_work[0]);
106:   for (k=0; k < fgmres->vv_allocated; k++) {
107:     fgmres->prevecs[k] = fgmres->prevecs_user_work[0][k];
108:   }

110:   /* specify how many work vectors have been allocated in this 
111:      chunck" (the first one) */
112:   fgmres->mwork_alloc[0] = fgmres->vv_allocated;
113:   fgmres->nwork_alloc    = 1;

115:   return(0);
116: }

118: /* 
119:     FGMRESResidual - This routine computes the initial residual (NOT PRECONDITIONED) 
120: */
123: static int FGMRESResidual(KSP ksp)
124: {
125:   KSP_FGMRES   *fgmres = (KSP_FGMRES *)(ksp->data);
126:   PetscScalar  mone = -1.0;
127:   Mat          Amat,Pmat;
128:   MatStructure pflag;
129:   int          ierr;

132:   PCGetOperators(ksp->B,&Amat,&Pmat,&pflag);

134:   /* put A*x into VEC_TEMP */
135:   MatMult(Amat,VEC_SOLN,VEC_TEMP);
136:   /* now put residual (-A*x + f) into vec_vv(0) */
137:   VecWAXPY(&mone,VEC_TEMP,VEC_RHS,VEC_VV(0));
138:   return(0);
139: }

141: /*

143:     FGMRESCycle - Run fgmres, possibly with restart.  Return residual 
144:                   history if requested.

146:     input parameters:
147: .         fgmres  - structure containing parameters and work areas

149:     output parameters:
150: .        itcount - number of iterations used.  If null, ignored.
151: .        converged - 0 if not converged

153:                   
154:     Notes:
155:     On entry, the value in vector VEC_VV(0) should be 
156:     the initial residual.


159:  */
162: int FGMREScycle(int *itcount,KSP ksp)
163: {

165:   KSP_FGMRES   *fgmres = (KSP_FGMRES *)(ksp->data);
166:   PetscReal    res_norm;
167:   PetscReal    hapbnd,tt;
168:   PetscScalar  zero = 0.0;
169:   PetscScalar  tmp;
170:   PetscTruth   hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
171:   int          ierr;
172:   int          loc_it;                /* local count of # of dir. in Krylov space */
173:   int          max_k = fgmres->max_k; /* max # of directions Krylov space */
174:   Mat          Amat,Pmat;
175:   MatStructure pflag;


179:   /* Number of pseudo iterations since last restart is the number 
180:      of prestart directions */
181:   loc_it = 0;

183:   /* initial residual is in VEC_VV(0)  - compute its norm*/
184:   VecNorm(VEC_VV(0),NORM_2,&res_norm);

186:   /* first entry in right-hand-side of hessenberg system is just 
187:      the initial residual norm */
188:   *RS(0) = res_norm;

190:   /* FYI: AMS calls are for memory snooper */
191:   PetscObjectTakeAccess(ksp);
192:   ksp->rnorm = res_norm;
193:   PetscObjectGrantAccess(ksp);
194:   KSPLogResidualHistory(ksp,res_norm);

196:   /* check for the convergence - maybe the current guess is good enough */
197:   (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);
198:   if (ksp->reason) {
199:     if (itcount) *itcount = 0;
200:     return(0);
201:   }

203:   /* scale VEC_VV (the initial residual) */
204:   tmp = 1.0/res_norm; VecScale(&tmp,VEC_VV(0));



208:   /* note: (fgmres->it) is always set one less than (loc_it) It is used in 
209:      KSPBUILDSolution_FGMRES, where it is passed to BuildFGmresSoln.  
210:      Note that when BuildFGmresSoln is called from this function, 
211:      (loc_it -1) is passed, so the two are equivalent */
212:   fgmres->it = (loc_it - 1);
213: 
214:   /* MAIN ITERATION LOOP BEGINNING*/
215:   /* keep iterating until we have converged OR generated the max number
216:      of directions OR reached the max number of iterations for the method */
217:   (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);
218:   while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
219:     KSPLogResidualHistory(ksp,res_norm);
220:     fgmres->it = (loc_it - 1);
221:     KSPMonitor(ksp,ksp->its,res_norm);

223:     /* see if more space is needed for work vectors */
224:     if (fgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
225:       FGMRESGetNewVectors(ksp,loc_it+1);
226:       /* (loc_it+1) is passed in as number of the first vector that should
227:          be allocated */
228:     }

230:     /* CHANGE THE PRECONDITIONER? */
231:     /* ModifyPC is the callback function that can be used to
232:        change the PC or its attributes before its applied */
233:     (*fgmres->modifypc)(ksp,ksp->its,loc_it,res_norm,fgmres->modifyctx);
234: 
235: 
236:     /* apply PRECONDITIONER to direction vector and store with 
237:        preconditioned vectors in prevec */
238:     PCApply(ksp->B,VEC_VV(loc_it),PREVEC(loc_it),PC_RIGHT);
239: 
240:     PCGetOperators(ksp->B,&Amat,&Pmat,&pflag);
241:     /* Multiply preconditioned vector by operator - put in VEC_VV(loc_it+1) */
242:     MatMult(Amat,PREVEC(loc_it),VEC_VV(1+loc_it));

244: 
245:     /* update hessenberg matrix and do Gram-Schmidt - new direction is in
246:        VEC_VV(1+loc_it)*/
247:     (*fgmres->orthog)(ksp,loc_it);

249:     /* new entry in hessenburg is the 2-norm of our new direction */
250:     VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);
251:     *HH(loc_it+1,loc_it)   = tt;
252:     *HES(loc_it+1,loc_it)  = tt;

254:     /* Happy Breakdown Check */
255:     hapbnd  = PetscAbsScalar((tt) / *RS(loc_it));
256:     /* RS(loc_it) contains the res_norm from the last iteration  */
257:     hapbnd = PetscMin(fgmres->haptol,hapbnd);
258:     if (tt > hapbnd) {
259:         tmp = 1.0/tt;
260:         /* scale new direction by its norm */
261:         VecScale(&tmp,VEC_VV(loc_it+1));
262:     } else {
263:         /* This happens when the solution is exactly reached. */
264:         /* So there is no new direction... */
265:           VecSet(&zero,VEC_TEMP); /* set VEC_TEMP to 0 */
266:           hapend = PETSC_TRUE;
267:     }
268:     /* note that for FGMRES we could get HES(loc_it+1, loc_it)  = 0 and the
269:        current solution would not be exact if HES was singular.  Note that 
270:        HH non-singular implies that HES is no singular, and HES is guaranteed
271:        to be nonsingular when PREVECS are linearly independent and A is 
272:        nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity 
273:        of HES). So we should really add a check to verify that HES is nonsingular.*/

275: 
276:     /* Now apply rotations to new col of hessenberg (and right side of system), 
277:        calculate new rotation, and get new residual norm at the same time*/
278:     FGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm);
279:     loc_it++;
280:     fgmres->it  = (loc_it-1);  /* Add this here in case it has converged */
281: 
282:     PetscObjectTakeAccess(ksp);
283:     ksp->its++;
284:     ksp->rnorm = res_norm;
285:     PetscObjectGrantAccess(ksp);

287:     (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);

289:     /* Catch error in happy breakdown and signal convergence and break from loop */
290:     if (hapend) {
291:       if (!ksp->reason) {
292:         SETERRQ(0,"You reached the happy break down,but convergence was not indicated.");
293:       }
294:       break;
295:     }
296:   }
297:   /* END OF ITERATION LOOP */

299:   KSPLogResidualHistory(ksp,res_norm);

301:   /*
302:      Monitor if we know that we will not return for a restart */
303:   if (ksp->reason || ksp->its >= ksp->max_it) {
304:     KSPMonitor(ksp,ksp->its,res_norm);
305:   }

307:   if (itcount) *itcount    = loc_it;

309:   /*
310:     Down here we have to solve for the "best" coefficients of the Krylov
311:     columns, add the solution values together, and possibly unwind the
312:     preconditioning from the solution
313:    */
314: 
315:   /* Form the solution (or the solution so far) */
316:   /* Note: must pass in (loc_it-1) for iteration count so that BuildFgmresSoln
317:      properly navigates */

319:   BuildFgmresSoln(RS(0),VEC_SOLN,VEC_SOLN,ksp,loc_it-1);

321:   return(0);
322: }

324: /*  
325:     KSPSolve_FGMRES - This routine applies the FGMRES method.


328:    Input Parameter:
329: .     ksp - the Krylov space object that was set to use fgmres

331:    Output Parameter:
332: .     outits - number of iterations used

334: */

338: int KSPSolve_FGMRES(KSP ksp)
339: {
340:   int        ierr;
341:   int        cycle_its; /* iterations done in a call to FGMREScycle */
342:   int        itcount;   /* running total of iterations, incl. those in restarts */
343:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
344:   PetscTruth diagonalscale;

347:   PCDiagonalScale(ksp->B,&diagonalscale);
348:   if (diagonalscale) SETERRQ1(1,"Krylov method %s does not support diagonal scaling",ksp->type_name);

350:   PetscObjectTakeAccess(ksp);
351:   ksp->its = 0;
352:   PetscObjectGrantAccess(ksp);

354:   /* initialize */
355:   itcount  = 0;

357:   /* Compute the initial (NOT preconditioned) residual */
358:   if (!ksp->guess_zero) {
359:     FGMRESResidual(ksp);
360:   } else { /* guess is 0 so residual is F (which is in VEC_RHS) */
361:     VecCopy(VEC_RHS,VEC_VV(0));
362:   }
363:   /* now the residual is in VEC_VV(0) - which is what 
364:      FGMREScycle expects... */
365: 
366:   FGMREScycle(&cycle_its,ksp);
367:   itcount += cycle_its;
368:   while (!ksp->reason) {
369:     FGMRESResidual(ksp);
370:     if (itcount >= ksp->max_it) break;
371:     FGMREScycle(&cycle_its,ksp);
372:     itcount += cycle_its;
373:   }
374:   /* mark lack of convergence */
375:   if (itcount >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;

377:   return(0);
378: }

380: /*

382:    KSPDestroy_FGMRES - Frees all memory space used by the Krylov method.

384: */
387: int KSPDestroy_FGMRES(KSP ksp)
388: {
389:   KSP_FGMRES *fgmres = (KSP_FGMRES*)ksp->data;
390:   int       i,ierr;

393:   /* Free the Hessenberg matrices */
394:   if (fgmres->hh_origin) {PetscFree(fgmres->hh_origin);}

396:   /* Free pointers to user variables */
397:   if (fgmres->vecs) {PetscFree(fgmres->vecs);}
398:   if (fgmres->prevecs) {PetscFree (fgmres->prevecs);}

400:   /* free work vectors */
401:   for (i=0; i < fgmres->nwork_alloc; i++) {
402:     VecDestroyVecs(fgmres->user_work[i],fgmres->mwork_alloc[i]);
403:   }
404:   if (fgmres->user_work)  {PetscFree(fgmres->user_work);}

406:   for (i=0; i < fgmres->nwork_alloc; i++) {
407:     VecDestroyVecs(fgmres->prevecs_user_work[i],fgmres->mwork_alloc[i]);
408:   }
409:   if (fgmres->prevecs_user_work) {PetscFree(fgmres->prevecs_user_work);}

411:   if (fgmres->mwork_alloc) {PetscFree(fgmres->mwork_alloc);}
412:   if (fgmres->nrs) {PetscFree(fgmres->nrs);}
413:   if (fgmres->sol_temp) {VecDestroy(fgmres->sol_temp);}
414:   if (fgmres->Rsvd) {PetscFree(fgmres->Rsvd);}
415:   if (fgmres->Dsvd) {PetscFree(fgmres->Dsvd);}
416:   if (fgmres->modifydestroy) {
417:     (*fgmres->modifydestroy)(fgmres->modifyctx);
418:   }
419:   PetscFree(fgmres);
420:   return(0);
421: }

423: /*
424:     BuildFgmresSoln - create the solution from the starting vector and the
425:                       current iterates.

427:     Input parameters:
428:         nrs - work area of size it + 1.
429:         vguess  - index of initial guess
430:         vdest - index of result.  Note that vguess may == vdest (replace
431:                 guess with the solution).
432:         it - HH upper triangular part is a block of size (it+1) x (it+1)  

434:      This is an internal routine that knows about the FGMRES internals.
435:  */
438: static int BuildFgmresSoln(PetscScalar* nrs,Vec vguess,Vec vdest,KSP ksp,int it)
439: {
440:   PetscScalar  tt,zero = 0.0,one = 1.0;
441:   int          ierr,ii,k,j;
442:   KSP_FGMRES   *fgmres = (KSP_FGMRES *)(ksp->data);

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

447:   /* If it is < 0, no fgmres steps have been performed */
448:   if (it < 0) {
449:     if (vdest != vguess) {
450:       VecCopy(vguess,vdest);
451:     }
452:     return(0);
453:   }

455:   /* so fgmres steps HAVE been performed */

457:   /* solve the upper triangular system - RS is the right side and HH is 
458:      the upper triangular matrix  - put soln in nrs */
459:   nrs[it] = *RS(it) / *HH(it,it);
460:   for (ii=1; ii<=it; ii++) {
461:     k   = it - ii;
462:     tt  = *RS(k);
463:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
464:     nrs[k]   = tt / *HH(k,k);
465:   }

467:   /* Accumulate the correction to the soln of the preconditioned prob. in 
468:      VEC_TEMP - note that we use the preconditioned vectors  */
469:   VecSet(&zero,VEC_TEMP); /* set VEC_TEMP components to 0 */
470:   VecMAXPY(it+1,nrs,VEC_TEMP,&PREVEC(0));

472:   /* put updated solution into vdest.*/
473:   if (vdest != vguess) {
474:     VecCopy(VEC_TEMP,vdest);
475:     VecAXPY(&one,vguess,vdest);
476:   } else  {/* replace guess with solution */
477:     VecAXPY(&one,VEC_TEMP,vdest);
478:   }
479:   return(0);
480: }

482: /*

484:     FGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.  
485:                             Return new residual.

487:     input parameters:

489: .        ksp -    Krylov space object
490: .         it  -    plane rotations are applied to the (it+1)th column of the 
491:                   modified hessenberg (i.e. HH(:,it))
492: .        hapend - PETSC_FALSE not happy breakdown ending.

494:     output parameters:
495: .        res - the new residual
496:         
497:  */
500: static int FGMRESUpdateHessenberg(KSP ksp,int it,PetscTruth hapend,PetscReal *res)
501: {
502:   PetscScalar   *hh,*cc,*ss,tt;
503:   int           j;
504:   KSP_FGMRES    *fgmres = (KSP_FGMRES *)(ksp->data);

507:   hh  = HH(0,it);  /* pointer to beginning of column to update - so 
508:                       incrementing hh "steps down" the (it+1)th col of HH*/
509:   cc  = CC(0);     /* beginning of cosine rotations */
510:   ss  = SS(0);     /* beginning of sine rotations */

512:   /* Apply all the previously computed plane rotations to the new column
513:      of the Hessenberg matrix */
514:   /* Note: this uses the rotation [conj(c)  s ; -s   c], c= cos(theta), s= sin(theta),
515:      and some refs have [c   s ; -conj(s)  c] (don't be confused!) */

517:   for (j=1; j<=it; j++) {
518:     tt  = *hh;
519: #if defined(PETSC_USE_COMPLEX)
520:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
521: #else
522:     *hh = *cc * tt + *ss * *(hh+1);
523: #endif
524:     hh++;
525:     *hh = *cc++ * *hh - (*ss++ * tt);
526:     /* hh, cc, and ss have all been incremented one by end of loop */
527:   }

529:   /*
530:     compute the new plane rotation, and apply it to:
531:      1) the right-hand-side of the Hessenberg system (RS)
532:         note: it affects RS(it) and RS(it+1)
533:      2) the new column of the Hessenberg matrix
534:         note: it affects HH(it,it) which is currently pointed to 
535:         by hh and HH(it+1, it) (*(hh+1))  
536:     thus obtaining the updated value of the residual...
537:   */

539:   /* compute new plane rotation */

541:   if (!hapend) {
542: #if defined(PETSC_USE_COMPLEX)
543:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
544: #else
545:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
546: #endif
547:     if (tt == 0.0) {SETERRQ(PETSC_ERR_KSP_BRKDWN,"Your matrix or preconditioner is the null operator");}
548:     *cc       = *hh / tt;   /* new cosine value */
549:     *ss       = *(hh+1) / tt;  /* new sine value */

551:     /* apply to 1) and 2) */
552:     *RS(it+1) = - (*ss * *RS(it));
553: #if defined(PETSC_USE_COMPLEX)
554:     *RS(it)   = PetscConj(*cc) * *RS(it);
555:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
556: #else
557:     *RS(it)   = *cc * *RS(it);
558:     *hh       = *cc * *hh + *ss * *(hh+1);
559: #endif

561:     /* residual is the last element (it+1) of right-hand side! */
562:     *res      = PetscAbsScalar(*RS(it+1));

564:   } else { /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
565:             another rotation matrix (so RH doesn't change).  The new residual is 
566:             always the new sine term times the residual from last time (RS(it)), 
567:             but now the new sine rotation would be zero...so the residual should
568:             be zero...so we will multiply "zero" by the last residual.  This might
569:             not be exactly what we want to do here -could just return "zero". */
570: 
571:     *res = 0.0;
572:   }
573:   return(0);
574: }

576: /*

578:    FGMRESGetNewVectors - This routine allocates more work vectors, starting from 
579:                          VEC_VV(it), and more preconditioned work vectors, starting 
580:                          from PREVEC(i).

582: */
585: static int FGMRESGetNewVectors(KSP ksp,int it)
586: {
587:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
588:   int        nwork = fgmres->nwork_alloc; /* number of work vector chunks allocated */
589:   int        nalloc;                      /* number to allocate */
590:   int        k,ierr;
591: 
593:   nalloc = fgmres->delta_allocate; /* number of vectors to allocate 
594:                                       in a single chunk */

596:   /* Adjust the number to allocate to make sure that we don't exceed the
597:      number of available slots (fgmres->vecs_allocated)*/
598:   if (it + VEC_OFFSET + nalloc >= fgmres->vecs_allocated){
599:     nalloc = fgmres->vecs_allocated - it - VEC_OFFSET;
600:   }
601:   if (!nalloc) return(0);

603:   fgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */

605:   /* work vectors */
606:   VecDuplicateVecs(VEC_RHS,nalloc,&fgmres->user_work[nwork]);
607:   PetscLogObjectParents(ksp,nalloc,fgmres->user_work[nwork]);
608:   for (k=0; k < nalloc; k++) {
609:     fgmres->vecs[it+VEC_OFFSET+k] = fgmres->user_work[nwork][k];
610:   }
611:   /* specify size of chunk allocated */
612:   fgmres->mwork_alloc[nwork] = nalloc;

614:   /* preconditioned vectors */
615:   VecDuplicateVecs(VEC_RHS,nalloc,&fgmres->prevecs_user_work[nwork]);
616:   PetscLogObjectParents(ksp,nalloc,fgmres->prevecs_user_work[nwork]);
617:   for (k=0; k < nalloc; k++) {
618:     fgmres->prevecs[it+VEC_OFFSET+k] = fgmres->prevecs_user_work[nwork][k];
619:   }

621:   /* increment the number of work vector chunks */
622:   fgmres->nwork_alloc++;
623:   return(0);
624: }

626: /* 

628:    KSPBuildSolution_FGMRES

630:      Input Parameter:
631: .     ksp - the Krylov space object
632: .     ptr-

634:    Output Parameter:
635: .     result - the solution

637:    Note: this calls BuildFgmresSoln - the same function that FGMREScycle
638:    calls directly.  

640: */
643: int KSPBuildSolution_FGMRES(KSP ksp,Vec ptr,Vec *result)
644: {
645:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
646:   int        ierr;

649:   if (!ptr) {
650:     if (!fgmres->sol_temp) {
651:       VecDuplicate(ksp->vec_sol,&fgmres->sol_temp);
652:       PetscLogObjectParent(ksp,fgmres->sol_temp);
653:     }
654:     ptr = fgmres->sol_temp;
655:   }
656:   if (!fgmres->nrs) {
657:     /* allocate the work area */
658:     PetscMalloc(fgmres->max_k*sizeof(PetscScalar),&fgmres->nrs);
659:     PetscLogObjectMemory(ksp,fgmres->max_k*sizeof(PetscScalar));
660:   }
661: 
662:   BuildFgmresSoln(fgmres->nrs,VEC_SOLN,ptr,ksp,fgmres->it);
663:   *result = ptr;
664: 
665:   return(0);
666: }


671: int KSPSetFromOptions_FGMRES(KSP ksp)
672: {
673:   int         ierr,restart,indx;
674:   PetscReal   haptol;
675:   KSP_FGMRES *gmres = (KSP_FGMRES*)ksp->data;
676:   PetscTruth  flg;
677:   const char  *types[] = {"never","ifneeded","always"};

680:   PetscOptionsHead("KSP flexible GMRES Options");
681:     PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
682:     if (flg) { KSPGMRESSetRestart(ksp,restart); }
683:     PetscOptionsReal("-ksp_gmres_haptol","Tolerance for declaring exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
684:     if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
685:     PetscOptionsName("-ksp_gmres_preallocate","Preallocate all Krylov vectors","KSPGMRESSetPreAllocateVectors",&flg);
686:     if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
687:     PetscOptionsLogicalGroupBegin("-ksp_gmres_classicalgramschmidt","Use classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
688:     if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
689:     PetscOptionsLogicalGroup("-ksp_gmres_modifiedgramschmidt","Use modified Gram-Schmidt (slow but more stable)","KSPGMRESSetOrthogonalization",&flg);
690:     if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
691:     PetscOptionsEList("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType()",types,3,types[gmres->cgstype],&indx,&flg);
692:     if (flg) {
693:       KSPGMRESSetCGSRefinementType(ksp,(KSPGMRESCGSRefinementType)indx);
694:     }
695:     PetscOptionsName("-ksp_gmres_krylov_monitor","Graphically plot the Krylov directions","KSPSetMonitor",&flg);
696:     if (flg) {
697:       PetscViewers viewers;
698:       PetscViewersCreate(ksp->comm,&viewers);
699:       KSPSetMonitor(ksp,KSPGMRESKrylovMonitor,viewers,(int (*)(void*))PetscViewersDestroy);
700:     }
701:     PetscOptionsLogicalGroupBegin("-ksp_fgmres_modifypcnochange","do not vary the preconditioner","KSPFGMRESSetModifyPC",&flg);
702:     if (flg) {KSPFGMRESSetModifyPC(ksp,KSPFGMRESModifyPCNoChange,0,0);}
703:     PetscOptionsLogicalGroupEnd("-ksp_fgmres_modifypcksp","vary the KSP based preconditioner","KSPFGMRESSetModifyPC",&flg);
704:     if (flg) {KSPFGMRESSetModifyPC(ksp,KSPFGMRESModifyPCKSP,0,0);}
705:   PetscOptionsTail();
706:   return(0);
707: }

709: EXTERN int KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
710: EXTERN int KSPComputeEigenvalues_GMRES(KSP,int,PetscReal *,PetscReal *,int *);

712: typedef int (*FCN1)(KSP,int,int,PetscReal,void*); /* force argument to next function to not be extern C*/
713: typedef int (*FCN2)(void*);
714: EXTERN_C_BEGIN
717: int KSPFGMRESSetModifyPC_FGMRES(KSP ksp,FCN1 fcn,void *ctx,FCN2 d)
718: {
721:   ((KSP_FGMRES *)ksp->data)->modifypc      = fcn;
722:   ((KSP_FGMRES *)ksp->data)->modifydestroy = d;
723:   ((KSP_FGMRES *)ksp->data)->modifyctx     = ctx;
724:   return(0);
725: }
726: EXTERN_C_END

728: EXTERN_C_BEGIN
729: EXTERN int KSPGMRESSetPreAllocateVectors_GMRES(KSP);
730: EXTERN int KSPGMRESSetRestart_GMRES(KSP,int);
731: EXTERN int KSPGMRESSetOrthogonalization_GMRES(KSP,int (*)(KSP,int));
732: EXTERN_C_END

736: int KSPDestroy_FGMRES_Internal(KSP ksp)
737: {
738:   KSP_FGMRES *gmres = (KSP_FGMRES*)ksp->data;
739:   int       i,ierr;

742:   /* Free the Hessenberg matrix */
743:   if (gmres->hh_origin) {PetscFree(gmres->hh_origin);}

745:   /* Free the pointer to user variables */
746:   if (gmres->vecs) {PetscFree(gmres->vecs);}

748:   /* free work vectors */
749:   for (i=0; i<gmres->nwork_alloc; i++) {
750:     VecDestroyVecs(gmres->user_work[i],gmres->mwork_alloc[i]);
751:   }
752:   if (gmres->user_work)  {PetscFree(gmres->user_work);}
753:   if (gmres->mwork_alloc) {PetscFree(gmres->mwork_alloc);}
754:   if (gmres->nrs) {PetscFree(gmres->nrs);}
755:   if (gmres->sol_temp) {VecDestroy(gmres->sol_temp);}
756:   if (gmres->Rsvd) {PetscFree(gmres->Rsvd);}
757:   if (gmres->Dsvd) {PetscFree(gmres->Dsvd);}

759:   return(0);
760: }

762: EXTERN_C_BEGIN
765: int KSPGMRESSetRestart_FGMRES(KSP ksp,int max_k)
766: {
767:   KSP_FGMRES *gmres = (KSP_FGMRES *)ksp->data;
768:   int        ierr;

771:   if (max_k < 1) SETERRQ(1,"Restart must be positive");
772:   if (!ksp->setupcalled) {
773:     gmres->max_k = max_k;
774:   } else if (gmres->max_k != max_k) {
775:      gmres->max_k = max_k;
776:      ksp->setupcalled = 0;
777:      /* free the data structures, then create them again */
778:      KSPDestroy_FGMRES_Internal(ksp);
779:   }
780:   return(0);
781: }
782: EXTERN_C_END

784: EXTERN_C_BEGIN
785: EXTERN int KSPGMRESSetCGSRefinementType_GMRES(KSP,KSPGMRESCGSRefinementType);
786: EXTERN_C_END

788: /*MC
789:      KSPFGMRES - Implements the Flexible Generalized Minimal Residual method.  
790:                 developed by Saad with restart


793:    Options Database Keys:
794: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
795: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
796: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of 
797:                              vectors are allocated as needed)
798: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
799: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
800: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the 
801:                                    stability of the classical Gram-Schmidt  orthogonalization.
802: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
803: .   -ksp_fgmres_modifypcnochange - do not change the preconditioner between iterations
804: -   -ksp_fgmres_modifypcksp - modify the preconditioner using KSPFGMRESModifyPCKSP()

806:    Level: beginner

808:     Notes: See KSPFGMRESSetModifyPC() for how to vary the preconditioner between iterations

810: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES,
811:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
812:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
813:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESKrylovMonitor(), KSPFGMRESSetModifyPC(),
814:            KSPFGMRESModifyPCKSP()

816: M*/

818: EXTERN_C_BEGIN
821: int KSPCreate_FGMRES(KSP ksp)
822: {
823:   KSP_FGMRES *fgmres;
824:   int        ierr;

827:   PetscNew(KSP_FGMRES,&fgmres);
828:   PetscMemzero(fgmres,sizeof(KSP_FGMRES));
829:   PetscLogObjectMemory(ksp,sizeof(KSP_FGMRES));
830:   ksp->data                              = (void*)fgmres;
831:   ksp->ops->buildsolution                = KSPBuildSolution_FGMRES;

833:   ksp->ops->setup                        = KSPSetUp_FGMRES;
834:   ksp->ops->solve                        = KSPSolve_FGMRES;
835:   ksp->ops->destroy                      = KSPDestroy_FGMRES;
836:   ksp->ops->view                         = KSPView_GMRES;
837:   ksp->ops->setfromoptions               = KSPSetFromOptions_FGMRES;
838:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
839:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

841:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
842:                                     "KSPGMRESSetPreAllocateVectors_GMRES",
843:                                      KSPGMRESSetPreAllocateVectors_GMRES);
844:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
845:                                     "KSPGMRESSetOrthogonalization_GMRES",
846:                                      KSPGMRESSetOrthogonalization_GMRES);
847:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
848:                                     "KSPGMRESSetRestart_FGMRES",
849:                                      KSPGMRESSetRestart_FGMRES);
850:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPFGMRESSetModifyPC_C",
851:                                     "KSPFGMRESSetModifyPC_FGMRES",
852:                                      KSPFGMRESSetModifyPC_FGMRES);
853:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
854:                                     "KSPGMRESSetCGSRefinementType_GMRES",
855:                                      KSPGMRESSetCGSRefinementType_GMRES);


858:   fgmres->haptol              = 1.0e-30;
859:   fgmres->q_preallocate       = 0;
860:   fgmres->delta_allocate      = FGMRES_DELTA_DIRECTIONS;
861:   fgmres->orthog              = KSPGMRESClassicalGramSchmidtOrthogonalization;
862:   fgmres->nrs                 = 0;
863:   fgmres->sol_temp            = 0;
864:   fgmres->max_k               = FGMRES_DEFAULT_MAXK;
865:   fgmres->Rsvd                = 0;
866:   fgmres->modifypc            = KSPFGMRESModifyPCNoChange;
867:   fgmres->modifyctx           = PETSC_NULL;
868:   fgmres->modifydestroy       = PETSC_NULL;
869:   fgmres->cgstype             = KSP_GMRES_CGS_REFINE_NEVER;
870:   /*
871:         This is not great since it changes this without explicit request from the user
872:      but there is no left preconditioning in the FGMRES
873:   */
874:   PetscLogInfo(ksp,"Warning: Setting PC_SIDE for FGMRES to right!\n");
875:   ksp->pc_side                = PC_RIGHT;

877:   return(0);
878: }
879: EXTERN_C_END