Actual source code: gmres.c
petsc-3.7.1 2016-05-15
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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>       /*I  "petscksp.h"  I*/
     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);

     39: PetscErrorCode    KSPSetUp_GMRES(KSP ksp)
     40: {
     41:   PetscInt       hh,hes,rs,cc;
     43:   PetscInt       max_k,k;
     44:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

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

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

     56:   if (ksp->calc_sings) {
     57:     /* Allocate workspace to hold Hessenberg matrix needed by lapack */
     58:     PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
     59:     PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
     60:     PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
     61:     PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
     62:   }

     64:   /* Allocate array to hold pointers to user vectors.  Note that we need
     65:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
     66:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;

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

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

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

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

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

     90:     gmres->mwork_alloc[0] = 5;
     91:     gmres->nwork_alloc    = 1;
     92:     for (k=0; k<gmres->vv_allocated; k++) {
     93:       gmres->vecs[k] = gmres->user_work[0][k];
     94:     }
     95:   }
     96:   return(0);
     97: }

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

    103: .        gmres  - structure containing parameters and work areas

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

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

    127:   if (itcount) *itcount = 0;
    128:   VecNormalize(VEC_VV(0),&res_norm);
    129:   KSPCheckNorm(ksp,res_norm);
    130:   res     = res_norm;
    131:   *GRS(0) = res_norm;

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

    146:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    147:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    148:     if (it) {
    149:       KSPLogResidualHistory(ksp,res);
    150:       KSPMonitor(ksp,ksp->its,res);
    151:     }
    152:     gmres->it = (it - 1);
    153:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
    154:       KSPGMRESGetNewVectors(ksp,it+1);
    155:     }
    156:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

    158:     /* update hessenberg matrix and do Gram-Schmidt */
    159:     (*gmres->orthog)(ksp,it);
    160:     if (ksp->reason) break;

    162:     /* vv(i+1) . vv(i+1) */
    163:     VecNormalize(VEC_VV(it+1),&tt);

    165:     /* save the magnitude */
    166:     *HH(it+1,it)  = tt;
    167:     *HES(it+1,it) = tt;

    169:     /* check for the happy breakdown */
    170:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    171:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
    172:     if (tt < hapbnd) {
    173:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
    174:       hapend = PETSC_TRUE;
    175:     }
    176:     KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);

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

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

    186:     /* Catch error in happy breakdown and signal convergence and break from loop */
    187:     if (hapend) {
    188:       if (!ksp->reason) {
    189:         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);
    190:         else {
    191:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    192:           break;
    193:         }
    194:       }
    195:     }
    196:   }

    198:   /* Monitor if we know that we will not return for a restart */
    199:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
    200:     KSPLogResidualHistory(ksp,res);
    201:     KSPMonitor(ksp,ksp->its,res);
    202:   }

    204:   if (itcount) *itcount = it;

    207:   /*
    208:     Down here we have to solve for the "best" coefficients of the Krylov
    209:     columns, add the solution values together, and possibly unwind the
    210:     preconditioning from the solution
    211:    */
    212:   /* Form the solution (or the solution so far) */
    213:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
    214:   return(0);
    215: }

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

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

    231:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    232:   ksp->its = 0;
    233:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    271: PetscErrorCode KSPReset_GMRES(KSP ksp)
    272: {
    273:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    275:   PetscInt       i;

    278:   /* Free the Hessenberg matrices */
    279:   PetscFree6(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin,gmres->hes_ritz);

    281:   /* free work vectors */
    282:   PetscFree(gmres->vecs);
    283:   for (i=0; i<gmres->nwork_alloc; i++) {
    284:     VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
    285:   }
    286:   gmres->nwork_alloc = 0;
    287:   if (gmres->vecb)  {
    288:     VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
    289:   }

    291:   PetscFree(gmres->user_work);
    292:   PetscFree(gmres->mwork_alloc);
    293:   PetscFree(gmres->nrs);
    294:   VecDestroy(&gmres->sol_temp);
    295:   PetscFree(gmres->Rsvd);
    296:   PetscFree(gmres->Dsvd);
    297:   PetscFree(gmres->orthogwork);

    299:   gmres->sol_temp       = 0;
    300:   gmres->vv_allocated   = 0;
    301:   gmres->vecs_allocated = 0;
    302:   gmres->sol_temp       = 0;
    303:   return(0);
    304: }

    308: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    309: {

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

    330:     Input parameters:
    331:         nrs - work area of size it + 1.
    332:         vs  - index of initial guess
    333:         vdest - index of result.  Note that vs may == vdest (replace
    334:                 guess with the solution).

    336:      This is an internal routine that knows about the GMRES internals.
    337:  */
    340: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    341: {
    342:   PetscScalar    tt;
    344:   PetscInt       ii,k,j;
    345:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);

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

    350:   /* If it is < 0, no gmres steps have been performed */
    351:   if (it < 0) {
    352:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
    353:     return(0);
    354:   }
    355:   if (*HH(it,it) != 0.0) {
    356:     nrs[it] = *GRS(it) / *HH(it,it);
    357:   } else {
    358:     ksp->reason = KSP_DIVERGED_BREAKDOWN;

    360:     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)));
    361:     return(0);
    362:   }
    363:   for (ii=1; ii<=it; ii++) {
    364:     k  = it - ii;
    365:     tt = *GRS(k);
    366:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    367:     if (*HH(k,k) == 0.0) {
    368:       ksp->reason = KSP_DIVERGED_BREAKDOWN;

    370:       PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    371:       return(0);
    372:     }
    373:     nrs[k] = tt / *HH(k,k);
    374:   }

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

    380:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    381:   /* add solution to previous solution */
    382:   if (vdest != vs) {
    383:     VecCopy(vs,vdest);
    384:   }
    385:   VecAXPY(vdest,1.0,VEC_TEMP);
    386:   return(0);
    387: }
    388: /*
    389:    Do the scalar work for the orthogonalization.  Return new residual norm.
    390:  */
    393: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    394: {
    395:   PetscScalar *hh,*cc,*ss,tt;
    396:   PetscInt    j;
    397:   KSP_GMRES   *gmres = (KSP_GMRES*)(ksp->data);

    400:   hh = HH(0,it);
    401:   cc = CC(0);
    402:   ss = SS(0);

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

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

    439:     *res = 0.0;
    440:   }
    441:   return(0);
    442: }
    443: /*
    444:    This routine allocates more work vectors, starting from VEC_VV(it).
    445:  */
    448: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
    449: {
    450:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    452:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

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

    463:   gmres->vv_allocated += nalloc;

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

    468:   gmres->mwork_alloc[nwork] = nalloc;
    469:   for (k=0; k<nalloc; k++) {
    470:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
    471:   }
    472:   gmres->nwork_alloc++;
    473:   return(0);
    474: }

    478: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
    479: {
    480:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

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

    497:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
    498:   if (result) *result = ptr;
    499:   return(0);
    500: }

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

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

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

    547:    Collective on KSP

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

    555:    Options Database Keys:
    556: .   -ksp_gmres_kyrlov_monitor

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

    561: .keywords: KSP, nonlinear, vector, monitor, view, Krylov space

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

    575:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
    576:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
    577:   if (!flg) {
    578:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
    579:     PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
    580:   }
    581:   x    = VEC_VV(gmres->it+1);
    582:   VecView(x,viewer);
    583:   return(0);
    584: }

    588: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    589: {
    591:   PetscInt       restart;
    592:   PetscReal      haptol;
    593:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    594:   PetscBool      flg;

    597:   PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
    598:   PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
    599:   if (flg) { KSPGMRESSetRestart(ksp,restart); }
    600:   PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
    601:   if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
    602:   flg  = PETSC_FALSE;
    603:   PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
    604:   if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
    605:   PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
    606:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
    607:   PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
    608:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
    609:   PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
    610:                           KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
    611:   flg  = PETSC_FALSE;
    612:   PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
    613:   if (flg) {
    614:     PetscViewers viewers;
    615:     PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
    616:     KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
    617:   }
    618:   PetscOptionsTail();
    619:   return(0);
    620: }

    622: extern PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal*,PetscReal*);
    623: extern PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

    627: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
    628: {
    629:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    632:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    633:   gmres->haptol = tol;
    634:   return(0);
    635: }

    639: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
    640: {
    641:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    644:   *max_k = gmres->max_k;
    645:   return(0);
    646: }

    650: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
    651: {
    652:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

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

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

    679: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
    680: {
    682:   *fcn = ((KSP_GMRES*)ksp->data)->orthog;
    683:   return(0);
    684: }

    688: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    689: {
    690:   KSP_GMRES *gmres;

    693:   gmres = (KSP_GMRES*)ksp->data;
    694:   gmres->q_preallocate = 1;
    695:   return(0);
    696: }

    700: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
    701: {
    702:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    705:   gmres->cgstype = type;
    706:   return(0);
    707: }

    711: PetscErrorCode  KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
    712: {
    713:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    716:   *type = gmres->cgstype;
    717:   return(0);
    718: }

    722: /*@
    723:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    724:          in the classical Gram Schmidt orthogonalization.

    726:    Logically Collective on KSP

    728:    Input Parameters:
    729: +  ksp - the Krylov space context
    730: -  type - the type of refinement

    732:   Options Database:
    733: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

    735:    Level: intermediate

    737: .keywords: KSP, GMRES, iterative refinement

    739: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
    740:           KSPGMRESGetOrthogonalization()
    741: @*/
    742: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
    743: {

    749:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
    750:   return(0);
    751: }

    755: /*@
    756:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    757:          in the classical Gram Schmidt orthogonalization.

    759:    Not Collective

    761:    Input Parameter:
    762: .  ksp - the Krylov space context

    764:    Output Parameter:
    765: .  type - the type of refinement

    767:   Options Database:
    768: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

    770:    Level: intermediate

    772: .keywords: KSP, GMRES, iterative refinement

    774: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
    775:           KSPGMRESGetOrthogonalization()
    776: @*/
    777: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
    778: {

    783:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
    784:   return(0);
    785: }

    790: /*@
    791:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    793:    Logically Collective on KSP

    795:    Input Parameters:
    796: +  ksp - the Krylov space context
    797: -  restart - integer restart value

    799:   Options Database:
    800: .  -ksp_gmres_restart <positive integer>

    802:     Note: The default value is 30.

    804:    Level: intermediate

    806: .keywords: KSP, GMRES, restart, iterations

    808: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
    809: @*/
    810: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    811: {

    817:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
    818:   return(0);
    819: }

    823: /*@
    824:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    826:    Not Collective

    828:    Input Parameter:
    829: .  ksp - the Krylov space context

    831:    Output Parameter:
    832: .   restart - integer restart value

    834:     Note: The default value is 30.

    836:    Level: intermediate

    838: .keywords: KSP, GMRES, restart, iterations

    840: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
    841: @*/
    842: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
    843: {

    847:   PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
    848:   return(0);
    849: }

    853: /*@
    854:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

    856:    Logically Collective on KSP

    858:    Input Parameters:
    859: +  ksp - the Krylov space context
    860: -  tol - the tolerance

    862:   Options Database:
    863: .  -ksp_gmres_haptol <positive real value>

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

    869:    Level: intermediate

    871: .keywords: KSP, GMRES, tolerance

    873: .seealso: KSPSetTolerances()
    874: @*/
    875: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
    876: {

    881:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
    882:   return(0);
    883: }

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

    890:    Options Database Keys:
    891: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    892: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    893: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    894:                              vectors are allocated as needed)
    895: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    896: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    897: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    898:                                    stability of the classical Gram-Schmidt  orthogonalization.
    899: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    901:    Level: beginner

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

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

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

    914: M*/

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

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

    927:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
    928:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
    929:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);

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

    952:   gmres->haptol         = 1.0e-30;
    953:   gmres->q_preallocate  = 0;
    954:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    955:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    956:   gmres->nrs            = 0;
    957:   gmres->sol_temp       = 0;
    958:   gmres->max_k          = GMRES_DEFAULT_MAXK;
    959:   gmres->Rsvd           = 0;
    960:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    961:   gmres->orthogwork     = 0;
    962:   return(0);
    963: }