Actual source code: gmres.c
petsc-3.15.0 2021-03-30
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      2: /*
      3:     This file implements GMRES (a Generalized Minimal Residual) method.
      4:     Reference:  Saad and Schultz, 1986.

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

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

     25:     Restarts:  Restarts are basically solves with x0 not equal to zero.
     26:     Note that we can eliminate an extra application of B^-1 between
     27:     restarts as long as we don't require that the solution at the end
     28:     of an unsuccessful gmres iteration always be the solution x.
     29:  */

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

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

     45:   max_k = gmres->max_k;          /* restart size */
     46:   hh    = (max_k + 2) * (max_k + 1);
     47:   hes   = (max_k + 1) * (max_k + 1);
     48:   rs    = (max_k + 2);
     49:   cc    = (max_k + 1);

     51:   PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);
     52:   PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));

     54:   if (ksp->calc_sings) {
     55:     /* Allocate workspace to hold Hessenberg matrix needed by lapack */
     56:     PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
     57:     PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
     58:     PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
     59:     PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
     60:   }

     62:   /* Allocate array to hold pointers to user vectors.  Note that we need
     63:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
     64:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;

     66:   PetscMalloc1(gmres->vecs_allocated,&gmres->vecs);
     67:   PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->user_work);
     68:   PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->mwork_alloc);
     69:   PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));

     71:   if (gmres->q_preallocate) {
     72:     gmres->vv_allocated = VEC_OFFSET + 2 + max_k;

     74:     KSPCreateVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);
     75:     PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);

     77:     gmres->mwork_alloc[0] = gmres->vv_allocated;
     78:     gmres->nwork_alloc    = 1;
     79:     for (k=0; k<gmres->vv_allocated; k++) {
     80:       gmres->vecs[k] = gmres->user_work[0][k];
     81:     }
     82:   } else {
     83:     gmres->vv_allocated = 5;

     85:     KSPCreateVecs(ksp,5,&gmres->user_work[0],0,NULL);
     86:     PetscLogObjectParents(ksp,5,gmres->user_work[0]);

     88:     gmres->mwork_alloc[0] = 5;
     89:     gmres->nwork_alloc    = 1;
     90:     for (k=0; k<gmres->vv_allocated; k++) {
     91:       gmres->vecs[k] = gmres->user_work[0][k];
     92:     }
     93:   }
     94:   return(0);
     95: }

     97: /*
     98:     Run gmres, possibly with restart.  Return residual history if requested.
     99:     input parameters:

    101: .        gmres  - structure containing parameters and work areas

    103:     output parameters:
    104: .        nres    - residuals (from preconditioned system) at each step.
    105:                   If restarting, consider passing nres+it.  If null,
    106:                   ignored
    107: .        itcount - number of iterations used.  nres[0] to nres[itcount]
    108:                   are defined.  If null, ignored.

    110:     Notes:
    111:     On entry, the value in vector VEC_VV(0) should be the initial residual
    112:     (this allows shortcuts where the initial preconditioned residual is 0).
    113:  */
    114: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
    115: {
    116:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);
    117:   PetscReal      res,hapbnd,tt;
    119:   PetscInt       it     = 0, max_k = gmres->max_k;
    120:   PetscBool      hapend = PETSC_FALSE;

    123:   if (itcount) *itcount = 0;
    124:   VecNormalize(VEC_VV(0),&res);
    125:   KSPCheckNorm(ksp,res);

    127:   /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
    128:   if ((ksp->rnorm > 0.0) && (PetscAbsReal(res-ksp->rnorm) > gmres->breakdowntol*gmres->rnorm0)) {
    129:       if (ksp->errorifnotconverged) SETERRQ3(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",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
    130:       else {
    131:         PetscInfo3(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",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
    132:         ksp->reason =  KSP_DIVERGED_BREAKDOWN;
    133:         return(0);
    134:       }
    135:   }
    136:   *GRS(0) = gmres->rnorm0 = res;

    138:   /* check for the convergence */
    139:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    140:   ksp->rnorm = res;
    141:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    142:   gmres->it  = (it - 1);
    143:   KSPLogResidualHistory(ksp,res);
    144:   KSPLogErrorHistory(ksp);
    145:   KSPMonitor(ksp,ksp->its,res);
    146:   if (!res) {
    147:     ksp->reason = KSP_CONVERGED_ATOL;
    148:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
    149:     return(0);
    150:   }

    152:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    153:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    154:     if (it) {
    155:       KSPLogResidualHistory(ksp,res);
    156:       KSPLogErrorHistory(ksp);
    157:       KSPMonitor(ksp,ksp->its,res);
    158:     }
    159:     gmres->it = (it - 1);
    160:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
    161:       KSPGMRESGetNewVectors(ksp,it+1);
    162:     }
    163:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

    165:     /* update hessenberg matrix and do Gram-Schmidt */
    166:     (*gmres->orthog)(ksp,it);
    167:     if (ksp->reason) break;

    169:     /* vv(i+1) . vv(i+1) */
    170:     VecNormalize(VEC_VV(it+1),&tt);
    171:     KSPCheckNorm(ksp,tt);

    173:     /* save the magnitude */
    174:     *HH(it+1,it)  = tt;
    175:     *HES(it+1,it) = tt;

    177:     /* check for the happy breakdown */
    178:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    179:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
    180:     if (tt < hapbnd) {
    181:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
    182:       hapend = PETSC_TRUE;
    183:     }
    184:     KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);

    186:     it++;
    187:     gmres->it = (it-1);   /* For converged */
    188:     ksp->its++;
    189:     ksp->rnorm = res;
    190:     if (ksp->reason) break;

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

    194:     /* Catch error in happy breakdown and signal convergence and break from loop */
    195:     if (hapend) {
    196:       if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
    197:         ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
    198:       } else if (!ksp->reason) {
    199:         if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res);
    200:         else {
    201:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    202:           break;
    203:         }
    204:       }
    205:     }
    206:   }

    208:   /* Monitor if we know that we will not return for a restart */
    209:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
    210:     KSPLogResidualHistory(ksp,res);
    211:     KSPLogErrorHistory(ksp);
    212:     KSPMonitor(ksp,ksp->its,res);
    213:   }

    215:   if (itcount) *itcount = it;

    218:   /*
    219:     Down here we have to solve for the "best" coefficients of the Krylov
    220:     columns, add the solution values together, and possibly unwind the
    221:     preconditioning from the solution
    222:    */
    223:   /* Form the solution (or the solution so far) */
    224:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
    225:   return(0);
    226: }

    228: PetscErrorCode KSPSolve_GMRES(KSP ksp)
    229: {
    231:   PetscInt       its,itcount,i;
    232:   KSP_GMRES      *gmres     = (KSP_GMRES*)ksp->data;
    233:   PetscBool      guess_zero = ksp->guess_zero;
    234:   PetscInt       N = gmres->max_k + 1;

    237:   if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

    239:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    240:   ksp->its = 0;
    241:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

    243:   itcount     = 0;
    244:   gmres->fullcycle = 0;
    245:   ksp->reason = KSP_CONVERGED_ITERATING;
    246:   ksp->rnorm  = -1.0; /* special marker for KSPGMRESCycle() */
    247:   while (!ksp->reason) {
    248:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    249:     KSPGMRESCycle(&its,ksp);
    250:     /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
    251:     if the cycle is complete for the computation of the Ritz pairs */
    252:     if (its == gmres->max_k) {
    253:       gmres->fullcycle++;
    254:       if (ksp->calc_ritz) {
    255:         if (!gmres->hes_ritz) {
    256:           PetscMalloc1(N*N,&gmres->hes_ritz);
    257:           PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
    258:           VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
    259:         }
    260:         PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,N*N);
    261:         for (i=0; i<gmres->max_k+1; i++) {
    262:           VecCopy(VEC_VV(i),gmres->vecb[i]);
    263:         }
    264:       }
    265:     }
    266:     itcount += its;
    267:     if (itcount >= ksp->max_it) {
    268:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    269:       break;
    270:     }
    271:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    272:   }
    273:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
    274:   return(0);
    275: }

    277: PetscErrorCode KSPReset_GMRES(KSP ksp)
    278: {
    279:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    281:   PetscInt       i;

    284:   /* Free the Hessenberg matrices */
    285:   PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
    286:   PetscFree(gmres->hes_ritz);

    288:   /* free work vectors */
    289:   PetscFree(gmres->vecs);
    290:   for (i=0; i<gmres->nwork_alloc; i++) {
    291:     VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
    292:   }
    293:   gmres->nwork_alloc = 0;
    294:   if (gmres->vecb)  {
    295:     VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
    296:   }

    298:   PetscFree(gmres->user_work);
    299:   PetscFree(gmres->mwork_alloc);
    300:   PetscFree(gmres->nrs);
    301:   VecDestroy(&gmres->sol_temp);
    302:   PetscFree(gmres->Rsvd);
    303:   PetscFree(gmres->Dsvd);
    304:   PetscFree(gmres->orthogwork);

    306:   gmres->vv_allocated   = 0;
    307:   gmres->vecs_allocated = 0;
    308:   gmres->sol_temp       = NULL;
    309:   return(0);
    310: }

    312: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    313: {

    317:   KSPReset_GMRES(ksp);
    318:   PetscFree(ksp->data);
    319:   /* clear composed functions */
    320:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
    321:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
    322:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
    323:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
    324:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
    325:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
    326:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",NULL);
    327:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
    328:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
    329:   return(0);
    330: }
    331: /*
    332:     KSPGMRESBuildSoln - create the solution from the starting vector and the
    333:     current iterates.

    335:     Input parameters:
    336:         nrs - work area of size it + 1.
    337:         vs  - index of initial guess
    338:         vdest - index of result.  Note that vs may == vdest (replace
    339:                 guess with the solution).

    341:      This is an internal routine that knows about the GMRES internals.
    342:  */
    343: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    344: {
    345:   PetscScalar    tt;
    347:   PetscInt       ii,k,j;
    348:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);

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

    353:   /* If it is < 0, no gmres steps have been performed */
    354:   if (it < 0) {
    355:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
    356:     return(0);
    357:   }
    358:   if (*HH(it,it) != 0.0) {
    359:     nrs[it] = *GRS(it) / *HH(it,it);
    360:   } else {
    361:     if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
    362:     else ksp->reason = KSP_DIVERGED_BREAKDOWN;

    364:     PetscInfo2(ksp,"Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %D GRS(it) = %g\n",it,(double)PetscAbsScalar(*GRS(it)));
    365:     return(0);
    366:   }
    367:   for (ii=1; ii<=it; ii++) {
    368:     k  = it - ii;
    369:     tt = *GRS(k);
    370:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    371:     if (*HH(k,k) == 0.0) {
    372:       if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    373:       else {
    374:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    375:         PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    376:         return(0);
    377:       }
    378:     }
    379:     nrs[k] = tt / *HH(k,k);
    380:   }

    382:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
    383:   VecSet(VEC_TEMP,0.0);
    384:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));

    386:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    387:   /* add solution to previous solution */
    388:   if (vdest != vs) {
    389:     VecCopy(vs,vdest);
    390:   }
    391:   VecAXPY(vdest,1.0,VEC_TEMP);
    392:   return(0);
    393: }
    394: /*
    395:    Do the scalar work for the orthogonalization.  Return new residual norm.
    396:  */
    397: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    398: {
    399:   PetscScalar *hh,*cc,*ss,tt;
    400:   PetscInt    j;
    401:   KSP_GMRES   *gmres = (KSP_GMRES*)(ksp->data);

    404:   hh = HH(0,it);
    405:   cc = CC(0);
    406:   ss = SS(0);

    408:   /* Apply all the previously computed plane rotations to the new column
    409:      of the Hessenberg matrix */
    410:   for (j=1; j<=it; j++) {
    411:     tt  = *hh;
    412:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    413:     hh++;
    414:     *hh = *cc++ * *hh - (*ss++ * tt);
    415:   }

    417:   /*
    418:     compute the new plane rotation, and apply it to:
    419:      1) the right-hand-side of the Hessenberg system
    420:      2) the new column of the Hessenberg matrix
    421:     thus obtaining the updated value of the residual
    422:   */
    423:   if (!hapend) {
    424:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    425:     if (tt == 0.0) {
    426:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
    427:       else {
    428:         ksp->reason = KSP_DIVERGED_NULL;
    429:         return(0);
    430:       }
    431:     }
    432:     *cc        = *hh / tt;
    433:     *ss        = *(hh+1) / tt;
    434:     *GRS(it+1) = -(*ss * *GRS(it));
    435:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    436:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
    437:     *res       = PetscAbsScalar(*GRS(it+1));
    438:   } else {
    439:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    440:             another rotation matrix (so RH doesn't change).  The new residual is
    441:             always the new sine term times the residual from last time (GRS(it)),
    442:             but now the new sine rotation would be zero...so the residual should
    443:             be zero...so we will multiply "zero" by the last residual.  This might
    444:             not be exactly what we want to do here -could just return "zero". */

    446:     *res = 0.0;
    447:   }
    448:   return(0);
    449: }
    450: /*
    451:    This routine allocates more work vectors, starting from VEC_VV(it).
    452:  */
    453: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
    454: {
    455:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    457:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

    460:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
    461:   /* Adjust the number to allocate to make sure that we don't exceed the
    462:     number of available slots */
    463:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
    464:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
    465:   }
    466:   if (!nalloc) return(0);

    468:   gmres->vv_allocated += nalloc;

    470:   KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
    471:   PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);

    473:   gmres->mwork_alloc[nwork] = nalloc;
    474:   for (k=0; k<nalloc; k++) {
    475:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
    476:   }
    477:   gmres->nwork_alloc++;
    478:   return(0);
    479: }

    481: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
    482: {
    483:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

    487:   if (!ptr) {
    488:     if (!gmres->sol_temp) {
    489:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
    490:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
    491:     }
    492:     ptr = gmres->sol_temp;
    493:   }
    494:   if (!gmres->nrs) {
    495:     /* allocate the work area */
    496:     PetscMalloc1(gmres->max_k,&gmres->nrs);
    497:     PetscLogObjectMemory((PetscObject)ksp,gmres->max_k);
    498:   }

    500:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
    501:   if (result) *result = ptr;
    502:   return(0);
    503: }

    505: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
    506: {
    507:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    508:   const char     *cstr;
    510:   PetscBool      iascii,isstring;

    513:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    514:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    515:   if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
    516:     switch (gmres->cgstype) {
    517:     case (KSP_GMRES_CGS_REFINE_NEVER):
    518:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
    519:       break;
    520:     case (KSP_GMRES_CGS_REFINE_ALWAYS):
    521:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
    522:       break;
    523:     case (KSP_GMRES_CGS_REFINE_IFNEEDED):
    524:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
    525:       break;
    526:     default:
    527:       SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
    528:     }
    529:   } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
    530:     cstr = "Modified Gram-Schmidt Orthogonalization";
    531:   } else {
    532:     cstr = "unknown orthogonalization";
    533:   }
    534:   if (iascii) {
    535:     PetscViewerASCIIPrintf(viewer,"  restart=%D, using %s\n",gmres->max_k,cstr);
    536:     PetscViewerASCIIPrintf(viewer,"  happy breakdown tolerance %g\n",(double)gmres->haptol);
    537:   } else if (isstring) {
    538:     PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
    539:   }
    540:   return(0);
    541: }

    543: /*@C
    544:    KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.

    546:    Collective on ksp

    548:    Input Parameters:
    549: +  ksp - the KSP context
    550: .  its - iteration number
    551: .  fgnorm - 2-norm of residual (or gradient)
    552: -  dummy - an collection of viewers created with KSPViewerCreate()

    554:    Options Database Keys:
    555: .   -ksp_gmres_kyrlov_monitor

    557:    Notes:
    558:     A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
    559:    Level: intermediate

    561: .seealso: KSPMonitorSet(), KSPMonitorResidual(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
    562: @*/
    563: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
    564: {
    565:   PetscViewers   viewers = (PetscViewers)dummy;
    566:   KSP_GMRES      *gmres  = (KSP_GMRES*)ksp->data;
    568:   Vec            x;
    569:   PetscViewer    viewer;
    570:   PetscBool      flg;

    573:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
    574:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
    575:   if (!flg) {
    576:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
    577:     PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
    578:   }
    579:   x    = VEC_VV(gmres->it+1);
    580:   VecView(x,viewer);
    581:   return(0);
    582: }

    584: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    585: {
    587:   PetscInt       restart;
    588:   PetscReal      haptol,breakdowntol;
    589:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    590:   PetscBool      flg;

    593:   PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
    594:   PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
    595:   if (flg) { KSPGMRESSetRestart(ksp,restart); }
    596:   PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
    597:   if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
    598:   PetscOptionsReal("-ksp_gmres_breakdown_tolerance","Divergence breakdown tolerance during GMRES restart","KSPGMRESSetBreakdownTolerance",gmres->breakdowntol,&breakdowntol,&flg);
    599:   if (flg) { KSPGMRESSetBreakdownTolerance(ksp,breakdowntol); }
    600:   flg  = PETSC_FALSE;
    601:   PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
    602:   if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
    603:   PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
    604:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
    605:   PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
    606:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
    607:   PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
    608:                           KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
    609:   flg  = PETSC_FALSE;
    610:   PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
    611:   if (flg) {
    612:     PetscViewers viewers;
    613:     PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
    614:     KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
    615:   }
    616:   PetscOptionsTail();
    617:   return(0);
    618: }

    620: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
    621: {
    622:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    625:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    626:   gmres->haptol = tol;
    627:   return(0);
    628: }

    630: PetscErrorCode  KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp,PetscReal tol)
    631: {
    632:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    635:   if (tol == PETSC_DEFAULT) {
    636:     gmres->breakdowntol = 0.1;
    637:     return(0);
    638:   }
    639:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Breakdown tolerance must be non-negative");
    640:   gmres->breakdowntol = tol;
    641:   return(0);
    642: }

    644: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
    645: {
    646:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    649:   *max_k = gmres->max_k;
    650:   return(0);
    651: }

    653: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
    654: {
    655:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

    659:   if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
    660:   if (!ksp->setupstage) {
    661:     gmres->max_k = max_k;
    662:   } else if (gmres->max_k != max_k) {
    663:     gmres->max_k    = max_k;
    664:     ksp->setupstage = KSP_SETUP_NEW;
    665:     /* free the data structures, then create them again */
    666:     KSPReset_GMRES(ksp);
    667:   }
    668:   return(0);
    669: }

    671: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
    672: {
    674:   ((KSP_GMRES*)ksp->data)->orthog = fcn;
    675:   return(0);
    676: }

    678: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
    679: {
    681:   *fcn = ((KSP_GMRES*)ksp->data)->orthog;
    682:   return(0);
    683: }

    685: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    686: {
    687:   KSP_GMRES *gmres;

    690:   gmres = (KSP_GMRES*)ksp->data;
    691:   gmres->q_preallocate = 1;
    692:   return(0);
    693: }

    695: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
    696: {
    697:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    700:   gmres->cgstype = type;
    701:   return(0);
    702: }

    704: PetscErrorCode  KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
    705: {
    706:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    709:   *type = gmres->cgstype;
    710:   return(0);
    711: }

    713: /*@
    714:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    715:          in the classical Gram Schmidt orthogonalization.

    717:    Logically Collective on ksp

    719:    Input Parameters:
    720: +  ksp - the Krylov space context
    721: -  type - the type of refinement

    723:   Options Database:
    724: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    726:    Level: intermediate

    728: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
    729:           KSPGMRESGetOrthogonalization()
    730: @*/
    731: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
    732: {

    738:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
    739:   return(0);
    740: }

    742: /*@
    743:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    744:          in the classical Gram Schmidt orthogonalization.

    746:    Not Collective

    748:    Input Parameter:
    749: .  ksp - the Krylov space context

    751:    Output Parameter:
    752: .  type - the type of refinement

    754:   Options Database:
    755: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    757:    Level: intermediate

    759: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
    760:           KSPGMRESGetOrthogonalization()
    761: @*/
    762: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
    763: {

    768:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
    769:   return(0);
    770: }

    773: /*@
    774:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    776:    Logically Collective on ksp

    778:    Input Parameters:
    779: +  ksp - the Krylov space context
    780: -  restart - integer restart value

    782:   Options Database:
    783: .  -ksp_gmres_restart <positive integer>

    785:     Note: The default value is 30.

    787:    Level: intermediate

    789: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
    790: @*/
    791: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    792: {

    798:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
    799:   return(0);
    800: }

    802: /*@
    803:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    805:    Not Collective

    807:    Input Parameter:
    808: .  ksp - the Krylov space context

    810:    Output Parameter:
    811: .   restart - integer restart value

    813:     Note: The default value is 30.

    815:    Level: intermediate

    817: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
    818: @*/
    819: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
    820: {

    824:   PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
    825:   return(0);
    826: }

    828: /*@
    829:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

    831:    Logically Collective on ksp

    833:    Input Parameters:
    834: +  ksp - the Krylov space context
    835: -  tol - the tolerance

    837:   Options Database:
    838: .  -ksp_gmres_haptol <positive real value>

    840:    Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
    841:          a certain number of iterations. If you attempt more iterations after this point unstable
    842:          things can happen hence very occasionally you may need to set this value to detect this condition

    844:    Level: intermediate

    846: .seealso: KSPSetTolerances()
    847: @*/
    848: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
    849: {

    854:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
    855:   return(0);
    856: }

    858: /*@
    859:    KSPGMRESSetBreakdownTolerance - Sets tolerance for determining divergence breakdown in GMRES.

    861:    Logically Collective on ksp

    863:    Input Parameters:
    864: +  ksp - the Krylov space context
    865: -  tol - the tolerance

    867:   Options Database:
    868: .  -ksp_gmres_breakdown_tolerance <positive real value>

    870:    Note: divergence breakdown occurs when GMRES residual increases significantly
    871:          during restart

    873:    Level: intermediate

    875: .seealso: KSPSetTolerances(), KSPGMRESSetHapTol()
    876: @*/
    877: PetscErrorCode  KSPGMRESSetBreakdownTolerance(KSP ksp,PetscReal tol)
    878: {

    883:   PetscTryMethod((ksp),"KSPGMRESSetBreakdownTolerance_C",(KSP,PetscReal),(ksp,tol));
    884:   return(0);
    885: }

    887: /*MC
    888:      KSPGMRES - Implements the Generalized Minimal Residual method.
    889:                 (Saad and Schultz, 1986) with restart

    892:    Options Database Keys:
    893: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    894: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    895: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    896:                              vectors are allocated as needed)
    897: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    898: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    899: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
    900:                                    stability of the classical Gram-Schmidt  orthogonalization.
    901: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    903:    Level: beginner

    905:    Notes:
    906:     Left and right preconditioning are supported, but not symmetric preconditioning.

    908:    References:
    909: .     1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
    910:           SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.

    912: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
    913:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    914:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    915:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

    917: M*/

    919: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
    920: {
    921:   KSP_GMRES      *gmres;

    925:   PetscNewLog(ksp,&gmres);
    926:   ksp->data = (void*)gmres;

    928:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
    929:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
    930:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
    931:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
    932:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    934:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
    935:   ksp->ops->setup                        = KSPSetUp_GMRES;
    936:   ksp->ops->solve                        = KSPSolve_GMRES;
    937:   ksp->ops->reset                        = KSPReset_GMRES;
    938:   ksp->ops->destroy                      = KSPDestroy_GMRES;
    939:   ksp->ops->view                         = KSPView_GMRES;
    940:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
    941:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    942:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;
    943: #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
    944:   ksp->ops->computeritz                  = KSPComputeRitz_GMRES;
    945: #endif
    946:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    947:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    948:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    949:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    950:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    951:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
    952:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",KSPGMRESSetBreakdownTolerance_GMRES);
    953:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    954:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    956:   gmres->haptol         = 1.0e-30;
    957:   gmres->breakdowntol   = 0.1;
    958:   gmres->q_preallocate  = 0;
    959:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    960:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    961:   gmres->nrs            = NULL;
    962:   gmres->sol_temp       = NULL;
    963:   gmres->max_k          = GMRES_DEFAULT_MAXK;
    964:   gmres->Rsvd           = NULL;
    965:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    966:   gmres->orthogwork     = NULL;
    967:   return(0);
    968: }