Date: 2022-03-31T04:48:10+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: {
     23:   KSPSetUp_GMRES(ksp);
     24:   return 0;
     25: }

     27: /*

     29:     KSPPGMRESCycle - Run pgmres, possibly with restart.  Return residual
     30:                   history if requested.

     32:     input parameters:
     33: .        pgmres  - structure containing parameters and work areas

     35:     output parameters:
     36: .        itcount - number of iterations used.  If null, ignored.
     37: .        converged - 0 if not converged

     39:     Notes:
     40:     On entry, the value in vector VEC_VV(0) should be
     41:     the initial residual.

     43:  */
     44: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp)
     45: {
     46:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);
     47:   PetscReal      res_norm,res,newnorm;
     48:   PetscInt       it     = 0,j,k;
     49:   PetscBool      hapend = PETSC_FALSE;

     51:   if (itcount) *itcount = 0;
     52:   VecNormalize(VEC_VV(0),&res_norm);
     53:   KSPCheckNorm(ksp,res_norm);
     54:   res    = res_norm;
     55:   *RS(0) = res_norm;

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

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

     82:     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. */
     83:       KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);
     84:     }

     86:     if (it > 1) {               /* Complete the pending reduction */
     87:       VecNormEnd(VEC_VV(it-1),NORM_2,&newnorm);
     88:       *HH(it-1,it-2) = newnorm;
     89:     }
     90:     if (it > 0) {               /* Finish the reduction computing the latest column of H */
     91:       VecMDotEnd(Zcur,it,&(VEC_VV(0)),HH(0,it-1));
     92:     }

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

     98:       KSPPGMRESUpdateHessenberg(ksp,it-2,&hapend,&res);
     99:       pgmres->it = it-2;
    100:       ksp->its++;
    101:       if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
    102:       else ksp->rnorm = 0;

    104:       (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
    105:       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. */
    106:         KSPLogResidualHistory(ksp,ksp->rnorm);
    107:         KSPMonitor(ksp,ksp->its,ksp->rnorm);
    108:       }
    109:       if (ksp->reason) break;
    110:       /* Catch error in happy breakdown and signal convergence and break from loop */
    111:       if (hapend) {
    113:         else {
    114:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    115:           break;
    116:         }
    117:       }

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

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

    126:       /* 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. */
    127:       for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
    128:       /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
    129:        * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
    130:       *HH(it-1,it-1) /= *HH(it-1,it-2);
    131:     }

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

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

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

    174:     /* Start an asynchronous split-mode reduction, the result of the MDot and Norm will be collected on the next iteration. */
    175:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Znext));
    176:   }

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

    180:   /*
    181:     Down here we have to solve for the "best" coefficients of the Krylov
    182:     columns, add the solution values together, and possibly unwind the
    183:     preconditioning from the solution
    184:    */
    185:   /* Form the solution (or the solution so far) */
    186:   KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);
    187:   return 0;
    188: }

    190: /*
    191:     KSPSolve_PGMRES - This routine applies the PGMRES method.

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

    196:    Output Parameter:
    197: .     outits - number of iterations used

    199: */
    200: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
    201: {
    202:   PetscInt       its,itcount;
    203:   KSP_PGMRES     *pgmres    = (KSP_PGMRES*)ksp->data;
    204:   PetscBool      guess_zero = ksp->guess_zero;

    207:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    208:   ksp->its = 0;
    209:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    227: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)
    228: {
    229:   KSPDestroy_GMRES(ksp);
    230:   return 0;
    231: }

    233: /*
    234:     KSPPGMRESBuildSoln - create the solution from the starting vector and the
    235:                       current iterates.

    237:     Input parameters:
    238:         nrs - work area of size it + 1.
    239:         vguess  - index of initial guess
    240:         vdest - index of result.  Note that vguess may == vdest (replace
    241:                 guess with the solution).
    242:         it - HH upper triangular part is a block of size (it+1) x (it+1)

    244:      This is an internal routine that knows about the PGMRES internals.
    245:  */
    246: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    247: {
    248:   PetscScalar    tt;
    249:   PetscInt       k,j;
    250:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

    254:   if (it < 0) {                                 /* no pgmres steps have been performed */
    255:     VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
    256:     return 0;
    257:   }

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

    264:   for (k=it-1; k>=0; k--) {
    265:     tt = *RS(k);
    266:     for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
    267:     nrs[k] = tt / *HH(k,k);
    268:   }

    270:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
    271:   VecZeroEntries(VEC_TEMP);
    272:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
    273:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    274:   /* add solution to previous solution */
    275:   if (vdest == vguess) {
    276:     VecAXPY(vdest,1.0,VEC_TEMP);
    277:   } else {
    278:     VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
    279:   }
    280:   return 0;
    281: }

    283: /*

    285:     KSPPGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    286:                             Return new residual.

    288:     input parameters:

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

    295:     output parameters:
    296: .        res - the new residual

    298:  */
    299: /*
    300: .  it - column of the Hessenberg that is complete, PGMRES is actually computing two columns ahead of this
    301:  */
    302: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)
    303: {
    304:   PetscScalar    *hh,*cc,*ss,*rs;
    305:   PetscInt       j;
    306:   PetscReal      hapbnd;
    307:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)(ksp->data);

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

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

    317:   /* check for the happy breakdown */
    318:   hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pgmres->haptol);
    319:   if (PetscAbsScalar(hh[it+1]) < hapbnd) {
    320:     PetscInfo(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)));
    321:     *hapend = PETSC_TRUE;
    322:   }

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

    329:   for (j=0; j<it; j++) {
    330:     PetscScalar hhj = hh[j];
    331:     hh[j]   = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
    332:     hh[j+1] =          -ss[j] *hhj + cc[j]*hh[j+1];
    333:   }

    335:   /*
    336:     compute the new plane rotation, and apply it to:
    337:      1) the right-hand-side of the Hessenberg system (RS)
    338:         note: it affects RS(it) and RS(it+1)
    339:      2) the new column of the Hessenberg matrix
    340:         note: it affects HH(it,it) which is currently pointed to
    341:         by hh and HH(it+1, it) (*(hh+1))
    342:     thus obtaining the updated value of the residual...
    343:   */

    345:   /* compute new plane rotation */

    347:   if (!*hapend) {
    348:     PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
    349:     if (delta == 0.0) {
    350:       ksp->reason = KSP_DIVERGED_NULL;
    351:       return 0;
    352:     }

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

    357:     hh[it]   = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
    358:     rs[it+1] = -ss[it]*rs[it];
    359:     rs[it]   = PetscConj(cc[it])*rs[it];
    360:     *res     = PetscAbsScalar(rs[it+1]);
    361:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
    362:             another rotation matrix (so RH doesn't change).  The new residual is
    363:             always the new sine term times the residual from last time (RS(it)),
    364:             but now the new sine rotation would be zero...so the residual should
    365:             be zero...so we will multiply "zero" by the last residual.  This might
    366:             not be exactly what we want to do here -could just return "zero". */

    368:     *res = 0.0;
    369:   }
    370:   return 0;
    371: }

    373: /*
    374:    KSPBuildSolution_PGMRES

    376:      Input Parameter:
    377: .     ksp - the Krylov space object
    378: .     ptr-

    380:    Output Parameter:
    381: .     result - the solution

    383:    Note: this calls KSPPGMRESBuildSoln - the same function that KSPPGMRESCycle
    384:    calls directly.

    386: */
    387: PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp,Vec ptr,Vec *result)
    388: {
    389:   KSP_PGMRES     *pgmres = (KSP_PGMRES*)ksp->data;

    391:   if (!ptr) {
    392:     if (!pgmres->sol_temp) {
    393:       VecDuplicate(ksp->vec_sol,&pgmres->sol_temp);
    394:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)pgmres->sol_temp);
    395:     }
    396:     ptr = pgmres->sol_temp;
    397:   }
    398:   if (!pgmres->nrs) {
    399:     /* allocate the work area */
    400:     PetscMalloc1(pgmres->max_k,&pgmres->nrs);
    401:     PetscLogObjectMemory((PetscObject)ksp,pgmres->max_k*sizeof(PetscScalar));
    402:   }

    404:   KSPPGMRESBuildSoln(pgmres->nrs,ksp->vec_sol,ptr,ksp,pgmres->it);
    405:   if (result) *result = ptr;
    406:   return 0;
    407: }

    409: PetscErrorCode KSPSetFromOptions_PGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    410: {
    411:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    412:   PetscOptionsHead(PetscOptionsObject,"KSP pipelined GMRES Options");
    413:   PetscOptionsTail();
    414:   return 0;
    415: }

    417: PetscErrorCode KSPReset_PGMRES(KSP ksp)
    418: {
    419:   KSPReset_GMRES(ksp);
    420:   return 0;
    421: }

    423: /*MC
    424:      KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method.

    426:    Options Database Keys:
    427: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    428: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    429: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    430:                              vectors are allocated as needed)
    431: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    432: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    433: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
    434:                                    stability of the classical Gram-Schmidt  orthogonalization.
    435: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    437:    Level: beginner

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

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

    446:    Developer Notes:
    447:     This object is subclassed off of KSPGMRES

    449: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES, KSPPIPECG, KSPPIPECR,
    450:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    451:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    452:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(),  KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov()
    453: M*/

    455: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)
    456: {
    457:   KSP_PGMRES     *pgmres;

    459:   PetscNewLog(ksp,&pgmres);

    461:   ksp->data                              = (void*)pgmres;
    462:   ksp->ops->buildsolution                = KSPBuildSolution_PGMRES;
    463:   ksp->ops->setup                        = KSPSetUp_PGMRES;
    464:   ksp->ops->solve                        = KSPSolve_PGMRES;
    465:   ksp->ops->reset                        = KSPReset_PGMRES;
    466:   ksp->ops->destroy                      = KSPDestroy_PGMRES;
    467:   ksp->ops->view                         = KSPView_GMRES;
    468:   ksp->ops->setfromoptions               = KSPSetFromOptions_PGMRES;
    469:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    470:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    472:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    473:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
    474:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);

    476:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    477:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    478:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    479:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    480:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    481:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    482:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    484:   pgmres->nextra_vecs    = 1;
    485:   pgmres->haptol         = 1.0e-30;
    486:   pgmres->q_preallocate  = 0;
    487:   pgmres->delta_allocate = PGMRES_DELTA_DIRECTIONS;
    488:   pgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    489:   pgmres->nrs            = NULL;
    490:   pgmres->sol_temp       = NULL;
    491:   pgmres->max_k          = PGMRES_DEFAULT_MAXK;
    492:   pgmres->Rsvd           = NULL;
    493:   pgmres->orthogwork     = NULL;
    494:   pgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    495:   return 0;
    496: }