Actual source code: dgmres.c
petsc-3.10.5 2019-03-28
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      1: /*
      2:  This file implements the deflated GMRES.

      4:  */

      6:  #include <../src/ksp/ksp/impls/gmres/dgmres/dgmresimpl.h>

      8: PetscLogEvent KSP_DGMRESComputeDeflationData, KSP_DGMRESApplyDeflation;

     10: #define GMRES_DELTA_DIRECTIONS 10
     11: #define GMRES_DEFAULT_MAXK     30
     12: static PetscErrorCode    KSPDGMRESGetNewVectors(KSP,PetscInt);
     13: static PetscErrorCode    KSPDGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
     14: static PetscErrorCode    KSPDGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

     16: PetscErrorCode  KSPDGMRESSetEigen(KSP ksp,PetscInt nb_eig)
     17: {

     21:   PetscTryMethod((ksp),"KSPDGMRESSetEigen_C",(KSP,PetscInt),(ksp,nb_eig));
     22:   return(0);
     23: }
     24: PetscErrorCode  KSPDGMRESSetMaxEigen(KSP ksp,PetscInt max_neig)
     25: {

     29:   PetscTryMethod((ksp),"KSPDGMRESSetMaxEigen_C",(KSP,PetscInt),(ksp,max_neig));
     30:   return(0);
     31: }
     32: PetscErrorCode  KSPDGMRESForce(KSP ksp,PetscBool force)
     33: {

     37:   PetscTryMethod((ksp),"KSPDGMRESForce_C",(KSP,PetscBool),(ksp,force));
     38:   return(0);
     39: }
     40: PetscErrorCode  KSPDGMRESSetRatio(KSP ksp,PetscReal ratio)
     41: {

     45:   PetscTryMethod((ksp),"KSPDGMRESSetRatio_C",(KSP,PetscReal),(ksp,ratio));
     46:   return(0);
     47: }
     48: PetscErrorCode  KSPDGMRESComputeSchurForm(KSP ksp,PetscInt *neig)
     49: {

     53:   PetscUseMethod((ksp),"KSPDGMRESComputeSchurForm_C",(KSP, PetscInt*),(ksp, neig));
     54:   return(0);
     55: }
     56: PetscErrorCode  KSPDGMRESComputeDeflationData(KSP ksp,PetscInt *curneigh)
     57: {

     61:   PetscUseMethod((ksp),"KSPDGMRESComputeDeflationData_C",(KSP,PetscInt*),(ksp,curneigh));
     62:   return(0);
     63: }
     64: PetscErrorCode  KSPDGMRESApplyDeflation(KSP ksp, Vec x, Vec y)
     65: {

     69:   PetscUseMethod((ksp),"KSPDGMRESApplyDeflation_C",(KSP, Vec, Vec),(ksp, x, y));
     70:   return(0);
     71: }

     73: PetscErrorCode  KSPDGMRESImproveEig(KSP ksp, PetscInt neig)
     74: {

     78:   PetscUseMethod((ksp), "KSPDGMRESImproveEig_C",(KSP, PetscInt),(ksp, neig));
     79:   return(0);
     80: }

     82: PetscErrorCode  KSPSetUp_DGMRES(KSP ksp)
     83: {
     85:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
     86:   PetscInt       neig    = dgmres->neig+EIG_OFFSET;
     87:   PetscInt       max_k   = dgmres->max_k+1;

     90:   KSPSetUp_GMRES(ksp);
     91:   if (!dgmres->neig) return(0);

     93:   /* Allocate workspace for the Schur vectors*/
     94:   PetscMalloc1(neig*max_k, &SR);
     95:   dgmres->wr    = NULL;
     96:   dgmres->wi    = NULL;
     97:   dgmres->perm  = NULL;
     98:   dgmres->modul = NULL;
     99:   dgmres->Q     = NULL;
    100:   dgmres->Z     = NULL;

    102:   UU   = NULL;
    103:   XX   = NULL;
    104:   MX   = NULL;
    105:   AUU  = NULL;
    106:   XMX  = NULL;
    107:   XMU  = NULL;
    108:   UMX  = NULL;
    109:   AUAU = NULL;
    110:   TT   = NULL;
    111:   TTF  = NULL;
    112:   INVP = NULL;
    113:   X1   = NULL;
    114:   X2   = NULL;
    115:   MU   = NULL;
    116:   return(0);
    117: }

    119: /*
    120:  Run GMRES, possibly with restart.  Return residual history if requested.
    121:  input parameters:

    123:  .       gmres  - structure containing parameters and work areas

    125:  output parameters:
    126:  .        nres    - residuals (from preconditioned system) at each step.
    127:  If restarting, consider passing nres+it.  If null,
    128:  ignored
    129:  .        itcount - number of iterations used.  nres[0] to nres[itcount]
    130:  are defined.  If null, ignored.

    132:  Notes:
    133:  On entry, the value in vector VEC_VV(0) should be the initial residual
    134:  (this allows shortcuts where the initial preconditioned residual is 0).
    135:  */
    136: PetscErrorCode KSPDGMRESCycle(PetscInt *itcount,KSP ksp)
    137: {
    138:   KSP_DGMRES     *dgmres = (KSP_DGMRES*)(ksp->data);
    139:   PetscReal      res_norm,res,hapbnd,tt;
    141:   PetscInt       it     = 0;
    142:   PetscInt       max_k  = dgmres->max_k;
    143:   PetscBool      hapend = PETSC_FALSE;
    144:   PetscReal      res_old;
    145:   PetscInt       test = 0;

    148:   VecNormalize(VEC_VV(0),&res_norm);
    149:   KSPCheckNorm(ksp,res_norm);
    150:   res     = res_norm;
    151:   *GRS(0) = res_norm;

    153:   /* check for the convergence */
    154:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    155:   ksp->rnorm = res;
    156:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    157:   dgmres->it = (it - 1);
    158:   KSPLogResidualHistory(ksp,res);
    159:   KSPMonitor(ksp,ksp->its,res);
    160:   if (!res) {
    161:     if (itcount) *itcount = 0;
    162:     ksp->reason = KSP_CONVERGED_ATOL;
    163:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
    164:     return(0);
    165:   }
    166:   /* record the residual norm to test if deflation is needed */
    167:   res_old = res;

    169:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    170:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
    171:     if (it) {
    172:       KSPLogResidualHistory(ksp,res);
    173:       KSPMonitor(ksp,ksp->its,res);
    174:     }
    175:     dgmres->it = (it - 1);
    176:     if (dgmres->vv_allocated <= it + VEC_OFFSET + 1) {
    177:       KSPDGMRESGetNewVectors(ksp,it+1);
    178:     }
    179:     if (dgmres->r > 0) {
    180:       if (ksp->pc_side == PC_LEFT) {
    181:         /* Apply the first preconditioner */
    182:         KSP_PCApplyBAorAB(ksp,VEC_VV(it), VEC_TEMP,VEC_TEMP_MATOP);
    183:         /* Then apply Deflation as a preconditioner */
    184:         KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_VV(1+it));
    185:       } else if (ksp->pc_side == PC_RIGHT) {
    186:         KSPDGMRESApplyDeflation(ksp, VEC_VV(it), VEC_TEMP);
    187:         KSP_PCApplyBAorAB(ksp, VEC_TEMP, VEC_VV(1+it), VEC_TEMP_MATOP);
    188:       }
    189:     } else {
    190:       KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
    191:     }
    192:     dgmres->matvecs += 1;
    193:     /* update hessenberg matrix and do Gram-Schmidt */
    194:     (*dgmres->orthog)(ksp,it);

    196:     /* vv(i+1) . vv(i+1) */
    197:     VecNormalize(VEC_VV(it+1),&tt);
    198:     /* save the magnitude */
    199:     *HH(it+1,it)  = tt;
    200:     *HES(it+1,it) = tt;

    202:     /* check for the happy breakdown */
    203:     hapbnd = PetscAbsScalar(tt / *GRS(it));
    204:     if (hapbnd > dgmres->haptol) hapbnd = dgmres->haptol;
    205:     if (tt < hapbnd) {
    206:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
    207:       hapend = PETSC_TRUE;
    208:     }
    209:     KSPDGMRESUpdateHessenberg(ksp,it,hapend,&res);

    211:     it++;
    212:     dgmres->it = (it-1);     /* For converged */
    213:     ksp->its++;
    214:     ksp->rnorm = res;
    215:     if (ksp->reason) break;

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

    219:     /* Catch error in happy breakdown and signal convergence and break from loop */
    220:     if (hapend) {
    221:       if (!ksp->reason) {
    222:         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);
    223:         else {
    224:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    225:           break;
    226:         }
    227:       }
    228:     }
    229:   }

    231:   /* Monitor if we know that we will not return for a restart */
    232:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
    233:     KSPLogResidualHistory(ksp,res);
    234:     KSPMonitor(ksp,ksp->its,res);
    235:   }
    236:   if (itcount) *itcount = it;

    238:   /*
    239:    Down here we have to solve for the "best" coefficients of the Krylov
    240:    columns, add the solution values together, and possibly unwind the
    241:    preconditioning from the solution
    242:    */
    243:   /* Form the solution (or the solution so far) */
    244:   KSPDGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);

    246:   /* Compute data for the deflation to be used during the next restart */
    247:   if (!ksp->reason && ksp->its < ksp->max_it) {
    248:     test = max_k *PetscLogReal(ksp->rtol/res) /PetscLogReal(res/res_old);
    249:     /* Compute data for the deflation if the residual rtol will not be reached in the remaining number of steps allowed  */
    250:     if ((test > dgmres->smv*(ksp->max_it-ksp->its)) || dgmres->force) {
    251:        KSPDGMRESComputeDeflationData(ksp,NULL);
    252:     }
    253:   }
    254:   return(0);
    255: }

    257: PetscErrorCode KSPSolve_DGMRES(KSP ksp)
    258: {
    260:   PetscInt       i,its,itcount;
    261:   KSP_DGMRES     *dgmres    = (KSP_DGMRES*) ksp->data;
    262:   PetscBool      guess_zero = ksp->guess_zero;

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

    267:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    268:   ksp->its        = 0;
    269:   dgmres->matvecs = 0;
    270:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

    272:   itcount     = 0;
    273:   ksp->reason = KSP_CONVERGED_ITERATING;
    274:   while (!ksp->reason) {
    275:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    276:     if (ksp->pc_side == PC_LEFT) {
    277:       dgmres->matvecs += 1;
    278:       if (dgmres->r > 0) {
    279:         KSPDGMRESApplyDeflation(ksp, VEC_VV(0), VEC_TEMP);
    280:         VecCopy(VEC_TEMP, VEC_VV(0));
    281:       }
    282:     }

    284:     KSPDGMRESCycle(&its,ksp);
    285:     itcount += its;
    286:     if (itcount >= ksp->max_it) {
    287:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    288:       break;
    289:     }
    290:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    291:   }
    292:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */

    294:   for (i = 0; i < dgmres->r; i++) {
    295:     VecViewFromOptions(UU[i],(PetscObject)ksp,"-ksp_dgmres_view_deflation_vecs");
    296:   }
    297:   return(0);
    298: }

    300: PetscErrorCode KSPDestroy_DGMRES(KSP ksp)
    301: {
    303:   KSP_DGMRES     *dgmres  = (KSP_DGMRES*) ksp->data;
    304:   PetscInt       neig1    = dgmres->neig+EIG_OFFSET;
    305:   PetscInt       max_neig = dgmres->max_neig;

    308:   if (dgmres->r) {
    309:     VecDestroyVecs(max_neig, &UU);
    310:     VecDestroyVecs(max_neig, &MU);
    311:     if (XX) {
    312:       VecDestroyVecs(neig1, &XX);
    313:       VecDestroyVecs(neig1, &MX);
    314:     }

    316:     PetscFree(TT);
    317:     PetscFree(TTF);
    318:     PetscFree(INVP);

    320:     PetscFree(XMX);
    321:     PetscFree(UMX);
    322:     PetscFree(XMU);
    323:     PetscFree(X1);
    324:     PetscFree(X2);
    325:     PetscFree(dgmres->work);
    326:     PetscFree(dgmres->iwork);
    327:     PetscFree(dgmres->wr);
    328:     PetscFree(dgmres->wi);
    329:     PetscFree(dgmres->modul);
    330:     PetscFree(dgmres->Q);
    331:     PetscFree(ORTH);
    332:     PetscFree(AUAU);
    333:     PetscFree(AUU);
    334:     PetscFree(SR2);
    335:   }
    336:   PetscFree(SR);
    337:   KSPDestroy_GMRES(ksp);
    338:   return(0);
    339: }
    340: /*
    341:  KSPDGMRESBuildSoln - create the solution from the starting vector and the
    342:  current iterates.

    344:  Input parameters:
    345:  nrs - work area of size it + 1.
    346:  vs  - index of initial guess
    347:  vdest - index of result.  Note that vs may == vdest (replace
    348:  guess with the solution).

    350:  This is an internal routine that knows about the GMRES internals.
    351:  */
    352: static PetscErrorCode KSPDGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
    353: {
    354:   PetscScalar    tt;
    356:   PetscInt       ii,k,j;
    357:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) (ksp->data);

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

    362:   /* If it is < 0, no gmres steps have been performed */
    363:   if (it < 0) {
    364:     VecCopy(vs,vdest);     /* VecCopy() is smart, exists immediately if vguess == vdest */
    365:     return(0);
    366:   }
    367:   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)));
    368:   if (*HH(it,it) != 0.0) nrs[it] = *GRS(it) / *HH(it,it);
    369:   else nrs[it] = 0.0;

    371:   for (ii=1; ii<=it; ii++) {
    372:     k  = it - ii;
    373:     tt = *GRS(k);
    374:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    375:     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);
    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:   /* Apply deflation */
    384:   if (ksp->pc_side==PC_RIGHT && dgmres->r > 0) {
    385:     KSPDGMRESApplyDeflation(ksp, VEC_TEMP, VEC_TEMP_MATOP);
    386:     VecCopy(VEC_TEMP_MATOP, VEC_TEMP);
    387:   }
    388:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

    390:   /* add solution to previous solution */
    391:   if (vdest != vs) {
    392:     VecCopy(vs,vdest);
    393:   }
    394:   VecAXPY(vdest,1.0,VEC_TEMP);
    395:   return(0);
    396: }
    397: /*
    398:  Do the scalar work for the orthogonalization.  Return new residual norm.
    399:  */
    400: static PetscErrorCode KSPDGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    401: {
    402:   PetscScalar *hh,*cc,*ss,tt;
    403:   PetscInt    j;
    404:   KSP_DGMRES  *dgmres = (KSP_DGMRES*) (ksp->data);

    407:   hh = HH(0,it);
    408:   cc = CC(0);
    409:   ss = SS(0);

    411:   /* Apply all the previously computed plane rotations to the new column
    412:    of the Hessenberg matrix */
    413:   for (j=1; j<=it; j++) {
    414:     tt  = *hh;
    415:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    416:     hh++;
    417:     *hh = *cc++ * *hh -(*ss++ * tt);
    418:   }

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

    446:     *res = 0.0;
    447:   }
    448:   return(0);
    449: }
    450: /*
    451:  This routine allocates more work vectors, starting from VEC_VV(it).
    452:  */
    453: static PetscErrorCode KSPDGMRESGetNewVectors(KSP ksp,PetscInt it)
    454: {
    455:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    457:   PetscInt       nwork = dgmres->nwork_alloc,k,nalloc;

    460:   nalloc = PetscMin(ksp->max_it,dgmres->delta_allocate);
    461:   /* Adjust the number to allocate to make sure that we don't exceed the
    462:    number of available slots */
    463:   if (it + VEC_OFFSET + nalloc >= dgmres->vecs_allocated) {
    464:     nalloc = dgmres->vecs_allocated - it - VEC_OFFSET;
    465:   }
    466:   if (!nalloc) return(0);

    468:   dgmres->vv_allocated += nalloc;

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

    473:   dgmres->mwork_alloc[nwork] = nalloc;
    474:   for (k=0; k<nalloc; k++) {
    475:     dgmres->vecs[it+VEC_OFFSET+k] = dgmres->user_work[nwork][k];
    476:   }
    477:   dgmres->nwork_alloc++;
    478:   return(0);
    479: }

    481: PetscErrorCode KSPBuildSolution_DGMRES(KSP ksp,Vec ptr,Vec *result)
    482: {
    483:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;

    487:   if (!ptr) {
    488:     if (!dgmres->sol_temp) {
    489:       VecDuplicate(ksp->vec_sol,&dgmres->sol_temp);
    490:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)dgmres->sol_temp);
    491:     }
    492:     ptr = dgmres->sol_temp;
    493:   }
    494:   if (!dgmres->nrs) {
    495:     /* allocate the work area */
    496:     PetscMalloc1(dgmres->max_k,&dgmres->nrs);
    497:     PetscLogObjectMemory((PetscObject)ksp,dgmres->max_k*sizeof(PetscScalar));
    498:   }

    500:   KSPDGMRESBuildSoln(dgmres->nrs,ksp->vec_sol,ptr,ksp,dgmres->it);
    501:   if (result) *result = ptr;
    502:   return(0);
    503: }

    505: PetscErrorCode KSPView_DGMRES(KSP ksp,PetscViewer viewer)
    506: {
    507:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    509:   PetscBool      iascii,isharmonic;

    512:   KSPView_GMRES(ksp,viewer);
    513:   PetscObjectTypeCompare((PetscObject) viewer,PETSCVIEWERASCII,&iascii);
    514:   if (iascii) {
    515:     if (dgmres->force) PetscViewerASCIIPrintf(viewer, "    Adaptive strategy is used: FALSE\n");
    516:     else PetscViewerASCIIPrintf(viewer, "    Adaptive strategy is used: TRUE\n");
    517:     PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &isharmonic);
    518:     if (isharmonic) {
    519:       PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %D using Harmonic Ritz values \n", dgmres->neig);
    520:     } else {
    521:       PetscViewerASCIIPrintf(viewer, "   Frequency of extracted eigenvalues = %D using Ritz values \n", dgmres->neig);
    522:     }
    523:     PetscViewerASCIIPrintf(viewer, "   Total number of extracted eigenvalues = %D\n", dgmres->r);
    524:     PetscViewerASCIIPrintf(viewer, "   Maximum number of eigenvalues set to be extracted = %D\n", dgmres->max_neig);
    525:     PetscViewerASCIIPrintf(viewer, "   relaxation parameter for the adaptive strategy(smv)  = %g\n", dgmres->smv);
    526:     PetscViewerASCIIPrintf(viewer, "   Number of matvecs : %D\n", dgmres->matvecs);
    527:   }
    528:   return(0);
    529: }

    531: /* New DGMRES functions */

    533: PetscErrorCode  KSPDGMRESSetEigen_DGMRES(KSP ksp,PetscInt neig)
    534: {
    535:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    538:   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 ");
    539:   dgmres->neig=neig;
    540:   return(0);
    541: }

    543: static PetscErrorCode  KSPDGMRESSetMaxEigen_DGMRES(KSP ksp,PetscInt max_neig)
    544: {
    545:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    548:   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 ");
    549:   dgmres->max_neig=max_neig;
    550:   return(0);
    551: }

    553: static PetscErrorCode  KSPDGMRESSetRatio_DGMRES(KSP ksp,PetscReal ratio)
    554: {
    555:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    558:   if (ratio <= 0) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE,"The relaxation parameter value must be positive");
    559:   dgmres->smv=ratio;
    560:   return(0);
    561: }

    563: static PetscErrorCode  KSPDGMRESForce_DGMRES(KSP ksp,PetscBool force)
    564: {
    565:   KSP_DGMRES *dgmres = (KSP_DGMRES*) ksp->data;

    568:   dgmres->force = force;
    569:   return(0);
    570: }

    572: PetscErrorCode KSPSetFromOptions_DGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    573: {
    575:   PetscInt       neig;
    576:   PetscInt       max_neig;
    577:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    578:   PetscBool      flg;

    581:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    582:   PetscOptionsHead(PetscOptionsObject,"KSP DGMRES Options");
    583:   PetscOptionsInt("-ksp_dgmres_eigen","Number of smallest eigenvalues to extract at each restart","KSPDGMRESSetEigen",dgmres->neig, &neig, &flg);
    584:   if (flg) {
    585:     KSPDGMRESSetEigen(ksp, neig);
    586:   }
    587:   PetscOptionsInt("-ksp_dgmres_max_eigen","Maximum Number of smallest eigenvalues to extract ","KSPDGMRESSetMaxEigen",dgmres->max_neig, &max_neig, &flg);
    588:   if (flg) {
    589:     KSPDGMRESSetMaxEigen(ksp, max_neig);
    590:   }
    591:   PetscOptionsReal("-ksp_dgmres_ratio","Relaxation parameter for the smaller number of matrix-vectors product allowed","KSPDGMRESSetRatio",dgmres->smv,&dgmres->smv,NULL);
    592:   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);
    593:   PetscOptionsBool("-ksp_dgmres_force","Sets DGMRES always at restart active, i.e do not use the adaptive strategy","KSPDGMRESForce",dgmres->force,&dgmres->force,NULL);
    594:   PetscOptionsTail();
    595:   return(0);
    596: }

    598: PetscErrorCode  KSPDGMRESComputeDeflationData_DGMRES(KSP ksp, PetscInt *ExtrNeig)
    599: {
    600:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    602:   PetscInt       i,j, k;
    603:   PetscBLASInt   nr, bmax;
    604:   PetscInt       r = dgmres->r;
    605:   PetscInt       neig;          /* number of eigenvalues to extract at each restart */
    606:   PetscInt       neig1    = dgmres->neig + EIG_OFFSET;  /* max number of eig that can be extracted at each restart */
    607:   PetscInt       max_neig = dgmres->max_neig;  /* Max number of eigenvalues to extract during the iterative process */
    608:   PetscInt       N        = dgmres->max_k+1;
    609:   PetscInt       n        = dgmres->it+1;
    610:   PetscReal      alpha;

    613:   PetscLogEventBegin(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    614:   if (dgmres->neig == 0 || (max_neig < (r+neig1) && !dgmres->improve)) {
    615:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    616:     return(0);
    617:   }

    619:    KSPDGMRESComputeSchurForm(ksp, &neig);
    620:   /* Form the extended Schur vectors X=VV*Sr */
    621:   if (!XX) {
    622:     VecDuplicateVecs(VEC_VV(0), neig1, &XX);
    623:   }
    624:   for (j = 0; j<neig; j++) {
    625:     VecZeroEntries(XX[j]);
    626:     VecMAXPY(XX[j], n, &SR[j*N], &VEC_VV(0));
    627:   }

    629:   /* Orthogonalize X against U */
    630:   if (!ORTH) {
    631:     PetscMalloc1(max_neig, &ORTH);
    632:   }
    633:   if (r > 0) {
    634:     /* modified Gram-Schmidt */
    635:     for (j = 0; j<neig; j++) {
    636:       for (i=0; i<r; i++) {
    637:         /* First, compute U'*X[j] */
    638:         VecDot(XX[j], UU[i], &alpha);
    639:         /* Then, compute X(j)=X(j)-U*U'*X(j) */
    640:         VecAXPY(XX[j], -alpha, UU[i]);
    641:       }
    642:     }
    643:   }
    644:   /* Compute MX = M^{-1}*A*X */
    645:   if (!MX) {
    646:     VecDuplicateVecs(VEC_VV(0), neig1, &MX);
    647:   }
    648:   for (j = 0; j<neig; j++) {
    649:     KSP_PCApplyBAorAB(ksp, XX[j], MX[j], VEC_TEMP_MATOP);
    650:   }
    651:   dgmres->matvecs += neig;

    653:   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 */
    654:     KSPDGMRESImproveEig(ksp, neig);
    655:     PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    656:     return(0);   /* We return here since data for M have been improved in  KSPDGMRESImproveEig()*/
    657:   }

    659:   /* Compute XMX = X'*M^{-1}*A*X -- size (neig, neig) */
    660:   if (!XMX) {
    661:     PetscMalloc1(neig1*neig1, &XMX);
    662:   }
    663:   for (j = 0; j < neig; j++) {
    664:     VecMDot(MX[j], neig, XX, &(XMX[j*neig1]));
    665:   }

    667:   if (r > 0) {
    668:     /* Compute UMX = U'*M^{-1}*A*X -- size (r, neig) */
    669:     if (!UMX) {
    670:       PetscMalloc1(max_neig*neig1, &UMX);
    671:     }
    672:     for (j = 0; j < neig; j++) {
    673:       VecMDot(MX[j], r, UU, &(UMX[j*max_neig]));
    674:     }
    675:     /* Compute XMU = X'*M^{-1}*A*U -- size(neig, r) */
    676:     if (!XMU) {
    677:       PetscMalloc1(max_neig*neig1, &XMU);
    678:     }
    679:     for (j = 0; j<r; j++) {
    680:       VecMDot(MU[j], neig, XX, &(XMU[j*neig1]));
    681:     }
    682:   }

    684:   /* Form the new matrix T = [T UMX; XMU XMX]; */
    685:   if (!TT) {
    686:     PetscMalloc1(max_neig*max_neig, &TT);
    687:   }
    688:   if (r > 0) {
    689:     /* Add XMU to T */
    690:     for (j = 0; j < r; j++) {
    691:       PetscMemcpy(&(TT[max_neig*j+r]), &(XMU[neig1*j]), neig*sizeof(PetscReal));
    692:     }
    693:     /* Add [UMX; XMX] to T */
    694:     for (j = 0; j < neig; j++) {
    695:       k = r+j;
    696:       PetscMemcpy(&(TT[max_neig*k]), &(UMX[max_neig*j]), r*sizeof(PetscReal));
    697:       PetscMemcpy(&(TT[max_neig*k + r]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
    698:     }
    699:   } else { /* Add XMX to T */
    700:     for (j = 0; j < neig; j++) {
    701:       PetscMemcpy(&(TT[max_neig*j]), &(XMX[neig1*j]), neig*sizeof(PetscReal));
    702:     }
    703:   }

    705:   dgmres->r += neig;
    706:   r          = dgmres->r;
    707:   PetscBLASIntCast(r,&nr);
    708:   /*LU Factorize T with Lapack xgetrf routine */

    710:   PetscBLASIntCast(max_neig,&bmax);
    711:   if (!TTF) {
    712:     PetscMalloc1(bmax*bmax, &TTF);
    713:   }
    714:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
    715:   if (!INVP) {
    716:     PetscMalloc1(bmax, &INVP);
    717:   }
    718: #if defined(PETSC_MISSING_LAPACK_GETRF)
    719:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
    720: #else
    721:   {
    722:     PetscBLASInt info;
    723:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bmax, INVP, &info));
    724:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
    725:   }
    726: #endif

    728:   /* Save X in U and MX in MU for the next cycles and increase the size of the invariant subspace */
    729:   if (!UU) {
    730:     VecDuplicateVecs(VEC_VV(0), max_neig, &UU);
    731:     VecDuplicateVecs(VEC_VV(0), max_neig, &MU);
    732:   }
    733:   for (j=0; j<neig; j++) {
    734:     VecCopy(XX[j], UU[r-neig+j]);
    735:     VecCopy(MX[j], MU[r-neig+j]);
    736:   }
    737:   PetscLogEventEnd(KSP_DGMRESComputeDeflationData, ksp, 0,0,0);
    738:   return(0);
    739: }

    741: PetscErrorCode  KSPDGMRESComputeSchurForm_DGMRES(KSP ksp, PetscInt *neig)
    742: {
    743:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    745:   PetscInt       N = dgmres->max_k + 1, n=dgmres->it+1;
    746:   PetscBLASInt   bn, bN;
    747:   PetscReal      *A;
    748:   PetscBLASInt   ihi;
    749:   PetscBLASInt   ldA;          /* leading dimension of A */
    750:   PetscBLASInt   ldQ;          /* leading dimension of Q */
    751:   PetscReal      *Q;           /*  orthogonal matrix of  (left) schur vectors */
    752:   PetscReal      *work;        /* working vector */
    753:   PetscBLASInt   lwork;        /* size of the working vector */
    754:   PetscInt       *perm;        /* Permutation vector to sort eigenvalues */
    755:   PetscInt       i, j;
    756:   PetscBLASInt   NbrEig;       /* Number of eigenvalues really extracted */
    757:   PetscReal      *wr, *wi, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
    758:   PetscBLASInt   *select;
    759:   PetscBLASInt   *iwork;
    760:   PetscBLASInt   liwork;
    761:   PetscScalar    *Ht;           /* Transpose of the Hessenberg matrix */
    762:   PetscScalar    *t;            /* Store the result of the solution of H^T*t=h_{m+1,m}e_m */
    763:   PetscBLASInt   *ipiv;         /* Permutation vector to be used in LAPACK */
    764:   PetscBool      flag;            /* determine whether to use Ritz vectors or harmonic Ritz vectors */

    767:   PetscBLASIntCast(n,&bn);
    768:   PetscBLASIntCast(N,&bN);
    769:   ihi  = ldQ = bn;
    770:   ldA  = bN;
    771:   PetscBLASIntCast(5*N,&lwork);

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

    777:   PetscMalloc1(ldA*ldA, &A);
    778:   PetscMalloc1(ldQ*n, &Q);
    779:   PetscMalloc1(lwork, &work);
    780:   if (!dgmres->wr) {
    781:     PetscMalloc1(n, &dgmres->wr);
    782:     PetscMalloc1(n, &dgmres->wi);
    783:   }
    784:   wr   = dgmres->wr;
    785:   wi   = dgmres->wi;
    786:   PetscMalloc1(n,&modul);
    787:   PetscMalloc1(n,&perm);
    788:   /* copy the Hessenberg matrix to work space */
    789:   PetscMemcpy(A, dgmres->hes_origin, ldA*ldA*sizeof(PetscReal));
    790:   PetscOptionsHasName(((PetscObject)ksp)->options,((PetscObject)ksp)->prefix, "-ksp_dgmres_harmonic_ritz", &flag);
    791:   if (flag) {
    792:     /* Compute the matrix H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    793:     /* Transpose the Hessenberg matrix */
    794:     PetscMalloc1(bn*bn, &Ht);
    795:     for (i = 0; i < bn; i++) {
    796:       for (j = 0; j < bn; j++) {
    797:         Ht[i * bn + j] = dgmres->hes_origin[j * ldA + i];
    798:       }
    799:     }

    801:     /* Solve the system H^T*t = h_{m+1,m}e_m */
    802:     PetscCalloc1(bn, &t);
    803:     t[bn-1] = dgmres->hes_origin[(bn -1) * ldA + bn]; /* Pick the last element H(m+1,m) */
    804:     PetscMalloc1(bn, &ipiv);
    805:     /* Call the LAPACK routine dgesv to solve the system Ht^-1 * t */
    806: #if   defined(PETSC_MISSING_LAPACK_GESV)
    807:     SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GESV - Lapack routine is unavailable.");
    808: #else
    809:     {
    810:       PetscBLASInt info;
    811:       PetscBLASInt nrhs = 1;
    812:       PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&bn, &nrhs, Ht, &bn, ipiv, t, &bn, &info));
    813:       if (info) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB, "Error while calling the Lapack routine DGESV");
    814:     }
    815: #endif
    816:     /* Now form H + H^{-T}*h^2_{m+1,m}e_m*e_m^T */
    817:     for (i = 0; i < bn; i++) A[(bn-1)*bn+i] += t[i];
    818:     PetscFree(t);
    819:     PetscFree(Ht);
    820:   }
    821:   /* Compute eigenvalues with the Schur form */
    822: #if defined(PETSC_MISSING_LAPACK_HSEQR)
    823:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable.");
    824: #else
    825:   {
    826:     PetscBLASInt info;
    827:     PetscBLASInt ilo = 1;
    828:     PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S", "I", &bn, &ilo, &ihi, A, &ldA, wr, wi, Q, &ldQ, work, &lwork, &info));
    829:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XHSEQR %d",(int) info);
    830:   }
    831: #endif
    832:   PetscFree(work);

    834:   /* sort the eigenvalues */
    835:   for (i=0; i<n; i++) modul[i] = PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
    836:   for (i=0; i<n; i++) perm[i] = i;

    838:   PetscSortRealWithPermutation(n, modul, perm);
    839:   /* save the complex modulus of the largest eigenvalue in magnitude */
    840:   if (dgmres->lambdaN < modul[perm[n-1]]) dgmres->lambdaN=modul[perm[n-1]];
    841:   /* count the number of extracted eigenvalues (with complex conjugates) */
    842:   NbrEig = 0;
    843:   while (NbrEig < dgmres->neig) {
    844:     if (wi[perm[NbrEig]] != 0) NbrEig += 2;
    845:     else NbrEig += 1;
    846:   }
    847:   /* Reorder the Schur decomposition so that the cluster of smallest eigenvalues appears in the leading diagonal blocks of A */

    849:   PetscCalloc1(n, &select);

    851:   if (!dgmres->GreatestEig) {
    852:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
    853:   } else {
    854:     for (j = 0; j < NbrEig; j++) select[perm[n-j-1]] = 1;
    855:   }
    856:   /* call Lapack dtrsen */
    857:   lwork  =  PetscMax(1, 4 * NbrEig *(bn-NbrEig));
    858:   liwork = PetscMax(1, 2 * NbrEig *(bn-NbrEig));
    859:   PetscMalloc1(lwork, &work);
    860:   PetscMalloc1(liwork, &iwork);
    861: #if defined(PETSC_MISSING_LAPACK_TRSEN)
    862:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable.");
    863: #else
    864:   {
    865:     PetscBLASInt info;
    866:     PetscReal    CondEig;         /* lower bound on the reciprocal condition number for the selected cluster of eigenvalues */
    867:     PetscReal    CondSub;         /* estimated reciprocal condition number of the specified invariant subspace. */
    868:     PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("B", "V", select, &bn, A, &ldA, Q, &ldQ, wr, wi, &NbrEig, &CondEig, &CondSub, work, &lwork, iwork, &liwork, &info));
    869:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
    870:   }
    871: #endif
    872:   PetscFree(select);

    874:   /* Extract the Schur vectors */
    875:   for (j = 0; j < NbrEig; j++) {
    876:     PetscMemcpy(&SR[j*N], &(Q[j*ldQ]), n*sizeof(PetscReal));
    877:   }
    878:   *neig = NbrEig;
    879:   PetscFree(A);
    880:   PetscFree(work);
    881:   PetscFree(perm);
    882:   PetscFree(work);
    883:   PetscFree(iwork);
    884:   PetscFree(modul);
    885:   PetscFree(Q);
    886:   return(0);
    887: }

    889: PetscErrorCode  KSPDGMRESApplyDeflation_DGMRES(KSP ksp, Vec x, Vec y)
    890: {
    891:   KSP_DGMRES     *dgmres = (KSP_DGMRES*) ksp->data;
    892:   PetscInt       i, r     = dgmres->r;
    894:   PetscReal      alpha    = 1.0;
    895:   PetscInt       max_neig = dgmres->max_neig;
    896:   PetscBLASInt   br,bmax;
    897:   PetscReal      lambda = dgmres->lambdaN;

    900:   PetscBLASIntCast(r,&br);
    901:   PetscBLASIntCast(max_neig,&bmax);
    902:   PetscLogEventBegin(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
    903:   if (!r) {
    904:     VecCopy(x,y);
    905:     return(0);
    906:   }
    907:   /* Compute U'*x */
    908:   if (!X1) {
    909:     PetscMalloc1(bmax, &X1);
    910:     PetscMalloc1(bmax, &X2);
    911:   }
    912:   VecMDot(x, r, UU, X1);

    914:   /* Solve T*X1=X2 for X1*/
    915:   PetscMemcpy(X2, X1, br*sizeof(PetscReal));
    916: #if defined(PETSC_MISSING_LAPACK_GETRS)
    917:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRS - Lapack routine is unavailable.");
    918: #else
    919:   {
    920:     PetscBLASInt info;
    921:     PetscBLASInt nrhs = 1;
    922:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N", &br, &nrhs, TTF, &bmax, INVP, X1, &bmax, &info));
    923:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRS %d", (int) info);
    924:   }
    925: #endif
    926:   /* Iterative refinement -- is it really necessary ?? */
    927:   if (!WORK) {
    928:     PetscMalloc1(3*bmax, &WORK);
    929:     PetscMalloc1(bmax, &IWORK);
    930:   }
    931: #if defined(PETSC_MISSING_LAPACK_GERFS)
    932:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GERFS - Lapack routine is unavailable.");
    933: #else
    934:   {
    935:     PetscBLASInt info;
    936:     PetscReal    berr, ferr;
    937:     PetscBLASInt nrhs = 1;
    938:     PetscStackCallBLAS("LAPACKgerfs",LAPACKgerfs_("N", &br, &nrhs, TT, &bmax, TTF, &bmax, INVP, X2, &bmax,X1, &bmax, &ferr, &berr, WORK, IWORK, &info));
    939:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGERFS %d", (int) info);
    940:   }
    941: #endif

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

    945:   /* Compute X2=U*X2 */
    946:   VecZeroEntries(y);
    947:   VecMAXPY(y, r, X2, UU);
    948:   VecAXPY(y, alpha, x);

    950:   PetscLogEventEnd(KSP_DGMRESApplyDeflation, ksp, 0, 0, 0);
    951:   return(0);
    952: }

    954: static PetscErrorCode  KSPDGMRESImproveEig_DGMRES(KSP ksp, PetscInt neig)
    955: {
    956:   KSP_DGMRES   *dgmres = (KSP_DGMRES*) ksp->data;
    957:   PetscInt     j,r_old, r = dgmres->r;
    958:   PetscBLASInt i     = 0;
    959:   PetscInt     neig1 = dgmres->neig + EIG_OFFSET;
    960:   PetscInt     bmax  = dgmres->max_neig;
    961:   PetscInt     aug   = r + neig;         /* actual size of the augmented invariant basis */
    962:   PetscInt     aug1  = bmax+neig1;       /* maximum size of the augmented invariant basis */
    963:   PetscBLASInt ldA;            /* leading dimension of AUAU and AUU*/
    964:   PetscBLASInt N;              /* size of AUAU */
    965:   PetscReal    *Q;             /*  orthogonal matrix of  (left) schur vectors */
    966:   PetscReal    *Z;             /*  orthogonal matrix of  (right) schur vectors */
    967:   PetscReal    *work;          /* working vector */
    968:   PetscBLASInt lwork;          /* size of the working vector */
    969:   PetscInt     *perm;          /* Permutation vector to sort eigenvalues */
    970:   PetscReal    *wr, *wi, *beta, *modul; /* Real and imaginary part and modul of the eigenvalues of A*/
    971:   PetscInt     ierr;
    972:   PetscBLASInt NbrEig = 0,nr,bm;
    973:   PetscBLASInt *select;
    974:   PetscBLASInt liwork, *iwork;

    977:   /* Block construction of the matrices AUU=(AU)'*U and (AU)'*AU*/
    978:   if (!AUU) {
    979:     PetscMalloc1(aug1*aug1, &AUU);
    980:     PetscMalloc1(aug1*aug1, &AUAU);
    981:   }
    982:   /* AUU = (AU)'*U = [(MU)'*U (MU)'*X; (MX)'*U (MX)'*X]
    983:    * Note that MU and MX have been computed previously either in ComputeDataDeflation() or down here in a previous call to this function */
    984:   /* (MU)'*U size (r x r) -- store in the <r> first columns of AUU*/
    985:   for (j=0; j < r; j++) {
    986:     VecMDot(UU[j], r, MU, &AUU[j*aug1]);
    987:   }
    988:   /* (MU)'*X size (r x neig) -- store in AUU from the column <r>*/
    989:   for (j = 0; j < neig; j++) {
    990:     VecMDot(XX[j], r, MU, &AUU[(r+j) *aug1]);
    991:   }
    992:   /* (MX)'*U size (neig x r) -- store in the <r> first columns of AUU from the row <r>*/
    993:   for (j = 0; j < r; j++) {
    994:     VecMDot(UU[j], neig, MX, &AUU[j*aug1+r]);
    995:   }
    996:   /* (MX)'*X size (neig neig) --  store in AUU from the column <r> and the row <r>*/
    997:   for (j = 0; j < neig; j++) {
    998:     VecMDot(XX[j], neig, MX, &AUU[(r+j) *aug1 + r]);
    999:   }

    1001:   /* AUAU = (AU)'*AU = [(MU)'*MU (MU)'*MX; (MX)'*MU (MX)'*MX] */
    1002:   /* (MU)'*MU size (r x r) -- store in the <r> first columns of AUAU*/
    1003:   for (j=0; j < r; j++) {
    1004:     VecMDot(MU[j], r, MU, &AUAU[j*aug1]);
    1005:   }
    1006:   /* (MU)'*MX size (r x neig) -- store in AUAU from the column <r>*/
    1007:   for (j = 0; j < neig; j++) {
    1008:     VecMDot(MX[j], r, MU, &AUAU[(r+j) *aug1]);
    1009:   }
    1010:   /* (MX)'*MU size (neig x r) -- store in the <r> first columns of AUAU from the row <r>*/
    1011:   for (j = 0; j < r; j++) {
    1012:     VecMDot(MU[j], neig, MX, &AUAU[j*aug1+r]);
    1013:   }
    1014:   /* (MX)'*MX size (neig neig) --  store in AUAU from the column <r> and the row <r>*/
    1015:   for (j = 0; j < neig; j++) {
    1016:     VecMDot(MX[j], neig, MX, &AUAU[(r+j) *aug1 + r]);
    1017:   }

    1019:   /* Computation of the eigenvectors */
    1020:   PetscBLASIntCast(aug1,&ldA);
    1021:   PetscBLASIntCast(aug,&N);
    1022:   lwork = 8 * N + 20; /* sizeof the working space */
    1023:   PetscMalloc1(N, &wr);
    1024:   PetscMalloc1(N, &wi);
    1025:   PetscMalloc1(N, &beta);
    1026:   PetscMalloc1(N, &modul);
    1027:   PetscMalloc1(N, &perm);
    1028:   PetscMalloc1(N*N, &Q);
    1029:   PetscMalloc1(N*N, &Z);
    1030:   PetscMalloc1(lwork, &work);
    1031: #if defined(PETSC_MISSING_LAPACK_GGES)
    1032:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GGES - Lapack routine is unavailable.");
    1033: #else
    1034:   {
    1035:     PetscBLASInt info;
    1036:     PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V", "V", "N", NULL, &N, AUAU, &ldA, AUU, &ldA, &i, wr, wi, beta, Q, &N, Z, &N, work, &lwork, NULL, &info));
    1037:     if (info) SETERRQ1 (PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGGES %d", (int) info);
    1038:   }
    1039: #endif
    1040:   for (i=0; i<N; i++) {
    1041:     if (beta[i] !=0.0) {
    1042:       wr[i] /=beta[i];
    1043:       wi[i] /=beta[i];
    1044:     }
    1045:   }
    1046:   /* sort the eigenvalues */
    1047:   for (i=0; i<N; i++) modul[i]=PetscSqrtReal(wr[i]*wr[i]+wi[i]*wi[i]);
    1048:   for (i=0; i<N; i++) perm[i] = i;
    1049:   PetscSortRealWithPermutation(N, modul, perm);
    1050:   /* Save the norm of the largest eigenvalue */
    1051:   if (dgmres->lambdaN < modul[perm[N-1]]) dgmres->lambdaN = modul[perm[N-1]];
    1052:   /* Allocate space to extract the first r schur vectors   */
    1053:   if (!SR2) {
    1054:     PetscMalloc1(aug1*bmax, &SR2);
    1055:   }
    1056:   /* count the number of extracted eigenvalues (complex conjugates count as 2) */
    1057:   while (NbrEig < bmax) {
    1058:     if (wi[perm[NbrEig]] == 0) NbrEig += 1;
    1059:     else NbrEig += 2;
    1060:   }
    1061:   if (NbrEig > bmax) NbrEig = bmax - 1;
    1062:   r_old     = r; /* previous size of r */
    1063:   dgmres->r = r = NbrEig;

    1065:   /* Select the eigenvalues to reorder */
    1066:   PetscCalloc1(N, &select);
    1067:   if (!dgmres->GreatestEig) {
    1068:     for (j = 0; j < NbrEig; j++) select[perm[j]] = 1;
    1069:   } else {
    1070:     for (j = 0; j < NbrEig; j++) select[perm[N-j-1]] = 1;
    1071:   }
    1072:   /* Reorder and extract the new <r> schur vectors */
    1073:   lwork  = PetscMax(4 * N + 16,  2 * NbrEig *(N - NbrEig));
    1074:   liwork = PetscMax(N + 6,  2 * NbrEig *(N - NbrEig));
    1075:   PetscFree(work);
    1076:   PetscMalloc1(lwork, &work);
    1077:   PetscMalloc1(liwork, &iwork);
    1078: #if defined(PETSC_MISSING_LAPACK_TGSEN)
    1079:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable.");
    1080: #else
    1081:   {
    1082:     PetscBLASInt info;
    1083:     PetscReal    Dif[2];
    1084:     PetscBLASInt ijob  = 2;
    1085:     PetscBLASInt wantQ = 1, wantZ = 1;
    1086:     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));
    1087:     if (info == 1) SETERRQ(PetscObjectComm((PetscObject)ksp), -1, "UNABLE TO REORDER THE EIGENVALUES WITH THE LAPACK ROUTINE : ILL-CONDITIONED PROBLEM");
    1088:   }
    1089: #endif
    1090:   PetscFree(select);

    1092:   for (j=0; j<r; j++) {
    1093:     PetscMemcpy(&SR2[j*aug1], &(Z[j*N]), N*sizeof(PetscReal));
    1094:   }

    1096:   /* Multiply the Schur vectors SR2 by U (and X)  to get a new U
    1097:    -- save it temporarily in MU */
    1098:   for (j = 0; j < r; j++) {
    1099:     VecZeroEntries(MU[j]);
    1100:     VecMAXPY(MU[j], r_old, &SR2[j*aug1], UU);
    1101:     VecMAXPY(MU[j], neig, &SR2[j*aug1+r_old], XX);
    1102:   }
    1103:   /* Form T = U'*MU*U */
    1104:   for (j = 0; j < r; j++) {
    1105:     VecCopy(MU[j], UU[j]);
    1106:     KSP_PCApplyBAorAB(ksp, UU[j], MU[j], VEC_TEMP_MATOP);
    1107:   }
    1108:   dgmres->matvecs += r;
    1109:   for (j = 0; j < r; j++) {
    1110:     VecMDot(MU[j], r, UU, &TT[j*bmax]);
    1111:   }
    1112:   /* Factorize T */
    1113:   PetscMemcpy(TTF, TT, bmax*r*sizeof(PetscReal));
    1114:   PetscBLASIntCast(r,&nr);
    1115:   PetscBLASIntCast(bmax,&bm);
    1116: #if defined(PETSC_MISSING_LAPACK_GETRF)
    1117:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GETRF - Lapack routine is unavailable.");
    1118: #else
    1119:   {
    1120:     PetscBLASInt info;
    1121:     PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&nr, &nr, TTF, &bm, INVP, &info));
    1122:     if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGETRF INFO=%d",(int) info);
    1123:   }
    1124: #endif
    1125:   /* Free Memory */
    1126:   PetscFree(wr);
    1127:   PetscFree(wi);
    1128:   PetscFree(beta);
    1129:   PetscFree(modul);
    1130:   PetscFree(perm);
    1131:   PetscFree(Q);
    1132:   PetscFree(Z);
    1133:   PetscFree(work);
    1134:   PetscFree(iwork);
    1135:   return(0);
    1136: }

    1138: /* end new DGMRES functions */

    1140: /*MC
    1141:      KSPDGMRES - Implements the deflated GMRES as defined in [1,2].
    1142:                  In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the
    1143:                  stagnation occurs.

    1145:    Options Database Keys:
    1146:    GMRES Options (inherited):
    1147: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    1148: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    1149: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    1150:                              vectors are allocated as needed)
    1151: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    1152: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    1153: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    1154:                                    stability of the classical Gram-Schmidt  orthogonalization.
    1155: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

    1157:    DGMRES Options Database Keys:
    1158: +   -ksp_dgmres_eigen <neig> - number of smallest eigenvalues to extract at each restart
    1159: .   -ksp_dgmres_max_eigen <max_neig> - maximum number of eigenvalues that can be extracted during the iterative
    1160:                                        process
    1161: .   -ksp_dgmres_force - use the deflation at each restart; switch off the adaptive strategy.
    1162: -   -ksp_dgmres_view_deflation_vecs <viewerspec> - View the deflation vectors, where viewerspec is a key that can be
    1163:                                                    parsed by PetscOptionsGetViewer().  If neig > 1, viewerspec should
    1164:                                                    end with ":append".  No vectors will be viewed if the adaptive
    1165:                                                    strategy chooses not to deflate, so -ksp_dgmres_force should also
    1166:                                                    be given.
    1167:                                                    The deflation vectors span a subspace that may be a good
    1168:                                                    approximation of the subspace of smallest eigenvectors of the
    1169:                                                    preconditioned operator, so this option can aid in understanding
    1170:                                                    the performance of a preconditioner.

    1172:  Level: beginner

    1174:  Notes:
    1175:     Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

    1177:  References:
    1178: +  1. - J. Erhel, K. Burrage and B. Pohl,  Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).
    1179: -  2. - D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids,
    1180:    In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

    1182:  Contributed by: Desire NUENTSA WAKAM,INRIA

    1184:  .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
    1185:  KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    1186:  KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    1187:  KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

    1189:  M*/

    1191: PETSC_EXTERN PetscErrorCode KSPCreate_DGMRES(KSP ksp)
    1192: {
    1193:   KSP_DGMRES     *dgmres;

    1197:   PetscNewLog(ksp,&dgmres);
    1198:   ksp->data = (void*) dgmres;

    1200:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    1201:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

    1203:   ksp->ops->buildsolution                = KSPBuildSolution_DGMRES;
    1204:   ksp->ops->setup                        = KSPSetUp_DGMRES;
    1205:   ksp->ops->solve                        = KSPSolve_DGMRES;
    1206:   ksp->ops->destroy                      = KSPDestroy_DGMRES;
    1207:   ksp->ops->view                         = KSPView_DGMRES;
    1208:   ksp->ops->setfromoptions               = KSPSetFromOptions_DGMRES;
    1209:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    1210:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    1212:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    1213:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    1214:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    1215:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
    1216:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    1217:   /* -- New functions defined in DGMRES -- */
    1218:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetEigen_C",KSPDGMRESSetEigen_DGMRES);
    1219:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetMaxEigen_C",KSPDGMRESSetMaxEigen_DGMRES);
    1220:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESSetRatio_C",KSPDGMRESSetRatio_DGMRES);
    1221:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESForce_C",KSPDGMRESForce_DGMRES);
    1222:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeSchurForm_C",KSPDGMRESComputeSchurForm_DGMRES);
    1223:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESComputeDeflationData_C",KSPDGMRESComputeDeflationData_DGMRES);
    1224:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESApplyDeflation_C",KSPDGMRESApplyDeflation_DGMRES);
    1225:   PetscObjectComposeFunction((PetscObject)ksp, "KSPDGMRESImproveEig_C", KSPDGMRESImproveEig_DGMRES);

    1227:   PetscLogEventRegister("DGMRESCompDefl",  KSP_CLASSID, &KSP_DGMRESComputeDeflationData);
    1228:   PetscLogEventRegister("DGMRESApplyDefl", KSP_CLASSID, &KSP_DGMRESApplyDeflation);

    1230:   dgmres->haptol         = 1.0e-30;
    1231:   dgmres->q_preallocate  = 0;
    1232:   dgmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
    1233:   dgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    1234:   dgmres->nrs            = 0;
    1235:   dgmres->sol_temp       = 0;
    1236:   dgmres->max_k          = GMRES_DEFAULT_MAXK;
    1237:   dgmres->Rsvd           = 0;
    1238:   dgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    1239:   dgmres->orthogwork     = 0;

    1241:   /* Default values for the deflation */
    1242:   dgmres->r           = 0;
    1243:   dgmres->neig        = DGMRES_DEFAULT_EIG;
    1244:   dgmres->max_neig    = DGMRES_DEFAULT_MAXEIG-1;
    1245:   dgmres->lambdaN     = 0.0;
    1246:   dgmres->smv         = SMV;
    1247:   dgmres->matvecs     = 0;
    1248:   dgmres->GreatestEig = PETSC_FALSE; /* experimental */
    1249:   dgmres->HasSchur    = PETSC_FALSE;
    1250:   return(0);
    1251: }