Date: 2021-03-03T22:27:23+00:00

Actual source code: gmres.c
petsc-3.14.5 2021-03-03
Report Typos and Errors

      2: /*
      3:     This file implements GMRES (a Generalized Minimal Residual) method.
      4:     Reference:  Saad and Schultz, 1986.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    101: .        gmres  - structure containing parameters and work areas

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

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

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

    127:   /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
    128:   if ((ksp->rnorm > 0.0) && (PetscAbsReal(res-ksp->rnorm) > gmres->breakdowntol*gmres->rnorm0)) {
    129:       if (ksp->errorifnotconverged) SETERRQ3(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
    130:       else {
    131:         PetscInfo3(ksp,"Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
    132:         ksp->reason =  KSP_DIVERGED_BREAKDOWN;
    133:         return(0);
    134:       }
    135:   }
    136:   *GRS(0) = gmres->rnorm0 = res;

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

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

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

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

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

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

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

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

    192:     /* Catch error in happy breakdown and signal convergence and break from loop */
    193:     if (hapend) {
    194:       if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
    195:         ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
    196:       } else if (!ksp->reason) {
    197:         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);
    198:         else {
    199:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    200:           break;
    201:         }
    202:       }
    203:     }
    204:   }

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

    212:   if (itcount) *itcount = it;

    215:   /*
    216:     Down here we have to solve for the "best" coefficients of the Krylov
    217:     columns, add the solution values together, and possibly unwind the
    218:     preconditioning from the solution
    219:    */
    220:   /* Form the solution (or the solution so far) */
    221:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
    222:   return(0);
    223: }

    225: PetscErrorCode KSPSolve_GMRES(KSP ksp)
    226: {
    228:   PetscInt       its,itcount,i;
    229:   KSP_GMRES      *gmres     = (KSP_GMRES*)ksp->data;
    230:   PetscBool      guess_zero = ksp->guess_zero;
    231:   PetscInt       N = gmres->max_k + 1;

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

    236:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    237:   ksp->its = 0;
    238:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

    274: PetscErrorCode KSPReset_GMRES(KSP ksp)
    275: {
    276:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    278:   PetscInt       i;

    281:   /* Free the Hessenberg matrices */
    282:   PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
    283:   PetscFree(gmres->hes_ritz);

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

    295:   PetscFree(gmres->user_work);
    296:   PetscFree(gmres->mwork_alloc);
    297:   PetscFree(gmres->nrs);
    298:   VecDestroy(&gmres->sol_temp);
    299:   PetscFree(gmres->Rsvd);
    300:   PetscFree(gmres->Dsvd);
    301:   PetscFree(gmres->orthogwork);

    303:   gmres->vv_allocated   = 0;
    304:   gmres->vecs_allocated = 0;
    305:   gmres->sol_temp       = NULL;
    306:   return(0);
    307: }

    309: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
    310: {

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

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

    338:      This is an internal routine that knows about the GMRES internals.
    339:  */
    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:     if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
    359:     else ksp->reason = KSP_DIVERGED_BREAKDOWN;

    361:     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)));
    362:     return(0);
    363:   }
    364:   for (ii=1; ii<=it; ii++) {
    365:     k  = it - ii;
    366:     tt = *GRS(k);
    367:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    368:     if (*HH(k,k) == 0.0) {
    369:       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);
    370:       else {
    371:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    372:         PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
    373:         return(0);
    374:       }
    375:     }
    376:     nrs[k] = tt / *HH(k,k);
    377:   }

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

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

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

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

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

    443:     *res = 0.0;
    444:   }
    445:   return(0);
    446: }
    447: /*
    448:    This routine allocates more work vectors, starting from VEC_VV(it).
    449:  */
    450: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
    451: {
    452:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    454:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

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

    465:   gmres->vv_allocated += nalloc;

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

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

    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);
    495:   }

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

    502: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
    503: {
    504:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    505:   const char     *cstr;
    507:   PetscBool      iascii,isstring;

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

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

    543:    Collective on ksp

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

    551:    Options Database Keys:
    552: .   -ksp_gmres_kyrlov_monitor

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

    558: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
    559: @*/
    560: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
    561: {
    562:   PetscViewers   viewers = (PetscViewers)dummy;
    563:   KSP_GMRES      *gmres  = (KSP_GMRES*)ksp->data;
    565:   Vec            x;
    566:   PetscViewer    viewer;
    567:   PetscBool      flg;

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

    581: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    582: {
    584:   PetscInt       restart;
    585:   PetscReal      haptol,breakdowntol;
    586:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
    587:   PetscBool      flg;

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

    617: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
    618: {
    619:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

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

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

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

    641: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
    642: {
    643:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    646:   *max_k = gmres->max_k;
    647:   return(0);
    648: }

    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: }

    668: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
    669: {
    671:   ((KSP_GMRES*)ksp->data)->orthog = fcn;
    672:   return(0);
    673: }

    675: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
    676: {
    678:   *fcn = ((KSP_GMRES*)ksp->data)->orthog;
    679:   return(0);
    680: }

    682: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
    683: {
    684:   KSP_GMRES *gmres;

    687:   gmres = (KSP_GMRES*)ksp->data;
    688:   gmres->q_preallocate = 1;
    689:   return(0);
    690: }

    692: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
    693: {
    694:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

    697:   gmres->cgstype = type;
    698:   return(0);
    699: }

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

    706:   *type = gmres->cgstype;
    707:   return(0);
    708: }

    710: /*@
    711:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
    712:          in the classical Gram Schmidt orthogonalization.

    714:    Logically Collective on ksp

    716:    Input Parameters:
    717: +  ksp - the Krylov space context
    718: -  type - the type of refinement

    720:   Options Database:
    721: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    723:    Level: intermediate

    725: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
    726:           KSPGMRESGetOrthogonalization()
    727: @*/
    728: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
    729: {

    735:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
    736:   return(0);
    737: }

    739: /*@
    740:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
    741:          in the classical Gram Schmidt orthogonalization.

    743:    Not Collective

    745:    Input Parameter:
    746: .  ksp - the Krylov space context

    748:    Output Parameter:
    749: .  type - the type of refinement

    751:   Options Database:
    752: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

    754:    Level: intermediate

    756: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
    757:           KSPGMRESGetOrthogonalization()
    758: @*/
    759: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
    760: {

    765:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
    766:   return(0);
    767: }

    770: /*@
    771:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    773:    Logically Collective on ksp

    775:    Input Parameters:
    776: +  ksp - the Krylov space context
    777: -  restart - integer restart value

    779:   Options Database:
    780: .  -ksp_gmres_restart <positive integer>

    782:     Note: The default value is 30.

    784:    Level: intermediate

    786: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
    787: @*/
    788: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
    789: {

    795:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
    796:   return(0);
    797: }

    799: /*@
    800:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

    802:    Not Collective

    804:    Input Parameter:
    805: .  ksp - the Krylov space context

    807:    Output Parameter:
    808: .   restart - integer restart value

    810:     Note: The default value is 30.

    812:    Level: intermediate

    814: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
    815: @*/
    816: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
    817: {

    821:   PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
    822:   return(0);
    823: }

    825: /*@
    826:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

    828:    Logically Collective on ksp

    830:    Input Parameters:
    831: +  ksp - the Krylov space context
    832: -  tol - the tolerance

    834:   Options Database:
    835: .  -ksp_gmres_haptol <positive real value>

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

    841:    Level: intermediate

    843: .seealso: KSPSetTolerances()
    844: @*/
    845: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
    846: {

    851:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
    852:   return(0);
    853: }

    855: /*@
    856:    KSPGMRESSetBreakdownTolerance - Sets tolerance for determining divergence breakdown in GMRES.

    858:    Logically Collective on ksp

    860:    Input Parameters:
    861: +  ksp - the Krylov space context
    862: -  tol - the tolerance

    864:   Options Database:
    865: .  -ksp_gmres_breakdown_tolerance <positive real value>

    867:    Note: divergence breakdown occurs when GMRES residual increases significantly
    868:          during restart

    870:    Level: intermediate

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

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

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

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

    900:    Level: beginner

    902:    Notes:
    903:     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*/

    916: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
    917: {
    918:   KSP_GMRES      *gmres;

    922:   PetscNewLog(ksp,&gmres);
    923:   ksp->data = (void*)gmres;

    925:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
    926:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
    927:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
    928:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
    929:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    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,"KSPGMRESSetBreakdownTolerance_C",KSPGMRESSetBreakdownTolerance_GMRES);
    950:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    951:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

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