Actual source code: lgmres.c


  2: #include <../src/ksp/ksp/impls/gmres/lgmres/lgmresimpl.h>

  4: #define LGMRES_DELTA_DIRECTIONS 10
  5: #define LGMRES_DEFAULT_MAXK     30
  6: #define LGMRES_DEFAULT_AUGDIM   2 /*default number of augmentation vectors */
  7: static PetscErrorCode    KSPLGMRESGetNewVectors(KSP,PetscInt);
  8: static PetscErrorCode    KSPLGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
  9: static PetscErrorCode    KSPLGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

 11: PetscErrorCode  KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
 12: {

 16:   PetscTryMethod((ksp),"KSPLGMRESSetAugDim_C",(KSP,PetscInt),(ksp,dim));
 17:   return(0);
 18: }

 20: PetscErrorCode  KSPLGMRESSetConstant(KSP ksp)
 21: {

 25:   PetscTryMethod((ksp),"KSPLGMRESSetConstant_C",(KSP),(ksp));
 26:   return(0);
 27: }

 29: /*
 30:     KSPSetUp_LGMRES - Sets up the workspace needed by lgmres.

 32:     This is called once, usually automatically by KSPSolve() or KSPSetUp(),
 33:     but can be called directly by KSPSetUp().

 35: */
 36: PetscErrorCode    KSPSetUp_LGMRES(KSP ksp)
 37: {
 39:   PetscInt       max_k,k, aug_dim;
 40:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

 43:   max_k   = lgmres->max_k;
 44:   aug_dim = lgmres->aug_dim;
 45:   KSPSetUp_GMRES(ksp);

 47:   /* need array of pointers to augvecs*/
 48:   PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs);

 50:   lgmres->aug_vecs_allocated = 2 *aug_dim + AUG_OFFSET;

 52:   PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs_user_work);
 53:   PetscMalloc1(aug_dim,&lgmres->aug_order);
 54:   PetscLogObjectMemory((PetscObject)ksp,(aug_dim)*(4*sizeof(void*) + sizeof(PetscInt)) + AUG_OFFSET*2*sizeof(void*));

 56:   /*  for now we will preallocate the augvecs - because aug_dim << restart
 57:      ... also keep in mind that we need to keep augvecs from cycle to cycle*/
 58:   lgmres->aug_vv_allocated = 2* aug_dim + AUG_OFFSET;
 59:   lgmres->augwork_alloc    =  2* aug_dim + AUG_OFFSET;

 61:   KSPCreateVecs(ksp,lgmres->aug_vv_allocated,&lgmres->augvecs_user_work[0],0,NULL);
 62:   PetscMalloc1(max_k+1,&lgmres->hwork);
 63:   PetscLogObjectParents(ksp,lgmres->aug_vv_allocated,lgmres->augvecs_user_work[0]);
 64:   for (k=0; k<lgmres->aug_vv_allocated; k++) {
 65:     lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
 66:   }
 67:   return(0);
 68: }

 70: /*

 72:     KSPLGMRESCycle - Run lgmres, possibly with restart.  Return residual
 73:                   history if requested.

 75:     input parameters:
 76: .        lgmres  - structure containing parameters and work areas

 78:     output parameters:
 79: .        nres    - residuals (from preconditioned system) at each step.
 80:                   If restarting, consider passing nres+it.  If null,
 81:                   ignored
 82: .        itcount - number of iterations used.   nres[0] to nres[itcount]
 83:                   are defined.  If null, ignored.  If null, ignored.
 84: .        converged - 0 if not converged

 86:     Notes:
 87:     On entry, the value in vector VEC_VV(0) should be
 88:     the initial residual.

 90:  */
 91: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount,KSP ksp)
 92: {
 93:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)(ksp->data);
 94:   PetscReal      res_norm, res;
 95:   PetscReal      hapbnd, tt;
 96:   PetscScalar    tmp;
 97:   PetscBool      hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
 99:   PetscInt       loc_it;                /* local count of # of dir. in Krylov space */
100:   PetscInt       max_k  = lgmres->max_k; /* max approx space size */
101:   PetscInt       max_it = ksp->max_it;  /* max # of overall iterations for the method */

103:   /* LGMRES_MOD - new variables*/
104:   PetscInt    aug_dim = lgmres->aug_dim;
105:   PetscInt    spot    = 0;
106:   PetscInt    order   = 0;
107:   PetscInt    it_arnoldi;                /* number of arnoldi steps to take */
108:   PetscInt    it_total;                  /* total number of its to take (=approx space size)*/
109:   PetscInt    ii, jj;
110:   PetscReal   tmp_norm;
111:   PetscScalar inv_tmp_norm;
112:   PetscScalar *avec;

115:   /* Number of pseudo iterations since last restart is the number
116:      of prestart directions */
117:   loc_it = 0;

119:   /* LGMRES_MOD: determine number of arnoldi steps to take */
120:   /* if approx_constant then we keep the space the same size even if
121:      we don't have the full number of aug vectors yet*/
122:   if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
123:   else it_arnoldi = max_k - aug_dim;

125:   it_total =  it_arnoldi + lgmres->aug_ct;

127:   /* initial residual is in VEC_VV(0)  - compute its norm*/
128:   VecNorm(VEC_VV(0),NORM_2,&res_norm);
129:   KSPCheckNorm(ksp,res_norm);
130:   res  = res_norm;

132:   /* first entry in right-hand-side of hessenberg system is just
133:      the initial residual norm */
134:   *GRS(0) = res_norm;

136:   /* check for the convergence */
137:   if (!res) {
138:     if (itcount) *itcount = 0;
139:     ksp->reason = KSP_CONVERGED_ATOL;
140:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
141:     return(0);
142:   }

144:   /* scale VEC_VV (the initial residual) */
145:   tmp = 1.0/res_norm; VecScale(VEC_VV(0),tmp);

147:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
148:   else ksp->rnorm = 0.0;

150:   /* note: (lgmres->it) is always set one less than (loc_it) It is used in
151:      KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
152:      Note that when KSPLGMRESBuildSoln is called from this function,
153:      (loc_it -1) is passed, so the two are equivalent */
154:   lgmres->it = (loc_it - 1);

156:   /* MAIN ITERATION LOOP BEGINNING*/

158:   /* keep iterating until we have converged OR generated the max number
159:      of directions OR reached the max number of iterations for the method */
160:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);

162:   while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
163:     KSPLogResidualHistory(ksp,res);
164:     lgmres->it = (loc_it - 1);
165:     KSPMonitor(ksp,ksp->its,res);

167:     /* see if more space is needed for work vectors */
168:     if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
169:       KSPLGMRESGetNewVectors(ksp,loc_it+1);
170:       /* (loc_it+1) is passed in as number of the first vector that should
171:           be allocated */
172:     }

174:     /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
175:     if (loc_it < it_arnoldi) { /* Arnoldi */
176:       KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);
177:     } else { /*aug step */
178:       order = loc_it - it_arnoldi + 1; /* which aug step */
179:       for (ii=0; ii<aug_dim; ii++) {
180:         if (lgmres->aug_order[ii] == order) {
181:           spot = ii;
182:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
183:         }
184:       }

186:       VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));
187:       /*note: an alternate implementation choice would be to only save the AUGVECS and
188:         not A_AUGVEC and then apply the PC here to the augvec */
189:     }

191:     /* update hessenberg matrix and do Gram-Schmidt - new direction is in
192:        VEC_VV(1+loc_it)*/
193:     (*lgmres->orthog)(ksp,loc_it);

195:     /* new entry in hessenburg is the 2-norm of our new direction */
196:     VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);

198:     *HH(loc_it+1,loc_it)  = tt;
199:     *HES(loc_it+1,loc_it) = tt;

201:     /* check for the happy breakdown */
202:     hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration  */
203:     if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
204:     if (tt > hapbnd) {
205:       tmp  = 1.0/tt;
206:       VecScale(VEC_VV(loc_it+1),tmp); /* scale new direction by its norm */
207:     } else {
208:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
209:       hapend = PETSC_TRUE;
210:     }

212:     /* Now apply rotations to new col of hessenberg (and right side of system),
213:        calculate new rotation, and get new residual norm at the same time*/
214:     KSPLGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);
215:     if (ksp->reason) break;

217:     loc_it++;
218:     lgmres->it = (loc_it-1);   /* Add this here in case it has converged */

220:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
221:     ksp->its++;
222:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
223:     else ksp->rnorm = 0.0;
224:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

228:     /* Catch error in happy breakdown and signal convergence and break from loop */
229:     if (hapend) {
230:       if (!ksp->reason) {
231:         if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res);
232:         else {
233:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
234:           break;
235:         }
236:       }
237:     }
238:   }
239:   /* END OF ITERATION LOOP */
240:   KSPLogResidualHistory(ksp,res);

242:   /* Monitor if we know that we will not return for a restart */
243:   if (ksp->reason || ksp->its >= max_it) {
244:     KSPMonitor(ksp, ksp->its, res);
245:   }

247:   if (itcount) *itcount = loc_it;

249:   /*
250:     Down here we have to solve for the "best" coefficients of the Krylov
251:     columns, add the solution values together, and possibly unwind the
252:     preconditioning from the solution
253:    */

255:   /* Form the solution (or the solution so far) */
256:   /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
257:      properly navigates */

259:   KSPLGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);

261:   /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
262:      only if we will be restarting (i.e. this cycle performed it_total
263:      iterations)  */
264:   if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {

266:     /*AUG_TEMP contains the new augmentation vector (assigned in  KSPLGMRESBuildSoln) */
267:     if (!lgmres->aug_ct) {
268:       spot = 0;
269:       lgmres->aug_ct++;
270:     } else if (lgmres->aug_ct < aug_dim) {
271:       spot = lgmres->aug_ct;
272:       lgmres->aug_ct++;
273:     } else { /* truncate */
274:       for (ii=0; ii<aug_dim; ii++) {
275:         if (lgmres->aug_order[ii] == aug_dim) spot = ii;
276:       }
277:     }

279:     VecCopy(AUG_TEMP, AUGVEC(spot));
280:     /*need to normalize */
281:     VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);

283:     inv_tmp_norm = 1.0/tmp_norm;

285:     VecScale(AUGVEC(spot),inv_tmp_norm);

287:     /*set new aug vector to order 1  - move all others back one */
288:     for (ii=0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
289:     AUG_ORDER(spot) = 1;

291:     /*now add the A*aug vector to A_AUGVEC(spot)  - this is independ. of preconditioning type*/
292:     /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */

294:     /* first do H+*y */
295:     avec = lgmres->hwork;
296:     PetscArrayzero(avec,it_total+1);
297:     for (ii=0; ii < it_total + 1; ii++) {
298:       for (jj=0; jj <= ii+1 && jj < it_total+1; jj++) {
299:         avec[jj] += *HES(jj ,ii) * *GRS(ii);
300:       }
301:     }

303:     /*now multiply result by V+ */
304:     VecSet(VEC_TEMP,0.0);
305:     VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/

307:     /*copy answer to aug location  and scale*/
308:     VecCopy(VEC_TEMP,  A_AUGVEC(spot));
309:     VecScale(A_AUGVEC(spot),inv_tmp_norm);
310:   }
311:   return(0);
312: }

314: /*
315:     KSPSolve_LGMRES - This routine applies the LGMRES method.

317:    Input Parameter:
318: .     ksp - the Krylov space object that was set to use lgmres

320:    Output Parameter:
321: .     outits - number of iterations used

323: */

325: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
326: {
328:   PetscInt       cycle_its; /* iterations done in a call to KSPLGMRESCycle */
329:   PetscInt       itcount;   /* running total of iterations, incl. those in restarts */
330:   KSP_LGMRES     *lgmres    = (KSP_LGMRES*)ksp->data;
331:   PetscBool      guess_zero = ksp->guess_zero;
332:   PetscInt       ii;        /*LGMRES_MOD variable */

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

337:   PetscObjectSAWsTakeAccess((PetscObject)ksp);

339:   ksp->its        = 0;
340:   lgmres->aug_ct  = 0;
341:   lgmres->matvecs = 0;

343:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

345:   /* initialize */
346:   itcount     = 0;
347:   ksp->reason = KSP_CONVERGED_ITERATING;
348:   /*LGMRES_MOD*/
349:   for (ii=0; ii<lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;

351:   while (!ksp->reason) {
352:     /* calc residual - puts in VEC_VV(0) */
353:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
354:     KSPLGMRESCycle(&cycle_its,ksp);
355:     itcount += cycle_its;
356:     if (itcount >= ksp->max_it) {
357:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
358:       break;
359:     }
360:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
361:   }
362:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
363:   return(0);
364: }

366: /*

368:    KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.

370: */
371: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
372: {
373:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

377:   PetscFree(lgmres->augvecs);
378:   if (lgmres->augwork_alloc) {
379:     VecDestroyVecs(lgmres->augwork_alloc,&lgmres->augvecs_user_work[0]);
380:   }
381:   PetscFree(lgmres->augvecs_user_work);
382:   PetscFree(lgmres->aug_order);
383:   PetscFree(lgmres->hwork);
384:   KSPDestroy_GMRES(ksp);
385:   return(0);
386: }

388: /*
389:     KSPLGMRESBuildSoln - create the solution from the starting vector and the
390:                       current iterates.

392:     Input parameters:
393:         nrs - work area of size it + 1.
394:         vguess  - index of initial guess
395:         vdest - index of result.  Note that vguess may == vdest (replace
396:                 guess with the solution).
397:         it - HH upper triangular part is a block of size (it+1) x (it+1)

399:      This is an internal routine that knows about the LGMRES internals.
400:  */
401: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
402: {
403:   PetscScalar    tt;
405:   PetscInt       ii,k,j;
406:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)(ksp->data);
407:   /*LGMRES_MOD */
408:   PetscInt it_arnoldi, it_aug;
409:   PetscInt jj, spot = 0;

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

414:   /* If it is < 0, no lgmres steps have been performed */
415:   if (it < 0) {
416:     VecCopy(vguess,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
417:     return(0);
418:   }

420:   /* so (it+1) lgmres steps HAVE been performed */

422:   /* LGMRES_MOD - determine if we need to use augvecs for the soln  - do not assume that
423:      this is called after the total its allowed for an approx space */
424:   if (lgmres->approx_constant) {
425:     it_arnoldi = lgmres->max_k - lgmres->aug_ct;
426:   } else {
427:     it_arnoldi = lgmres->max_k - lgmres->aug_dim;
428:   }
429:   if (it_arnoldi >= it +1) {
430:     it_aug     = 0;
431:     it_arnoldi = it+1;
432:   } else {
433:     it_aug = (it + 1) - it_arnoldi;
434:   }

436:   /* now it_arnoldi indicates the number of matvecs that took place */
437:   lgmres->matvecs += it_arnoldi;

439:   /* solve the upper triangular system - GRS is the right side and HH is
440:      the upper triangular matrix  - put soln in nrs */
441:   if (*HH(it,it) == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %g",it,(double)PetscAbsScalar(*GRS(it)));
442:   if (*HH(it,it) != 0.0) {
443:     nrs[it] = *GRS(it) / *HH(it,it);
444:   } else {
445:     nrs[it] = 0.0;
446:   }

448:   for (ii=1; ii<=it; ii++) {
449:     k  = it - ii;
450:     tt = *GRS(k);
451:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
452:     nrs[k] = tt / *HH(k,k);
453:   }

455:   /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
456:   VecSet(VEC_TEMP,0.0); /* set VEC_TEMP components to 0 */

458:   /*LGMRES_MOD - if augmenting has happened we need to form the solution
459:     using the augvecs */
460:   if (!it_aug) { /* all its are from arnoldi */
461:     VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
462:   } else { /*use aug vecs */
463:     /*first do regular krylov directions */
464:     VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));
465:     /*now add augmented portions - add contribution of aug vectors one at a time*/

467:     for (ii=0; ii<it_aug; ii++) {
468:       for (jj=0; jj<lgmres->aug_dim; jj++) {
469:         if (lgmres->aug_order[jj] == (ii+1)) {
470:           spot = jj;
471:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
472:         }
473:       }
474:       VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));
475:     }
476:   }
477:   /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
478:      preconditioner is "unwound" from right-precondtioning*/
479:   VecCopy(VEC_TEMP, AUG_TEMP);

481:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

483:   /* add solution to previous solution */
484:   /* put updated solution into vdest.*/
485:   VecCopy(vguess,vdest);
486:   VecAXPY(vdest,1.0,VEC_TEMP);
487:   return(0);
488: }

490: /*

492:     KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
493:                             Return new residual.

495:     input parameters:

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

502:     output parameters:
503: .        res - the new residual

505:  */
506: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
507: {
508:   PetscScalar *hh,*cc,*ss,tt;
509:   PetscInt    j;
510:   KSP_LGMRES  *lgmres = (KSP_LGMRES*)(ksp->data);

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

518:   /* Apply all the previously computed plane rotations to the new column
519:      of the Hessenberg matrix */
520:   /* Note: this uses the rotation [conj(c)  s ; -s   c], c= cos(theta), s= sin(theta) */

522:   for (j=1; j<=it; j++) {
523:     tt  = *hh;
524:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
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 (GRS)
533:         note: it affects GRS(it) and GRS(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:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
544:     if (tt == 0.0) {
545:       ksp->reason = KSP_DIVERGED_NULL;
546:       return(0);
547:     }
548:     *cc = *hh / tt;         /* new cosine value */
549:     *ss = *(hh+1) / tt;        /* new sine value */

551:     /* apply to 1) and 2) */
552:     *GRS(it+1) = -(*ss * *GRS(it));
553:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
554:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);

556:     /* residual is the last element (it+1) of right-hand side! */
557:     *res = PetscAbsScalar(*GRS(it+1));

559:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
560:             another rotation matrix (so RH doesn't change).  The new residual is
561:             always the new sine term times the residual from last time (GRS(it)),
562:             but now the new sine rotation would be zero...so the residual should
563:             be zero...so we will multiply "zero" by the last residual.  This might
564:             not be exactly what we want to do here -could just return "zero". */

566:     *res = 0.0;
567:   }
568:   return(0);
569: }

571: /*

573:    KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
574:                          VEC_VV(it)

576: */
577: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp,PetscInt it)
578: {
579:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;
580:   PetscInt       nwork   = lgmres->nwork_alloc; /* number of work vector chunks allocated */
581:   PetscInt       nalloc;                      /* number to allocate */
583:   PetscInt       k;

586:   nalloc = lgmres->delta_allocate; /* number of vectors to allocate
587:                                       in a single chunk */

589:   /* Adjust the number to allocate to make sure that we don't exceed the
590:      number of available slots (lgmres->vecs_allocated)*/
591:   if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) {
592:     nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
593:   }
594:   if (!nalloc) return(0);

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

598:   /* work vectors */
599:   KSPCreateVecs(ksp,nalloc,&lgmres->user_work[nwork],0,NULL);
600:   PetscLogObjectParents(ksp,nalloc,lgmres->user_work[nwork]);
601:   /* specify size of chunk allocated */
602:   lgmres->mwork_alloc[nwork] = nalloc;

604:   for (k=0; k < nalloc; k++) {
605:     lgmres->vecs[it+VEC_OFFSET+k] = lgmres->user_work[nwork][k];
606:   }

608:   /* LGMRES_MOD - for now we are preallocating the augmentation vectors */

610:   /* increment the number of work vector chunks */
611:   lgmres->nwork_alloc++;
612:   return(0);
613: }

615: /*

617:    KSPBuildSolution_LGMRES

619:      Input Parameter:
620: .     ksp - the Krylov space object
621: .     ptr-

623:    Output Parameter:
624: .     result - the solution

626:    Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
627:    calls directly.

629: */
630: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
631: {
632:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

636:   if (!ptr) {
637:     if (!lgmres->sol_temp) {
638:       VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
639:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)lgmres->sol_temp);
640:     }
641:     ptr = lgmres->sol_temp;
642:   }
643:   if (!lgmres->nrs) {
644:     /* allocate the work area */
645:     PetscMalloc1(lgmres->max_k,&lgmres->nrs);
646:     PetscLogObjectMemory((PetscObject)ksp,lgmres->max_k*sizeof(PetscScalar));
647:   }

649:   KSPLGMRESBuildSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
650:   if (result) *result = ptr;
651:   return(0);
652: }

654: PetscErrorCode KSPView_LGMRES(KSP ksp,PetscViewer viewer)
655: {
656:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;
658:   PetscBool      iascii;

661:   KSPView_GMRES(ksp,viewer);
662:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
663:   if (iascii) {
664:     /*LGMRES_MOD */
665:     PetscViewerASCIIPrintf(viewer,"  aug. dimension=%D\n",lgmres->aug_dim);
666:     if (lgmres->approx_constant) {
667:       PetscViewerASCIIPrintf(viewer,"  approx. space size was kept constant.\n");
668:     }
669:     PetscViewerASCIIPrintf(viewer,"  number of matvecs=%D\n",lgmres->matvecs);
670:   }
671:   return(0);
672: }

674: PetscErrorCode KSPSetFromOptions_LGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
675: {
677:   PetscInt       aug;
678:   KSP_LGMRES     *lgmres = (KSP_LGMRES*) ksp->data;
679:   PetscBool      flg     = PETSC_FALSE;

682:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
683:   PetscOptionsHead(PetscOptionsObject,"KSP LGMRES Options");
684:   PetscOptionsBool("-ksp_lgmres_constant","Use constant approx. space size","KSPGMRESSetConstant",lgmres->approx_constant,&lgmres->approx_constant,NULL);
685:   PetscOptionsInt("-ksp_lgmres_augment","Number of error approximations to augment the Krylov space with","KSPLGMRESSetAugDim",lgmres->aug_dim,&aug,&flg);
686:   if (flg) { KSPLGMRESSetAugDim(ksp,aug); }
687:   PetscOptionsTail();
688:   return(0);
689: }

691: /*functions for extra lgmres options here*/
692: static PetscErrorCode  KSPLGMRESSetConstant_LGMRES(KSP ksp)
693: {
694:   KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;

697:   lgmres->approx_constant = PETSC_TRUE;
698:   return(0);
699: }

701: static PetscErrorCode  KSPLGMRESSetAugDim_LGMRES(KSP ksp,PetscInt aug_dim)
702: {
703:   KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;

706:   if (aug_dim < 0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be positive");
707:   if (aug_dim > (lgmres->max_k -1)) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be <= (restart size-1)");
708:   lgmres->aug_dim = aug_dim;
709:   return(0);
710: }

712: /* end new lgmres functions */

714: /*MC
715:     KSPLGMRES - Augments the standard GMRES approximation space with approximations to
716:                 the error from previous restart cycles.

718:   Options Database Keys:
719: +   -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
720: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
721: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
722:                             vectors are allocated as needed)
723: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
724: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
725: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
726:                                   stability of the classical Gram-Schmidt  orthogonalization.
727: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
728: .   -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
729: -   -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

731:     To run LGMRES(m, k) as described in the above paper, use:
732:        -ksp_gmres_restart <m+k>
733:        -ksp_lgmres_augment <k>

735:   Level: beginner

737:    Notes:
738:     Supports both left and right preconditioning, but not symmetric.

740:    References:
741: .    1. - A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).

743:   Developer Notes:
744:     This object is subclassed off of KSPGMRES

746:   Contributed by: Allison Baker

748: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
749:           KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
750:           KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
751:           KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(),
752:           KSPGMRESSetConstant()

754: M*/

756: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
757: {
758:   KSP_LGMRES     *lgmres;

762:   PetscNewLog(ksp,&lgmres);

764:   ksp->data               = (void*)lgmres;
765:   ksp->ops->buildsolution = KSPBuildSolution_LGMRES;

767:   ksp->ops->setup                        = KSPSetUp_LGMRES;
768:   ksp->ops->solve                        = KSPSolve_LGMRES;
769:   ksp->ops->destroy                      = KSPDestroy_LGMRES;
770:   ksp->ops->view                         = KSPView_LGMRES;
771:   ksp->ops->setfromoptions               = KSPSetFromOptions_LGMRES;
772:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
773:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

775:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
776:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
777:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);

779:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
780:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
781:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
782:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
783:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
784:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
785:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
786:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

788:   /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
789:   PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetConstant_C",KSPLGMRESSetConstant_LGMRES);
790:   PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetAugDim_C",KSPLGMRESSetAugDim_LGMRES);

792:   /*defaults */
793:   lgmres->haptol         = 1.0e-30;
794:   lgmres->q_preallocate  = 0;
795:   lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
796:   lgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
797:   lgmres->nrs            = NULL;
798:   lgmres->sol_temp       = NULL;
799:   lgmres->max_k          = LGMRES_DEFAULT_MAXK;
800:   lgmres->Rsvd           = NULL;
801:   lgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
802:   lgmres->orthogwork     = NULL;

804:   /*LGMRES_MOD - new defaults */
805:   lgmres->aug_dim         = LGMRES_DEFAULT_AUGDIM;
806:   lgmres->aug_ct          = 0;     /* start with no aug vectors */
807:   lgmres->approx_constant = PETSC_FALSE;
808:   lgmres->matvecs         = 0;
809:   return(0);
810: }