Actual source code: fgmres.c

  1: #define PETSCKSP_DLL

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

  7:     Preconditioning:  If the preconditioner is constant then this fgmres
  8:     code is equivalent to RIGHT-PRECONDITIONED GMRES.
  9:     FGMRES is a modification of gmres that allows the preconditioner to change
 10:     at each iteration.

 12:     Restarts:  Restarts are basically solves with x0 not equal to zero.
 13:  
 14:        Contributed by Allison Baker

 16: */

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

 25: EXTERN PetscErrorCode KSPView_GMRES(KSP,PetscViewer);
 26: /*

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

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

 33: */
 36: PetscErrorCode    KSPSetUp_FGMRES(KSP ksp)
 37: {
 38:   PetscInt       size,hh,hes,rs,cc;
 40:   PetscInt       max_k,k;
 41:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)ksp->data;

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

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

 66:   if (ksp->calc_sings) {
 67:     /* Allocate workspace to hold Hessenberg matrix needed by Eispack */
 68:     size = (max_k + 3)*(max_k + 9)*sizeof(PetscScalar);
 69:     PetscMalloc(size,&fgmres->Rsvd);
 70:     PetscMalloc(5*(max_k+2)*sizeof(PetscReal),&fgmres->Dsvd);
 71:     PetscLogObjectMemory(ksp,size+5*(max_k+2)*sizeof(PetscReal));
 72:   }

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

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


 89:   /* if q_preallocate = 0 then only allocate one "chunck" of space (for 
 90:      5 vectors) - additional will then be allocated from FGMREScycle() 
 91:      as needed.  Otherwise, allocate all of the space that could be needed */
 92:   if (fgmres->q_preallocate) {
 93:     fgmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
 94:   } else {
 95:     fgmres->vv_allocated    = 5;
 96:   }

 98:   /* space for work vectors */
 99:   KSPGetVecs(ksp,fgmres->vv_allocated,&fgmres->user_work[0],0,PETSC_NULL);
100:   PetscLogObjectParents(ksp,fgmres->vv_allocated,fgmres->user_work[0]);
101:   for (k=0; k < fgmres->vv_allocated; k++) {
102:     fgmres->vecs[k] = fgmres->user_work[0][k];
103:   }

105:   /* space for preconditioned vectors */
106:   KSPGetVecs(ksp,fgmres->vv_allocated,&fgmres->prevecs_user_work[0],0,PETSC_NULL);
107:   PetscLogObjectParents(ksp,fgmres->vv_allocated,fgmres->prevecs_user_work[0]);
108:   for (k=0; k < fgmres->vv_allocated; k++) {
109:     fgmres->prevecs[k] = fgmres->prevecs_user_work[0][k];
110:   }

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

117:   return(0);
118: }

120: /* 
121:     FGMRESResidual - This routine computes the initial residual (NOT PRECONDITIONED) 
122: */
125: static PetscErrorCode FGMRESResidual(KSP ksp)
126: {
127:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)(ksp->data);
128:   Mat            Amat,Pmat;
129:   MatStructure   pflag;

133:   PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);

135:   /* put A*x into VEC_TEMP */
136:   MatMult(Amat,ksp->vec_sol,VEC_TEMP);
137:   /* now put residual (-A*x + f) into vec_vv(0) */
138:   VecWAXPY(VEC_VV(0),-1.0,VEC_TEMP,ksp->vec_rhs);
139:   return(0);
140: }

142: /*

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

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

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

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


160:  */
163: PetscErrorCode FGMREScycle(PetscInt *itcount,KSP ksp)
164: {

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


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

182:   /* note: (fgmres->it) is always set one less than (loc_it) It is used in 
183:      KSPBUILDSolution_FGMRES, where it is passed to BuildFGmresSoln.  
184:      Note that when BuildFGmresSoln is called from this function, 
185:      (loc_it -1) is passed, so the two are equivalent */
186:   fgmres->it = (loc_it - 1);

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

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

195:   ksp->rnorm = res_norm;
196:   KSPLogResidualHistory(ksp,res_norm);

198:   /* check for the convergence - maybe the current guess is good enough */
199:   (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);
200:   if (ksp->reason) {
201:     if (itcount) *itcount = 0;
202:     return(0);
203:   }

205:   /* scale VEC_VV (the initial residual) */
206:   VecScale(VEC_VV(0),1.0/res_norm);
207: 
208:   /* MAIN ITERATION LOOP BEGINNING*/
209:   /* keep iterating until we have converged OR generated the max number
210:      of directions OR reached the max number of iterations for the method */
211:   while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
212:     if (loc_it) KSPLogResidualHistory(ksp,res_norm);
213:     fgmres->it = (loc_it - 1);
214:     KSPMonitor(ksp,ksp->its,res_norm);

216:     /* see if more space is needed for work vectors */
217:     if (fgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
218:       FGMRESGetNewVectors(ksp,loc_it+1);
219:       /* (loc_it+1) is passed in as number of the first vector that should
220:          be allocated */
221:     }

223:     /* CHANGE THE PRECONDITIONER? */
224:     /* ModifyPC is the callback function that can be used to
225:        change the PC or its attributes before its applied */
226:     (*fgmres->modifypc)(ksp,ksp->its,loc_it,res_norm,fgmres->modifyctx);
227: 
228: 
229:     /* apply PRECONDITIONER to direction vector and store with 
230:        preconditioned vectors in prevec */
231:     KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));
232: 
233:     PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
234:     /* Multiply preconditioned vector by operator - put in VEC_VV(loc_it+1) */
235:     MatMult(Amat,PREVEC(loc_it),VEC_VV(1+loc_it));

237: 
238:     /* update hessenberg matrix and do Gram-Schmidt - new direction is in
239:        VEC_VV(1+loc_it)*/
240:     (*fgmres->orthog)(ksp,loc_it);

242:     /* new entry in hessenburg is the 2-norm of our new direction */
243:     VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);
244:     *HH(loc_it+1,loc_it)   = tt;
245:     *HES(loc_it+1,loc_it)  = tt;

247:     /* Happy Breakdown Check */
248:     hapbnd  = PetscAbsScalar((tt) / *RS(loc_it));
249:     /* RS(loc_it) contains the res_norm from the last iteration  */
250:     hapbnd = PetscMin(fgmres->haptol,hapbnd);
251:     if (tt > hapbnd) {
252:         /* scale new direction by its norm */
253:         VecScale(VEC_VV(loc_it+1),1.0/tt);
254:     } else {
255:         /* This happens when the solution is exactly reached. */
256:         /* So there is no new direction... */
257:           VecSet(VEC_TEMP,0.0); /* set VEC_TEMP to 0 */
258:           hapend = PETSC_TRUE;
259:     }
260:     /* note that for FGMRES we could get HES(loc_it+1, loc_it)  = 0 and the
261:        current solution would not be exact if HES was singular.  Note that 
262:        HH non-singular implies that HES is no singular, and HES is guaranteed
263:        to be nonsingular when PREVECS are linearly independent and A is 
264:        nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity 
265:        of HES). So we should really add a check to verify that HES is nonsingular.*/

267: 
268:     /* Now apply rotations to new col of hessenberg (and right side of system), 
269:        calculate new rotation, and get new residual norm at the same time*/
270:     FGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm);
271:     if (ksp->reason) break;

273:     loc_it++;
274:     fgmres->it  = (loc_it-1);  /* Add this here in case it has converged */
275: 
276:     PetscObjectTakeAccess(ksp);
277:     ksp->its++;
278:     ksp->rnorm = res_norm;
279:     PetscObjectGrantAccess(ksp);

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

283:     /* Catch error in happy breakdown and signal convergence and break from loop */
284:     if (hapend) {
285:       if (!ksp->reason) {
286:         SETERRQ(0,"You reached the happy break down,but convergence was not indicated.");
287:       }
288:       break;
289:     }
290:   }
291:   /* END OF ITERATION LOOP */

293:   KSPLogResidualHistory(ksp,res_norm);

295:   /*
296:      Monitor if we know that we will not return for a restart */
297:   if (ksp->reason || ksp->its >= ksp->max_it) {
298:     KSPMonitor(ksp,ksp->its,res_norm);
299:   }

301:   if (itcount) *itcount    = loc_it;

303:   /*
304:     Down here we have to solve for the "best" coefficients of the Krylov
305:     columns, add the solution values together, and possibly unwind the
306:     preconditioning from the solution
307:    */
308: 
309:   /* Form the solution (or the solution so far) */
310:   /* Note: must pass in (loc_it-1) for iteration count so that BuildFgmresSoln
311:      properly navigates */

313:   BuildFgmresSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);

315:   return(0);
316: }

318: /*  
319:     KSPSolve_FGMRES - This routine applies the FGMRES method.


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

325:    Output Parameter:
326: .     outits - number of iterations used

328: */

332: PetscErrorCode KSPSolve_FGMRES(KSP ksp)
333: {
335:   PetscInt       cycle_its = 0; /* iterations done in a call to FGMREScycle */
336:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)ksp->data;
337:   PetscTruth     diagonalscale;

340:   PCDiagonalScale(ksp->pc,&diagonalscale);
341:   if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
342:   if (ksp->normtype != KSP_NORM_UNPRECONDITIONED) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Can only use FGMRES with unpreconditioned residual (it is coded with right preconditioning)");

344:   PetscObjectTakeAccess(ksp);
345:   ksp->its = 0;
346:   PetscObjectGrantAccess(ksp);

348:   /* Compute the initial (NOT preconditioned) residual */
349:   if (!ksp->guess_zero) {
350:     FGMRESResidual(ksp);
351:   } else { /* guess is 0 so residual is F (which is in ksp->vec_rhs) */
352:     VecCopy(ksp->vec_rhs,VEC_VV(0));
353:   }
354:   /* now the residual is in VEC_VV(0) - which is what 
355:      FGMREScycle expects... */
356: 
357:   FGMREScycle(&cycle_its,ksp);
358:   while (!ksp->reason) {
359:     FGMRESResidual(ksp);
360:     if (ksp->its >= ksp->max_it) break;
361:     FGMREScycle(&cycle_its,ksp);
362:   }
363:   /* mark lack of convergence */
364:   if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

366:   return(0);
367: }

369: /*

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

373: */
376: PetscErrorCode KSPDestroy_FGMRES(KSP ksp)
377: {
378:   KSP_FGMRES     *fgmres = (KSP_FGMRES*)ksp->data;
380:   PetscInt       i;

383:   /* Free the Hessenberg matrices */
384:   PetscFree(fgmres->hh_origin);

386:   /* Free pointers to user variables */
387:   PetscFree(fgmres->vecs);
388:   PetscFree (fgmres->prevecs);

390:   /* free work vectors */
391:   for (i=0; i < fgmres->nwork_alloc; i++) {
392:     VecDestroyVecs(fgmres->user_work[i],fgmres->mwork_alloc[i]);
393:   }
394:   PetscFree(fgmres->user_work);

396:   for (i=0; i < fgmres->nwork_alloc; i++) {
397:     VecDestroyVecs(fgmres->prevecs_user_work[i],fgmres->mwork_alloc[i]);
398:   }
399:   PetscFree(fgmres->prevecs_user_work);

401:   PetscFree(fgmres->mwork_alloc);
402:   PetscFree(fgmres->nrs);
403:   if (fgmres->sol_temp) {VecDestroy(fgmres->sol_temp);}
404:   PetscFree(fgmres->Rsvd);
405:   PetscFree(fgmres->Dsvd);
406:   PetscFree(fgmres->orthogwork);
407:   if (fgmres->modifydestroy) {
408:     (*fgmres->modifydestroy)(fgmres->modifyctx);
409:   }
410:   PetscFree(ksp->data);

412:   /* clear composed functions */
413:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C","",PETSC_NULL);
414:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C","",PETSC_NULL);
415:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C","",PETSC_NULL);
416:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPFGMRESSetModifyPC_C","",PETSC_NULL);
417:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C","",PETSC_NULL);
418:   return(0);
419: }

421: /*
422:     BuildFgmresSoln - create the solution from the starting vector and the
423:                       current iterates.

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

432:      This is an internal routine that knows about the FGMRES internals.
433:  */
436: static PetscErrorCode BuildFgmresSoln(PetscScalar* nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
437: {
438:   PetscScalar    tt;
440:   PetscInt       ii,k,j;
441:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)(ksp->data);

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

446:   /* If it is < 0, no fgmres steps have been performed */
447:   if (it < 0) {
448:     VecCopy(vguess,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
449:     return(0);
450:   }

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

454:   /* solve the upper triangular system - RS is the right side and HH is 
455:      the upper triangular matrix  - put soln in nrs */
456:   if (*HH(it,it) != 0.0) {
457:     nrs[it] = *RS(it) / *HH(it,it);
458:   } else {
459:     nrs[it] = 0.0;
460:   }
461:   for (ii=1; ii<=it; ii++) {
462:     k   = it - ii;
463:     tt  = *RS(k);
464:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
465:     nrs[k]   = tt / *HH(k,k);
466:   }

468:   /* Accumulate the correction to the soln of the preconditioned prob. in 
469:      VEC_TEMP - note that we use the preconditioned vectors  */
470:   VecSet(VEC_TEMP,0.0); /* set VEC_TEMP components to 0 */
471:   VecMAXPY(VEC_TEMP,it+1,nrs,&PREVEC(0));

473:   /* put updated solution into vdest.*/
474:   if (vdest != vguess) {
475:     VecCopy(VEC_TEMP,vdest);
476:     VecAXPY(vdest,1.0,vguess);
477:   } else  {/* replace guess with solution */
478:     VecAXPY(vdest,1.0,VEC_TEMP);
479:   }
480:   return(0);
481: }

483: /*

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

488:     input parameters:

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

495:     output parameters:
496: .        res - the new residual
497:         
498:  */
501: static PetscErrorCode FGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
502: {
503:   PetscScalar   *hh,*cc,*ss,tt;
504:   PetscInt      j;
505:   KSP_FGMRES    *fgmres = (KSP_FGMRES *)(ksp->data);

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

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

518:   for (j=1; j<=it; j++) {
519:     tt  = *hh;
520: #if defined(PETSC_USE_COMPLEX)
521:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
522: #else
523:     *hh = *cc * tt + *ss * *(hh+1);
524: #endif
525:     hh++;
526:     *hh = *cc++ * *hh - (*ss++ * tt);
527:     /* hh, cc, and ss have all been incremented one by end of loop */
528:   }

530:   /*
531:     compute the new plane rotation, and apply it to:
532:      1) the right-hand-side of the Hessenberg system (RS)
533:         note: it affects RS(it) and RS(it+1)
534:      2) the new column of the Hessenberg matrix
535:         note: it affects HH(it,it) which is currently pointed to 
536:         by hh and HH(it+1, it) (*(hh+1))  
537:     thus obtaining the updated value of the residual...
538:   */

540:   /* compute new plane rotation */

542:   if (!hapend) {
543: #if defined(PETSC_USE_COMPLEX)
544:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
545: #else
546:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
547: #endif
548:     if (tt == 0.0) {
549:       ksp->reason = KSP_DIVERGED_NULL;
550:       return(0);
551:     }

553:     *cc       = *hh / tt;   /* new cosine value */
554:     *ss       = *(hh+1) / tt;  /* new sine value */

556:     /* apply to 1) and 2) */
557:     *RS(it+1) = - (*ss * *RS(it));
558: #if defined(PETSC_USE_COMPLEX)
559:     *RS(it)   = PetscConj(*cc) * *RS(it);
560:     *hh       = PetscConj(*cc) * *hh + *ss * *(hh+1);
561: #else
562:     *RS(it)   = *cc * *RS(it);
563:     *hh       = *cc * *hh + *ss * *(hh+1);
564: #endif

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

569:   } else { /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply 
570:             another rotation matrix (so RH doesn't change).  The new residual is 
571:             always the new sine term times the residual from last time (RS(it)), 
572:             but now the new sine rotation would be zero...so the residual should
573:             be zero...so we will multiply "zero" by the last residual.  This might
574:             not be exactly what we want to do here -could just return "zero". */
575: 
576:     *res = 0.0;
577:   }
578:   return(0);
579: }

581: /*

583:    FGMRESGetNewVectors - This routine allocates more work vectors, starting from 
584:                          VEC_VV(it), and more preconditioned work vectors, starting 
585:                          from PREVEC(i).

587: */
590: static PetscErrorCode FGMRESGetNewVectors(KSP ksp,PetscInt it)
591: {
592:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)ksp->data;
593:   PetscInt       nwork = fgmres->nwork_alloc; /* number of work vector chunks allocated */
594:   PetscInt       nalloc;                      /* number to allocate */
596:   PetscInt       k;
597: 
599:   nalloc = fgmres->delta_allocate; /* number of vectors to allocate 
600:                                       in a single chunk */

602:   /* Adjust the number to allocate to make sure that we don't exceed the
603:      number of available slots (fgmres->vecs_allocated)*/
604:   if (it + VEC_OFFSET + nalloc >= fgmres->vecs_allocated){
605:     nalloc = fgmres->vecs_allocated - it - VEC_OFFSET;
606:   }
607:   if (!nalloc) return(0);

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

611:   /* work vectors */
612:   KSPGetVecs(ksp,nalloc,&fgmres->user_work[nwork],0,PETSC_NULL);
613:   PetscLogObjectParents(ksp,nalloc,fgmres->user_work[nwork]);
614:   for (k=0; k < nalloc; k++) {
615:     fgmres->vecs[it+VEC_OFFSET+k] = fgmres->user_work[nwork][k];
616:   }
617:   /* specify size of chunk allocated */
618:   fgmres->mwork_alloc[nwork] = nalloc;

620:   /* preconditioned vectors */
621:   KSPGetVecs(ksp,nalloc,&fgmres->prevecs_user_work[nwork],0,PETSC_NULL);
622:   PetscLogObjectParents(ksp,nalloc,fgmres->prevecs_user_work[nwork]);
623:   for (k=0; k < nalloc; k++) {
624:     fgmres->prevecs[it+VEC_OFFSET+k] = fgmres->prevecs_user_work[nwork][k];
625:   }

627:   /* increment the number of work vector chunks */
628:   fgmres->nwork_alloc++;
629:   return(0);
630: }

632: /* 

634:    KSPBuildSolution_FGMRES

636:      Input Parameter:
637: .     ksp - the Krylov space object
638: .     ptr-

640:    Output Parameter:
641: .     result - the solution

643:    Note: this calls BuildFgmresSoln - the same function that FGMREScycle
644:    calls directly.  

646: */
649: PetscErrorCode KSPBuildSolution_FGMRES(KSP ksp,Vec ptr,Vec *result)
650: {
651:   KSP_FGMRES     *fgmres = (KSP_FGMRES *)ksp->data;

655:   if (!ptr) {
656:     if (!fgmres->sol_temp) {
657:       VecDuplicate(ksp->vec_sol,&fgmres->sol_temp);
658:       PetscLogObjectParent(ksp,fgmres->sol_temp);
659:     }
660:     ptr = fgmres->sol_temp;
661:   }
662:   if (!fgmres->nrs) {
663:     /* allocate the work area */
664:     PetscMalloc(fgmres->max_k*sizeof(PetscScalar),&fgmres->nrs);
665:     PetscLogObjectMemory(ksp,fgmres->max_k*sizeof(PetscScalar));
666:   }
667: 
668:   BuildFgmresSoln(fgmres->nrs,ksp->vec_sol,ptr,ksp,fgmres->it);
669:   if (result) *result = ptr;
670: 
671:   return(0);
672: }


678: PetscErrorCode KSPSetFromOptions_FGMRES(KSP ksp)
679: {
681:   PetscTruth     flg;

684:   KSPSetFromOptions_GMRES(ksp);
685:   PetscOptionsHead("KSP flexible GMRES Options");
686:     PetscOptionsTruthGroupBegin("-ksp_fgmres_modifypcnochange","do not vary the preconditioner","KSPFGMRESSetModifyPC",&flg);
687:     if (flg) {KSPFGMRESSetModifyPC(ksp,KSPFGMRESModifyPCNoChange,0,0);}
688:     PetscOptionsTruthGroupEnd("-ksp_fgmres_modifypcksp","vary the KSP based preconditioner","KSPFGMRESSetModifyPC",&flg);
689:     if (flg) {KSPFGMRESSetModifyPC(ksp,KSPFGMRESModifyPCKSP,0,0);}
690:   PetscOptionsTail();
691:   return(0);
692: }

694: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
695: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);

698: typedef PetscErrorCode (*FCN2)(void*);
702: PetscErrorCode  KSPFGMRESSetModifyPC_FGMRES(KSP ksp,FCN1 fcn,void *ctx,FCN2 d)
703: {
706:   ((KSP_FGMRES *)ksp->data)->modifypc      = fcn;
707:   ((KSP_FGMRES *)ksp->data)->modifydestroy = d;
708:   ((KSP_FGMRES *)ksp->data)->modifyctx     = ctx;
709:   return(0);
710: }

714: EXTERN PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP);
715: EXTERN PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP,PetscInt);
716: EXTERN PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP,PetscErrorCode (*)(KSP,PetscInt));

719: EXTERN PetscErrorCode KSPDestroy_GMRES_Internal(KSP);

723: PetscErrorCode KSPDestroy_FGMRES_Internal(KSP ksp)
724: {
725:   KSP_FGMRES     *gmres = (KSP_FGMRES*)ksp->data;

729:   KSPDestroy_GMRES_Internal(ksp);
730:   PetscFree (gmres->prevecs);
731:   PetscFree(gmres->prevecs_user_work);
732:   if (gmres->modifydestroy) {
733:     (*gmres->modifydestroy)(gmres->modifyctx);
734:   }
735:   return(0);
736: }

741: PetscErrorCode  KSPGMRESSetRestart_FGMRES(KSP ksp,PetscInt max_k)
742: {
743:   KSP_FGMRES     *gmres = (KSP_FGMRES *)ksp->data;

747:   if (max_k < 1) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
748:   if (!ksp->setupcalled) {
749:     gmres->max_k = max_k;
750:   } else if (gmres->max_k != max_k) {
751:      gmres->max_k = max_k;
752:      ksp->setupcalled = 0;
753:      /* free the data structures, then create them again */
754:      KSPDestroy_FGMRES_Internal(ksp);
755:   }
756:   return(0);
757: }

761: EXTERN PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP,KSPGMRESCGSRefinementType);

764: /*MC
765:      KSPFGMRES - Implements the Flexible Generalized Minimal Residual method.  
766:                 developed by Saad with restart


769:    Options Database Keys:
770: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
771: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
772: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of 
773:                              vectors are allocated as needed)
774: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
775: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
776: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the 
777:                                    stability of the classical Gram-Schmidt  orthogonalization.
778: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
779: .   -ksp_fgmres_modifypcnochange - do not change the preconditioner between iterations
780: -   -ksp_fgmres_modifypcksp - modify the preconditioner using KSPFGMRESModifyPCKSP()

782:    Level: beginner

784:     Notes: See KSPFGMRESSetModifyPC() for how to vary the preconditioner between iterations
785:            This object is subclassed off of KSPGMRES

787: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES,
788:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
789:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
790:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPFGMRESSetModifyPC(),
791:            KSPFGMRESModifyPCKSP()

793: M*/

798: PetscErrorCode  KSPCreate_FGMRES(KSP ksp)
799: {
800:   KSP_FGMRES     *fgmres;

804:   PetscNewLog(ksp,KSP_FGMRES,&fgmres);
805:   ksp->data                              = (void*)fgmres;
806:   ksp->ops->buildsolution                = KSPBuildSolution_FGMRES;
807:   ksp->ops->setup                        = KSPSetUp_FGMRES;
808:   ksp->ops->solve                        = KSPSolve_FGMRES;
809:   ksp->ops->destroy                      = KSPDestroy_FGMRES;
810:   ksp->ops->view                         = KSPView_GMRES;
811:   ksp->ops->setfromoptions               = KSPSetFromOptions_FGMRES;
812:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
813:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

815:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
816:                                     "KSPGMRESSetPreAllocateVectors_GMRES",
817:                                      KSPGMRESSetPreAllocateVectors_GMRES);
818:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
819:                                     "KSPGMRESSetOrthogonalization_GMRES",
820:                                      KSPGMRESSetOrthogonalization_GMRES);
821:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
822:                                     "KSPGMRESSetRestart_FGMRES",
823:                                      KSPGMRESSetRestart_FGMRES);
824:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPFGMRESSetModifyPC_C",
825:                                     "KSPFGMRESSetModifyPC_FGMRES",
826:                                      KSPFGMRESSetModifyPC_FGMRES);
827:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
828:                                     "KSPGMRESSetCGSRefinementType_GMRES",
829:                                      KSPGMRESSetCGSRefinementType_GMRES);


832:   fgmres->haptol              = 1.0e-30;
833:   fgmres->q_preallocate       = 0;
834:   fgmres->delta_allocate      = FGMRES_DELTA_DIRECTIONS;
835:   fgmres->orthog              = KSPGMRESClassicalGramSchmidtOrthogonalization;
836:   fgmres->nrs                 = 0;
837:   fgmres->sol_temp            = 0;
838:   fgmres->max_k               = FGMRES_DEFAULT_MAXK;
839:   fgmres->Rsvd                = 0;
840:   fgmres->orthogwork          = 0;
841:   fgmres->modifypc            = KSPFGMRESModifyPCNoChange;
842:   fgmres->modifyctx           = PETSC_NULL;
843:   fgmres->modifydestroy       = PETSC_NULL;
844:   fgmres->cgstype             = KSP_GMRES_CGS_REFINE_NEVER;
845:   /*
846:         This is not great since it changes this without explicit request from the user
847:      but there is no left preconditioning in the FGMRES
848:   */
849:   PetscInfo(ksp,"WARNING! Setting PC_SIDE for FGMRES to right!\n");
850:   ksp->pc_side  = PC_RIGHT;
851:   ksp->normtype = KSP_NORM_UNPRECONDITIONED;
852:   return(0);
853: }