Actual source code: pgmres.c

      2: /*
      3:     This file implements PGMRES (a Pipelined Generalized Minimal Residual method)
      4: */

      6: #include <../src/ksp/ksp/impls/gmres/pgmres/pgmresimpl.h>
      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: */
     21: static PetscErrorCode KSPSetUp_PGMRES(KSP ksp)
     22: {

     26:   KSPSetUp_GMRES(ksp);
     27:   return(0);
     28: }

     30: /*

     32:     KSPPGMRESCycle - Run pgmres, possibly with restart.  Return residual
     33:                   history if requested.

     35:     input parameters:
     36: .        pgmres  - structure containing parameters and work areas

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

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

     47:  */
     48: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp)
     49: {
     50:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);
     51:   PetscReal      res_norm,res,newnorm;
     53:   PetscInt       it     = 0,j,k;
     54:   PetscBool      hapend = PETSC_FALSE;

     57:   if (itcount) *itcount = 0;
     58:   VecNormalize(VEC_VV(0),&res_norm);
     59:   KSPCheckNorm(ksp,res_norm);
     60:   res    = res_norm;
     61:   *RS(0) = res_norm;

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

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

     88:     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. */
     89:       KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);
     90:     }

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

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

    104:       KSPPGMRESUpdateHessenberg(ksp,it-2,&hapend,&res);
    105:       pgmres->it = it-2;
    106:       ksp->its++;
    107:       if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
    108:       else ksp->rnorm = 0;

    110:       (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
    111:       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. */
    112:         KSPLogResidualHistory(ksp,ksp->rnorm);
    113:         KSPMonitor(ksp,ksp->its,ksp->rnorm);
    114:       }
    115:       if (ksp->reason) break;
    116:       /* Catch error in happy breakdown and signal convergence and break from loop */
    117:       if (hapend) {
    118:         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);
    119:         else {
    120:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    121:           break;
    122:         }
    123:       }

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

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

    132:       /* 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. */
    133:       for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
    134:       /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
    135:        * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
    136:       *HH(it-1,it-1) /= *HH(it-1,it-2);
    137:     }

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

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

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

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

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

    186:   /*
    187:     Down here we have to solve for the "best" coefficients of the Krylov
    188:     columns, add the solution values together, and possibly unwind the
    189:     preconditioning from the solution
    190:    */
    191:   /* Form the solution (or the solution so far) */
    192:   KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);
    193:   return(0);
    194: }

    196: /*
    197:     KSPSolve_PGMRES - This routine applies the PGMRES method.

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

    203:    Output Parameter:
    204: .     outits - number of iterations used

    206: */
    207: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
    208: {
    210:   PetscInt       its,itcount;
    211:   KSP_PGMRES     *pgmres    = (KSP_PGMRES*)ksp->data;
    212:   PetscBool      guess_zero = ksp->guess_zero;

    215:   if (ksp->calc_sings && !pgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
    216:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    217:   ksp->its = 0;
    218:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    236: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)
    237: {

    241:   KSPDestroy_GMRES(ksp);
    242:   return(0);
    243: }

    245: /*
    246:     KSPPGMRESBuildSoln - create the solution from the starting vector and the
    247:                       current iterates.

    249:     Input parameters:
    250:         nrs - work area of size it + 1.
    251:         vguess  - index of initial guess
    252:         vdest - index of result.  Note that vguess may == vdest (replace
    253:                 guess with the solution).
    254:         it - HH upper triangular part is a block of size (it+1) x (it+1)

    256:      This is an internal routine that knows about the PGMRES internals.
    257:  */
    258: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    259: {
    260:   PetscScalar    tt;
    262:   PetscInt       k,j;
    263:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

    268:   if (it < 0) {                                 /* no pgmres steps have been performed */
    269:     VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
    270:     return(0);
    271:   }

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

    278:   for (k=it-1; k>=0; k--) {
    279:     tt = *RS(k);
    280:     for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
    281:     nrs[k] = tt / *HH(k,k);
    282:   }

    284:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
    285:   VecZeroEntries(VEC_TEMP);
    286:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
    287:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    288:   /* add solution to previous solution */
    289:   if (vdest == vguess) {
    290:     VecAXPY(vdest,1.0,VEC_TEMP);
    291:   } else {
    292:     VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
    293:   }
    294:   return(0);
    295: }

    297: /*

    299:     KSPPGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    300:                             Return new residual.

    302:     input parameters:

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

    309:     output parameters:
    310: .        res - the new residual

    312:  */
    313: /*
    314: .  it - column of the Hessenberg that is complete, PGMRES is actually computing two columns ahead of this
    315:  */
    316: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)
    317: {
    318:   PetscScalar    *hh,*cc,*ss,*rs;
    319:   PetscInt       j;
    320:   PetscReal      hapbnd;
    321:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

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

    333:   /* check for the happy breakdown */
    334:   hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pgmres->haptol);
    335:   if (PetscAbsScalar(hh[it+1]) < hapbnd) {
    336:     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)));
    337:     *hapend = PETSC_TRUE;
    338:   }

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

    345:   for (j=0; j<it; j++) {
    346:     PetscScalar hhj = hh[j];
    347:     hh[j]   = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
    348:     hh[j+1] =          -ss[j] *hhj + cc[j]*hh[j+1];
    349:   }

    351:   /*
    352:     compute the new plane rotation, and apply it to:
    353:      1) the right-hand-side of the Hessenberg system (RS)
    354:         note: it affects RS(it) and RS(it+1)
    355:      2) the new column of the Hessenberg matrix
    356:         note: it affects HH(it,it) which is currently pointed to
    357:         by hh and HH(it+1, it) (*(hh+1))
    358:     thus obtaining the updated value of the residual...
    359:   */

    361:   /* compute new plane rotation */

    363:   if (!*hapend) {
    364:     PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
    365:     if (delta == 0.0) {
    366:       ksp->reason = KSP_DIVERGED_NULL;
    367:       return(0);
    368:     }

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

    373:     hh[it]   = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
    374:     rs[it+1] = -ss[it]*rs[it];
    375:     rs[it]   = PetscConj(cc[it])*rs[it];
    376:     *res     = PetscAbsScalar(rs[it+1]);
    377:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
    378:             another rotation matrix (so RH doesn't change).  The new residual is
    379:             always the new sine term times the residual from last time (RS(it)),
    380:             but now the new sine rotation would be zero...so the residual should
    381:             be zero...so we will multiply "zero" by the last residual.  This might
    382:             not be exactly what we want to do here -could just return "zero". */

    384:     *res = 0.0;
    385:   }
    386:   return(0);
    387: }

    389: /*
    390:    KSPBuildSolution_PGMRES

    392:      Input Parameter:
    393: .     ksp - the Krylov space object
    394: .     ptr-

    396:    Output Parameter:
    397: .     result - the solution

    399:    Note: this calls KSPPGMRESBuildSoln - the same function that KSPPGMRESCycle
    400:    calls directly.

    402: */
    403: PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp,Vec ptr,Vec *result)
    404: {
    405:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)ksp->data;

    409:   if (!ptr) {
    410:     if (!pgmres->sol_temp) {
    411:       VecDuplicate(ksp->vec_sol,&pgmres->sol_temp);
    412:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)pgmres->sol_temp);
    413:     }
    414:     ptr = pgmres->sol_temp;
    415:   }
    416:   if (!pgmres->nrs) {
    417:     /* allocate the work area */
    418:     PetscMalloc1(pgmres->max_k,&pgmres->nrs);
    419:     PetscLogObjectMemory((PetscObject)ksp,pgmres->max_k*sizeof(PetscScalar));
    420:   }

    422:   KSPPGMRESBuildSoln(pgmres->nrs,ksp->vec_sol,ptr,ksp,pgmres->it);
    423:   if (result) *result = ptr;
    424:   return(0);
    425: }

    427: PetscErrorCode KSPSetFromOptions_PGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    428: {

    432:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    433:   PetscOptionsHead(PetscOptionsObject,"KSP pipelined GMRES Options");
    434:   PetscOptionsTail();
    435:   return(0);
    436: }

    438: PetscErrorCode KSPReset_PGMRES(KSP ksp)
    439: {

    443:   KSPReset_GMRES(ksp);
    444:   return(0);
    445: }

    447: /*MC
    448:      KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method.

    450:    Options Database Keys:
    451: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    452: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    453: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    454:                              vectors are allocated as needed)
    455: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    456: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    457: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
    458:                                    stability of the classical Gram-Schmidt  orthogonalization.
    459: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    461:    Level: beginner

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

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

    470:    Developer Notes:
    471:     This object is subclassed off of KSPGMRES

    473: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES, KSPPIPECG, KSPPIPECR,
    474:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    475:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    476:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(),  KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov()
    477: M*/

    479: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)
    480: {
    481:   KSP_PGMRES     *pgmres;

    485:   PetscNewLog(ksp,&pgmres);

    487:   ksp->data                              = (void*)pgmres;
    488:   ksp->ops->buildsolution                = KSPBuildSolution_PGMRES;
    489:   ksp->ops->setup                        = KSPSetUp_PGMRES;
    490:   ksp->ops->solve                        = KSPSolve_PGMRES;
    491:   ksp->ops->reset                        = KSPReset_PGMRES;
    492:   ksp->ops->destroy                      = KSPDestroy_PGMRES;
    493:   ksp->ops->view                         = KSPView_GMRES;
    494:   ksp->ops->setfromoptions               = KSPSetFromOptions_PGMRES;
    495:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    496:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    498:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    499:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
    500:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);

    502:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    503:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    504:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    505:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    506:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    507:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    508:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    510:   pgmres->nextra_vecs    = 1;
    511:   pgmres->haptol         = 1.0e-30;
    512:   pgmres->q_preallocate  = 0;
    513:   pgmres->delta_allocate = PGMRES_DELTA_DIRECTIONS;
    514:   pgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    515:   pgmres->nrs            = NULL;
    516:   pgmres->sol_temp       = NULL;
    517:   pgmres->max_k          = PGMRES_DEFAULT_MAXK;
    518:   pgmres->Rsvd           = NULL;
    519:   pgmres->orthogwork     = NULL;
    520:   pgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    521:   return(0);
    522: }