Date: 2022-03-04T17:39:03+00:00

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.

     46:  */
     47: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp)
     48: {
     49:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);
     50:   PetscReal      res_norm,res,newnorm;
     52:   PetscInt       it     = 0,j,k;
     53:   PetscBool      hapend = PETSC_FALSE;

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

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

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

     87:     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. */
     88:       KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);
     89:     }

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

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

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

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

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

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

    131:       /* 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. */
    132:       for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
    133:       /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
    134:        * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
    135:       *HH(it-1,it-1) /= *HH(it-1,it-2);
    136:     }

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

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

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

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

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

    185:   /*
    186:     Down here we have to solve for the "best" coefficients of the Krylov
    187:     columns, add the solution values together, and possibly unwind the
    188:     preconditioning from the solution
    189:    */
    190:   /* Form the solution (or the solution so far) */
    191:   KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);
    192:   return(0);
    193: }

    195: /*
    196:     KSPSolve_PGMRES - This routine applies the PGMRES method.

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

    201:    Output Parameter:
    202: .     outits - number of iterations used

    204: */
    205: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
    206: {
    208:   PetscInt       its,itcount;
    209:   KSP_PGMRES     *pgmres    = (KSP_PGMRES*)ksp->data;
    210:   PetscBool      guess_zero = ksp->guess_zero;

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

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

    234: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)
    235: {

    239:   KSPDestroy_GMRES(ksp);
    240:   return(0);
    241: }

    243: /*
    244:     KSPPGMRESBuildSoln - create the solution from the starting vector and the
    245:                       current iterates.

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

    254:      This is an internal routine that knows about the PGMRES internals.
    255:  */
    256: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    257: {
    258:   PetscScalar    tt;
    260:   PetscInt       k,j;
    261:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

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

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

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

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

    295: /*

    297:     KSPPGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    298:                             Return new residual.

    300:     input parameters:

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

    307:     output parameters:
    308: .        res - the new residual

    310:  */
    311: /*
    312: .  it - column of the Hessenberg that is complete, PGMRES is actually computing two columns ahead of this
    313:  */
    314: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)
    315: {
    316:   PetscScalar    *hh,*cc,*ss,*rs;
    317:   PetscInt       j;
    318:   PetscReal      hapbnd;
    319:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

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

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

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

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

    349:   /*
    350:     compute the new plane rotation, and apply it to:
    351:      1) the right-hand-side of the Hessenberg system (RS)
    352:         note: it affects RS(it) and RS(it+1)
    353:      2) the new column of the Hessenberg matrix
    354:         note: it affects HH(it,it) which is currently pointed to
    355:         by hh and HH(it+1, it) (*(hh+1))
    356:     thus obtaining the updated value of the residual...
    357:   */

    359:   /* compute new plane rotation */

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

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

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

    382:     *res = 0.0;
    383:   }
    384:   return(0);
    385: }

    387: /*
    388:    KSPBuildSolution_PGMRES

    390:      Input Parameter:
    391: .     ksp - the Krylov space object
    392: .     ptr-

    394:    Output Parameter:
    395: .     result - the solution

    397:    Note: this calls KSPPGMRESBuildSoln - the same function that KSPPGMRESCycle
    398:    calls directly.

    400: */
    401: PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp,Vec ptr,Vec *result)
    402: {
    403:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)ksp->data;

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

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

    425: PetscErrorCode KSPSetFromOptions_PGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    426: {

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

    436: PetscErrorCode KSPReset_PGMRES(KSP ksp)
    437: {

    441:   KSPReset_GMRES(ksp);
    442:   return(0);
    443: }

    445: /*MC
    446:      KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method.

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

    459:    Level: beginner

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

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

    468:    Developer Notes:
    469:     This object is subclassed off of KSPGMRES

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

    477: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)
    478: {
    479:   KSP_PGMRES     *pgmres;

    483:   PetscNewLog(ksp,&pgmres);

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

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

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

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