Actual source code: fgmres.c

      1: /*
      2:     This file implements FGMRES (a Generalized Minimal Residual) method.
      3:     Reference:  Saad, 1993.

      5:     Preconditioning:  If the preconditioner is constant then this fgmres
      6:     code is equivalent to RIGHT-PRECONDITIONED GMRES.
      7:     FGMRES is a modification of gmres that allows the preconditioner to change
      8:     at each iteration.

     10:     Restarts:  Restarts are basically solves with x0 not equal to zero.
     11: */

     13: #include <../src/ksp/ksp/impls/gmres/fgmres/fgmresimpl.h>
     14: #define FGMRES_DELTA_DIRECTIONS 10
     15: #define FGMRES_DEFAULT_MAXK     30
     16: static PetscErrorCode KSPFGMRESGetNewVectors(KSP, PetscInt);
     17: static PetscErrorCode KSPFGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
     18: static PetscErrorCode KSPFGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);

     20: static PetscErrorCode KSPSetUp_FGMRES(KSP ksp)
     21: {
     22:   PetscInt    max_k, k;
     23:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;

     25:   PetscFunctionBegin;
     26:   max_k = fgmres->max_k;

     28:   PetscCall(KSPSetUp_GMRES(ksp));

     30:   PetscCall(PetscMalloc1(max_k + 2, &fgmres->prevecs));
     31:   PetscCall(PetscMalloc1(max_k + 2, &fgmres->prevecs_user_work));

     33:   /* fgmres->vv_allocated includes extra work vectors, which are not used in the additional
     34:      block of vectors used to store the preconditioned directions, hence  the -VEC_OFFSET
     35:      term for this first allocation of vectors holding preconditioned directions */
     36:   PetscCall(KSPCreateVecs(ksp, fgmres->vv_allocated - VEC_OFFSET, &fgmres->prevecs_user_work[0], 0, NULL));
     37:   for (k = 0; k < fgmres->vv_allocated - VEC_OFFSET; k++) fgmres->prevecs[k] = fgmres->prevecs_user_work[0][k];
     38:   PetscFunctionReturn(PETSC_SUCCESS);
     39: }

     41: static PetscErrorCode KSPFGMRESResidual(KSP ksp)
     42: {
     43:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
     44:   Mat         Amat, Pmat;

     46:   PetscFunctionBegin;
     47:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

     49:   /* put A*x into VEC_TEMP */
     50:   PetscCall(KSP_MatMult(ksp, Amat, ksp->vec_sol, VEC_TEMP));
     51:   /* now put residual (-A*x + f) into vec_vv(0) */
     52:   PetscCall(VecWAXPY(VEC_VV(0), -1.0, VEC_TEMP, ksp->vec_rhs));
     53:   PetscFunctionReturn(PETSC_SUCCESS);
     54: }

     56: static PetscErrorCode KSPFGMRESCycle(PetscInt *itcount, KSP ksp)
     57: {
     58:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
     59:   PetscReal   res_norm;
     60:   PetscReal   hapbnd, tt;
     61:   PetscBool   hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
     62:   PetscInt    loc_it;                /* local count of # of dir. in Krylov space */
     63:   PetscInt    max_k = fgmres->max_k; /* max # of directions Krylov space */
     64:   Mat         Amat, Pmat;

     66:   PetscFunctionBegin;
     67:   /* Number of pseudo iterations since last restart is the number
     68:      of prestart directions */
     69:   loc_it = 0;

     71:   /* note: (fgmres->it) is always set one less than (loc_it) It is used in
     72:      KSPBUILDSolution_FGMRES, where it is passed to KSPFGMRESBuildSoln.
     73:      Note that when KSPFGMRESBuildSoln is called from this function,
     74:      (loc_it -1) is passed, so the two are equivalent */
     75:   fgmres->it = (loc_it - 1);

     77:   /* initial residual is in VEC_VV(0)  - compute its norm*/
     78:   PetscCall(VecNorm(VEC_VV(0), NORM_2, &res_norm));
     79:   KSPCheckNorm(ksp, res_norm);

     81:   /* The first entry in the right-hand side of the Hessenberg system is just
     82:      the initial residual norm */
     83:   *RS(0) = res_norm;

     85:   ksp->rnorm = res_norm;
     86:   PetscCall(KSPLogResidualHistory(ksp, res_norm));
     87:   PetscCall(KSPMonitor(ksp, ksp->its, res_norm));

     89:   /* check for the convergence - maybe the current guess is good enough */
     90:   PetscCall((*ksp->converged)(ksp, ksp->its, res_norm, &ksp->reason, ksp->cnvP));
     91:   if (ksp->reason) {
     92:     if (itcount) *itcount = 0;
     93:     PetscFunctionReturn(PETSC_SUCCESS);
     94:   }

     96:   /* scale VEC_VV (the initial residual) */
     97:   PetscCall(VecScale(VEC_VV(0), 1.0 / res_norm));

     99:   /* MAIN ITERATION LOOP BEGINNING*/
    100:   /* keep iterating until we have converged OR generated the max number
    101:      of directions OR reached the max number of iterations for the method */
    102:   while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
    103:     if (loc_it) {
    104:       PetscCall(KSPLogResidualHistory(ksp, res_norm));
    105:       PetscCall(KSPMonitor(ksp, ksp->its, res_norm));
    106:     }
    107:     fgmres->it = (loc_it - 1);

    109:     /* see if more space is needed for work vectors */
    110:     if (fgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
    111:       PetscCall(KSPFGMRESGetNewVectors(ksp, loc_it + 1));
    112:       /* (loc_it+1) is passed in as number of the first vector that should
    113:          be allocated */
    114:     }

    116:     /* CHANGE THE PRECONDITIONER? */
    117:     /* ModifyPC is the callback function that can be used to
    118:        change the PC or its attributes before its applied */
    119:     PetscCall((*fgmres->modifypc)(ksp, ksp->its, loc_it, res_norm, fgmres->modifyctx));

    121:     /* apply PRECONDITIONER to direction vector and store with
    122:        preconditioned vectors in prevec */
    123:     PetscCall(KSP_PCApply(ksp, VEC_VV(loc_it), PREVEC(loc_it)));

    125:     PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
    126:     /* Multiply preconditioned vector by operator - put in VEC_VV(loc_it+1) */
    127:     PetscCall(KSP_MatMult(ksp, Amat, PREVEC(loc_it), VEC_VV(1 + loc_it)));

    129:     /* update Hessenberg matrix and do Gram-Schmidt - new direction is in
    130:        VEC_VV(1+loc_it)*/
    131:     PetscCall((*fgmres->orthog)(ksp, loc_it));

    133:     /* new entry in hessenburg is the 2-norm of our new direction */
    134:     PetscCall(VecNorm(VEC_VV(loc_it + 1), NORM_2, &tt));
    135:     KSPCheckNorm(ksp, tt);

    137:     *HH(loc_it + 1, loc_it)  = tt;
    138:     *HES(loc_it + 1, loc_it) = tt;

    140:     /* Happy Breakdown Check */
    141:     hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
    142:     /* RS(loc_it) contains the res_norm from the last iteration  */
    143:     hapbnd = PetscMin(fgmres->haptol, hapbnd);
    144:     if (tt > hapbnd) {
    145:       /* scale new direction by its norm */
    146:       PetscCall(VecScale(VEC_VV(loc_it + 1), 1.0 / tt));
    147:     } else {
    148:       /* This happens when the solution is exactly reached. */
    149:       /* So there is no new direction... */
    150:       PetscCall(VecSet(VEC_TEMP, 0.0)); /* set VEC_TEMP to 0 */
    151:       hapend = PETSC_TRUE;
    152:     }
    153:     /* note that for FGMRES we could get HES(loc_it+1, loc_it)  = 0 and the
    154:        current solution would not be exact if HES was singular.  Note that
    155:        HH non-singular implies that HES is no singular, and HES is guaranteed
    156:        to be nonsingular when PREVECS are linearly independent and A is
    157:        nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
    158:        of HES). So we should really add a check to verify that HES is nonsingular.*/

    160:     /* Now apply rotations to the new column of Hessenberg (and the right-hand side of the system),
    161:        calculate new rotation, and get new residual norm at the same time*/
    162:     PetscCall(KSPFGMRESUpdateHessenberg(ksp, loc_it, hapend, &res_norm));
    163:     if (ksp->reason) break;

    165:     loc_it++;
    166:     fgmres->it = (loc_it - 1); /* Add this here in case it has converged */

    168:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
    169:     ksp->its++;
    170:     ksp->rnorm = res_norm;
    171:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

    173:     PetscCall((*ksp->converged)(ksp, ksp->its, res_norm, &ksp->reason, ksp->cnvP));

    175:     /* Catch error in happy breakdown and signal convergence and break from loop */
    176:     if (hapend) {
    177:       if (!ksp->reason) {
    178:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res_norm);
    179:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    180:         break;
    181:       }
    182:     }
    183:   }
    184:   /* END OF ITERATION LOOP */

    186:   if (itcount) *itcount = loc_it;

    188:   /*
    189:     Down here we have to solve for the "best" coefficients of the Krylov
    190:     columns, add the solution values together, and possibly unwind the
    191:     preconditioning from the solution
    192:    */

    194:   /* Form the solution (or the solution so far) */
    195:   /* Note: must pass in (loc_it-1) for iteration count so that KSPFGMRESBuildSoln
    196:      properly navigates */

    198:   PetscCall(KSPFGMRESBuildSoln(RS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1));

    200:   /*  Monitor if we know that we will not return for a restart */
    201:   if (ksp->reason == KSP_CONVERGED_ITERATING && ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    202:   if (loc_it && ksp->reason) {
    203:     PetscCall(KSPMonitor(ksp, ksp->its, res_norm));
    204:     PetscCall(KSPLogResidualHistory(ksp, res_norm));
    205:   }
    206:   PetscFunctionReturn(PETSC_SUCCESS);
    207: }

    209: static PetscErrorCode KSPSolve_FGMRES(KSP ksp)
    210: {
    211:   PetscInt    cycle_its = 0; /* iterations done in a call to KSPFGMRESCycle */
    212:   KSP_FGMRES *fgmres    = (KSP_FGMRES *)ksp->data;
    213:   PetscBool   diagonalscale;

    215:   PetscFunctionBegin;
    216:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
    217:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

    219:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
    220:   ksp->its = 0;
    221:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

    223:   /* Compute the initial (NOT preconditioned) residual */
    224:   if (!ksp->guess_zero) {
    225:     PetscCall(KSPFGMRESResidual(ksp));
    226:   } else { /* guess is 0 so residual is F (which is in ksp->vec_rhs) */
    227:     PetscCall(VecCopy(ksp->vec_rhs, VEC_VV(0)));
    228:   }
    229:   /* This may be true only on a subset of MPI ranks; setting it here so it will be detected by the first norm computation in the Krylov method */
    230:   PetscCall(VecFlag(VEC_VV(0), ksp->reason == KSP_DIVERGED_PC_FAILED));

    232:   /* now the residual is in VEC_VV(0) - which is what
    233:      KSPFGMRESCycle expects... */

    235:   PetscCall(KSPFGMRESCycle(&cycle_its, ksp));
    236:   while (!ksp->reason) {
    237:     PetscCall(KSPFGMRESResidual(ksp));
    238:     if (ksp->its >= ksp->max_it) break;
    239:     PetscCall(KSPFGMRESCycle(&cycle_its, ksp));
    240:   }
    241:   /* mark lack of convergence */
    242:   if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    243:   PetscFunctionReturn(PETSC_SUCCESS);
    244: }

    246: extern PetscErrorCode KSPReset_FGMRES(KSP);

    248: static PetscErrorCode KSPDestroy_FGMRES(KSP ksp)
    249: {
    250:   PetscFunctionBegin;
    251:   PetscCall(KSPReset_FGMRES(ksp));
    252:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFlexibleSetModifyPC_C", NULL));
    253:   PetscCall(KSPDestroy_GMRES(ksp));
    254:   PetscFunctionReturn(PETSC_SUCCESS);
    255: }

    257: static PetscErrorCode KSPFGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
    258: {
    259:   PetscScalar tt;
    260:   PetscInt    ii, k, j;
    261:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;

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

    266:   /* If it is < 0, no fgmres steps have been performed */
    267:   if (it < 0) {
    268:     PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
    269:     PetscFunctionReturn(PETSC_SUCCESS);
    270:   }

    272:   /* so fgmres steps HAVE been performed */

    274:   /* solve the upper triangular system - RS is the right side and HH is
    275:      the upper triangular matrix  - put soln in nrs */
    276:   if (*HH(it, it) != 0.0) {
    277:     nrs[it] = *RS(it) / *HH(it, it);
    278:   } else {
    279:     nrs[it] = 0.0;
    280:   }
    281:   for (ii = 1; ii <= it; ii++) {
    282:     k  = it - ii;
    283:     tt = *RS(k);
    284:     for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
    285:     nrs[k] = tt / *HH(k, k);
    286:   }

    288:   /* Accumulate the correction to the soln of the preconditioned prob. in
    289:      VEC_TEMP - note that we use the preconditioned vectors  */
    290:   PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &PREVEC(0)));

    292:   /* put updated solution into vdest.*/
    293:   if (vdest != vguess) {
    294:     PetscCall(VecCopy(VEC_TEMP, vdest));
    295:     PetscCall(VecAXPY(vdest, 1.0, vguess));
    296:   } else { /* replace guess with solution */
    297:     PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
    298:   }
    299:   PetscFunctionReturn(PETSC_SUCCESS);
    300: }

    302: static PetscErrorCode KSPFGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
    303: {
    304:   PetscScalar *hh, *cc, *ss, tt;
    305:   PetscInt     j;
    306:   KSP_FGMRES  *fgmres = (KSP_FGMRES *)ksp->data;

    308:   PetscFunctionBegin;
    309:   hh = HH(0, it); /* pointer to beginning of column to update - so
    310:                       incrementing hh "steps down" the (it+1)th col of HH*/
    311:   cc = CC(0);     /* beginning of cosine rotations */
    312:   ss = SS(0);     /* beginning of sine rotations */

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

    319:   for (j = 1; j <= it; j++) {
    320:     tt  = *hh;
    321:     *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
    322:     hh++;
    323:     *hh = *cc++ * *hh - (*ss++ * tt);
    324:     /* hh, cc, and ss have all been incremented one by end of loop */
    325:   }

    327:   /*
    328:     compute the new plane rotation, and apply it to:
    329:      1) the right-hand side of the Hessenberg system (RS)
    330:         note: it affects RS(it) and RS(it+1)
    331:      2) the new column of the Hessenberg matrix
    332:         note: it affects HH(it,it) which is currently pointed to
    333:         by hh and HH(it+1, it) (*(hh+1))
    334:     thus obtaining the updated value of the residual...
    335:   */

    337:   /* compute new plane rotation */

    339:   if (!hapend) {
    340:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
    341:     if (tt == 0.0) {
    342:       ksp->reason = KSP_DIVERGED_NULL;
    343:       PetscFunctionReturn(PETSC_SUCCESS);
    344:     }

    346:     *cc = *hh / tt;       /* new cosine value */
    347:     *ss = *(hh + 1) / tt; /* new sine value */

    349:     /* apply to 1) and 2) */
    350:     *RS(it + 1) = -(*ss * *RS(it));
    351:     *RS(it)     = PetscConj(*cc) * *RS(it);
    352:     *hh         = PetscConj(*cc) * *hh + *ss * *(hh + 1);

    354:     /* residual is the last element (it+1) of right-hand side! */
    355:     *res = PetscAbsScalar(*RS(it + 1));

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

    364:     *res = 0.0;
    365:   }
    366:   PetscFunctionReturn(PETSC_SUCCESS);
    367: }

    369: static PetscErrorCode KSPFGMRESGetNewVectors(KSP ksp, PetscInt it)
    370: {
    371:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
    372:   PetscInt    nwork  = fgmres->nwork_alloc; /* number of work vector chunks allocated */
    373:   PetscInt    nalloc;                       /* number to allocate */
    374:   PetscInt    k;

    376:   PetscFunctionBegin;
    377:   nalloc = fgmres->delta_allocate; /* number of vectors to allocate
    378:                                       in a single chunk */

    380:   /* Adjust the number to allocate to make sure that we don't exceed the
    381:      number of available slots (fgmres->vecs_allocated)*/
    382:   if (it + VEC_OFFSET + nalloc >= fgmres->vecs_allocated) nalloc = fgmres->vecs_allocated - it - VEC_OFFSET;
    383:   if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);

    385:   fgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */

    387:   /* work vectors */
    388:   PetscCall(KSPCreateVecs(ksp, nalloc, &fgmres->user_work[nwork], 0, NULL));
    389:   for (k = 0; k < nalloc; k++) fgmres->vecs[it + VEC_OFFSET + k] = fgmres->user_work[nwork][k];
    390:   /* specify size of chunk allocated */
    391:   fgmres->mwork_alloc[nwork] = nalloc;

    393:   /* preconditioned vectors */
    394:   PetscCall(KSPCreateVecs(ksp, nalloc, &fgmres->prevecs_user_work[nwork], 0, NULL));
    395:   for (k = 0; k < nalloc; k++) fgmres->prevecs[it + k] = fgmres->prevecs_user_work[nwork][k];

    397:   /* increment the number of work vector chunks */
    398:   fgmres->nwork_alloc++;
    399:   PetscFunctionReturn(PETSC_SUCCESS);
    400: }

    402: static PetscErrorCode KSPBuildSolution_FGMRES(KSP ksp, Vec ptr, Vec *result)
    403: {
    404:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;

    406:   PetscFunctionBegin;
    407:   if (!ptr) {
    408:     if (!fgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &fgmres->sol_temp));
    409:     ptr = fgmres->sol_temp;
    410:   }
    411:   if (!fgmres->nrs) {
    412:     /* allocate the work area */
    413:     PetscCall(PetscMalloc1(fgmres->max_k, &fgmres->nrs));
    414:   }

    416:   PetscCall(KSPFGMRESBuildSoln(fgmres->nrs, ksp->vec_sol, ptr, ksp, fgmres->it));
    417:   if (result) *result = ptr;
    418:   PetscFunctionReturn(PETSC_SUCCESS);
    419: }

    421: static PetscErrorCode KSPSetFromOptions_FGMRES(KSP ksp, PetscOptionItems PetscOptionsObject)
    422: {
    423:   PetscBool flg;

    425:   PetscFunctionBegin;
    426:   PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
    427:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP flexible GMRES Options");
    428:   PetscCall(PetscOptionsBoolGroupBegin("-ksp_fgmres_modifypcnochange", "do not vary the preconditioner", "KSPFlexibleSetModifyPC", &flg));
    429:   if (flg) PetscCall(KSPFlexibleSetModifyPC(ksp, KSPFlexibleModifyPCNoChange, NULL, NULL));
    430:   PetscCall(PetscOptionsBoolGroupEnd("-ksp_fgmres_modifypcksp", "vary the KSP based preconditioner", "KSPFlexibleSetModifyPC", &flg));
    431:   if (flg) PetscCall(KSPFlexibleSetModifyPC(ksp, KSPFlexibleModifyPCKSP, NULL, NULL));
    432:   PetscOptionsHeadEnd();
    433:   PetscFunctionReturn(PETSC_SUCCESS);
    434: }

    436: static PetscErrorCode KSPFlexibleSetModifyPC_FGMRES(KSP ksp, KSPFlexibleModifyPCFn *fcn, PetscCtx ctx, PetscCtxDestroyFn *d)
    437: {
    438:   PetscFunctionBegin;
    440:   ((KSP_FGMRES *)ksp->data)->modifypc      = fcn;
    441:   ((KSP_FGMRES *)ksp->data)->modifydestroy = d;
    442:   ((KSP_FGMRES *)ksp->data)->modifyctx     = ctx;
    443:   PetscFunctionReturn(PETSC_SUCCESS);
    444: }

    446: PetscErrorCode KSPReset_FGMRES(KSP ksp)
    447: {
    448:   KSP_FGMRES *fgmres = (KSP_FGMRES *)ksp->data;
    449:   PetscInt    i;

    451:   PetscFunctionBegin;
    452:   PetscCall(PetscFree(fgmres->prevecs));
    453:   if (fgmres->nwork_alloc > 0) {
    454:     i = 0;
    455:     /* In the first allocation we allocated VEC_OFFSET fewer vectors in prevecs */
    456:     PetscCall(VecDestroyVecs(fgmres->mwork_alloc[i] - VEC_OFFSET, &fgmres->prevecs_user_work[i]));
    457:     for (i = 1; i < fgmres->nwork_alloc; i++) PetscCall(VecDestroyVecs(fgmres->mwork_alloc[i], &fgmres->prevecs_user_work[i]));
    458:   }
    459:   PetscCall(PetscFree(fgmres->prevecs_user_work));
    460:   if (fgmres->modifydestroy) PetscCall((*fgmres->modifydestroy)(&fgmres->modifyctx));
    461:   PetscCall(KSPReset_GMRES(ksp));
    462:   PetscFunctionReturn(PETSC_SUCCESS);
    463: }

    465: static PetscErrorCode KSPGMRESSetRestart_FGMRES(KSP ksp, PetscInt max_k)
    466: {
    467:   KSP_FGMRES *gmres = (KSP_FGMRES *)ksp->data;

    469:   PetscFunctionBegin;
    470:   PetscCheck(max_k >= 1, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Restart must be positive");
    471:   if (!ksp->setupstage) {
    472:     gmres->max_k = max_k;
    473:   } else if (gmres->max_k != max_k) {
    474:     gmres->max_k    = max_k;
    475:     ksp->setupstage = KSP_SETUP_NEW;
    476:     /* free the data structures, then create them again */
    477:     PetscCall(KSPReset_FGMRES(ksp));
    478:   }
    479:   PetscFunctionReturn(PETSC_SUCCESS);
    480: }

    482: static PetscErrorCode KSPGMRESGetRestart_FGMRES(KSP ksp, PetscInt *max_k)
    483: {
    484:   KSP_FGMRES *gmres = (KSP_FGMRES *)ksp->data;

    486:   PetscFunctionBegin;
    487:   *max_k = gmres->max_k;
    488:   PetscFunctionReturn(PETSC_SUCCESS);
    489: }

    491: /*MC
    492:    KSPFGMRES - Implements the Flexible Generalized Minimal Residual method, flexible GMRES. [](sec_flexibleksp)

    494:    Options Database Keys:
    495: +   -ksp_gmres_restart restart                                                  - the number of Krylov directions to orthogonalize against
    496: .   -ksp_gmres_haptol tol                                                       - sets the tolerance for "happy ending" (exact convergence)
    497: .   -ksp_gmres_preallocate                                                      - preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)
    498: .   -ksp_gmres_classicalgramschmidt                                             - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    499: .   -ksp_gmres_modifiedgramschmidt                                              - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    500: .   -ksp_gmres_cgs_refinement_type (refine_never|refine_ifneeded|refine_always) - determine if iterative refinement is used to increase the
    501:                                                                                   stability of the classical Gram-Schmidt orthogonalization.
    502: .   -ksp_gmres_krylov_monitor                                                   - plot the Krylov space generated
    503: .   -ksp_fgmres_modifypcnochange                                                - do not change the preconditioner between iterations
    504: -   -ksp_fgmres_modifypcksp                                                     - modify the preconditioner using `KSPFlexibleModifyPCKSP()`

    506:    Level: beginner

    508:    Notes:
    509:    See `KSPFlexibleSetModifyPC()` for how to vary the preconditioner between iterations

    511:    GMRES requires that the preconditioner used is a linear operator. Flexible GMRES allows the preconditioner to be a nonlinear operator. This
    512:    allows, for example, Flexible GMRES to use GMRES solvers or other Krylov solvers (which are nonlinear operators in general) inside the preconditioner
    513:    used by `KSPFGMRES`. For example, the options `-ksp_type fgmres -pc_type ksp -ksp_ksp_type bcgs -ksp_view -ksp_pc_type jacobi` make the preconditioner
    514:    (or inner solver) be bi-CG-stab with a preconditioner of `PCJACOBI`. `KSPFCG` provides a flexible version of the preconditioned conjugate gradient method.

    516:    Only right preconditioning is supported.

    518:    The following options `-ksp_type fgmres -pc_type ksp -ksp_ksp_type bcgs -ksp_view -ksp_pc_type jacobi` make the preconditioner (or inner solver)
    519:    be bi-CG-stab with a preconditioner of `PCJACOBI`

    521:    Developer Note:
    522:    This object is subclassed off of `KSPGMRES`, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code

    524:    Contributed by:
    525:    Allison Baker

    527: .seealso: [](ch_ksp), [](sec_flexibleksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPGMRES`, `KSPLGMRES`, `KSPFCG`,
    528:           `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
    529:           `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
    530:           `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPFlexibleSetModifyPC()`,
    531:           `KSPFlexibleModifyPCKSP()`
    532: M*/

    534: PETSC_EXTERN PetscErrorCode KSPCreate_FGMRES(KSP ksp)
    535: {
    536:   KSP_FGMRES *fgmres;

    538:   PetscFunctionBegin;
    539:   PetscCall(PetscNew(&fgmres));

    541:   ksp->data                              = (void *)fgmres;
    542:   ksp->ops->buildsolution                = KSPBuildSolution_FGMRES;
    543:   ksp->ops->setup                        = KSPSetUp_FGMRES;
    544:   ksp->ops->solve                        = KSPSolve_FGMRES;
    545:   ksp->ops->reset                        = KSPReset_FGMRES;
    546:   ksp->ops->destroy                      = KSPDestroy_FGMRES;
    547:   ksp->ops->view                         = KSPView_GMRES;
    548:   ksp->ops->setfromoptions               = KSPSetFromOptions_FGMRES;
    549:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    550:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    552:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));
    553:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

    555:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
    556:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
    557:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
    558:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_FGMRES));
    559:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_FGMRES));
    560:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFlexibleSetModifyPC_C", KSPFlexibleSetModifyPC_FGMRES));
    561:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
    562:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));

    564:   fgmres->haptol         = 1.0e-30;
    565:   fgmres->q_preallocate  = PETSC_FALSE;
    566:   fgmres->delta_allocate = FGMRES_DELTA_DIRECTIONS;
    567:   fgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    568:   fgmres->nrs            = NULL;
    569:   fgmres->sol_temp       = NULL;
    570:   fgmres->max_k          = FGMRES_DEFAULT_MAXK;
    571:   fgmres->Rsvd           = NULL;
    572:   fgmres->orthogwork     = NULL;
    573:   fgmres->modifypc       = KSPFlexibleModifyPCNoChange;
    574:   fgmres->modifyctx      = NULL;
    575:   fgmres->modifydestroy  = NULL;
    576:   fgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    577:   PetscFunctionReturn(PETSC_SUCCESS);
    578: }