Date: 2016-07-24T17:06:47+00:00

Actual source code: pgmres.c
petsc-3.7.3 2016-07-24
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      2: /*
      3:     This file implements PGMRES (a Pipelined Generalized Minimal Residual method)
      4: */

      6: #include <../src/ksp/ksp/impls/gmres/pgmres/pgmresimpl.h>       /*I  "petscksp.h"  I*/
      7: #define PGMRES_DELTA_DIRECTIONS 10
      8: #define PGMRES_DEFAULT_MAXK     30

     10: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool*,PetscReal*);
     11: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

     13: /*

     15:     KSPSetUp_PGMRES - Sets up the workspace needed by pgmres.

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

     20: */
     23: static PetscErrorCode KSPSetUp_PGMRES(KSP ksp)
     24: {

     28:   KSPSetUp_GMRES(ksp);
     29:   return(0);
     30: }

     32: /*

     34:     KSPPGMRESCycle - Run pgmres, possibly with restart.  Return residual
     35:                   history if requested.

     37:     input parameters:
     38: .        pgmres  - structure containing parameters and work areas

     40:     output parameters:
     41: .        itcount - number of iterations used.  If null, ignored.
     42: .        converged - 0 if not converged

     44:     Notes:
     45:     On entry, the value in vector VEC_VV(0) should be
     46:     the initial residual.

     49:  */
     52: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp)
     53: {
     54:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);
     55:   PetscReal      res_norm,res,newnorm;
     57:   PetscInt       it     = 0,j,k;
     58:   PetscBool      hapend = PETSC_FALSE;

     61:   if (itcount) *itcount = 0;
     62:   VecNormalize(VEC_VV(0),&res_norm);
     63:   KSPCheckNorm(ksp,res_norm);
     64:   res    = res_norm;
     65:   *RS(0) = res_norm;

     67:   /* check for the convergence */
     68:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
     69:   ksp->rnorm = res;
     70:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
     71:   pgmres->it = it-2;
     72:   KSPLogResidualHistory(ksp,res);
     73:   KSPMonitor(ksp,ksp->its,res);
     74:   if (!res) {
     75:     ksp->reason = KSP_CONVERGED_ATOL;
     76:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
     77:     return(0);
     78:   }

     80:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
     81:   for (; !ksp->reason; it++) {
     82:     Vec Zcur,Znext;
     83:     if (pgmres->vv_allocated <= it + VEC_OFFSET + 1) {
     84:       KSPGMRESGetNewVectors(ksp,it+1);
     85:     }
     86:     /* VEC_VV(it-1) is orthogonal, it will be normalized once the VecNorm arrives. */
     87:     Zcur  = VEC_VV(it);         /* Zcur is not yet orthogonal, but the VecMDot to orthogonalize it has been started. */
     88:     Znext = VEC_VV(it+1);       /* This iteration will compute Znext, update with a deferred correction once we know how
     89:                                  * Zcur relates to the previous vectors, and start the reduction to orthogonalize it. */

     91:     if (it < pgmres->max_k+1 && ksp->its+1 < PetscMax(2,ksp->max_it)) { /* We don't know whether what we have computed is enough, so apply the matrix. */
     92:       KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);
     93:     }

     95:     if (it > 1) {               /* Complete the pending reduction */
     96:       VecNormEnd(VEC_VV(it-1),NORM_2,&newnorm);
     97:       *HH(it-1,it-2) = newnorm;
     98:     }
     99:     if (it > 0) {               /* Finish the reduction computing the latest column of H */
    100:       VecMDotEnd(Zcur,it,&(VEC_VV(0)),HH(0,it-1));
    101:     }

    103:     if (it > 1) {
    104:       /* normalize the base vector from two iterations ago, basis is complete up to here */
    105:       VecScale(VEC_VV(it-1),1./ *HH(it-1,it-2));

    107:       KSPPGMRESUpdateHessenberg(ksp,it-2,&hapend,&res);
    108:       pgmres->it = it-2;
    109:       ksp->its++;
    110:       ksp->rnorm = res;

    112:       (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    113:       if (it < pgmres->max_k+1 || ksp->reason || ksp->its == ksp->max_it) {  /* Monitor if we are done or still iterating, but not before a restart. */
    114:         KSPLogResidualHistory(ksp,res);
    115:         KSPMonitor(ksp,ksp->its,res);
    116:       }
    117:       if (ksp->reason) break;
    118:       /* Catch error in happy breakdown and signal convergence and break from loop */
    119:       if (hapend) {
    120:         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);
    121:         else {
    122:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    123:           break;
    124:         }
    125:       }

    127:       if (!(it < pgmres->max_k+1 && ksp->its < ksp->max_it)) break;

    129:       /* The it-2 column of H was not scaled when we computed Zcur, apply correction */
    130:       VecScale(Zcur,1./ *HH(it-1,it-2));
    131:       /* And Znext computed in this iteration was computed using the under-scaled Zcur */
    132:       VecScale(Znext,1./ *HH(it-1,it-2));

    134:       /* In the previous iteration, we projected an unnormalized Zcur against the Krylov basis, so we need to fix the column of H resulting from that projection. */
    135:       for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
    136:       /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
    137:        * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
    138:       *HH(it-1,it-1) /= *HH(it-1,it-2);
    139:     }

    141:     if (it > 0) {
    142:       PetscScalar *work;
    143:       if (!pgmres->orthogwork) {PetscMalloc1(pgmres->max_k + 2,&pgmres->orthogwork);}
    144:       work = pgmres->orthogwork;
    145:       /* Apply correction computed by the VecMDot in the last iteration to Znext. The original form is
    146:        *
    147:        *   Znext -= sum_{j=0}^{i-1} Z[j+1] * H[j,i-1]
    148:        *
    149:        * where
    150:        *
    151:        *   Z[j] = sum_{k=0}^j V[k] * H[k,j-1]
    152:        *
    153:        * substituting
    154:        *
    155:        *   Znext -= sum_{j=0}^{i-1} sum_{k=0}^{j+1} V[k] * H[k,j] * H[j,i-1]
    156:        *
    157:        * rearranging the iteration space from row-column to column-row
    158:        *
    159:        *   Znext -= sum_{k=0}^i sum_{j=k-1}^{i-1} V[k] * H[k,j] * H[j,i-1]
    160:        *
    161:        * Note that column it-1 of HH is correct. For all previous columns, we must look at HES because HH has already
    162:        * been transformed to upper triangular form.
    163:        */
    164:       for (k=0; k<it+1; k++) {
    165:         work[k] = 0;
    166:         for (j=PetscMax(0,k-1); j<it-1; j++) work[k] -= *HES(k,j) * *HH(j,it-1);
    167:       }
    168:       VecMAXPY(Znext,it+1,work,&VEC_VV(0));
    169:       VecAXPY(Znext,-*HH(it-1,it-1),Zcur);

    171:       /* Orthogonalize Zcur against existing basis vectors. */
    172:       for (k=0; k<it; k++) work[k] = -*HH(k,it-1);
    173:       VecMAXPY(Zcur,it,work,&VEC_VV(0));
    174:       /* Zcur is now orthogonal, and will be referred to as VEC_VV(it) again, though it is still not normalized. */
    175:       /* Begin computing the norm of the new vector, will be normalized after the MatMult in the next iteration. */
    176:       VecNormBegin(VEC_VV(it),NORM_2,&newnorm);
    177:     }

    179:     /* Compute column of H (to the diagonal, but not the subdiagonal) to be able to orthogonalize the newest vector. */
    180:     VecMDotBegin(Znext,it+1,&VEC_VV(0),HH(0,it));

    182:     /* Start an asynchronous split-mode reduction, the result of the MDot and Norm will be collected on the next iteration. */
    183:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Znext));
    184:   }

    186:   if (itcount) *itcount = it-1; /* Number of iterations actually completed. */

    188:   /*
    189:     Down here we have to solve for the "best" coefficients of the Krylov
    190:     columns, add the solution values together, and possibly unwind the
    191:     preconditioning from the solution
    192:    */
    193:   /* Form the solution (or the solution so far) */
    194:   KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);
    195:   return(0);
    196: }

    198: /*
    199:     KSPSolve_PGMRES - This routine applies the PGMRES method.

    202:    Input Parameter:
    203: .     ksp - the Krylov space object that was set to use pgmres

    205:    Output Parameter:
    206: .     outits - number of iterations used

    208: */
    211: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
    212: {
    214:   PetscInt       its,itcount;
    215:   KSP_PGMRES     *pgmres    = (KSP_PGMRES*)ksp->data;
    216:   PetscBool      guess_zero = ksp->guess_zero;

    219:   if (ksp->calc_sings && !pgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
    220:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    221:   ksp->its = 0;
    222:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    242: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)
    243: {

    247:   KSPDestroy_GMRES(ksp);
    248:   return(0);
    249: }

    251: /*
    252:     KSPPGMRESBuildSoln - create the solution from the starting vector and the
    253:                       current iterates.

    255:     Input parameters:
    256:         nrs - work area of size it + 1.
    257:         vguess  - index of initial guess
    258:         vdest - index of result.  Note that vguess may == vdest (replace
    259:                 guess with the solution).
    260:         it - HH upper triangular part is a block of size (it+1) x (it+1)

    262:      This is an internal routine that knows about the PGMRES internals.
    263:  */
    266: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    267: {
    268:   PetscScalar    tt;
    270:   PetscInt       k,j;
    271:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

    276:   if (it < 0) {                                 /* no pgmres steps have been performed */
    277:     VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
    278:     return(0);
    279:   }

    281:   /* solve the upper triangular system - RS is the right side and HH is
    282:      the upper triangular matrix  - put soln in nrs */
    283:   if (*HH(it,it) != 0.0) nrs[it] = *RS(it) / *HH(it,it);
    284:   else nrs[it] = 0.0;

    286:   for (k=it-1; k>=0; k--) {
    287:     tt = *RS(k);
    288:     for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
    289:     nrs[k] = tt / *HH(k,k);
    290:   }

    292:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
    293:   VecZeroEntries(VEC_TEMP);
    294:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
    295:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    296:   /* add solution to previous solution */
    297:   if (vdest == vguess) {
    298:     VecAXPY(vdest,1.0,VEC_TEMP);
    299:   } else {
    300:     VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
    301:   }
    302:   return(0);
    303: }

    305: /*

    307:     KSPPGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    308:                             Return new residual.

    310:     input parameters:

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

    317:     output parameters:
    318: .        res - the new residual

    320:  */
    323: /*
    324: .  it - column of the Hessenberg that is complete, PGMRES is actually computing two columns ahead of this
    325:  */
    326: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)
    327: {
    328:   PetscScalar    *hh,*cc,*ss,*rs;
    329:   PetscInt       j;
    330:   PetscReal      hapbnd;
    331:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

    335:   hh = HH(0,it);   /* pointer to beginning of column to update */
    336:   cc = CC(0);      /* beginning of cosine rotations */
    337:   ss = SS(0);      /* beginning of sine rotations */
    338:   rs = RS(0);      /* right hand side of least squares system */

    340:   /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
    341:   for (j=0; j<=it+1; j++) *HES(j,it) = hh[j];

    343:   /* check for the happy breakdown */
    344:   hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pgmres->haptol);
    345:   if (PetscAbsScalar(hh[it+1]) < hapbnd) {
    346:     PetscInfo4(ksp,"Detected happy breakdown, current hapbnd = %14.12e H(%D,%D) = %14.12e\n",(double)hapbnd,it+1,it,(double)PetscAbsScalar(*HH(it+1,it)));
    347:     *hapend = PETSC_TRUE;
    348:   }

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

    355:   for (j=0; j<it; j++) {
    356:     PetscScalar hhj = hh[j];
    357:     hh[j]   = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
    358:     hh[j+1] =          -ss[j] *hhj + cc[j]*hh[j+1];
    359:   }

    361:   /*
    362:     compute the new plane rotation, and apply it to:
    363:      1) the right-hand-side of the Hessenberg system (RS)
    364:         note: it affects RS(it) and RS(it+1)
    365:      2) the new column of the Hessenberg matrix
    366:         note: it affects HH(it,it) which is currently pointed to
    367:         by hh and HH(it+1, it) (*(hh+1))
    368:     thus obtaining the updated value of the residual...
    369:   */

    371:   /* compute new plane rotation */

    373:   if (!*hapend) {
    374:     PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
    375:     if (delta == 0.0) {
    376:       ksp->reason = KSP_DIVERGED_NULL;
    377:       return(0);
    378:     }

    380:     cc[it] = hh[it] / delta;    /* new cosine value */
    381:     ss[it] = hh[it+1] / delta;  /* new sine value */

    383:     hh[it]   = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
    384:     rs[it+1] = -ss[it]*rs[it];
    385:     rs[it]   = PetscConj(cc[it])*rs[it];
    386:     *res     = PetscAbsScalar(rs[it+1]);
    387:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
    388:             another rotation matrix (so RH doesn't change).  The new residual is
    389:             always the new sine term times the residual from last time (RS(it)),
    390:             but now the new sine rotation would be zero...so the residual should
    391:             be zero...so we will multiply "zero" by the last residual.  This might
    392:             not be exactly what we want to do here -could just return "zero". */

    394:     *res = 0.0;
    395:   }
    396:   return(0);
    397: }

    399: /*
    400:    KSPBuildSolution_PGMRES

    402:      Input Parameter:
    403: .     ksp - the Krylov space object
    404: .     ptr-

    406:    Output Parameter:
    407: .     result - the solution

    409:    Note: this calls KSPPGMRESBuildSoln - the same function that KSPPGMRESCycle
    410:    calls directly.

    412: */
    415: PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp,Vec ptr,Vec *result)
    416: {
    417:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)ksp->data;

    421:   if (!ptr) {
    422:     if (!pgmres->sol_temp) {
    423:       VecDuplicate(ksp->vec_sol,&pgmres->sol_temp);
    424:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)pgmres->sol_temp);
    425:     }
    426:     ptr = pgmres->sol_temp;
    427:   }
    428:   if (!pgmres->nrs) {
    429:     /* allocate the work area */
    430:     PetscMalloc1(pgmres->max_k,&pgmres->nrs);
    431:     PetscLogObjectMemory((PetscObject)ksp,pgmres->max_k*sizeof(PetscScalar));
    432:   }

    434:   KSPPGMRESBuildSoln(pgmres->nrs,ksp->vec_sol,ptr,ksp,pgmres->it);
    435:   if (result) *result = ptr;
    436:   return(0);
    437: }

    441: PetscErrorCode KSPSetFromOptions_PGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    442: {

    446:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    447:   PetscOptionsHead(PetscOptionsObject,"KSP pipelined GMRES Options");
    448:   PetscOptionsTail();
    449:   return(0);
    450: }

    454: PetscErrorCode KSPReset_PGMRES(KSP ksp)
    455: {

    459:   KSPReset_GMRES(ksp);
    460:   return(0);
    461: }

    463: /*MC
    464:      KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method.

    466:    Options Database Keys:
    467: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    468: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    469: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    470:                              vectors are allocated as needed)
    471: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    472: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    473: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    474:                                    stability of the classical Gram-Schmidt  orthogonalization.
    475: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    477:    Level: beginner

    479:    Notes:
    480:    MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
    481:    See the FAQ on the PETSc website for details.

    483:    Reference:
    484:    Ghysels, Ashby, Meerbergen, Vanroose, Hiding global communication latencies in the GMRES algorithm on massively parallel machines, 2012.

    486:    Developer Notes: This object is subclassed off of KSPGMRES

    488: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES, KSPPIPECG, KSPPIPECR,
    489:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    490:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    491:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(),  KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov()
    492: M*/

    496: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)
    497: {
    498:   KSP_PGMRES     *pgmres;

    502:   PetscNewLog(ksp,&pgmres);

    504:   ksp->data                              = (void*)pgmres;
    505:   ksp->ops->buildsolution                = KSPBuildSolution_PGMRES;
    506:   ksp->ops->setup                        = KSPSetUp_PGMRES;
    507:   ksp->ops->solve                        = KSPSolve_PGMRES;
    508:   ksp->ops->reset                        = KSPReset_PGMRES;
    509:   ksp->ops->destroy                      = KSPDestroy_PGMRES;
    510:   ksp->ops->view                         = KSPView_GMRES;
    511:   ksp->ops->setfromoptions               = KSPSetFromOptions_PGMRES;
    512:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    513:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    515:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    516:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

    518:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    519:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    520:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    521:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    522:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    523:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    524:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    526:   pgmres->nextra_vecs    = 1;
    527:   pgmres->haptol         = 1.0e-30;
    528:   pgmres->q_preallocate  = 0;
    529:   pgmres->delta_allocate = PGMRES_DELTA_DIRECTIONS;
    530:   pgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    531:   pgmres->nrs            = 0;
    532:   pgmres->sol_temp       = 0;
    533:   pgmres->max_k          = PGMRES_DEFAULT_MAXK;
    534:   pgmres->Rsvd           = 0;
    535:   pgmres->orthogwork     = 0;
    536:   pgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    537:   return(0);
    538: }