Date: 2015-10-02T22:21:18+00:00

Actual source code: dgmres.c
petsc-3.6.2 2015-10-02
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      2: /*
      3:  This file implements the deflated GMRES.
      4:  References:
      5:  [1]J. Erhel, K. Burrage and B. Pohl,  Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318.
      6:  [2] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

      8:  */

     10: #include <../src/ksp/ksp/impls/gmres/dgmres/dgmresimpl.h>       /*I  "petscksp.h"  I*/

     12: PetscLogEvent KSP_DGMRESComputeDeflationData, KSP_DGMRESApplyDeflation;

     14: #define GMRES_DELTA_DIRECTIONS 10
     15: #define GMRES_DEFAULT_MAXK     30
     16: static PetscErrorCode    KSPDGMRESGetNewVectors(KSP,PetscInt);
     17: static PetscErrorCode    KSPDGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
     18: static PetscErrorCode    KSPDGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

     22: PetscErrorCode  KSPDGMRESSetEigen(KSP ksp,PetscInt nb_eig)
     23: {

     27:   PetscTryMethod((ksp),"KSPDGMRESSetEigen_C",(KSP,PetscInt),(ksp,nb_eig));
     28:   return(0);
     29: }
     32: PetscErrorCode  KSPDGMRESSetMaxEigen(KSP ksp,PetscInt max_neig)
     33: {

     37:   PetscTryMethod((ksp),"KSPDGMRESSetMaxEigen_C",(KSP,PetscInt),(ksp,max_neig));
     38:   return(0);
     39: }
     42: PetscErrorCode  KSPDGMRESForce(KSP ksp,PetscBool force)
     43: {

     47:   PetscTryMethod((ksp),"KSPDGMRESForce_C",(KSP,PetscBool),(ksp,force));
     48:   return(0);
     49: }
     52: PetscErrorCode  KSPDGMRESSetRatio(KSP ksp,PetscReal ratio)
     53: {

     57:   PetscTryMethod((ksp),"KSPDGMRESSetRatio_C",(KSP,PetscReal),(ksp,ratio));
     58:   return(0);
     59: }
     62: PetscErrorCode  KSPDGMRESComputeSchurForm(KSP ksp,PetscInt *neig)
     63: {

     67:   PetscTryMethod((ksp),"KSPDGMRESComputeSchurForm_C",(KSP, PetscInt*),(ksp, neig));
     68:   return(0);
     69: }
     72: PetscErrorCode  KSPDGMRESComputeDeflationData(KSP ksp)
     73: {

     77:   PetscTryMethod((ksp),"KSPDGMRESComputeDeflationData_C",(KSP),(ksp));
     78:   return(0);
     79: }
     82: PetscErrorCode  KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
     83: {

     87:   PetscTryMethod((ksp),"KSPDGMRESApplyDeflation_C",(KSP, Vec, Vec),(ksp, x, y));
     88:   return(0);
     89: }

     93: PetscErrorCode  KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
     94: {

     98:   PetscTryMethod((ksp), "KSPDGMRESImproveEig_C",(KSP, PetscInt),(ksp, neig));
     99:   return(0);
    100: }

    104: PetscErrorCode  KSPSetUp_DGMRES(KSP ksp)
    105: {
    107:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    108:   PetscInt       neig    = dgmres->neig+EIG_OFFSET;
    109:   PetscInt       max_k   = dgmres->max_k+1;

    112:   KSPSetUp_GMRES(ksp);
    113:   if (!dgmres->neig) return(0);

    115:   /* Allocate workspace for the Schur vectors*/
    116:   PetscMalloc1(neig*max_k, &SR);
    117:   dgmres->wr    = NULL;
    118:   dgmres->wi    = NULL;
    119:   dgmres->perm  = NULL;
    120:   dgmres->modul = NULL;
    121:   dgmres->Q     = NULL;
    122:   dgmres->Z     = NULL;

    124:   UU   = NULL;
    125:   XX   = NULL;
    126:   MX   = NULL;
    127:   AUU  = NULL;
    128:   XMX  = NULL;
    129:   XMU  = NULL;
    130:   UMX  = NULL;
    131:   AUAU = NULL;
    132:   TT   = NULL;
    133:   TTF  = NULL;
    134:   INVP = NULL;
    135:   X1   = NULL;
    136:   X2   = NULL;
    137:   MU   = NULL;
    138:   return(0);
    139: }

    141: /*
    142:  Run GMRES, possibly with restart.  Return residual history if requested.
    143:  input parameters:

    145:  .       gmres  - structure containing parameters and work areas

    147:  output parameters:
    148:  .        nres    - residuals (from preconditioned system) at each step.
    149:  If restarting, consider passing nres+it.  If null,
    150:  ignored
    151:  .        itcount - number of iterations used.  nres[0] to nres[itcount]
    152:  are defined.  If null, ignored.

    154:  Notes:
    155:  On entry, the value in vector VEC_VV(0) should be the initial residual
    156:  (this allows shortcuts where the initial preconditioned residual is 0).
    157:  */
    160: PetscErrorCode KSPDGMRESCycle(PetscInt *itcount,KSP ksp)
    161: {
    162:   KSP_DGMRES     *dgmres = (KSP_DGMRES*)(ksp->data);
    163:   PetscReal      res_norm,res,hapbnd,tt;
    165:   PetscInt       it     = 0;
    166:   PetscInt       max_k  = dgmres->max_k;
    167:   PetscBool      hapend = PETSC_FALSE;
    168:   PetscReal      res_old;
    169:   PetscInt       test = 0;

    172:   VecNormalize(VEC_VV(0),&res_norm);
    173:   res     = res_norm;
    174:   *GRS(0) = res_norm;

    176:   /* check for the convergence */
    177:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    178:   ksp->rnorm = res;
    179:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    180:   dgmres->it = (it - 1);
    181:   KSPLogResidualHistory(ksp,res);
    182:   KSPMonitor(ksp,ksp->its,res);
    183:   if (!res) {
    184:     if (itcount) *itcount = 0;
    185:     ksp->reason = KSP_CONVERGED_ATOL;
    186:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
    187:     return(0);
    188:   }
    189:   /* record the residual norm to test if deflation is needed */
    190:   res_old = res;

    192:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    193:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    194:     if (it) {
    195:       KSPLogResidualHistory(ksp,res);
    196:       KSPMonitor(ksp,ksp->its,res);
    197:     }
    198:     dgmres->it = (it - 1);
    199:     if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) {
    200:       KSPDGMRESGetNewVectors(ksp,it+1);
    201:     }
    202:     if (dgmres->r > 0) {
    203:       if (ksp->pc_side == PC_LEFT) {
    204:         /* Apply the first preconditioner */
    205:         KSP_PCApplyBAorAB(ksp,VEC_VV(it), VEC_TEMP,VEC_TEMP_MATOP);
    206:         /* Then apply Deflation as a preconditioner */
    207:         KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1+it));
    208:       } else if (ksp->pc_side == PC_RIGHT) {
    209:         KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP);
    210:         KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1+it), VEC_TEMP_MATOP);
    211:       }
    212:     } else {
    213:       KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
    214:     }
    215:     dgmres->matvecs += 1;
    216:     /* update hessenberg matrix and do Gram-Schmidt */
    217:     (*dgmres->orthog)(ksp,it);

    219:     /* vv(i+1) . vv(i+1) */
    220:     VecNormalize(VEC_VV(it+1),&tt);
    221:     /* save the magnitude */
    222:     *HH(it+1,it)  = tt;
    223:     *HES(it+1,it) = tt;

    225:     /* check for the happy breakdown */
    226:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    227:     if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
    228:     if (tt < hapbnd) {
    229:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
    230:       hapend = PETSC_TRUE;
    231:     }
    232:     KSPDGMRESUpdateHessenberg(ksp,it,hapend,&res);

    234:     it++;
    235:     dgmres->it = (it-1);     /* For converged */
    236:     ksp->its++;
    237:     ksp->rnorm = res;
    238:     if (ksp->reason) break;

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

    242:     /* Catch error in happy breakdown and signal convergence and break from loop */
    243:     if (hapend) {
    244:       if (!ksp->reason) {
    245:         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);
    246:         else {
    247:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    248:           break;
    249:         }
    250:       }
    251:     }
    252:   }

    254:   /* Monitor if we know that we will not return for a restart */
    255:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
    256:     KSPLogResidualHistory(ksp,res);
    257:     KSPMonitor(ksp,ksp->its,res);
    258:   }
    259:   if (itcount) *itcount = it;

    261:   /*
    262:    Down here we have to solve for the "best" coefficients of the Krylov
    263:    columns, add the solution values together, and possibly unwind the
    264:    preconditioning from the solution
    265:    */
    266:   /* Form the solution (or the solution so far) */
    267:   KSPDGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

    269:   /* Compute data for the deflation to be used during the next restart */
    270:   if (!ksp->reason && ksp->its < ksp->max_it) {
    271:     test = max_k *PetscLogReal(ksp->rtol/res) /PetscLogReal(res/res_old);
    272:     /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed  */
    273:     if ((test > dgmres->smv*(ksp->max_it-ksp->its)) || dgmres->force) {
    274:        KSPDGMRESComputeDeflationData(ksp);
    275:     }
    276:   }
    277:   return(0);
    278: }

    282: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
    283: {
    285:   PetscInt       i,its,itcount;
    286:   KSP_DGMRES     *dgmres    = (KSP_DGMRES*) ksp->data;
    287:   PetscBool      guess_zero = ksp->guess_zero;

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

    292:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    293:   ksp->its        = 0;
    294:   dgmres->matvecs = 0;
    295:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

    297:   itcount     = 0;
    298:   ksp->reason = KSP_CONVERGED_ITERATING;
    299:   while (!ksp->reason) {
    300:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    301:     if (ksp->pc_side == PC_LEFT) {
    302:       dgmres->matvecs += 1;
    303:       if (dgmres->r > 0) {
    304:         KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP);
    305:         VecCopy(VEC_TEMP, VEC_VV(0));
    306:       }
    307:     }

    309:     KSPDGMRESCycle(&its,ksp);
    310:     itcount += its;
    311:     if (itcount >= ksp->max_it) {
    312:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    313:       break;
    314:     }
    315:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    316:   }
    317:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */

    319:   for (i = 0; i < dgmres->r; i++) {
    320:     VecViewFromOptions(UU[i],(PetscObject)ksp,"-ksp_dgmres_view_deflation_vecs");
    321:   }
    322:   return(0);
    323: }

    327: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
    328: {
    330:   KSP_DGMRES     *dgmres  = (KSP_DGMRES*) ksp->data;
    331:   PetscInt       neig1    = dgmres->neig+EIG_OFFSET;
    332:   PetscInt       max_neig = dgmres->max_neig;

    335:   if (dgmres->r) {
    336:     VecDestroyVecs(max_neig, &UU);
    337:     VecDestroyVecs(max_neig, &MU);
    338:     if (XX) {
    339:       VecDestroyVecs(neig1, &XX);
    340:       VecDestroyVecs(neig1, &MX);
    341:     }

    343:     PetscFree(TT);
    344:     PetscFree(TTF);
    345:     PetscFree(INVP);

    347:     PetscFree(XMX);
    348:     PetscFree(UMX);
    349:     PetscFree(XMU);
    350:     PetscFree(X1);
    351:     PetscFree(X2);
    352:     PetscFree(dgmres->work);
    353:     PetscFree(dgmres->iwork);
    354:     PetscFree(dgmres->wr);
    355:     PetscFree(dgmres->wi);
    356:     PetscFree(dgmres->modul);
    357:     PetscFree(dgmres->Q);
    358:     PetscFree(ORTH);
    359:     PetscFree(AUAU);
    360:     PetscFree(AUU);
    361:     PetscFree(SR2);
    362:   }
    363:   PetscFree(SR);
    364:   KSPDestroy_GMRES(ksp);
    365:   return(0);
    366: }
    367: /*
    368:  KSPDGMRESBuildSoln - create the solution from the starting vector and the
    369:  current iterates.

    371:  Input parameters:
    372:  nrs - work area of size it + 1.
    373:  vs  - index of initial guess
    374:  vdest - index of result.  Note that vs may == vdest (replace
    375:  guess with the solution).

    377:  This is an internal routine that knows about the GMRES internals.
    378:  */
    381: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    382: {
    383:   PetscScalar    tt;
    385:   PetscInt       ii,k,j;
    386:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) (ksp->data);

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

    391:   /* If it is < 0, no gmres steps have been performed */
    392:   if (it < 0) {
    393:     VecCopy(vs,vdest);     /* VecCopy() is smart, exists immediately if vguess == vdest */
    394:     return(0);
    395:   }
    396:   if (*HH(it,it) == 0.0) SETERRQ2(PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED,"Likely your matrix is the zero operator. HH(it,it) is identically zero; it = %D GRS(it) = %g",it,(double)PetscAbsScalar(*GRS(it)));
    397:   if (*HH(it,it) != 0.0) nrs[it] = *GRS(it) / *HH(it,it);
    398:   else nrs[it] = 0.0;

    400:   for (ii=1; ii<=it; ii++) {
    401:     k  = it - ii;
    402:     tt = *GRS(k);
    403:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    404:     if (*HH(k,k) == 0.0) SETERRQ2(PetscObjectComm((PetscObject)ksp), PETSC_ERR_CONV_FAILED,"Likely your matrix is singular. HH(k,k) is identically zero; it = %D k = %D",it,k);
    405:     nrs[k] = tt / *HH(k,k);
    406:   }

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

    412:   /* Apply deflation */
    413:   if (ksp->pc_side==PC_RIGHT && dgmres->r > 0) {
    414:     KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP);
    415:     VecCopy(VEC_TEMP_MATOP, VEC_TEMP);
    416:   }
    417:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

    419:   /* add solution to previous solution */
    420:   if (vdest != vs) {
    421:     VecCopy(vs,vdest);
    422:   }
    423:   VecAXPY(vdest,1.0,VEC_TEMP);
    424:   return(0);
    425: }
    426: /*
    427:  Do the scalar work for the orthogonalization.  Return new residual norm.
    428:  */
    431: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    432: {
    433:   PetscScalar *hh,*cc,*ss,tt;
    434:   PetscInt    j;
    435:   KSP_DGMRES  *dgmres = (KSP_DGMRES*) (ksp->data);

    438:   hh = HH(0,it);
    439:   cc = CC(0);
    440:   ss = SS(0);

    442:   /* Apply all the previously computed plane rotations to the new column
    443:    of the Hessenberg matrix */
    444:   for (j=1; j<=it; j++) {
    445:     tt  = *hh;
    446:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    447:     hh++;
    448:     *hh = *cc++ * *hh -(*ss++ * tt);
    449:   }

    451:   /*
    452:    compute the new plane rotation, and apply it to:
    453:    1) the right-hand-side of the Hessenberg system
    454:    2) the new column of the Hessenberg matrix
    455:    thus obtaining the updated value of the residual
    456:    */
    457:   if (!hapend) {
    458:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    459:     if (tt == 0.0) {
    460:       ksp->reason = KSP_DIVERGED_NULL;
    461:       return(0);
    462:     }
    463:     *cc        = *hh / tt;
    464:     *ss        = *(hh+1) / tt;
    465:     *GRS(it+1) = -(*ss * *GRS(it));
    466:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    467:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
    468:     *res       = PetscAbsScalar(*GRS(it+1));
    469:   } else {
    470:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    471:      another rotation matrix (so RH doesn't change).  The new residual is
    472:      always the new sine term times the residual from last time (GRS(it)),
    473:      but now the new sine rotation would be zero...so the residual should
    474:      be zero...so we will multiply "zero" by the last residual.  This might
    475:      not be exactly what we want to do here -could just return "zero". */

    477:     *res = 0.0;
    478:   }
    479:   return(0);
    480: }
    481: /*
    482:  This routine allocates more work vectors, starting from VEC_VV(it).
    483:  */
    486: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp,PetscInt it)
    487: {
    488:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    490:   PetscInt       nwork = dgmres->nwork_alloc,k,nalloc;

    493:   nalloc = PetscMin(ksp->max_it,dgmres->delta_allocate);
    494:   /* Adjust the number to allocate to make sure that we don't exceed the
    495:    number of available slots */
    496:   if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) {
    497:     nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
    498:   }
    499:   if (!nalloc) return(0);

    501:   dgmres->vv_allocated += nalloc;

    503:   KSPCreateVecs(ksp,nalloc,&dgmres->user_work[nwork],0,NULL);
    504:   PetscLogObjectParents(ksp,nalloc,dgmres->user_work[nwork]);

    506:   dgmres->mwork_alloc[nwork] = nalloc;
    507:   for (k=0; k<nalloc; k++) {
    508:     dgmres->vecs[it+VEC_OFFSET+k] = dgmres->user_work[nwork][k];
    509:   }
    510:   dgmres->nwork_alloc++;
    511:   return(0);
    512: }

    516: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp,Vec ptr,Vec *result)
    517: {
    518:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;

    522:   if (!ptr) {
    523:     if (!dgmres->sol_temp) {
    524:       VecDuplicate(ksp->vec_sol,&dgmres->sol_temp);
    525:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)dgmres->sol_temp);
    526:     }
    527:     ptr = dgmres->sol_temp;
    528:   }
    529:   if (!dgmres->nrs) {
    530:     /* allocate the work area */
    531:     PetscMalloc1(dgmres->max_k,&dgmres->nrs);
    532:     PetscLogObjectMemory((PetscObject)ksp,dgmres->max_k*sizeof(PetscScalar));
    533:   }

    535:   KSPDGMRESBuildSoln(dgmres->nrs,ksp->vec_sol,ptr,ksp,dgmres->it);
    536:   if (result) *result = ptr;
    537:   return(0);
    538: }

    542: PetscErrorCode KSPView_DGMRES(KSP ksp,PetscViewer viewer)
    543: {
    544:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    546:   PetscBool      iascii,isharmonic;

    549:   KSPView_GMRES(ksp,viewer);
    550:   PetscObjectTypeCompare((PetscObject) viewer,PETSCVIEWERASCII,&iascii);
    551:   if (iascii) {
    552:     if (dgmres->force) PetscViewerASCIIPrintf(viewer, "   DGMRES: Adaptive strategy is used: FALSE\n");
    553:     else PetscViewerASCIIPrintf(viewer, "   DGMRES: Adaptive strategy is used: TRUE\n");
    554:     PetscOptionsHasName(NULL, "-ksp_dgmres_harmonic_ritz", &isharmonic);
    555:     if (isharmonic) {
    556:       PetscViewerASCIIPrintf(viewer, "  DGMRES: Frequency of extracted eigenvalues = %D using Harmonic Ritz values \n", dgmres->neig);
    557:     } else {
    558:       PetscViewerASCIIPrintf(viewer, "  DGMRES: Frequency of extracted eigenvalues = %D using Ritz values \n", dgmres->neig);
    559:     }
    560:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Total number of extracted eigenvalues = %D\n", dgmres->r);
    561:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Maximum number of eigenvalues set to be extracted = %D\n", dgmres->max_neig);
    562:     PetscViewerASCIIPrintf(viewer, "  DGMRES: relaxation parameter for the adaptive strategy(smv)  = %g\n", dgmres->smv);
    563:     PetscViewerASCIIPrintf(viewer, "  DGMRES: Number of matvecs : %D\n", dgmres->matvecs);
    564:   }
    565:   return(0);
    566: }

    568: /* New DGMRES functions */

    572: static PetscErrorCode  KSPDGMRESSetEigen_DGMRES(KSP ksp,PetscInt neig)
    573: {
    574:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    577:   if (neig< 0 && neig >dgmres->max_k) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The value of neig must be positive and less than the restart value ");
    578:   dgmres->neig=neig;
    579:   return(0);
    580: }

    584: static PetscErrorCode  KSPDGMRESSetMaxEigen_DGMRES(KSP ksp,PetscInt max_neig)
    585: {
    586:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    589:   if (max_neig < 0 && max_neig >dgmres->max_k) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The value of max_neig must be positive and less than the restart value ");
    590:   dgmres->max_neig=max_neig;
    591:   return(0);
    592: }

    596: static PetscErrorCode  KSPDGMRESSetRatio_DGMRES(KSP ksp,PetscReal ratio)
    597: {
    598:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    601:   if (ratio <= 0) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The relaxation parameter value must be positive");
    602:   dgmres->smv=ratio;
    603:   return(0);
    604: }

    608: static PetscErrorCode  KSPDGMRESForce_DGMRES(KSP ksp,PetscBool force)
    609: {
    610:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    613:   dgmres->force = force;
    614:   return(0);
    615: }

    617: extern PetscErrorCode KSPSetFromOptions_GMRES(PetscOptions *PetscOptionsObject,KSP);

    621: PetscErrorCode KSPSetFromOptions_DGMRES(PetscOptions *PetscOptionsObject,KSP ksp)
    622: {
    624:   PetscInt       neig;
    625:   PetscInt       max_neig;
    626:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    627:   PetscBool      flg;

    630:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    631:   PetscOptionsHead(PetscOptionsObject,"KSP DGMRES Options");
    632:   PetscOptionsInt("-ksp_dgmres_eigen","Number of smallest eigenvalues to extract at each restart","KSPDGMRESSetEigen",dgmres->neig, &neig, &flg);
    633:   if (flg) {
    634:     KSPDGMRESSetEigen(ksp, neig);
    635:   }
    636:   PetscOptionsInt("-ksp_dgmres_max_eigen","Maximum Number of smallest eigenvalues to extract ","KSPDGMRESSetMaxEigen",dgmres->max_neig, &max_neig, &flg);
    637:   if (flg) {
    638:     KSPDGMRESSetMaxEigen(ksp, max_neig);
    639:   }
    640:   PetscOptionsReal("-ksp_dgmres_ratio","Relaxation parameter for the smaller number of matrix-vectors product allowed","KSPDGMRESSetRatio",dgmres->smv,&dgmres->smv,NULL);
    641:   PetscOptionsBool("-ksp_dgmres_improve","Improve the computation of eigenvalues by solving a new generalized eigenvalue problem (experimental - not stable at this time)",NULL,dgmres->improve,&dgmres->improve,NULL);
    642:   PetscOptionsBool("-ksp_dgmres_force","Sets DGMRES always at restart active, i.e do not use the adaptive strategy","KSPDGMRESForce",dgmres->force,&dgmres->force,NULL);
    643:   PetscOptionsTail();
    644:   return(0);
    645: }

    649: static PetscErrorCode  KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
    650: {
    651:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    653:   PetscInt       i,j, k;
    654:   PetscBLASInt   nr, bmax;
    655:   PetscInt       r = dgmres->r;
    656:   PetscInt       neig;          /* number of eigenvalues to extract at each restart */
    657:   PetscInt       neig1    = dgmres->neig + EIG_OFFSET;  /* max number of eig that can be extracted at each restart */
    658:   PetscInt       max_neig = dgmres->max_neig;  /* Max number of eigenvalues to extract during the iterative process */
    659:   PetscInt       N        = dgmres->max_k+1;
    660:   PetscInt       n        = dgmres->it+1;
    661:   PetscReal      alpha;

    664:   PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    665:   if (dgmres->neig == 0) return(0);
    666:   if (max_neig < (r+neig1) && !dgmres->improve) {
    667:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    668:     return(0);
    669:   }

    671:    KSPDGMRESComputeSchurForm(ksp, &neig);
    672:   /* Form the extended Schur vectors X=VV*Sr */
    673:   if (!XX) {
    674:     VecDuplicateVecs(VEC_VV(0), neig1, &XX);
    675:   }
    676:   for (j = 0; j<neig; j++) {
    677:     VecZeroEntries(XX[j]);
    678:     VecMAXPY(XX[j], n, &SR[j*N], &VEC_VV(0));
    679:   }

    681:   /* Orthogonalize X against U */
    682:   if (!ORTH) {
    683:     PetscMalloc1(max_neig, &ORTH);
    684:   }
    685:   if (r > 0) {
    686:     /* modified Gram-Schmidt */
    687:     for (j = 0; j<neig; j++) {
    688:       for (i=0; i<r; i++) {
    689:         /* First, compute U'*X[j] */
    690:         VecDot(XX[j], UU[i], &alpha);
    691:         /* Then, compute X(j)=X(j)-U*U'*X(j) */
    692:         VecAXPY(XX[j], -alpha, UU[i]);
    693:       }
    694:     }
    695:   }
    696:   /* Compute MX = M^{-1}*A*X */
    697:   if (!MX) {
    698:     VecDuplicateVecs(VEC_VV(0), neig1, &MX);
    699:   }
    700:   for (j = 0; j<neig; j++) {
    701:     KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP);
    702:   }
    703:   dgmres->matvecs += neig;

    705:   if ((r+neig1) > max_neig && dgmres->improve) {    /* Improve the approximate eigenvectors in X by solving a new generalized eigenvalue -- Quite expensive to do this actually */
    706:     KSPDGMRESImproveEig(ksp, neig);
    707:     return(0);   /* We return here since data for M have been improved in  KSPDGMRESImproveEig()*/
    708:   }

    710:   /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
    711:   if (!XMX) {
    712:     PetscMalloc1(neig1*neig1, &XMX);
    713:   }
    714:   for (j = 0; j < neig; j++) {
    715:     VecMDot(MX[j], neig, XX, &(XMX[j*neig1]));
    716:   }

    718:   if (r > 0) {
    719:     /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
    720:     if (!UMX) {
    721:       PetscMalloc1(max_neig*neig1, &UMX);
    722:     }
    723:     for (j = 0; j < neig; j++) {
    724:       VecMDot(MX[j], r, UU, &(UMX[j*max_neig]));
    725:     }
    726:     /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
    727:     if (!XMU) {
    728:       PetscMalloc1(max_neig*neig1, &XMU);
    729:     }
    730:     for (j = 0; j<r; j++) {
    731:       VecMDot(MU[j], neig, XX, &(XMU[j*neig1]));
    732:     }
    733:   }

    735:   /* Form the new matrix T = [T UMX; XMU XMX]; */
    736:   if (!TT) {
    737:     PetscMalloc1(max_neig*max_neig, &TT);
    738:   }
    739:   if (r > 0) {
    740:     /* Add XMU to T */
    741:     for (j = 0; j < r; j++) {
    742:       PetscMemcpy(&(TT[max_neig*j+r]), &(XMU[neig1*j]), neig*sizeof(PetscReal));
    743:     }
    744:     /* Add [UMX; XMX] to T */
    745:     for (j = 0; j < neig; j++) {
    746:       k = r+j;
    747:       PetscMemcpy(&(TT[max_neig*k]), &(UMX[max_neig*j]), r*sizeof(PetscReal));
    748:       PetscMemcpy(&(TT[max_neig*k + r]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
    749:     }
    750:   } else { /* Add XMX to T */
    751:     for (j = 0; j < neig; j++) {
    752:       PetscMemcpy(&(TT[max_neig*j]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
    753:     }
    754:   }

    756:   dgmres->r += neig;
    757:   r          = dgmres->r;
    758:   PetscBLASIntCast(r,&nr);
    759:   /*LU Factorize T with Lapack xgetrf routine */

    761:   PetscBLASIntCast(max_neig,&bmax);
    762:   if (!TTF) {
    763:     PetscMalloc1(bmax*bmax, &TTF);
    764:   }
    765:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
    766:   if (!INVP) {
    767:     PetscMalloc1(bmax, &INVP);
    768:   }
    769: #if defined(PETSC_MISSING_LAPACK_GETRF)
    770:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
    771: #else
    772:   {
    773:     PetscBLASInt info;
    774:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
    775:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
    776:   }
    777: #endif

    779:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
    780:   if (!UU) {
    781:     VecDuplicateVecs(VEC_VV(0), max_neig, &UU);
    782:     VecDuplicateVecs(VEC_VV(0), max_neig, &MU);
    783:   }
    784:   for (j=0; j<neig; j++) {
    785:     VecCopy(XX[j], UU[r-neig+j]);
    786:     VecCopy(MX[j], MU[r-neig+j]);
    787:   }
    788:   PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    789:   return(0);
    790: }

    794: static PetscErrorCode  KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
    795: {
    796:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    798:   PetscInt       N = dgmres->max_k + 1, n=dgmres->it+1;
    799:   PetscBLASInt   bn, bN;
    800:   PetscReal      *A;
    801:   PetscBLASInt   ihi;
    802:   PetscBLASInt   ldA;          /* leading dimension of A */
    803:   PetscBLASInt   ldQ;          /* leading dimension of Q */
    804:   PetscReal      *Q;           /*  orthogonal matrix of  (left) schur vectors */
    805:   PetscReal      *work;        /* working vector */
    806:   PetscBLASInt   lwork;        /* size of the working vector */
    807:   PetscInt       *perm;        /* Permutation vector to sort eigenvalues */
    808:   PetscInt       i, j;
    809:   PetscBLASInt   NbrEig;       /* Number of eigenvalues really extracted */
    810:   PetscReal      *wr, *wi, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
    811:   PetscBLASInt   *select;
    812:   PetscBLASInt   *iwork;
    813:   PetscBLASInt   liwork;
    814:   PetscScalar    *Ht;           /* Transpose of the Hessenberg matrix */
    815:   PetscScalar    *t;            /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
    816:   PetscBLASInt   *ipiv;         /* Permutation vector to be used in LAPACK */
    817:   PetscBool      flag;            /* determine whether to use Ritz vectors or harmonic Ritz vectors */

    820:   PetscBLASIntCast(n,&bn);
    821:   PetscBLASIntCast(N,&bN);
    822:   ihi  = ldQ = bn;
    823:   ldA  = bN;
    824:   PetscBLASIntCast(5*N,&lwork);

    826: #if defined(PETSC_USE_COMPLEX)
    827:   SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "NO SUPPORT FOR COMPLEX VALUES AT THIS TIME");
    828: #endif

    830:   PetscMalloc1(ldA*ldA, &A);
    831:   PetscMalloc1(ldQ*n, &Q);
    832:   PetscMalloc1(lwork, &work);
    833:   if (!dgmres->wr) {
    834:     PetscMalloc1(n, &dgmres->wr);
    835:     PetscMalloc1(n, &dgmres->wi);
    836:   }
    837:   wr   = dgmres->wr;
    838:   wi   = dgmres->wi;
    839:   PetscMalloc1(n,&modul);
    840:   PetscMalloc1(n,&perm);
    841:   /* copy the Hessenberg matrix to work space */
    842:   PetscMemcpy(A, dgmres->hes_origin, ldA*ldA*sizeof(PetscReal));
    843:   PetscOptionsHasName(NULL, "-ksp_dgmres_harmonic_ritz", &flag);
    844:   if (flag) {
    845:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    846:     /* Transpose the Hessenberg matrix */
    847:     PetscMalloc1(bn*bn, &Ht);
    848:     for (i = 0; i < bn; i++) {
    849:       for (j = 0; j < bn; j++) {
    850:         Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
    851:       }
    852:     }

    854:     /* Solve the system H^T*t = h_{m+1,m}e_m */
    855:     PetscCalloc1(bn, &t);
    856:     t[bn-1] = dgmres->hes_origin[(bn -1) * ldA + bn]; /* Pick the last element H(m+1,m) */
    857:     PetscMalloc1(bn, &ipiv);
    858:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
    859: #if   defined(PETSC_MISSING_LAPACK_GESV)
    860:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GESV - Lapack routine is unavailable.");
    861: #else
    862:     {
    863:       PetscBLASInt info;
    864:       PetscBLASInt nrhs = 1;
    865:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
    866:       if (info) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB, "Error while calling the Lapack routine DGESV");
    867:     }
    868: #endif
    869:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    870:     for (i = 0; i < bn; i++) A[(bn-1)*bn+i] += t[i];
    871:     PetscFree(t);
    872:     PetscFree(Ht);
    873:   }
    874:   /* Compute eigenvalues with the Schur form */
    875: #if defined(PETSC_MISSING_LAPACK_HSEQR)
    876:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable.");
    877: #else
    878:   {
    879:     PetscBLASInt info;
    880:     PetscBLASInt ilo = 1;
    881:     PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
    882:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XHSEQR %d",(int) info);
    883:   }
    884: #endif
    885:   PetscFree(work);

    887:   /* sort the eigenvalues */
    888:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
    889:   for (i=0; i<n; i++) perm[i] = i;

    891:   PetscSortRealWithPermutation(n, modul, perm);
    892:   /* save the complex modulus of the largest eigenvalue in magnitude */
    893:   if (dgmres->lambdaN < modul[perm[n-1]]) dgmres->lambdaN=modul[perm[n-1]];
    894:   /* count the number of extracted eigenvalues (with complex conjugates) */
    895:   NbrEig = 0;
    896:   while (NbrEig < dgmres->neig) {
    897:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
    898:     else NbrEig += 1;
    899:   }
    900:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

    902:   PetscCalloc1(n, &select);

    904:   if (!dgmres->GreatestEig) {
    905:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
    906:   } else {
    907:     for (j = 0; j < NbrEig; j++) select[perm[n-j-1]] = 1;
    908:   }
    909:   /* call Lapack dtrsen */
    910:   lwork  =  PetscMax(1, 4 * NbrEig *(bn-NbrEig));
    911:   liwork = PetscMax(1, 2 * NbrEig *(bn-NbrEig));
    912:   PetscMalloc1(lwork, &work);
    913:   PetscMalloc1(liwork, &iwork);
    914: #if defined(PETSC_MISSING_LAPACK_TRSEN)
    915:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable.");
    916: #else
    917:   {
    918:     PetscBLASInt info;
    919:     PetscReal    CondEig;         /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
    920:     PetscReal    CondSub;         /* estimated reciprocal condition number of the specified invariant subspace. */
    921:     PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
    922:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
    923:   }
    924: #endif
    925:   PetscFree(select);

    927:   /* Extract the Schur vectors */
    928:   for (j = 0; j < NbrEig; j++) {
    929:     PetscMemcpy(&SR[j*N], &(Q[j*ldQ]), n*sizeof(PetscReal));
    930:   }
    931:   *neig = NbrEig;
    932:   PetscFree(A);
    933:   PetscFree(work);
    934:   PetscFree(perm);
    935:   PetscFree(work);
    936:   PetscFree(iwork);
    937:   PetscFree(modul);
    938:   PetscFree(Q);
    939:   return(0);
    940: }

    944: static PetscErrorCode  KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
    945: {
    946:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    947:   PetscInt       i, r     = dgmres->r;
    949:   PetscReal      alpha    = 1.0;
    950:   PetscInt       max_neig = dgmres->max_neig;
    951:   PetscBLASInt   br,bmax;
    952:   PetscReal      lambda = dgmres->lambdaN;

    955:   PetscBLASIntCast(r,&br);
    956:   PetscBLASIntCast(max_neig,&bmax);
    957:   PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
    958:   if (!r) {
    959:     VecCopy(x,y);
    960:     return(0);
    961:   }
    962:   /* Compute U'*x */
    963:   if (!X1) {
    964:     PetscMalloc1(bmax, &X1);
    965:     PetscMalloc1(bmax, &X2);
    966:   }
    967:   VecMDot(x, r, UU, X1);

    969:   /* Solve T*X1=X2 for X1*/
    970:   PetscMemcpy(X2, X1, br*sizeof(PetscReal));
    971: #if defined(PETSC_MISSING_LAPACK_GETRS)
    972:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable.");
    973: #else
    974:   {
    975:     PetscBLASInt info;
    976:     PetscBLASInt nrhs = 1;
    977:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
    978:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRS %d", (int) info);
    979:   }
    980: #endif
    981:   /* Iterative refinement -- is it really necessary ?? */
    982:   if (!WORK) {
    983:     PetscMalloc1(3*bmax, &WORK);
    984:     PetscMalloc1(bmax, &IWORK);
    985:   }
    986: #if defined(PETSC_MISSING_LAPACK_GERFS)
    987:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GERFS - Lapack routine is unavailable.");
    988: #else
    989:   {
    990:     PetscBLASInt info;
    991:     PetscReal    berr, ferr;
    992:     PetscBLASInt nrhs = 1;
    993:     PetscStackCallBLAS("LAPACKgerfs",LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax,X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
    994:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGERFS %d", (int) info);
    995:   }
    996: #endif

    998:   for (i = 0; i < r; i++) X2[i] =  X1[i]/lambda - X2[i];

    1000:   /* Compute X2=U*X2 */
    1001:   VecZeroEntries(y);
    1002:   VecMAXPY(y, r, X2, UU);
    1003:   VecAXPY(y, alpha, x);

    1005:   PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
    1006:   return(0);
    1007: }

    1011: static PetscErrorCode  KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
    1012: {
    1013:   KSP_DGMRES   *dgmres = (KSP_DGMRES*) ksp->data;
    1014:   PetscInt     j,r_old, r = dgmres->r;
    1015:   PetscBLASInt i     = 0;
    1016:   PetscInt     neig1 = dgmres->neig + EIG_OFFSET;
    1017:   PetscInt     bmax  = dgmres->max_neig;
    1018:   PetscInt     aug   = r + neig;         /* actual size of the augmented invariant basis */
    1019:   PetscInt     aug1  = bmax+neig1;       /* maximum size of the augmented invariant basis */
    1020:   PetscBLASInt ldA;            /* leading dimension of AUAU and AUU*/
    1021:   PetscBLASInt N;              /* size of AUAU */
    1022:   PetscReal    *Q;             /*  orthogonal matrix of  (left) schur vectors */
    1023:   PetscReal    *Z;             /*  orthogonal matrix of  (right) schur vectors */
    1024:   PetscReal    *work;          /* working vector */
    1025:   PetscBLASInt lwork;          /* size of the working vector */
    1026:   PetscInt     *perm;          /* Permutation vector to sort eigenvalues */
    1027:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
    1028:   PetscInt     ierr;
    1029:   PetscBLASInt NbrEig = 0,nr,bm;
    1030:   PetscBLASInt *select;
    1031:   PetscBLASInt liwork, *iwork;

    1034:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
    1035:   if (!AUU) {
    1036:     PetscMalloc1(aug1*aug1, &AUU);
    1037:     PetscMalloc1(aug1*aug1, &AUAU);
    1038:   }
    1039:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
    1040:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
    1041:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
    1042:   for (j=0; j < r; j++) {
    1043:     VecMDot(UU[j], r, MU, &AUU[j*aug1]);
    1044:   }
    1045:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
    1046:   for (j = 0; j < neig; j++) {
    1047:     VecMDot(XX[j], r, MU, &AUU[(r+j) *aug1]);
    1048:   }
    1049:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
    1050:   for (j = 0; j < r; j++) {
    1051:     VecMDot(UU[j], neig, MX, &AUU[j*aug1+r]);
    1052:   }
    1053:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
    1054:   for (j = 0; j < neig; j++) {
    1055:     VecMDot(XX[j], neig, MX, &AUU[(r+j) *aug1 + r]);
    1056:   }

    1058:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
    1059:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
    1060:   for (j=0; j < r; j++) {
    1061:     VecMDot(MU[j], r, MU, &AUAU[j*aug1]);
    1062:   }
    1063:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
    1064:   for (j = 0; j < neig; j++) {
    1065:     VecMDot(MX[j], r, MU, &AUAU[(r+j) *aug1]);
    1066:   }
    1067:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
    1068:   for (j = 0; j < r; j++) {
    1069:     VecMDot(MU[j], neig, MX, &AUAU[j*aug1+r]);
    1070:   }
    1071:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
    1072:   for (j = 0; j < neig; j++) {
    1073:     VecMDot(MX[j], neig, MX, &AUAU[(r+j) *aug1 + r]);
    1074:   }

    1076:   /* Computation of the eigenvectors */
    1077:   PetscBLASIntCast(aug1,&ldA);
    1078:   PetscBLASIntCast(aug,&N);
    1079:   lwork = 8 * N + 20; /* sizeof the working space */
    1080:   PetscMalloc1(N, &wr);
    1081:   PetscMalloc1(N, &wi);
    1082:   PetscMalloc1(N, &beta);
    1083:   PetscMalloc1(N, &modul);
    1084:   PetscMalloc1(N, &perm);
    1085:   PetscMalloc1(N*N, &Q);
    1086:   PetscMalloc1(N*N, &Z);
    1087:   PetscMalloc1(lwork, &work);
    1088: #if defined(PETSC_MISSING_LAPACK_GGES)
    1089:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
    1090: #else
    1091:   {
    1092:     PetscBLASInt info;
    1093:     PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
    1094:     if (info) SETERRQ1 (PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGGES %d", (int) info);
    1095:   }
    1096: #endif
    1097:   for (i=0; i<N; i++) {
    1098:     if (beta[i] !=0.0) {
    1099:       wr[i] /=beta[i];
    1100:       wi[i] /=beta[i];
    1101:     }
    1102:   }
    1103:   /* sort the eigenvalues */
    1104:   for (i=0; i<N; i++) modul[i]=PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
    1105:   for (i=0; i<N; i++) perm[i] = i;
    1106:   PetscSortRealWithPermutation(N, modul, perm);
    1107:   /* Save the norm of the largest eigenvalue */
    1108:   if (dgmres->lambdaN < modul[perm[N-1]]) dgmres->lambdaN = modul[perm[N-1]];
    1109:   /* Allocate space to extract the first r schur vectors   */
    1110:   if (!SR2) {
    1111:     PetscMalloc1(aug1*bmax, &SR2);
    1112:   }
    1113:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
    1114:   while (NbrEig < bmax) {
    1115:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
    1116:     else NbrEig += 2;
    1117:   }
    1118:   if (NbrEig > bmax) NbrEig = bmax - 1;
    1119:   r_old     = r; /* previous size of r */
    1120:   dgmres->r = r = NbrEig;

    1122:   /* Select the eigenvalues to reorder */
    1123:   PetscCalloc1(N, &select);
    1124:   if (!dgmres->GreatestEig) {
    1125:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
    1126:   } else {
    1127:     for (j = 0; j < NbrEig; j++) select[perm[N-j-1]] = 1;
    1128:   }
    1129:   /* Reorder and extract the new <r> schur vectors */
    1130:   lwork  = PetscMax(4 * N + 16,  2 * NbrEig *(N - NbrEig));
    1131:   liwork = PetscMax(N + 6,  2 * NbrEig *(N - NbrEig));
    1132:   PetscFree(work);
    1133:   PetscMalloc1(lwork, &work);
    1134:   PetscMalloc1(liwork, &iwork);
    1135: #if defined(PETSC_MISSING_LAPACK_TGSEN)
    1136:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable.");
    1137: #else
    1138:   {
    1139:     PetscBLASInt info;
    1140:     PetscReal    Dif[2];
    1141:     PetscBLASInt ijob  = 2;
    1142:     PetscBLASInt wantQ = 1, wantZ = 1;
    1143:     PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&ijob, &wantQ, &wantZ, select, &N, AUAU, &ldA, AUU, &ldA, wr, wi, beta, Q, &N, Z, &N, &NbrEig, NULL, NULL, &(Dif[0]), work, &lwork, iwork, &liwork, &info));
    1144:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
    1145:   }
    1146: #endif
    1147:   PetscFree(select);

    1149:   for (j=0; j<r; j++) {
    1150:     PetscMemcpy(&SR2[j*aug1], &(Z[j*N]), N*sizeof(PetscReal));
    1151:   }

    1153:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
    1154:    -- save it temporarily in MU */
    1155:   for (j = 0; j < r; j++) {
    1156:     VecZeroEntries(MU[j]);
    1157:     VecMAXPY(MU[j], r_old, &SR2[j*aug1], UU);
    1158:     VecMAXPY(MU[j], neig, &SR2[j*aug1+r_old], XX);
    1159:   }
    1160:   /* Form T = U'*MU*U */
    1161:   for (j = 0; j < r; j++) {
    1162:     VecCopy(MU[j], UU[j]);
    1163:     KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP);
    1164:   }
    1165:   dgmres->matvecs += r;
    1166:   for (j = 0; j < r; j++) {
    1167:     VecMDot(MU[j], r, UU, &TT[j*bmax]);
    1168:   }
    1169:   /* Factorize T */
    1170:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
    1171:   PetscBLASIntCast(r,&nr);
    1172:   PetscBLASIntCast(bmax,&bm);
    1173: #if defined(PETSC_MISSING_LAPACK_GETRF)
    1174:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
    1175: #else
    1176:   {
    1177:     PetscBLASInt info;
    1178:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
    1179:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
    1180:   }
    1181: #endif
    1182:   /* Free Memory */
    1183:   PetscFree(wr);
    1184:   PetscFree(wi);
    1185:   PetscFree(beta);
    1186:   PetscFree(modul);
    1187:   PetscFree(perm);
    1188:   PetscFree(Q);
    1189:   PetscFree(Z);
    1190:   PetscFree(work);
    1191:   PetscFree(iwork);
    1192:   return(0);
    1193: }

    1195: /* end new DGMRES functions */

    1197: /*MC
    1198:      KSPDGMRES - Implements the deflated GMRES as defined in [1,2].
    1199:                  In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the
    1200:                  stagnation occurs.

    1202:    Options Database Keys:
    1203:    GMRES Options (inherited):
    1204: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    1205: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    1206: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    1207:                              vectors are allocated as needed)
    1208: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    1209: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    1210: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    1211:                                    stability of the classical Gram-Schmidt  orthogonalization.
    1212: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    1214:    DGMRES Options Database Keys:
    1215: +   -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
    1216: .   -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative
    1217:                                        process
    1218: .   -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
    1219: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
    1220:                                                    parsed by PetscOptionsGetViewer().  If neig > 1, viewerspec should
    1221:                                                    end with ":append".  No vectors will be viewed if the adaptive
    1222:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
    1223:                                                    be given.
    1224:                                                    The deflation vectors span a subspace that may be a good
    1225:                                                    approximation of the subspace of smallest eigenvectors of the
    1226:                                                    preconditioned operator, so this option can aid in understanding
    1227:                                                    the performance of a preconditioner.

    1229:  Level: beginner

    1231:  Notes: Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

    1233:  References:

    1235:  [1]Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318.
    1236:  [2]On the performance of various adaptive preconditioned GMRES strategies, 5(1998), 101-121.
    1237:  [3] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

    1239:  Contributed by: Desire NUENTSA WAKAM,INRIA

    1241:  .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
    1242:  KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    1243:  KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    1244:  KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

    1246:  M*/

    1250: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
    1251: {
    1252:   KSP_DGMRES     *dgmres;

    1256:   PetscNewLog(ksp,&dgmres);
    1257:   ksp->data = (void*) dgmres;

    1259:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    1260:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

    1262:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
    1263:   ksp->ops->setup                        = KSPSetUp_DGMRES;
    1264:   ksp->ops->solve                        = KSPSolve_DGMRES;
    1265:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
    1266:   ksp->ops->view                         = KSPView_DGMRES;
    1267:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
    1268:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    1269:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    1271:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    1272:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    1273:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    1274:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
    1275:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    1276:   /* -- New functions defined in DGMRES -- */
    1277:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C",KSPDGMRESSetEigen_DGMRES);
    1278:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C",KSPDGMRESSetMaxEigen_DGMRES);
    1279:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C",KSPDGMRESSetRatio_DGMRES);
    1280:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C",KSPDGMRESForce_DGMRES);
    1281:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C",KSPDGMRESComputeSchurForm_DGMRES);
    1282:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C",KSPDGMRESComputeDeflationData_DGMRES);
    1283:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C",KSPDGMRESApplyDeflation_DGMRES);
    1284:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES);

    1286:   PetscLogEventRegister("DGMRESComputeDefl", KSP_CLASSID, &KSP_DGMRESComputeDeflationData);
    1287:   PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation);

    1289:   dgmres->haptol         = 1.0e-30;
    1290:   dgmres->q_preallocate  = 0;
    1291:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    1292:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    1293:   dgmres->nrs            = 0;
    1294:   dgmres->sol_temp       = 0;
    1295:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
    1296:   dgmres->Rsvd           = 0;
    1297:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    1298:   dgmres->orthogwork     = 0;

    1300:   /* Default values for the deflation */
    1301:   dgmres->r           = 0;
    1302:   dgmres->neig        = DGMRES_DEFAULT_EIG;
    1303:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG-1;
    1304:   dgmres->lambdaN     = 0.0;
    1305:   dgmres->smv         = SMV;
    1306:   dgmres->matvecs     = 0;
    1307:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
    1308:   dgmres->HasSchur    = PETSC_FALSE;
    1309:   return(0);
    1310: }