Actual source code: gmres.c
petsc-3.10.5 2019-03-28
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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_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);

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

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

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

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

    182:     /* Catch error in happy breakdown and signal convergence and break from loop */
    183:     if (hapend) {
    184:       if (!ksp->reason) {
    185:         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);
    186:         else {
    187:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    188:           break;
    189:         }
    190:       }
    191:     }
    192:   }

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

    200:   if (itcount) *itcount = it;

    203:   /*
    204:     Down here we have to solve for the "best" coefficients of the Krylov
    205:     columns, add the solution values together, and possibly unwind the
    206:     preconditioning from the solution
    207:    */
    208:   /* Form the solution (or the solution so far) */
    209:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
    210:   return(0);
    211: }

    213: PetscErrorCode KSPSolve_GMRES(KSP ksp)
    214: {
    216:   PetscInt       its,itcount,i;
    217:   KSP_GMRES      *gmres     = (KSP_GMRES*)ksp->data;
    218:   PetscBool      guess_zero = ksp->guess_zero;
    219:   PetscInt       N = gmres->max_k + 1;
    220:   PetscBLASInt   bN;

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

    225:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    226:   ksp->its = 0;
    227:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    263: PetscErrorCode KSPReset_GMRES(KSP ksp)
    264: {
    265:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    267:   PetscInt       i;

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

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

    283:   PetscFree(gmres->user_work);
    284:   PetscFree(gmres->mwork_alloc);
    285:   PetscFree(gmres->nrs);
    286:   VecDestroy(&gmres->sol_temp);
    287:   PetscFree(gmres->Rsvd);
    288:   PetscFree(gmres->Dsvd);
    289:   PetscFree(gmres->orthogwork);

    291:   gmres->sol_temp       = 0;
    292:   gmres->vv_allocated   = 0;
    293:   gmres->vecs_allocated = 0;
    294:   gmres->sol_temp       = 0;
    295:   return(0);
    296: }

    298: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    299: {

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

    320:     Input parameters:
    321:         nrs - work area of size it + 1.
    322:         vs  - index of initial guess
    323:         vdest - index of result.  Note that vs may == vdest (replace
    324:                 guess with the solution).

    326:      This is an internal routine that knows about the GMRES internals.
    327:  */
    328: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    329: {
    330:   PetscScalar    tt;
    332:   PetscInt       ii,k,j;
    333:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);

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

    338:   /* If it is < 0, no gmres steps have been performed */
    339:   if (it < 0) {
    340:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
    341:     return(0);
    342:   }
    343:   if (*HH(it,it) != 0.0) {
    344:     nrs[it] = *GRS(it) / *HH(it,it);
    345:   } else {
    346:     ksp->reason = KSP_DIVERGED_BREAKDOWN;

    348:     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)));
    349:     return(0);
    350:   }
    351:   for (ii=1; ii<=it; ii++) {
    352:     k  = it - ii;
    353:     tt = *GRS(k);
    354:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    355:     if (*HH(k,k) == 0.0) {
    356:       ksp->reason = KSP_DIVERGED_BREAKDOWN;

    358:       PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    359:       return(0);
    360:     }
    361:     nrs[k] = tt / *HH(k,k);
    362:   }

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

    368:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
    369:   /* add solution to previous solution */
    370:   if (vdest != vs) {
    371:     VecCopy(vs,vdest);
    372:   }
    373:   VecAXPY(vdest,1.0,VEC_TEMP);
    374:   return(0);
    375: }
    376: /*
    377:    Do the scalar work for the orthogonalization.  Return new residual norm.
    378:  */
    379: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    380: {
    381:   PetscScalar *hh,*cc,*ss,tt;
    382:   PetscInt    j;
    383:   KSP_GMRES   *gmres = (KSP_GMRES*)(ksp->data);

    386:   hh = HH(0,it);
    387:   cc = CC(0);
    388:   ss = SS(0);

    390:   /* Apply all the previously computed plane rotations to the new column
    391:      of the Hessenberg matrix */
    392:   for (j=1; j<=it; j++) {
    393:     tt  = *hh;
    394:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    395:     hh++;
    396:     *hh = *cc++ * *hh - (*ss++ * tt);
    397:   }

    399:   /*
    400:     compute the new plane rotation, and apply it to:
    401:      1) the right-hand-side of the Hessenberg system
    402:      2) the new column of the Hessenberg matrix
    403:     thus obtaining the updated value of the residual
    404:   */
    405:   if (!hapend) {
    406:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    407:     if (tt == 0.0) {
    408:       ksp->reason = KSP_DIVERGED_NULL;
    409:       return(0);
    410:     }
    411:     *cc        = *hh / tt;
    412:     *ss        = *(hh+1) / tt;
    413:     *GRS(it+1) = -(*ss * *GRS(it));
    414:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    415:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
    416:     *res       = PetscAbsScalar(*GRS(it+1));
    417:   } else {
    418:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    419:             another rotation matrix (so RH doesn't change).  The new residual is
    420:             always the new sine term times the residual from last time (GRS(it)),
    421:             but now the new sine rotation would be zero...so the residual should
    422:             be zero...so we will multiply "zero" by the last residual.  This might
    423:             not be exactly what we want to do here -could just return "zero". */

    425:     *res = 0.0;
    426:   }
    427:   return(0);
    428: }
    429: /*
    430:    This routine allocates more work vectors, starting from VEC_VV(it).
    431:  */
    432: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
    433: {
    434:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    436:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

    439:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
    440:   /* Adjust the number to allocate to make sure that we don't exceed the
    441:     number of available slots */
    442:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
    443:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
    444:   }
    445:   if (!nalloc) return(0);

    447:   gmres->vv_allocated += nalloc;

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

    452:   gmres->mwork_alloc[nwork] = nalloc;
    453:   for (k=0; k<nalloc; k++) {
    454:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
    455:   }
    456:   gmres->nwork_alloc++;
    457:   return(0);
    458: }

    460: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
    461: {
    462:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

    466:   if (!ptr) {
    467:     if (!gmres->sol_temp) {
    468:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
    469:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
    470:     }
    471:     ptr = gmres->sol_temp;
    472:   }
    473:   if (!gmres->nrs) {
    474:     /* allocate the work area */
    475:     PetscMalloc1(gmres->max_k,&gmres->nrs);
    476:     PetscLogObjectMemory((PetscObject)ksp,gmres->max_k*sizeof(PetscScalar));
    477:   }

    479:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
    480:   if (result) *result = ptr;
    481:   return(0);
    482: }

    484: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
    485: {
    486:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    487:   const char     *cstr;
    489:   PetscBool      iascii,isstring;

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

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

    525:    Collective on KSP

    527:    Input Parameters:
    528: +  ksp - the KSP context
    529: .  its - iteration number
    530: .  fgnorm - 2-norm of residual (or gradient)
    531: -  dummy - an collection of viewers created with KSPViewerCreate()

    533:    Options Database Keys:
    534: .   -ksp_gmres_kyrlov_monitor

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

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

    542: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
    543: @*/
    544: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
    545: {
    546:   PetscViewers   viewers = (PetscViewers)dummy;
    547:   KSP_GMRES      *gmres  = (KSP_GMRES*)ksp->data;
    549:   Vec            x;
    550:   PetscViewer    viewer;
    551:   PetscBool      flg;

    554:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
    555:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
    556:   if (!flg) {
    557:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
    558:     PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
    559:   }
    560:   x    = VEC_VV(gmres->it+1);
    561:   VecView(x,viewer);
    562:   return(0);
    563: }

    565: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    566: {
    568:   PetscInt       restart;
    569:   PetscReal      haptol;
    570:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    571:   PetscBool      flg;

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

    599: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
    600: {
    601:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    604:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
    605:   gmres->haptol = tol;
    606:   return(0);
    607: }

    609: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
    610: {
    611:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    614:   *max_k = gmres->max_k;
    615:   return(0);
    616: }

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

    624:   if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
    625:   if (!ksp->setupstage) {
    626:     gmres->max_k = max_k;
    627:   } else if (gmres->max_k != max_k) {
    628:     gmres->max_k    = max_k;
    629:     ksp->setupstage = KSP_SETUP_NEW;
    630:     /* free the data structures, then create them again */
    631:     KSPReset_GMRES(ksp);
    632:   }
    633:   return(0);
    634: }

    636: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
    637: {
    639:   ((KSP_GMRES*)ksp->data)->orthog = fcn;
    640:   return(0);
    641: }

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

    650: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    651: {
    652:   KSP_GMRES *gmres;

    655:   gmres = (KSP_GMRES*)ksp->data;
    656:   gmres->q_preallocate = 1;
    657:   return(0);
    658: }

    660: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
    661: {
    662:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    665:   gmres->cgstype = type;
    666:   return(0);
    667: }

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

    674:   *type = gmres->cgstype;
    675:   return(0);
    676: }

    678: /*@
    679:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    680:          in the classical Gram Schmidt orthogonalization.

    682:    Logically Collective on KSP

    684:    Input Parameters:
    685: +  ksp - the Krylov space context
    686: -  type - the type of refinement

    688:   Options Database:
    689: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    691:    Level: intermediate

    693: .keywords: KSP, GMRES, iterative refinement

    695: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
    696:           KSPGMRESGetOrthogonalization()
    697: @*/
    698: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
    699: {

    705:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
    706:   return(0);
    707: }

    709: /*@
    710:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    711:          in the classical Gram Schmidt orthogonalization.

    713:    Not Collective

    715:    Input Parameter:
    716: .  ksp - the Krylov space context

    718:    Output Parameter:
    719: .  type - the type of refinement

    721:   Options Database:
    722: .  -ksp_gmres_cgs_refinement_type <never,ifneeded,always>

    724:    Level: intermediate

    726: .keywords: KSP, GMRES, iterative refinement

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

    737:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
    738:   return(0);
    739: }

    742: /*@
    743:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    745:    Logically Collective on KSP

    747:    Input Parameters:
    748: +  ksp - the Krylov space context
    749: -  restart - integer restart value

    751:   Options Database:
    752: .  -ksp_gmres_restart <positive integer>

    754:     Note: The default value is 30.

    756:    Level: intermediate

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

    760: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
    761: @*/
    762: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    763: {

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

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

    776:    Not Collective

    778:    Input Parameter:
    779: .  ksp - the Krylov space context

    781:    Output Parameter:
    782: .   restart - integer restart value

    784:     Note: The default value is 30.

    786:    Level: intermediate

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

    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: .keywords: KSP, GMRES, tolerance

    821: .seealso: KSPSetTolerances()
    822: @*/
    823: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
    824: {

    829:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
    830:   return(0);
    831: }

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

    838:    Options Database Keys:
    839: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    840: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    841: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    842:                              vectors are allocated as needed)
    843: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    844: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    845: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    846:                                    stability of the classical Gram-Schmidt  orthogonalization.
    847: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    849:    Level: beginner

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

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

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

    863: M*/

    865: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
    866: {
    867:   KSP_GMRES      *gmres;

    871:   PetscNewLog(ksp,&gmres);
    872:   ksp->data = (void*)gmres;

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

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

    901:   gmres->haptol         = 1.0e-30;
    902:   gmres->q_preallocate  = 0;
    903:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    904:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    905:   gmres->nrs            = 0;
    906:   gmres->sol_temp       = 0;
    907:   gmres->max_k          = GMRES_DEFAULT_MAXK;
    908:   gmres->Rsvd           = 0;
    909:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    910:   gmres->orthogwork     = 0;
    911:   return(0);
    912: }