Actual source code: gmres.c
petsc-3.13.6 2020-09-29
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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 Section 1.5 Writing Application Codes with PETSc 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_norm,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_norm);
    125:   KSPCheckNorm(ksp,res_norm);
    126:   res     = res_norm;
    127:   *GRS(0) = res_norm;

    129:   /* check for the convergence */
    130:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    131:   ksp->rnorm = res;
    132:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    133:   gmres->it  = (it - 1);
    134:   KSPLogResidualHistory(ksp,res);
    135:   KSPMonitor(ksp,ksp->its,res);
    136:   if (!res) {
    137:     ksp->reason = KSP_CONVERGED_ATOL;
    138:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
    139:     return(0);
    140:   }

    142:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    143:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    144:     if (it) {
    145:       KSPLogResidualHistory(ksp,res);
    146:       KSPMonitor(ksp,ksp->its,res);
    147:     }
    148:     gmres->it = (it - 1);
    149:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
    150:       KSPGMRESGetNewVectors(ksp,it+1);
    151:     }
    152:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

    154:     /* update hessenberg matrix and do Gram-Schmidt */
    155:     (*gmres->orthog)(ksp,it);
    156:     if (ksp->reason) break;

    158:     /* vv(i+1) . vv(i+1) */
    159:     VecNormalize(VEC_VV(it+1),&tt);
    160:     KSPCheckNorm(ksp,tt);

    162:     /* save the magnitude */
    163:     *HH(it+1,it)  = tt;
    164:     *HES(it+1,it) = tt;

    166:     /* check for the happy breakdown */
    167:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    168:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
    169:     if (tt < hapbnd) {
    170:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
    171:       hapend = PETSC_TRUE;
    172:     }
    173:     KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);

    175:     it++;
    176:     gmres->it = (it-1);   /* For converged */
    177:     ksp->its++;
    178:     ksp->rnorm = res;
    179:     if (ksp->reason) break;

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

    183:     /* Catch error in happy breakdown and signal convergence and break from loop */
    184:     if (hapend) {
    185:       if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
    186:         ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
    187:       } else if (!ksp->reason) {
    188:         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);
    189:         else {
    190:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    191:           break;
    192:         }
    193:       }
    194:     }
    195:   }

    197:   /* Monitor if we know that we will not return for a restart */
    198:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
    199:     KSPLogResidualHistory(ksp,res);
    200:     KSPMonitor(ksp,ksp->its,res);
    201:   }

    203:   if (itcount) *itcount = it;

    206:   /*
    207:     Down here we have to solve for the "best" coefficients of the Krylov
    208:     columns, add the solution values together, and possibly unwind the
    209:     preconditioning from the solution
    210:    */
    211:   /* Form the solution (or the solution so far) */
    212:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
    213:   return(0);
    214: }

    216: PetscErrorCode KSPSolve_GMRES(KSP ksp)
    217: {
    219:   PetscInt       its,itcount,i;
    220:   KSP_GMRES      *gmres     = (KSP_GMRES*)ksp->data;
    221:   PetscBool      guess_zero = ksp->guess_zero;
    222:   PetscInt       N = gmres->max_k + 1;
    223:   PetscBLASInt   bN;

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

    228:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    229:   ksp->its = 0;
    230:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

    232:   itcount     = 0;
    233:   gmres->fullcycle = 0;
    234:   ksp->reason = KSP_CONVERGED_ITERATING;
    235:   while (!ksp->reason) {
    236:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    237:     KSPGMRESCycle(&its,ksp);
    238:     /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
    239:     if the cycle is complete for the computation of the Ritz pairs */
    240:     if (its == gmres->max_k) {
    241:       gmres->fullcycle++;
    242:       if (ksp->calc_ritz) {
    243:         if (!gmres->hes_ritz) {
    244:           PetscMalloc1(N*N,&gmres->hes_ritz);
    245:           PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
    246:           VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
    247:         }
    248:         PetscBLASIntCast(N,&bN);
    249:         PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,bN*bN);
    250:         for (i=0; i<gmres->max_k+1; i++) {
    251:           VecCopy(VEC_VV(i),gmres->vecb[i]);
    252:         }
    253:       }
    254:     }
    255:     itcount += its;
    256:     if (itcount >= ksp->max_it) {
    257:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    258:       break;
    259:     }
    260:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    261:   }
    262:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
    263:   return(0);
    264: }

    266: PetscErrorCode KSPReset_GMRES(KSP ksp)
    267: {
    268:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    270:   PetscInt       i;

    273:   /* Free the Hessenberg matrices */
    274:   PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
    275:   PetscFree(gmres->hes_ritz);

    277:   /* free work vectors */
    278:   PetscFree(gmres->vecs);
    279:   for (i=0; i<gmres->nwork_alloc; i++) {
    280:     VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
    281:   }
    282:   gmres->nwork_alloc = 0;
    283:   if (gmres->vecb)  {
    284:     VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
    285:   }

    287:   PetscFree(gmres->user_work);
    288:   PetscFree(gmres->mwork_alloc);
    289:   PetscFree(gmres->nrs);
    290:   VecDestroy(&gmres->sol_temp);
    291:   PetscFree(gmres->Rsvd);
    292:   PetscFree(gmres->Dsvd);
    293:   PetscFree(gmres->orthogwork);

    295:   gmres->sol_temp       = 0;
    296:   gmres->vv_allocated   = 0;
    297:   gmres->vecs_allocated = 0;
    298:   gmres->sol_temp       = 0;
    299:   return(0);
    300: }

    302: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    303: {

    307:   KSPReset_GMRES(ksp);
    308:   PetscFree(ksp->data);
    309:   /* clear composed functions */
    310:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
    311:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
    312:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
    313:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
    314:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
    315:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
    316:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
    317:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
    318:   return(0);
    319: }
    320: /*
    321:     KSPGMRESBuildSoln - create the solution from the starting vector and the
    322:     current iterates.

    324:     Input parameters:
    325:         nrs - work area of size it + 1.
    326:         vs  - index of initial guess
    327:         vdest - index of result.  Note that vs may == vdest (replace
    328:                 guess with the solution).

    330:      This is an internal routine that knows about the GMRES internals.
    331:  */
    332: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    333: {
    334:   PetscScalar    tt;
    336:   PetscInt       ii,k,j;
    337:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);

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

    342:   /* If it is < 0, no gmres steps have been performed */
    343:   if (it < 0) {
    344:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
    345:     return(0);
    346:   }
    347:   if (*HH(it,it) != 0.0) {
    348:     nrs[it] = *GRS(it) / *HH(it,it);
    349:   } else {
    350:     if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
    351:     else ksp->reason = KSP_DIVERGED_BREAKDOWN;

    353:     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)));
    354:     return(0);
    355:   }
    356:   for (ii=1; ii<=it; ii++) {
    357:     k  = it - ii;
    358:     tt = *GRS(k);
    359:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    360:     if (*HH(k,k) == 0.0) {
    361:       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);
    362:       else {
    363:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    364:         PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    365:         return(0);
    366:       }
    367:     }
    368:     nrs[k] = tt / *HH(k,k);
    369:   }

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

    375:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    376:   /* add solution to previous solution */
    377:   if (vdest != vs) {
    378:     VecCopy(vs,vdest);
    379:   }
    380:   VecAXPY(vdest,1.0,VEC_TEMP);
    381:   return(0);
    382: }
    383: /*
    384:    Do the scalar work for the orthogonalization.  Return new residual norm.
    385:  */
    386: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    387: {
    388:   PetscScalar *hh,*cc,*ss,tt;
    389:   PetscInt    j;
    390:   KSP_GMRES   *gmres = (KSP_GMRES*)(ksp->data);

    393:   hh = HH(0,it);
    394:   cc = CC(0);
    395:   ss = SS(0);

    397:   /* Apply all the previously computed plane rotations to the new column
    398:      of the Hessenberg matrix */
    399:   for (j=1; j<=it; j++) {
    400:     tt  = *hh;
    401:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    402:     hh++;
    403:     *hh = *cc++ * *hh - (*ss++ * tt);
    404:   }

    406:   /*
    407:     compute the new plane rotation, and apply it to:
    408:      1) the right-hand-side of the Hessenberg system
    409:      2) the new column of the Hessenberg matrix
    410:     thus obtaining the updated value of the residual
    411:   */
    412:   if (!hapend) {
    413:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    414:     if (tt == 0.0) {
    415:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
    416:       else {
    417:         ksp->reason = KSP_DIVERGED_NULL;
    418:         return(0);
    419:       }
    420:     }
    421:     *cc        = *hh / tt;
    422:     *ss        = *(hh+1) / tt;
    423:     *GRS(it+1) = -(*ss * *GRS(it));
    424:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    425:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
    426:     *res       = PetscAbsScalar(*GRS(it+1));
    427:   } else {
    428:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    429:             another rotation matrix (so RH doesn't change).  The new residual is
    430:             always the new sine term times the residual from last time (GRS(it)),
    431:             but now the new sine rotation would be zero...so the residual should
    432:             be zero...so we will multiply "zero" by the last residual.  This might
    433:             not be exactly what we want to do here -could just return "zero". */

    435:     *res = 0.0;
    436:   }
    437:   return(0);
    438: }
    439: /*
    440:    This routine allocates more work vectors, starting from VEC_VV(it).
    441:  */
    442: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
    443: {
    444:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    446:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

    449:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
    450:   /* Adjust the number to allocate to make sure that we don't exceed the
    451:     number of available slots */
    452:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
    453:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
    454:   }
    455:   if (!nalloc) return(0);

    457:   gmres->vv_allocated += nalloc;

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

    462:   gmres->mwork_alloc[nwork] = nalloc;
    463:   for (k=0; k<nalloc; k++) {
    464:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
    465:   }
    466:   gmres->nwork_alloc++;
    467:   return(0);
    468: }

    470: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
    471: {
    472:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

    476:   if (!ptr) {
    477:     if (!gmres->sol_temp) {
    478:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
    479:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
    480:     }
    481:     ptr = gmres->sol_temp;
    482:   }
    483:   if (!gmres->nrs) {
    484:     /* allocate the work area */
    485:     PetscMalloc1(gmres->max_k,&gmres->nrs);
    486:     PetscLogObjectMemory((PetscObject)ksp,gmres->max_k);
    487:   }

    489:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
    490:   if (result) *result = ptr;
    491:   return(0);
    492: }

    494: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
    495: {
    496:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    497:   const char     *cstr;
    499:   PetscBool      iascii,isstring;

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

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

    535:    Collective on ksp

    537:    Input Parameters:
    538: +  ksp - the KSP context
    539: .  its - iteration number
    540: .  fgnorm - 2-norm of residual (or gradient)
    541: -  dummy - an collection of viewers created with KSPViewerCreate()

    543:    Options Database Keys:
    544: .   -ksp_gmres_kyrlov_monitor

    546:    Notes:
    547:     A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
    548:    Level: intermediate

    550: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
    551: @*/
    552: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
    553: {
    554:   PetscViewers   viewers = (PetscViewers)dummy;
    555:   KSP_GMRES      *gmres  = (KSP_GMRES*)ksp->data;
    557:   Vec            x;
    558:   PetscViewer    viewer;
    559:   PetscBool      flg;

    562:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
    563:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
    564:   if (!flg) {
    565:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
    566:     PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
    567:   }
    568:   x    = VEC_VV(gmres->it+1);
    569:   VecView(x,viewer);
    570:   return(0);
    571: }

    573: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    574: {
    576:   PetscInt       restart;
    577:   PetscReal      haptol;
    578:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    579:   PetscBool      flg;

    582:   PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
    583:   PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
    584:   if (flg) { KSPGMRESSetRestart(ksp,restart); }
    585:   PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
    586:   if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
    587:   flg  = PETSC_FALSE;
    588:   PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
    589:   if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
    590:   PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
    591:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
    592:   PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
    593:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
    594:   PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
    595:                           KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
    596:   flg  = PETSC_FALSE;
    597:   PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
    598:   if (flg) {
    599:     PetscViewers viewers;
    600:     PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
    601:     KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
    602:   }
    603:   PetscOptionsTail();
    604:   return(0);
    605: }

    607: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
    608: {
    609:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    612:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    613:   gmres->haptol = tol;
    614:   return(0);
    615: }

    617: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
    618: {
    619:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    622:   *max_k = gmres->max_k;
    623:   return(0);
    624: }

    626: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
    627: {
    628:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

    632:   if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
    633:   if (!ksp->setupstage) {
    634:     gmres->max_k = max_k;
    635:   } else if (gmres->max_k != max_k) {
    636:     gmres->max_k    = max_k;
    637:     ksp->setupstage = KSP_SETUP_NEW;
    638:     /* free the data structures, then create them again */
    639:     KSPReset_GMRES(ksp);
    640:   }
    641:   return(0);
    642: }

    644: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
    645: {
    647:   ((KSP_GMRES*)ksp->data)->orthog = fcn;
    648:   return(0);
    649: }

    651: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
    652: {
    654:   *fcn = ((KSP_GMRES*)ksp->data)->orthog;
    655:   return(0);
    656: }

    658: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    659: {
    660:   KSP_GMRES *gmres;

    663:   gmres = (KSP_GMRES*)ksp->data;
    664:   gmres->q_preallocate = 1;
    665:   return(0);
    666: }

    668: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
    669: {
    670:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    673:   gmres->cgstype = type;
    674:   return(0);
    675: }

    677: PetscErrorCode  KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
    678: {
    679:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    682:   *type = gmres->cgstype;
    683:   return(0);
    684: }

    686: /*@
    687:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    688:          in the classical Gram Schmidt orthogonalization.

    690:    Logically Collective on ksp

    692:    Input Parameters:
    693: +  ksp - the Krylov space context
    694: -  type - the type of refinement

    696:   Options Database:
    697: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    699:    Level: intermediate

    701: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
    702:           KSPGMRESGetOrthogonalization()
    703: @*/
    704: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
    705: {

    711:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
    712:   return(0);
    713: }

    715: /*@
    716:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    717:          in the classical Gram Schmidt orthogonalization.

    719:    Not Collective

    721:    Input Parameter:
    722: .  ksp - the Krylov space context

    724:    Output Parameter:
    725: .  type - the type of refinement

    727:   Options Database:
    728: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    730:    Level: intermediate

    732: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
    733:           KSPGMRESGetOrthogonalization()
    734: @*/
    735: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
    736: {

    741:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
    742:   return(0);
    743: }

    746: /*@
    747:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    749:    Logically Collective on ksp

    751:    Input Parameters:
    752: +  ksp - the Krylov space context
    753: -  restart - integer restart value

    755:   Options Database:
    756: .  -ksp_gmres_restart <positive integer>

    758:     Note: The default value is 30.

    760:    Level: intermediate

    762: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
    763: @*/
    764: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    765: {

    771:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
    772:   return(0);
    773: }

    775: /*@
    776:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    778:    Not Collective

    780:    Input Parameter:
    781: .  ksp - the Krylov space context

    783:    Output Parameter:
    784: .   restart - integer restart value

    786:     Note: The default value is 30.

    788:    Level: intermediate

    790: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
    791: @*/
    792: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
    793: {

    797:   PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
    798:   return(0);
    799: }

    801: /*@
    802:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

    804:    Logically Collective on ksp

    806:    Input Parameters:
    807: +  ksp - the Krylov space context
    808: -  tol - the tolerance

    810:   Options Database:
    811: .  -ksp_gmres_haptol <positive real value>

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

    817:    Level: intermediate

    819: .seealso: KSPSetTolerances()
    820: @*/
    821: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
    822: {

    827:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
    828:   return(0);
    829: }

    831: /*MC
    832:      KSPGMRES - Implements the Generalized Minimal Residual method.
    833:                 (Saad and Schultz, 1986) with restart

    836:    Options Database Keys:
    837: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    838: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    839: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    840:                              vectors are allocated as needed)
    841: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    842: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    843: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
    844:                                    stability of the classical Gram-Schmidt  orthogonalization.
    845: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    847:    Level: beginner

    849:    Notes:
    850:     Left and right preconditioning are supported, but not symmetric preconditioning.

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

    856: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
    857:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    858:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    859:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

    861: M*/

    863: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
    864: {
    865:   KSP_GMRES      *gmres;

    869:   PetscNewLog(ksp,&gmres);
    870:   ksp->data = (void*)gmres;

    872:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
    873:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
    874:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
    875:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
    876:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    878:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
    879:   ksp->ops->setup                        = KSPSetUp_GMRES;
    880:   ksp->ops->solve                        = KSPSolve_GMRES;
    881:   ksp->ops->reset                        = KSPReset_GMRES;
    882:   ksp->ops->destroy                      = KSPDestroy_GMRES;
    883:   ksp->ops->view                         = KSPView_GMRES;
    884:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
    885:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    886:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;
    887: #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
    888:   ksp->ops->computeritz                  = KSPComputeRitz_GMRES;
    889: #endif
    890:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    891:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    892:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    893:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    894:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    895:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
    896:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    897:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    899:   gmres->haptol         = 1.0e-30;
    900:   gmres->q_preallocate  = 0;
    901:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    902:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    903:   gmres->nrs            = 0;
    904:   gmres->sol_temp       = 0;
    905:   gmres->max_k          = GMRES_DEFAULT_MAXK;
    906:   gmres->Rsvd           = 0;
    907:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    908:   gmres->orthogwork     = 0;
    909:   return(0);
    910: }