Date: 2026-07-30T21:14:07+00:00

Actual source code: gmres.c

      1: /*
      2:     This file implements GMRES (a Generalized Minimal Residual) method.
      3:     Reference:  Saad and Schultz, 1986.

      5:     Some comments on left vs. right preconditioning, and restarts.
      6:     Left and right preconditioning.
      7:     If right preconditioning is chosen, then the problem being solved
      8:     by GMRES is actually
      9:        My =  AB^-1 y = f
     10:     so the initial residual is
     11:           r = f - M y
     12:     Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
     13:     residual is
     14:           r = f - A x
     15:     The final solution is then
     16:           x = B^-1 y

     18:     If left preconditioning is chosen, then the problem being solved is
     19:        My = B^-1 A x = B^-1 f,
     20:     and the initial residual is
     21:        r  = B^-1(f - Ax)

     23:     Restarts:  Restarts are basically solves with x0 not equal to zero.
     24:     Note that we can eliminate an extra application of B^-1 between
     25:     restarts as long as we don't require that the solution at the end
     26:     of an unsuccessful gmres iteration always be the solution x.
     27:  */

     29: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
     30: #define GMRES_DELTA_DIRECTIONS 10
     31: #define GMRES_DEFAULT_MAXK     30
     32: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
     33: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);

     35: PetscErrorCode KSPSetUp_GMRES(KSP ksp)
     36: {
     37:   PetscInt   hh, hes, rs, cc;
     38:   PetscInt   max_k, k;
     39:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

     41:   PetscFunctionBegin;
     42:   max_k = gmres->max_k; /* restart size */
     43:   hh    = (max_k + 2) * (max_k + 1);
     44:   hes   = (max_k + 1) * (max_k + 1);
     45:   rs    = (max_k + 2);
     46:   cc    = (max_k + 1);

     48:   PetscCall(PetscCalloc5(hh, &gmres->hh_origin, hes, &gmres->hes_origin, rs, &gmres->rs_origin, cc, &gmres->cc_origin, cc, &gmres->ss_origin));

     50:   if (ksp->calc_sings) {
     51:     /* Allocate workspace to hold Hessenberg matrix needed by LAPACK */
     52:     PetscCall(PetscMalloc1((max_k + 3) * (max_k + 9), &gmres->Rsvd));
     53:     PetscCall(PetscMalloc1(6 * (max_k + 2), &gmres->Dsvd));
     54:   }

     56:   /* Allocate array to hold pointers to user vectors.  Note that we need
     57:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
     58:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
     59:   PetscCall(PetscMalloc1(gmres->vecs_allocated, &gmres->vecs));
     60:   PetscCall(PetscMalloc1(VEC_OFFSET + 2 + max_k, &gmres->user_work));
     61:   PetscCall(PetscMalloc1(VEC_OFFSET + 2 + max_k, &gmres->mwork_alloc));
     62:   if (gmres->q_preallocate || ksp->normtype == KSP_NORM_NONE) gmres->vv_allocated = VEC_OFFSET + 2 + PetscMin(max_k, ksp->max_it);
     63:   else gmres->vv_allocated = VEC_OFFSET + 2 + PetscMin(PetscMin(5, max_k), ksp->max_it);
     64:   PetscCall(KSPCreateVecs(ksp, gmres->vv_allocated, &gmres->user_work[0], 0, NULL));
     65:   gmres->mwork_alloc[0] = gmres->vv_allocated;
     66:   gmres->nwork_alloc    = 1;
     67:   for (k = 0; k < gmres->vv_allocated; k++) gmres->vecs[k] = gmres->user_work[0][k];
     68:   PetscFunctionReturn(PETSC_SUCCESS);
     69: }

     71: /*
     72:     Run gmres, possibly with restart.  Return residual history if requested.
     73:     input parameters:

     75: .        gmres  - structure containing parameters and work areas

     77:     output parameters:
     78: .        nres    - residuals (from preconditioned system) at each step.
     79:                   If restarting, consider passing nres+it.  If null,
     80:                   ignored
     81: .        itcount - number of iterations used.  nres[0] to nres[itcount]
     82:                   are defined.  If null, ignored.

     84:     Notes:
     85:     On entry, the value in vector VEC_VV(0) should be the initial residual
     86:     (this allows shortcuts where the initial preconditioned residual is 0).
     87:  */
     88: static PetscErrorCode KSPGMRESCycle(PetscInt *itcount, KSP ksp)
     89: {
     90:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
     91:   PetscReal  res, hapbnd, tt;
     92:   PetscInt   it = 0, max_k = gmres->max_k;
     93:   PetscBool  hapend = PETSC_FALSE;

     95:   PetscFunctionBegin;
     96:   if (itcount) *itcount = 0;
     97:   PetscCall(VecNormalize(VEC_VV(0), &res));
     98:   KSPCheckNorm(ksp, res);

    100:   /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
    101:   if ((ksp->rnorm > 0.0) && (PetscAbsReal(res - ksp->rnorm) > gmres->breakdowntol * gmres->rnorm0)) {
    102:     PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED, "Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",
    103:                (double)ksp->rnorm, (double)res, (double)gmres->rnorm0);
    104:     PetscCall(PetscInfo(ksp, "Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g\n", (double)ksp->rnorm, (double)res, (double)gmres->rnorm0));
    105:     ksp->reason = KSP_DIVERGED_BREAKDOWN;
    106:     PetscFunctionReturn(PETSC_SUCCESS);
    107:   }
    108:   *GRS(0) = gmres->rnorm0 = res;

    110:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
    111:   ksp->rnorm = res;
    112:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
    113:   gmres->it = (it - 1);
    114:   PetscCall(KSPLogResidualHistory(ksp, res));
    115:   PetscCall(KSPLogErrorHistory(ksp));
    116:   PetscCall(KSPMonitor(ksp, ksp->its, res));
    117:   if (!res) {
    118:     ksp->reason = KSP_CONVERGED_ATOL;
    119:     PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
    120:     PetscFunctionReturn(PETSC_SUCCESS);
    121:   }

    123:   /* check for the convergence */
    124:   PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));
    125:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    126:     if (it) {
    127:       PetscCall(KSPLogResidualHistory(ksp, res));
    128:       PetscCall(KSPLogErrorHistory(ksp));
    129:       PetscCall(KSPMonitor(ksp, ksp->its, res));
    130:     }
    131:     gmres->it = (it - 1);
    132:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) PetscCall(KSPGMRESGetNewVectors(ksp, it + 1));
    133:     PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(it), VEC_VV(1 + it), VEC_TEMP_MATOP));

    135:     /* update Hessenberg matrix and do Gram-Schmidt */
    136:     PetscCall((*gmres->orthog)(ksp, it));
    137:     if (ksp->reason) break;

    139:     /* vv(i+1) . vv(i+1) */
    140:     PetscCall(VecNormalize(VEC_VV(it + 1), &tt));
    141:     KSPCheckNorm(ksp, tt);

    143:     /* save the magnitude */
    144:     *HH(it + 1, it)  = tt;
    145:     *HES(it + 1, it) = tt;

    147:     /* check for the happy breakdown */
    148:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    149:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
    150:     if (tt < hapbnd) {
    151:       PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n", (double)hapbnd, (double)tt));
    152:       hapend = PETSC_TRUE;
    153:     }
    154:     PetscCall(KSPGMRESUpdateHessenberg(ksp, it, hapend, &res));

    156:     it++;
    157:     gmres->it = (it - 1); /* For converged */
    158:     ksp->its++;
    159:     ksp->rnorm = res;
    160:     if (ksp->reason) break;

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

    164:     /* Catch error in happy breakdown and signal convergence and break from loop */
    165:     if (hapend) {
    166:       if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
    167:         ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
    168:       } else if (!ksp->reason) {
    169:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
    170:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    171:         break;
    172:       }
    173:     }
    174:   }

    176:   if (itcount) *itcount = it;

    178:   /*
    179:     Down here we have to solve for the "best" coefficients of the Krylov
    180:     columns, add the solution values together, and possibly unwind the
    181:     preconditioning from the solution
    182:    */
    183:   /* Form the solution (or the solution so far) */
    184:   PetscCall(KSPGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, it - 1));

    186:   /* Monitor if we know that we will not return for a restart */
    187:   if (ksp->reason == KSP_CONVERGED_ITERATING && ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    188:   if (it && ksp->reason) {
    189:     PetscCall(KSPLogResidualHistory(ksp, res));
    190:     PetscCall(KSPLogErrorHistory(ksp));
    191:     PetscCall(KSPMonitor(ksp, ksp->its, res));
    192:   }
    193:   PetscFunctionReturn(PETSC_SUCCESS);
    194: }

    196: static PetscErrorCode KSPSolve_GMRES(KSP ksp)
    197: {
    198:   PetscInt   its, itcount, i;
    199:   KSP_GMRES *gmres      = (KSP_GMRES *)ksp->data;
    200:   PetscBool  guess_zero = ksp->guess_zero;
    201:   PetscInt   N          = gmres->max_k + 1;

    203:   PetscFunctionBegin;
    204:   PetscCheck(!ksp->calc_sings || gmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

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

    210:   itcount          = 0;
    211:   gmres->fullcycle = 0;
    212:   ksp->rnorm       = -1.0; /* special marker for KSPGMRESCycle() */
    213:   while (!ksp->reason || (ksp->rnorm == -1 && ksp->reason == KSP_DIVERGED_PC_FAILED)) {
    214:     PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
    215:     PetscCall(KSPGMRESCycle(&its, ksp));
    216:     /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
    217:     if the cycle is complete for the computation of the Ritz pairs */
    218:     if (its == gmres->max_k) {
    219:       gmres->fullcycle++;
    220:       if (ksp->calc_ritz) {
    221:         if (!gmres->hes_ritz) {
    222:           PetscCall(PetscMalloc1(N * N, &gmres->hes_ritz));
    223:           PetscCall(VecDuplicateVecs(VEC_VV(0), N, &gmres->vecb));
    224:         }
    225:         PetscCall(PetscArraycpy(gmres->hes_ritz, gmres->hes_origin, N * N));
    226:         for (i = 0; i < gmres->max_k + 1; i++) PetscCall(VecCopy(VEC_VV(i), gmres->vecb[i]));
    227:       }
    228:     }
    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:   PetscFunctionReturn(PETSC_SUCCESS);
    238: }

    240: PetscErrorCode KSPReset_GMRES(KSP ksp)
    241: {
    242:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
    243:   PetscInt   i;

    245:   PetscFunctionBegin;
    246:   /* Free the Hessenberg matrices */
    247:   PetscCall(PetscFree5(gmres->hh_origin, gmres->hes_origin, gmres->rs_origin, gmres->cc_origin, gmres->ss_origin));
    248:   PetscCall(PetscFree(gmres->hes_ritz));

    250:   /* free work vectors */
    251:   PetscCall(PetscFree(gmres->vecs));
    252:   for (i = 0; i < gmres->nwork_alloc; i++) PetscCall(VecDestroyVecs(gmres->mwork_alloc[i], &gmres->user_work[i]));
    253:   gmres->nwork_alloc = 0;
    254:   if (gmres->vecb) PetscCall(VecDestroyVecs(gmres->max_k + 1, &gmres->vecb));

    256:   PetscCall(PetscFree(gmres->user_work));
    257:   PetscCall(PetscFree(gmres->mwork_alloc));
    258:   PetscCall(PetscFree(gmres->nrs));
    259:   PetscCall(VecDestroy(&gmres->sol_temp));
    260:   PetscCall(PetscFree(gmres->Rsvd));
    261:   PetscCall(PetscFree(gmres->Dsvd));
    262:   PetscCall(PetscFree(gmres->orthogwork));

    264:   gmres->vv_allocated   = 0;
    265:   gmres->vecs_allocated = 0;
    266:   gmres->sol_temp       = NULL;
    267:   PetscFunctionReturn(PETSC_SUCCESS);
    268: }

    270: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    271: {
    272:   PetscFunctionBegin;
    273:   PetscCall(KSPReset_GMRES(ksp));
    274:   PetscCall(PetscFree(ksp->data));
    275:   /* clear composed functions */
    276:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", NULL));
    277:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", NULL));
    278:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", NULL));
    279:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", NULL));
    280:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", NULL));
    281:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", NULL));
    282:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetBreakdownTolerance_C", NULL));
    283:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", NULL));
    284:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", NULL));
    285:   PetscFunctionReturn(PETSC_SUCCESS);
    286: }
    287: /*
    288:     KSPGMRESBuildSoln - create the solution from the starting vector and the
    289:     current iterates.

    291:     Input parameters:
    292:         nrs - work area of size it + 1.
    293:         vs  - index of initial guess
    294:         vdest - index of result.  Note that vs may == vdest (replace
    295:                 guess with the solution).

    297:      This is an internal routine that knows about the GMRES internals.
    298:  */
    299: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs, Vec vs, Vec vdest, KSP ksp, PetscInt it)
    300: {
    301:   PetscScalar tt;
    302:   PetscInt    ii, k, j;
    303:   KSP_GMRES  *gmres = (KSP_GMRES *)ksp->data;

    305:   PetscFunctionBegin;
    306:   /* Solve for solution vector that minimizes the residual */

    308:   /* If it is < 0, no gmres steps have been performed */
    309:   if (it < 0) {
    310:     PetscCall(VecCopy(vs, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
    311:     PetscFunctionReturn(PETSC_SUCCESS);
    312:   }
    313:   if (*HH(it, it) != 0.0) {
    314:     nrs[it] = *GRS(it) / *HH(it, it);
    315:   } else {
    316:     PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "You reached the break down in GMRES; HH(it,it) = 0");
    317:     ksp->reason = KSP_DIVERGED_BREAKDOWN;

    319:     PetscCall(PetscInfo(ksp, "Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g\n", it, (double)PetscAbsScalar(*GRS(it))));
    320:     PetscFunctionReturn(PETSC_SUCCESS);
    321:   }
    322:   for (ii = 1; ii <= it; ii++) {
    323:     k  = it - ii;
    324:     tt = *GRS(k);
    325:     for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
    326:     if (*HH(k, k) == 0.0) {
    327:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %" PetscInt_FMT, k);
    328:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
    329:       PetscCall(PetscInfo(ksp, "Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %" PetscInt_FMT "\n", k));
    330:       PetscFunctionReturn(PETSC_SUCCESS);
    331:     }
    332:     nrs[k] = tt / *HH(k, k);
    333:   }

    335:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
    336:   PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));

    338:   PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));
    339:   /* add solution to previous solution */
    340:   if (vdest != vs) PetscCall(VecCopy(vs, vdest));
    341:   PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
    342:   PetscFunctionReturn(PETSC_SUCCESS);
    343: }
    344: /*
    345:    Do the scalar work for the orthogonalization.  Return new residual norm.
    346:  */
    347: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
    348: {
    349:   PetscScalar *hh, *cc, *ss, tt;
    350:   PetscInt     j;
    351:   KSP_GMRES   *gmres = (KSP_GMRES *)ksp->data;

    353:   PetscFunctionBegin;
    354:   hh = HH(0, it);
    355:   cc = CC(0);
    356:   ss = SS(0);

    358:   /* Apply all the previously computed plane rotations to the new column
    359:      of the Hessenberg matrix */
    360:   for (j = 1; j <= it; j++) {
    361:     tt  = *hh;
    362:     *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
    363:     hh++;
    364:     *hh = *cc++ * *hh - (*ss++ * tt);
    365:   }

    367:   /*
    368:     compute the new plane rotation, and apply it to:
    369:      1) the right-hand side of the Hessenberg system
    370:      2) the new column of the Hessenberg matrix
    371:     thus obtaining the updated value of the residual
    372:   */
    373:   if (!hapend) {
    374:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
    375:     if (tt == 0.0) {
    376:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "tt == 0.0");
    377:       ksp->reason = KSP_DIVERGED_NULL;
    378:       PetscFunctionReturn(PETSC_SUCCESS);
    379:     }
    380:     *cc          = *hh / tt;
    381:     *ss          = *(hh + 1) / tt;
    382:     *GRS(it + 1) = -(*ss * *GRS(it));
    383:     *GRS(it)     = PetscConj(*cc) * *GRS(it);
    384:     *hh          = PetscConj(*cc) * *hh + *ss * *(hh + 1);
    385:     *res         = PetscAbsScalar(*GRS(it + 1));
    386:   } else {
    387:     /* 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 (GRS(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:   PetscFunctionReturn(PETSC_SUCCESS);
    397: }
    398: /*
    399:    This routine allocates more work vectors, starting from VEC_VV(it).
    400:  */
    401: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp, PetscInt it)
    402: {
    403:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
    404:   PetscInt   nwork = gmres->nwork_alloc, k, nalloc;

    406:   PetscFunctionBegin;
    407:   nalloc = PetscMin(ksp->max_it, gmres->delta_allocate);
    408:   /* Adjust the number to allocate to make sure that we don't exceed the
    409:     number of available slots */
    410:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
    411:   if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);

    413:   gmres->vv_allocated += nalloc;

    415:   PetscCall(KSPCreateVecs(ksp, nalloc, &gmres->user_work[nwork], 0, NULL));

    417:   gmres->mwork_alloc[nwork] = nalloc;
    418:   for (k = 0; k < nalloc; k++) gmres->vecs[it + VEC_OFFSET + k] = gmres->user_work[nwork][k];
    419:   gmres->nwork_alloc++;
    420:   PetscFunctionReturn(PETSC_SUCCESS);
    421: }

    423: static PetscErrorCode KSPBuildSolution_GMRES(KSP ksp, Vec ptr, Vec *result)
    424: {
    425:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    427:   PetscFunctionBegin;
    428:   if (!ptr) {
    429:     if (!gmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &gmres->sol_temp));
    430:     ptr = gmres->sol_temp;
    431:   }
    432:   if (!gmres->nrs) {
    433:     /* allocate the work area */
    434:     PetscCall(PetscMalloc1(gmres->max_k, &gmres->nrs));
    435:   }

    437:   PetscCall(KSPGMRESBuildSoln(gmres->nrs, ksp->vec_sol, ptr, ksp, gmres->it));
    438:   if (result) *result = ptr;
    439:   PetscFunctionReturn(PETSC_SUCCESS);
    440: }

    442: PetscErrorCode KSPView_GMRES(KSP ksp, PetscViewer viewer)
    443: {
    444:   KSP_GMRES  *gmres = (KSP_GMRES *)ksp->data;
    445:   const char *cstr;
    446:   PetscBool   isascii, isstring;

    448:   PetscFunctionBegin;
    449:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    450:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
    451:   if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
    452:     switch (gmres->cgstype) {
    453:     case KSP_GMRES_CGS_REFINE_NEVER:
    454:       cstr = "classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement";
    455:       break;
    456:     case KSP_GMRES_CGS_REFINE_ALWAYS:
    457:       cstr = "classical (unmodified) Gram-Schmidt orthogonalization with one step of iterative refinement";
    458:       break;
    459:     case KSP_GMRES_CGS_REFINE_IFNEEDED:
    460:       cstr = "classical (unmodified) Gram-Schmidt orthogonalization with one step of iterative refinement when needed";
    461:       break;
    462:     default:
    463:       SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Unknown orthogonalization");
    464:     }
    465:   } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
    466:     cstr = "modified Gram-Schmidt orthogonalization";
    467:   } else {
    468:     cstr = "unknown orthogonalization";
    469:   }
    470:   if (isascii) {
    471:     PetscCall(PetscViewerASCIIPrintf(viewer, "  restart=%" PetscInt_FMT ", using %s\n", gmres->max_k, cstr));
    472:     PetscCall(PetscViewerASCIIPrintf(viewer, "  happy breakdown tolerance=%g\n", (double)gmres->haptol));
    473:   } else if (isstring) {
    474:     PetscCall(PetscViewerStringSPrintf(viewer, "%s restart %" PetscInt_FMT, cstr, gmres->max_k));
    475:   }
    476:   PetscFunctionReturn(PETSC_SUCCESS);
    477: }

    479: /*@C
    480:   KSPGMRESMonitorKrylov - Calls `VecView()` to monitor each new direction in the `KSPGMRES` accumulated Krylov space.

    482:   Collective

    484:   Input Parameters:
    485: + ksp     - the `KSP` context
    486: . its     - iteration number
    487: . fgnorm  - 2-norm of residual (or gradient)
    488: - Viewers - a collection of viewers created with `PetscViewersCreate()`

    490:   Options Database Key:
    491: . -ksp_gmres_krylov_monitor (true|false) - Plot the Krylov directions

    493:   Level: intermediate

    495:   Note:
    496:   A new `PETSCVIEWERDRAW` is created for each Krylov vector so they can all be simultaneously viewed

    498: .seealso: [](ch_ksp), `KSPGMRES`, `KSPMonitorSet()`, `KSPMonitorResidual()`, `VecView()`, `PetscViewersCreate()`, `PetscViewersDestroy()`
    499: @*/
    500: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp, PetscInt its, PetscReal fgnorm, void *Viewers)
    501: {
    502:   PetscViewers viewers = (PetscViewers)Viewers;
    503:   KSP_GMRES   *gmres   = (KSP_GMRES *)ksp->data;
    504:   Vec          x;
    505:   PetscViewer  viewer;
    506:   PetscBool    flg;

    508:   PetscFunctionBegin;
    509:   PetscCall(PetscViewersGetViewer(viewers, gmres->it + 1, &viewer));
    510:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &flg));
    511:   if (!flg) {
    512:     PetscCall(PetscViewerSetType(viewer, PETSCVIEWERDRAW));
    513:     PetscCall(PetscViewerDrawSetInfo(viewer, NULL, "Krylov GMRES Monitor", PETSC_DECIDE, PETSC_DECIDE, 300, 300));
    514:   }
    515:   x = VEC_VV(gmres->it + 1);
    516:   PetscCall(VecView(x, viewer));
    517:   PetscFunctionReturn(PETSC_SUCCESS);
    518: }

    520: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp, PetscOptionItems PetscOptionsObject)
    521: {
    522:   PetscInt   restart;
    523:   PetscReal  haptol, breakdowntol;
    524:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;
    525:   PetscBool  flg, set;

    527:   PetscFunctionBegin;
    528:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP GMRES Options");
    529:   PetscCall(PetscOptionsInt("-ksp_gmres_restart", "Number of Krylov search directions", "KSPGMRESSetRestart", gmres->max_k, &restart, &flg));
    530:   if (flg) PetscCall(KSPGMRESSetRestart(ksp, restart));
    531:   PetscCall(PetscOptionsReal("-ksp_gmres_haptol", "Tolerance for exact convergence (happy breakdown)", "KSPGMRESSetHapTol", gmres->haptol, &haptol, &flg));
    532:   if (flg) PetscCall(KSPGMRESSetHapTol(ksp, haptol));
    533:   PetscCall(PetscOptionsReal("-ksp_gmres_breakdown_tolerance", "Divergence breakdown tolerance during GMRES restart", "KSPGMRESSetBreakdownTolerance", gmres->breakdowntol, &breakdowntol, &flg));
    534:   if (flg) PetscCall(KSPGMRESSetBreakdownTolerance(ksp, breakdowntol));
    535:   flg = PETSC_FALSE;
    536:   PetscCall(PetscOptionsBool("-ksp_gmres_preallocate", "Preallocate Krylov vectors", "KSPGMRESSetPreAllocateVectors", gmres->q_preallocate, &flg, &set));
    537:   PetscCheck(!set || flg, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Cannot turn off preallocation with -ksp_gmres_preallocate false");
    538:   if (set) PetscCall(KSPGMRESSetPreAllocateVectors(ksp));
    539:   PetscCall(PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt", "classical (unmodified) Gram-Schmidt (fast)", "KSPGMRESSetOrthogonalization", &flg));
    540:   if (flg) PetscCall(KSPGMRESSetOrthogonalization(ksp, KSPGMRESClassicalGramSchmidtOrthogonalization));
    541:   PetscCall(PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt", "modified Gram-Schmidt (slow, more stable)", "KSPGMRESSetOrthogonalization", &flg));
    542:   if (flg) PetscCall(KSPGMRESSetOrthogonalization(ksp, KSPGMRESModifiedGramSchmidtOrthogonalization));
    543:   PetscCall(PetscOptionsEnum("-ksp_gmres_cgs_refinement_type", "Type of iterative refinement for classical (unmodified) Gram-Schmidt", "KSPGMRESSetCGSRefinementType", KSPGMRESCGSRefinementTypes, (PetscEnum)gmres->cgstype, (PetscEnum *)&gmres->cgstype, &flg));
    544:   flg = PETSC_FALSE;
    545:   PetscCall(PetscOptionsBool("-ksp_gmres_krylov_monitor", "Plot the Krylov directions", "KSPMonitorSet", flg, &flg, NULL));
    546:   if (flg) {
    547:     PetscViewers viewers;

    549:     PetscCall(PetscViewersCreate(PetscObjectComm((PetscObject)ksp), &viewers));
    550:     PetscCall(KSPMonitorSet(ksp, KSPGMRESMonitorKrylov, viewers, (PetscCtxDestroyFn *)PetscViewersDestroy));
    551:   }
    552:   PetscOptionsHeadEnd();
    553:   PetscFunctionReturn(PETSC_SUCCESS);
    554: }

    556: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp, PetscReal tol)
    557: {
    558:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    560:   PetscFunctionBegin;
    561:   PetscCheck(tol >= 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Tolerance must be non-negative");
    562:   gmres->haptol = tol;
    563:   PetscFunctionReturn(PETSC_SUCCESS);
    564: }

    566: static PetscErrorCode KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp, PetscReal tol)
    567: {
    568:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    570:   PetscFunctionBegin;
    571:   if (tol == (PetscReal)PETSC_DEFAULT) {
    572:     gmres->breakdowntol = 0.1;
    573:     PetscFunctionReturn(PETSC_SUCCESS);
    574:   }
    575:   PetscCheck(tol >= 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Breakdown tolerance must be non-negative");
    576:   gmres->breakdowntol = tol;
    577:   PetscFunctionReturn(PETSC_SUCCESS);
    578: }

    580: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp, PetscInt *max_k)
    581: {
    582:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    584:   PetscFunctionBegin;
    585:   *max_k = gmres->max_k;
    586:   PetscFunctionReturn(PETSC_SUCCESS);
    587: }

    589: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp, PetscInt max_k)
    590: {
    591:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    593:   PetscFunctionBegin;
    594:   PetscCheck(max_k >= 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Restart must be positive");
    595:   if (!ksp->setupstage) {
    596:     gmres->max_k = max_k;
    597:   } else if (gmres->max_k != max_k) {
    598:     gmres->max_k    = max_k;
    599:     ksp->setupstage = KSP_SETUP_NEW;
    600:     /* free the data structures, then create them again */
    601:     PetscCall(KSPReset_GMRES(ksp));
    602:   }
    603:   PetscFunctionReturn(PETSC_SUCCESS);
    604: }

    606: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp, FCN fcn)
    607: {
    608:   PetscFunctionBegin;
    609:   ((KSP_GMRES *)ksp->data)->orthog = fcn;
    610:   PetscFunctionReturn(PETSC_SUCCESS);
    611: }

    613: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp, FCN *fcn)
    614: {
    615:   PetscFunctionBegin;
    616:   *fcn = ((KSP_GMRES *)ksp->data)->orthog;
    617:   PetscFunctionReturn(PETSC_SUCCESS);
    618: }

    620: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    621: {
    622:   KSP_GMRES *gmres;

    624:   PetscFunctionBegin;
    625:   gmres                = (KSP_GMRES *)ksp->data;
    626:   gmres->q_preallocate = PETSC_TRUE;
    627:   PetscFunctionReturn(PETSC_SUCCESS);
    628: }

    630: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp, KSPGMRESCGSRefinementType type)
    631: {
    632:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    634:   PetscFunctionBegin;
    635:   gmres->cgstype = type;
    636:   PetscFunctionReturn(PETSC_SUCCESS);
    637: }

    639: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp, KSPGMRESCGSRefinementType *type)
    640: {
    641:   KSP_GMRES *gmres = (KSP_GMRES *)ksp->data;

    643:   PetscFunctionBegin;
    644:   *type = gmres->cgstype;
    645:   PetscFunctionReturn(PETSC_SUCCESS);
    646: }

    648: /*@
    649:   KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    650:   in the classical Gram-Schmidt orthogonalization used by `KSPGMRES` and other PETSc GMRES implementations.

    652:   Logically Collective

    654:   Input Parameters:
    655: + ksp  - the Krylov space solver context
    656: - type - the type of refinement
    657: .vb
    658:   KSP_GMRES_CGS_REFINE_NEVER
    659:   KSP_GMRES_CGS_REFINE_IFNEEDED
    660:   KSP_GMRES_CGS_REFINE_ALWAYS
    661: .ve

    663:   Options Database Key:
    664: . -ksp_gmres_cgs_refinement_type (refine_never|refine_ifneeded|refine_always) - refinement type

    666:   Level: intermediate

    668:   Notes:
    669:   The default is `KSP_GMRES_CGS_REFINE_NEVER`

    671:   For a very small set of problems not using refinement, that is `KSP_GMRES_CGS_REFINE_NEVER` may be unstable, thus causing `KSPSolve()`
    672:   to not converge.

    674: .seealso: [](ch_ksp), `KSPGMRES`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESCGSRefinementType`, `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESGetCGSRefinementType()`,
    675:           `KSPGMRESGetOrthogonalization()`
    676: @*/
    677: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp, KSPGMRESCGSRefinementType type)
    678: {
    679:   PetscFunctionBegin;
    682:   PetscTryMethod(ksp, "KSPGMRESSetCGSRefinementType_C", (KSP, KSPGMRESCGSRefinementType), (ksp, type));
    683:   PetscFunctionReturn(PETSC_SUCCESS);
    684: }

    686: /*@
    687:   KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    688:   in the classical Gram-Schmidt orthogonalization used by `KSPGMRES` and other PETSc GMRES implementations.

    690:   Not Collective

    692:   Input Parameter:
    693: . ksp - the Krylov space solver context

    695:   Output Parameter:
    696: . type - the type of refinement

    698:   Level: intermediate

    700: .seealso: [](ch_ksp), `KSPGMRES`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESCGSRefinementType`, `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESSetCGSRefinementType()`,
    701:           `KSPGMRESGetOrthogonalization()`
    702: @*/
    703: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp, KSPGMRESCGSRefinementType *type)
    704: {
    705:   PetscFunctionBegin;
    707:   PetscUseMethod(ksp, "KSPGMRESGetCGSRefinementType_C", (KSP, KSPGMRESCGSRefinementType *), (ksp, type));
    708:   PetscFunctionReturn(PETSC_SUCCESS);
    709: }

    711: /*@
    712:   KSPGMRESSetRestart - Sets number of iterations at which GMRES (`KSPGMRES`, `KSPFGMRES`, `KSPPGMRES`, `KSPAGMRES`, `KSPDGMRES`, `KSPPIPEFGMRES`,
    713:   and `KSPLGMRES`) restarts.

    715:   Logically Collective

    717:   Input Parameters:
    718: + ksp     - the Krylov space solver context
    719: - restart - integer restart value, this corresponds to the number of iterations of GMRES to perform before restarting

    721:   Options Database Key:
    722: . -ksp_gmres_restart restart - integer restart value

    724:   Level: intermediate

    726:   Notes:
    727:   The default value is 30.

    729:   GMRES builds a Krylov subspace of increasing size, where each new vector is orthogonalized against the previous ones using a Gram-Schmidt process.
    730:   As the size of the Krylov subspace grows, the computational cost and memory requirements increase. To mitigate this issue, GMRES methods
    731:   usually employ restart strategies, which involve periodically deleting the Krylov subspace and beginning to generate a new one. This can help reduce
    732:   the computational cost and memory usage while still maintaining convergence. The maximum size of the Krylov subspace, that is the maximum number
    733:   of vectors orthogonalized is called the `restart` parameter.

    735:   A larger restart parameter generally leads to faster convergence of GMRES but the memory usage is higher than with a smaller `restart` parameter,
    736:   as is the average time to perform each iteration. For more ill-conditioned problems a larger restart value may be necessary.

    738:   `KSPBCGS` has the advantage over `KSPGMRES` in that it does not explicitly store the Krylov space and thus does not require as much memory
    739:   as GMRES might need.

    741: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESGetRestart()`,
    742:           `KSPFGMRES`, `KSPLGMRES`, `KSPPGMRES`, `KSPAGMRES`, `KSPDGMRES`, `KSPPIPEFGMRES`
    743: @*/
    744: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    745: {
    746:   PetscFunctionBegin;

    749:   PetscTryMethod(ksp, "KSPGMRESSetRestart_C", (KSP, PetscInt), (ksp, restart));
    750:   PetscFunctionReturn(PETSC_SUCCESS);
    751: }

    753: /*@
    754:   KSPGMRESGetRestart - Gets number of iterations at which GMRES (`KSPGMRES`, `KSPFGMRES`, `KSPPGMRES`, `KSPAGMRES`, `KSPDGMRES`, `KSPPIPEFGMRES`,
    755:   and `KSPLGMRES`) restarts.

    757:   Not Collective

    759:   Input Parameter:
    760: . ksp - the Krylov space solver context

    762:   Output Parameter:
    763: . restart - integer restart value

    765:   Level: intermediate

    767: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetRestart()`,
    768:           `KSPFGMRES`, `KSPLGMRES`, `KSPPGMRES`, `KSPAGMRES`, `KSPDGMRES`, `KSPPIPEFGMRES`
    769: @*/
    770: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
    771: {
    772:   PetscFunctionBegin;
    773:   PetscUseMethod(ksp, "KSPGMRESGetRestart_C", (KSP, PetscInt *), (ksp, restart));
    774:   PetscFunctionReturn(PETSC_SUCCESS);
    775: }

    777: /*@
    778:   KSPGMRESSetHapTol - Sets the tolerance for detecting a happy breakdown in GMRES (`KSPGMRES`, `KSPFGMRES` and `KSPLGMRES` and others)

    780:   Logically Collective

    782:   Input Parameters:
    783: + ksp - the Krylov space solver context
    784: - tol - the tolerance for detecting a happy breakdown

    786:   Options Database Key:
    787: . -ksp_gmres_haptol tol - set tolerance for determining happy breakdown

    789:   Level: intermediate

    791:   Note:
    792:   Happy breakdown is the rare case in `KSPGMRES` where a very near zero matrix entry is generated in the upper Hessenberg matrix indicating
    793:   an 'exact' solution has been obtained. If you attempt more iterations after this point with GMRES unstable
    794:   things can happen.

    796:   The default tolerance value for detecting a happy breakdown with GMRES in PETSc is 1.0e-30.

    798: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`
    799: @*/
    800: PetscErrorCode KSPGMRESSetHapTol(KSP ksp, PetscReal tol)
    801: {
    802:   PetscFunctionBegin;
    804:   PetscTryMethod(ksp, "KSPGMRESSetHapTol_C", (KSP, PetscReal), (ksp, tol));
    805:   PetscFunctionReturn(PETSC_SUCCESS);
    806: }

    808: /*@
    809:   KSPGMRESSetBreakdownTolerance - Sets the tolerance for determining divergence breakdown in `KSPGMRES` at restart.

    811:   Logically Collective

    813:   Input Parameters:
    814: + ksp - the Krylov space solver context
    815: - tol - the tolerance

    817:   Options Database Key:
    818: . -ksp_gmres_breakdown_tolerance tol - set tolerance for determining divergence breakdown

    820:   Level: intermediate

    822:   Note:
    823:   Divergence breakdown occurs when the norm of the GMRES residual increases significantly at a restart.
    824:   This is defined to be $ | truenorm - gmresnorm | > tol * gmresnorm $ where $ gmresnorm $ is the norm computed
    825:   by the GMRES process at a restart iteration using the standard GMRES recursion formula and $ truenorm $ is computed after
    826:   the restart using the definition $ \| r \| = \| b - A x \|$.

    828:   Divergence breakdown stops the iterative solve with a `KSPConvergedReason` of `KSP_DIVERGED_BREAKDOWN` indicating the
    829:   GMRES solver has not converged.

    831:   Divergence breakdown can occur when there is an error (bug) in either the application of the matrix or the preconditioner,
    832:   or the preconditioner is extremely ill-conditioned.

    834:   The default is .1

    836: .seealso: [](ch_ksp), `KSPGMRES`, `KSPSetTolerances()`, `KSPGMRESSetHapTol()`, `KSPConvergedReason`
    837: @*/
    838: PetscErrorCode KSPGMRESSetBreakdownTolerance(KSP ksp, PetscReal tol)
    839: {
    840:   PetscFunctionBegin;
    842:   PetscTryMethod(ksp, "KSPGMRESSetBreakdownTolerance_C", (KSP, PetscReal), (ksp, tol));
    843:   PetscFunctionReturn(PETSC_SUCCESS);
    844: }

    846: /*MC
    847:    KSPGMRES - Implements the Generalized Minimal Residual method {cite}`saad.schultz:gmres` with restart for solving linear systems using `KSP`.

    849:    Options Database Keys:
    850: +   -ksp_gmres_restart restart                                                  - the number of Krylov directions to orthogonalize against
    851: .   -ksp_gmres_haptol tol                                                       - sets the tolerance for happy breakdown (exact convergence) of `KSPGMRES`
    852: .   -ksp_gmres_preallocate                                                      - preallocate all the Krylov search directions initially (otherwise groups of
    853:                                                                                   vectors are allocated as needed), see `KSPGMRESSetPreAllocateVectors()`
    854: .   -ksp_gmres_classicalgramschmidt                                             - use classical (unmodified) Gram-Schmidt to orthogonalize against
    855:                                                                                   the Krylov space (fast) (the default)
    856: .   -ksp_gmres_modifiedgramschmidt                                              - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    857: .   -ksp_gmres_cgs_refinement_type (refine_never|refine_ifneeded|refine_always) - determine if iterative refinement is used to increase the
    858:                                                                                   stability of the classical Gram-Schmidt  orthogonalization.
    859: -   -ksp_gmres_krylov_monitor                                                   - plot the Krylov space generated

    861:    Level: beginner

    863:    Notes:
    864:    Left and right preconditioning are supported, but not symmetric preconditioning.

    866:    Using `KSPGMRESSetPreAllocateVectors()` or `-ksp_gmres_preallocate` can improve the efficiency of the orthogonalization step with certain vector implementations.

    868: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`, `KSPPGMRES`, `KSPAGMRES`, `KSPDGMRES`, `KSPPIPEFGMRES`,
    869:           `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
    870:           `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
    871:           `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
    872: M*/

    874: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
    875: {
    876:   KSP_GMRES *gmres;

    878:   PetscFunctionBegin;
    879:   PetscCall(PetscNew(&gmres));
    880:   ksp->data = (void *)gmres;

    882:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 4));
    883:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));
    884:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_SYMMETRIC, 2));
    885:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
    886:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

    888:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
    889:   ksp->ops->setup                        = KSPSetUp_GMRES;
    890:   ksp->ops->solve                        = KSPSolve_GMRES;
    891:   ksp->ops->reset                        = KSPReset_GMRES;
    892:   ksp->ops->destroy                      = KSPDestroy_GMRES;
    893:   ksp->ops->view                         = KSPView_GMRES;
    894:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
    895:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    896:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;
    897:   ksp->ops->computeritz                  = KSPComputeRitz_GMRES;
    898:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
    899:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
    900:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
    901:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
    902:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
    903:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
    904:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetBreakdownTolerance_C", KSPGMRESSetBreakdownTolerance_GMRES));
    905:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
    906:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));

    908:   gmres->haptol         = 1.0e-30;
    909:   gmres->breakdowntol   = 0.1;
    910:   gmres->q_preallocate  = PETSC_FALSE;
    911:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    912:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    913:   gmres->nrs            = NULL;
    914:   gmres->sol_temp       = NULL;
    915:   gmres->max_k          = GMRES_DEFAULT_MAXK;
    916:   gmres->Rsvd           = NULL;
    917:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    918:   gmres->orthogwork     = NULL;
    919:   PetscFunctionReturn(PETSC_SUCCESS);
    920: }