Date: 2022-11-02T11:47:22+00:00

Actual source code: qslice.c
slepc-3.18.1 2022-11-02
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    SLEPc polynomial eigensolver: "stoar"

     13:    Method: S-TOAR with spectrum slicing for symmetric quadratic eigenproblems

     15:    Algorithm:

     17:        Symmetric Two-Level Orthogonal Arnoldi.

     19:    References:

     21:        [1] C. Campos and J.E. Roman, "Inertia-based spectrum slicing
     22:            for symmetric quadratic eigenvalue problems", Numer. Linear
     23:            Algebra Appl. 27(4):e2293, 2020.
     24: */

     26: #include <slepc/private/pepimpl.h>
     27: #include "../src/pep/impls/krylov/pepkrylov.h"
     28: #include <slepcblaslapack.h>

     30: static PetscBool  cited = PETSC_FALSE;
     31: static const char citation[] =
     32:   "@Article{slepc-slice-qep,\n"
     33:   "   author = \"C. Campos and J. E. Roman\",\n"
     34:   "   title = \"Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems\",\n"
     35:   "   journal = \"Numer. Linear Algebra Appl.\",\n"
     36:   "   volume = \"27\",\n"
     37:   "   number = \"4\",\n"
     38:   "   pages = \"e2293\",\n"
     39:   "   year = \"2020,\"\n"
     40:   "   doi = \"https://doi.org/10.1002/nla.2293\"\n"
     41:   "}\n";

     43: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON

     45: static PetscErrorCode PEPQSliceResetSR(PEP pep)
     46: {
     47:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
     48:   PEP_SR         sr=ctx->sr;
     49:   PEP_shift      s;
     50:   PetscInt       i;

     52:   if (sr) {
     53:     /* Reviewing list of shifts to free memory */
     54:     s = sr->s0;
     55:     if (s) {
     56:       while (s->neighb[1]) {
     57:         s = s->neighb[1];
     58:         PetscFree(s->neighb[0]);
     59:       }
     60:       PetscFree(s);
     61:     }
     62:     PetscFree(sr->S);
     63:     for (i=0;i<pep->nconv;i++) PetscFree(sr->qinfo[i].q);
     64:     PetscFree(sr->qinfo);
     65:     for (i=0;i<3;i++) VecDestroy(&sr->v[i]);
     66:     EPSDestroy(&sr->eps);
     67:     PetscFree(sr);
     68:   }
     69:   ctx->sr = NULL;
     70:   return 0;
     71: }

     73: PetscErrorCode PEPReset_STOAR_QSlice(PEP pep)
     74: {
     75:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

     77:   PEPQSliceResetSR(pep);
     78:   PetscFree(ctx->inertias);
     79:   PetscFree(ctx->shifts);
     80:   return 0;
     81: }

     83: /*
     84:   PEPQSliceAllocateSolution - Allocate memory storage for common variables such
     85:   as eigenvalues and eigenvectors.
     86: */
     87: static PetscErrorCode PEPQSliceAllocateSolution(PEP pep)
     88: {
     89:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
     90:   PetscInt       k;
     91:   BVType         type;
     92:   Vec            t;
     93:   PEP_SR         sr = ctx->sr;

     95:   /* allocate space for eigenvalues and friends */
     96:   k = PetscMax(1,sr->numEigs);
     97:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
     98:   PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
     99:   PetscFree(sr->qinfo);
    100:   PetscCalloc1(k,&sr->qinfo);

    102:   /* allocate sr->V and transfer options from pep->V */
    103:   BVDestroy(&sr->V);
    104:   BVCreate(PetscObjectComm((PetscObject)pep),&sr->V);
    105:   if (!pep->V) PEPGetBV(pep,&pep->V);
    106:   if (!((PetscObject)(pep->V))->type_name) BVSetType(sr->V,BVSVEC);
    107:   else {
    108:     BVGetType(pep->V,&type);
    109:     BVSetType(sr->V,type);
    110:   }
    111:   STMatCreateVecsEmpty(pep->st,&t,NULL);
    112:   BVSetSizesFromVec(sr->V,t,k+1);
    113:   VecDestroy(&t);
    114:   sr->ld = k;
    115:   PetscFree(sr->S);
    116:   PetscMalloc1((k+1)*sr->ld*(pep->nmat-1),&sr->S);
    117:   return 0;
    118: }

    120: /* Convergence test to compute positive Ritz values */
    121: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    122: {
    123:   *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
    124:   return 0;
    125: }

    127: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    128: {
    129:   KSP            ksp,kspr;
    130:   PC             pc;
    131:   Mat            F;
    132:   PetscBool      flg;

    134:   if (!pep->solvematcoeffs) PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
    135:   if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
    136:     pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
    137:   } else PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL);
    138:   STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
    139:   STGetKSP(pep->st,&ksp);
    140:   KSPGetPC(ksp,&pc);
    141:   PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
    142:   if (flg) {
    143:     PCRedundantGetKSP(pc,&kspr);
    144:     KSPGetPC(kspr,&pc);
    145:   }
    146:   PCFactorGetMatrix(pc,&F);
    147:   MatGetInertia(F,inertia,zeros,NULL);
    148:   return 0;
    149: }

    151: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
    152: {
    153:   KSP            ksp;
    154:   Mat            P;
    155:   PetscReal      nzshift=0.0,dot;
    156:   PetscRandom    rand;
    157:   PetscInt       nconv;
    158:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    159:   PEP_SR         sr=ctx->sr;

    161:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    162:     *inertia = 0;
    163:   } else if (shift <= PETSC_MIN_REAL) {
    164:     *inertia = 0;
    165:     if (zeros) *zeros = 0;
    166:   } else {
    167:     /* If the shift is zero, perturb it to a very small positive value.
    168:        The goal is that the nonzero pattern is the same in all cases and reuse
    169:        the symbolic factorizations */
    170:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
    171:     PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
    172:     STSetShift(pep->st,nzshift);
    173:   }
    174:   if (!correction) {
    175:     if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
    176:     else if (shift>PETSC_MIN_REAL) {
    177:       STGetKSP(pep->st,&ksp);
    178:       KSPGetOperators(ksp,&P,NULL);
    179:       if (*inertia!=pep->n && !sr->v[0]) {
    180:         MatCreateVecs(P,&sr->v[0],NULL);
    181:         VecDuplicate(sr->v[0],&sr->v[1]);
    182:         VecDuplicate(sr->v[0],&sr->v[2]);
    183:         BVGetRandomContext(pep->V,&rand);
    184:         VecSetRandom(sr->v[0],rand);
    185:       }
    186:       if (*inertia<pep->n && *inertia>0) {
    187:         if (!sr->eps) {
    188:           EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
    189:           EPSSetProblemType(sr->eps,EPS_HEP);
    190:           EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
    191:         }
    192:         EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
    193:         EPSSetOperators(sr->eps,P,NULL);
    194:         EPSSolve(sr->eps);
    195:         EPSGetConverged(sr->eps,&nconv);
    197:         EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
    198:       }
    199:       if (*inertia!=pep->n) {
    200:         MatMult(pep->A[1],sr->v[0],sr->v[1]);
    201:         MatMult(pep->A[2],sr->v[0],sr->v[2]);
    202:         VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
    203:         VecDotRealPart(sr->v[1],sr->v[0],&dot);
    204:         if (dot>0.0) *inertia = 2*pep->n-*inertia;
    205:       }
    206:     }
    207:   } else if (correction<0) *inertia = 2*pep->n-*inertia;
    208:   return 0;
    209: }

    211: /*
    212:    Check eigenvalue type - used only in non-hyperbolic problems.
    213:    All computed eigenvalues must have the same definite type (positive or negative).
    214:    If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
    215:    closest to shift and determine its type.
    216:  */
    217: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
    218: {
    219:   PEP            pep2;
    220:   ST             st;
    221:   PetscInt       nconv;
    222:   PetscScalar    lambda;
    223:   PetscReal      dot;
    224:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    225:   PEP_SR         sr=ctx->sr;

    227:   if (!ini) {
    229:   } else {
    230:     PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
    231:     PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
    232:     PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
    233:     PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
    234:     PEPSetType(pep2,PEPTOAR);
    235:     PEPSetOperators(pep2,pep->nmat,pep->A);
    236:     PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
    237:     PEPGetRG(pep2,&pep2->rg);
    238:     RGSetType(pep2->rg,RGINTERVAL);
    239: #if defined(PETSC_USE_COMPLEX)
    240:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
    241: #else
    242:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
    243: #endif
    244:     pep2->target = shift;
    245:     st = pep2->st;
    246:     pep2->st = pep->st;
    247:     PEPSolve(pep2);
    248:     PEPGetConverged(pep2,&nconv);
    249:     if (nconv) {
    250:       PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
    251:       MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
    252:       MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
    253:       VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
    254:       VecDotRealPart(pep2->work[1],pep2->work[0],&dot);
    255:       PetscInfo(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(dot>0.0)?"positive":"negative");
    256:       if (!sr->type) sr->type = (dot>0.0)?1:-1;
    258:     }
    259:     pep2->st = st;
    260:     PEPDestroy(&pep2);
    261:   }
    262:   return 0;
    263: }

    265: static inline PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
    266: {
    267:   PetscReal      ap,bp,cp,dis;

    269:   MatMult(pep->A[0],u,w);
    270:   VecDotRealPart(w,u,&cp);
    271:   MatMult(pep->A[1],u,w);
    272:   VecDotRealPart(w,u,&bp);
    273:   MatMult(pep->A[2],u,w);
    274:   VecDotRealPart(w,u,&ap);
    275:   dis = bp*bp-4*ap*cp;
    276:   if (dis>=0.0 && smas) {
    277:     if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
    278:     else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
    279:     else {
    280:       if (bp >0) *smas = -cp/bp;
    281:       else *smas = PETSC_MAX_REAL;
    282:     }
    283:   }
    284:   if (dis>=0.0 && smenos) {
    285:     if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
    286:     else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
    287:     else {
    288:       if (bp<0) *smenos = -cp/bp;
    289:       else *smenos = PETSC_MAX_REAL;
    290:     }
    291:   }
    292:   if (d) *d = dis;
    293:   return 0;
    294: }

    296: static inline PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
    297: {
    298:   MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
    299:   MatAXPY(M,x,pep->A[1],str);
    300:   MatAXPY(M,x*x,pep->A[2],str);
    301:   return 0;
    302: }

    304: /*@
    305:    PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
    306:    is definite or not.

    308:    Logically Collective on pep

    310:    Input Parameter:
    311: .  pep  - eigensolver context

    313:    Output Parameters:
    314: +  xi - first computed parameter
    315: .  mu - second computed parameter
    316: .  definite - flag indicating that the problem is definite
    317: -  hyperbolic - flag indicating that the problem is hyperbolic

    319:    Notes:
    320:    This function is intended for quadratic eigenvalue problems, Q(lambda)=A*lambda^2+B*lambda+C,
    321:    with symmetric (or Hermitian) coefficient matrices A,B,C.

    323:    On output, the flag 'definite' may have the values -1 (meaning that the QEP is not
    324:    definite), 1 (if the problem is definite), or 0 if the algorithm was not able to
    325:    determine whether the problem is definite or not.

    327:    If definite=1, the output flag 'hyperbolic' informs in a similar way about whether the
    328:    problem is hyperbolic or not.

    330:    If definite=1, the computed values xi and mu satisfy Q(xi)<0 and Q(mu)>0, as
    331:    obtained via the method proposed in [Niendorf and Voss, LAA 2010]. Furthermore, if
    332:    hyperbolic=1 then only xi is computed.

    334:    Level: advanced

    336: .seealso: PEPSetProblemType()
    337: @*/
    338: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
    339: {
    340:   PetscRandom    rand;
    341:   Vec            u,w;
    342:   PetscReal      d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
    343:   PetscInt       k,its=10,hyp=0,check=0,nconv,inertia,n;
    344:   Mat            M=NULL;
    345:   MatStructure   str;
    346:   EPS            eps;
    347:   PetscBool      transform,ptypehyp;

    350:   ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
    351:   if (!pep->st) PEPGetST(pep,&pep->st);
    352:   PEPSetDefaultST(pep);
    353:   STSetMatrices(pep->st,pep->nmat,pep->A);
    354:   MatGetSize(pep->A[0],&n,NULL);
    355:   STGetTransform(pep->st,&transform);
    356:   STSetTransform(pep->st,PETSC_FALSE);
    357:   STSetUp(pep->st);
    358:   MatCreateVecs(pep->A[0],&u,&w);
    359:   PEPGetBV(pep,&pep->V);
    360:   BVGetRandomContext(pep->V,&rand);
    361:   VecSetRandom(u,rand);
    362:   VecNormalize(u,NULL);
    363:   PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
    364:   if (d<0.0) check = -1;
    365:   if (!check) {
    366:     EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
    367:     EPSSetProblemType(eps,EPS_HEP);
    368:     EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
    369:     EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
    370:     MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
    371:     STGetMatStructure(pep->st,&str);
    372:   }
    373:   for (k=0;k<its&&!check;k++) {
    374:     PEPQSliceEvaluateQEP(pep,s,M,str);
    375:     EPSSetOperators(eps,M,NULL);
    376:     EPSSolve(eps);
    377:     EPSGetConverged(eps,&nconv);
    378:     if (!nconv) break;
    379:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    380:     sp = s;
    381:     PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
    382:     if (d<0.0) {check = -1; break;}
    383:     if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
    384:     if (s>sp) {hyp = -1;}
    385:     mut = 2*s-sp;
    386:     PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    387:     if (inertia == n) {check = 1; break;}
    388:   }
    389:   for (;k<its&&!check;k++) {
    390:     mut = (s-omg)/2;
    391:     PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    392:     if (inertia == n) {check = 1; break;}
    393:     if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
    394:     PEPQSliceEvaluateQEP(pep,omg,M,str);
    395:     EPSSetOperators(eps,M,NULL);
    396:     EPSSolve(eps);
    397:     EPSGetConverged(eps,&nconv);
    398:     if (!nconv) break;
    399:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    400:     omgp = omg;
    401:     PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
    402:     if (d<0.0) {check = -1; break;}
    403:     if (omg<omgp) hyp = -1;
    404:   }
    405:   if (check==1) *xi = mut;
    407:   if (check==1 && hyp==0) {
    408:     PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
    409:     if (inertia == 0) hyp = 1;
    410:     else hyp = -1;
    411:   }
    412:   if (check==1 && hyp!=1) {
    413:     check = 0;
    414:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
    415:     for (;k<its&&!check;k++) {
    416:       PEPQSliceEvaluateQEP(pep,s,M,str);
    417:       EPSSetOperators(eps,M,NULL);
    418:       EPSSolve(eps);
    419:       EPSGetConverged(eps,&nconv);
    420:       if (!nconv) break;
    421:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    422:       sp = s;
    423:       PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
    424:       if (d<0.0) {check = -1; break;}
    425:       if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
    426:       mut = 2*s-sp;
    427:       PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    428:       if (inertia == 0) {check = 1; break;}
    429:     }
    430:     for (;k<its&&!check;k++) {
    431:       mut = (s-omg)/2;
    432:       PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    433:       if (inertia == 0) {check = 1; break;}
    434:       if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
    435:       PEPQSliceEvaluateQEP(pep,omg,M,str);
    436:       EPSSetOperators(eps,M,NULL);
    437:       EPSSolve(eps);
    438:       EPSGetConverged(eps,&nconv);
    439:       if (!nconv) break;
    440:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    441:       PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
    442:       if (d<0.0) {check = -1; break;}
    443:     }
    444:   }
    445:   if (check==1) *mu = mut;
    446:   *definite = check;
    447:   *hyperbolic = hyp;
    448:   if (M) MatDestroy(&M);
    449:   VecDestroy(&u);
    450:   VecDestroy(&w);
    451:   EPSDestroy(&eps);
    452:   STSetTransform(pep->st,transform);
    453:   return 0;
    454: }

    456: /*
    457:    Dummy backtransform operation
    458:  */
    459: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
    460: {
    461:   return 0;
    462: }

    464: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
    465: {
    466:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    467:   PEP_SR         sr;
    468:   PetscInt       ld,i,zeros=0;
    469:   SlepcSC        sc;
    470:   PetscReal      r;

    472:   PEPCheckSinvertCayley(pep);
    475:   PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
    476:   if (pep->tol==PETSC_DEFAULT) {
    477: #if defined(PETSC_USE_REAL_SINGLE)
    478:     pep->tol = SLEPC_DEFAULT_TOL;
    479: #else
    480:     /* use tighter tolerance */
    481:     pep->tol = SLEPC_DEFAULT_TOL*1e-2;
    482: #endif
    483:   }
    484:   if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n);  /* nev not set, use default value */
    486:   pep->ops->backtransform = PEPBackTransform_Skip;
    487:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;

    489:   /* create spectrum slicing context and initialize it */
    490:   PEPQSliceResetSR(pep);
    491:   PetscNew(&sr);
    492:   ctx->sr   = sr;
    493:   sr->itsKs = 0;
    494:   sr->nleap = 0;
    495:   sr->sPres = NULL;

    497:   if (pep->solvematcoeffs) PetscFree(pep->solvematcoeffs);
    498:   PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
    499:   if (!pep->st) PEPGetST(pep,&pep->st);
    500:   STSetTransform(pep->st,PETSC_FALSE);
    501:   STSetUp(pep->st);

    503:   ctx->hyperbolic = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;

    505:   /* check presence of ends and finding direction */
    506:   if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
    507:     sr->int0 = pep->inta;
    508:     sr->int1 = pep->intb;
    509:     sr->dir = 1;
    510:     if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
    511:       sr->hasEnd = PETSC_FALSE;
    512:     } else sr->hasEnd = PETSC_TRUE;
    513:   } else {
    514:     sr->int0 = pep->intb;
    515:     sr->int1 = pep->inta;
    516:     sr->dir = -1;
    517:     sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
    518:   }

    520:   /* compute inertia0 */
    521:   PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
    523:   if (!ctx->hyperbolic && ctx->checket) PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE);

    525:   /* compute inertia1 */
    526:   PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
    528:   if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
    529:     PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE);
    532:     if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
    533:       sr->intcorr = -1;
    534:       sr->inertia0 = 2*pep->n-sr->inertia0;
    535:       sr->inertia1 = 2*pep->n-sr->inertia1;
    536:     } else sr->intcorr = 1;
    537:   } else {
    538:     if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
    539:     else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
    540:   }

    542:   if (sr->hasEnd) {
    543:     sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
    544:     i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
    545:   }

    547:   /* number of eigenvalues in interval */
    548:   sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    549:   PetscInfo(pep,"QSlice setup: allocating for %" PetscInt_FMT " eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb);
    550:   if (sr->numEigs) {
    551:     PEPQSliceAllocateSolution(pep);
    552:     PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd);
    553:     pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
    554:     ld   = ctx->ncv+2;
    555:     DSSetType(pep->ds,DSGHIEP);
    556:     DSSetCompact(pep->ds,PETSC_TRUE);
    557:     DSSetExtraRow(pep->ds,PETSC_TRUE);
    558:     DSAllocate(pep->ds,ld);
    559:     DSGetSlepcSC(pep->ds,&sc);
    560:     sc->rg            = NULL;
    561:     sc->comparison    = SlepcCompareLargestMagnitude;
    562:     sc->comparisonctx = NULL;
    563:     sc->map           = NULL;
    564:     sc->mapobj        = NULL;
    565:   } else {pep->ncv = 0; pep->nev = 0; pep->mpd = 0;}
    566:   return 0;
    567: }

    569: /*
    570:    Fills the fields of a shift structure
    571: */
    572: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
    573: {
    574:   PEP_shift      s,*pending2;
    575:   PetscInt       i;
    576:   PEP_SR         sr;
    577:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

    579:   sr = ctx->sr;
    580:   PetscNew(&s);
    581:   s->value = val;
    582:   s->neighb[0] = neighb0;
    583:   if (neighb0) neighb0->neighb[1] = s;
    584:   s->neighb[1] = neighb1;
    585:   if (neighb1) neighb1->neighb[0] = s;
    586:   s->comp[0] = PETSC_FALSE;
    587:   s->comp[1] = PETSC_FALSE;
    588:   s->index = -1;
    589:   s->neigs = 0;
    590:   s->nconv[0] = s->nconv[1] = 0;
    591:   s->nsch[0] = s->nsch[1]=0;
    592:   /* Inserts in the stack of pending shifts */
    593:   /* If needed, the array is resized */
    594:   if (sr->nPend >= sr->maxPend) {
    595:     sr->maxPend *= 2;
    596:     PetscMalloc1(sr->maxPend,&pending2);
    597:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
    598:     PetscFree(sr->pending);
    599:     sr->pending = pending2;
    600:   }
    601:   sr->pending[sr->nPend++]=s;
    602:   return 0;
    603: }

    605: /* Provides next shift to be computed */
    606: static PetscErrorCode PEPExtractShift(PEP pep)
    607: {
    608:   PetscInt       iner,zeros=0;
    609:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    610:   PEP_SR         sr;
    611:   PetscReal      newShift,aux;
    612:   PEP_shift      sPres;

    614:   sr = ctx->sr;
    615:   if (sr->nPend > 0) {
    616:     if (sr->dirch) {
    617:       aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
    618:       iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
    619:       sr->dir *= -1;
    620:       PetscFree(sr->s0->neighb[1]);
    621:       PetscFree(sr->s0);
    622:       sr->nPend--;
    623:       PEPCreateShift(pep,sr->int0,NULL,NULL);
    624:       sr->sPrev = NULL;
    625:       sr->sPres = sr->pending[--sr->nPend];
    626:       pep->target = sr->sPres->value;
    627:       sr->s0 = sr->sPres;
    628:       pep->reason = PEP_CONVERGED_ITERATING;
    629:     } else {
    630:       sr->sPrev = sr->sPres;
    631:       sr->sPres = sr->pending[--sr->nPend];
    632:     }
    633:     sPres = sr->sPres;
    634:     PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
    635:     if (zeros) {
    636:       newShift = sPres->value*(1.0+SLICE_PTOL);
    637:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    638:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    639:       PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
    641:       sPres->value = newShift;
    642:     }
    643:     sr->sPres->inertia = iner;
    644:     pep->target = sr->sPres->value;
    645:     pep->reason = PEP_CONVERGED_ITERATING;
    646:     pep->its = 0;
    647:   } else sr->sPres = NULL;
    648:   return 0;
    649: }

    651: /*
    652:   Obtains value of subsequent shift
    653: */
    654: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
    655: {
    656:   PetscReal lambda,d_prev;
    657:   PetscInt  i,idxP;
    658:   PEP_SR    sr;
    659:   PEP_shift sPres,s;
    660:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

    662:   sr = ctx->sr;
    663:   sPres = sr->sPres;
    664:   if (sPres->neighb[side]) {
    665:   /* Completing a previous interval */
    666:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
    667:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
    668:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
    669:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
    670:   } else { /* (Only for side=1). Creating a new interval. */
    671:     if (sPres->neigs==0) {/* No value has been accepted*/
    672:       if (sPres->neighb[0]) {
    673:         /* Multiplying by 10 the previous distance */
    674:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    675:         sr->nleap++;
    676:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    678:       } else { /* First shift */
    679:         if (pep->nconv != 0) {
    680:           /* Unaccepted values give information for next shift */
    681:           idxP=0;/* Number of values left from shift */
    682:           for (i=0;i<pep->nconv;i++) {
    683:             lambda = PetscRealPart(pep->eigr[i]);
    684:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
    685:             else break;
    686:           }
    687:           /* Avoiding subtraction of eigenvalues (might be the same).*/
    688:           if (idxP>0) {
    689:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
    690:           } else {
    691:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
    692:           }
    693:           *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
    694:           sr->dirch = PETSC_FALSE;
    695:         } else { /* No values found, no information for next shift */
    697:           sr->dirch = PETSC_TRUE;
    698:           *newS = sr->int1;
    699:         }
    700:       }
    701:     } else { /* Accepted values found */
    702:       sr->dirch = PETSC_FALSE;
    703:       sr->nleap = 0;
    704:       /* Average distance of values in previous subinterval */
    705:       s = sPres->neighb[0];
    706:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    707:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    708:       }
    709:       if (s) {
    710:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    711:       } else { /* First shift. Average distance obtained with values in this shift */
    712:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    713:         if ((sr->dir)*(PetscRealPart(sr->eigr[0])-sPres->value)>0 && PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0]))/PetscRealPart(sr->eigr[0])) > PetscSqrtReal(pep->tol)) {
    714:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    715:         } else {
    716:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    717:         }
    718:       }
    719:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    720:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    721:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
    722:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    723:         *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
    724:       }
    725:     }
    726:     /* End of interval can not be surpassed */
    727:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
    728:   }/* of neighb[side]==null */
    729:   return 0;
    730: }

    732: /*
    733:   Function for sorting an array of real values
    734: */
    735: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    736: {
    737:   PetscReal re;
    738:   PetscInt  i,j,tmp;

    740:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    741:   /* Insertion sort */
    742:   for (i=1;i<nr;i++) {
    743:     re = PetscRealPart(r[perm[i]]);
    744:     j = i-1;
    745:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    746:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    747:     }
    748:   }
    749:   return 0;
    750: }

    752: /* Stores the pairs obtained since the last shift in the global arrays */
    753: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
    754: {
    755:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    756:   PetscReal      lambda,err,*errest;
    757:   PetscInt       i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
    758:   PetscBool      iscayley,divide=PETSC_FALSE;
    759:   PEP_SR         sr = ctx->sr;
    760:   PEP_shift      sPres;
    761:   Vec            w,vomega;
    762:   Mat            MS;
    763:   BV             tV;
    764:   PetscScalar    *S,*eigr,*tS,*omega;

    766:   sPres = sr->sPres;
    767:   sPres->index = sr->indexEig;

    769:   if (nconv>sr->ndef0+sr->ndef1) {
    770:     /* Back-transform */
    771:     STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
    772:     for (i=0;i<nconv;i++) {
    773: #if defined(PETSC_USE_COMPLEX)
    774:       if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
    775: #else
    776:       if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
    777: #endif
    778:     }
    779:     PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
    780:     /* Sort eigenvalues */
    781:     sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
    782:     VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
    783:     BVGetSignature(ctx->V,vomega);
    784:     VecGetArray(vomega,&omega);
    785:     BVGetSizes(pep->V,NULL,NULL,&ld);
    786:     BVTensorGetFactors(ctx->V,NULL,&MS);
    787:     MatDenseGetArray(MS,&S);
    788:     /* Values stored in global array */
    789:     PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
    790:     ndef = sr->ndef0+sr->ndef1;
    791:     for (i=0;i<nconv;i++) {
    792:       lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
    793:       err = pep->errest[pep->perm[i]];
    794:       if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    796:         PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
    797:         eigr[count] = lambda;
    798:         errest[count] = err;
    799:         if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
    800:         if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
    801:         PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
    802:         PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
    803:         count++;
    804:       }
    805:     }
    806:     VecRestoreArray(vomega,&omega);
    807:     VecDestroy(&vomega);
    808:     for (i=0;i<count;i++) {
    809:       PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
    810:       PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
    811:     }
    812:     MatDenseRestoreArray(MS,&S);
    813:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    814:     BVSetActiveColumns(ctx->V,0,count);
    815:     BVTensorCompress(ctx->V,count);
    816:     if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
    817:       divide = PETSC_TRUE;
    818:       BVTensorGetFactors(ctx->V,NULL,&MS);
    819:       MatDenseGetArray(MS,&S);
    820:       PetscArrayzero(tS,nconv*nconv*d);
    821:       for (i=0;i<count;i++) {
    822:         PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
    823:         PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
    824:       }
    825:       MatDenseRestoreArray(MS,&S);
    826:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    827:       BVSetActiveColumns(pep->V,0,count);
    828:       BVDuplicateResize(pep->V,count,&tV);
    829:       BVCopy(pep->V,tV);
    830:     }
    831:     if (sr->sPres->nconv[0]) {
    832:       if (divide) {
    833:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
    834:         BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
    835:       }
    836:       for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
    837:       for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
    838:       BVTensorGetFactors(ctx->V,NULL,&MS);
    839:       MatDenseGetArray(MS,&S);
    840:       for (i=0;i<sr->sPres->nconv[0];i++) {
    841:         sr->eigr[aux[i]] = eigr[i];
    842:         sr->errest[aux[i]] = errest[i];
    843:         BVGetColumn(pep->V,i,&w);
    844:         BVInsertVec(sr->V,aux[i],w);
    845:         BVRestoreColumn(pep->V,i,&w);
    846:         idx = sr->ld*d*aux[i];
    847:         PetscArrayzero(sr->S+idx,sr->ld*d);
    848:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
    849:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
    850:         PetscFree(sr->qinfo[aux[i]].q);
    851:         PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
    852:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
    853:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
    854:       }
    855:       MatDenseRestoreArray(MS,&S);
    856:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    857:     }

    859:     if (sr->sPres->nconv[1]) {
    860:       if (divide) {
    861:         BVTensorGetFactors(ctx->V,NULL,&MS);
    862:         MatDenseGetArray(MS,&S);
    863:         for (i=0;i<sr->sPres->nconv[1];i++) {
    864:           PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
    865:           PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
    866:         }
    867:         MatDenseRestoreArray(MS,&S);
    868:         BVTensorRestoreFactors(ctx->V,NULL,&MS);
    869:         BVSetActiveColumns(pep->V,0,count);
    870:         BVCopy(tV,pep->V);
    871:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
    872:         BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
    873:       }
    874:       for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
    875:       for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
    876:       BVTensorGetFactors(ctx->V,NULL,&MS);
    877:       MatDenseGetArray(MS,&S);
    878:       for (i=0;i<sr->sPres->nconv[1];i++) {
    879:         sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
    880:         sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
    881:         BVGetColumn(pep->V,i,&w);
    882:         BVInsertVec(sr->V,aux[i],w);
    883:         BVRestoreColumn(pep->V,i,&w);
    884:         idx = sr->ld*d*aux[i];
    885:         PetscArrayzero(sr->S+idx,sr->ld*d);
    886:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
    887:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
    888:         PetscFree(sr->qinfo[aux[i]].q);
    889:         PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
    890:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
    891:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
    892:       }
    893:       MatDenseRestoreArray(MS,&S);
    894:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    895:     }
    896:     sPres->neigs = count-sr->ndef0-sr->ndef1;
    897:     sr->indexEig += sPres->neigs;
    898:     sPres->nconv[0]-= sr->ndef0;
    899:     sPres->nconv[1]-= sr->ndef1;
    900:     PetscFree4(eigr,errest,tS,aux);
    901:   } else {
    902:     sPres->neigs = 0;
    903:     sPres->nconv[0]= 0;
    904:     sPres->nconv[1]= 0;
    905:   }
    906:   /* Global ordering array updating */
    907:   sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
    908:   /* Check for completion */
    909:   sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
    910:   sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
    912:   if (divide) BVDestroy(&tV);
    913:   return 0;
    914: }

    916: static PetscErrorCode PEPLookForDeflation(PEP pep)
    917: {
    918:   PetscReal val;
    919:   PetscInt  i,count0=0,count1=0;
    920:   PEP_shift sPres;
    921:   PetscInt  ini,fin;
    922:   PEP_SR    sr;
    923:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

    925:   sr = ctx->sr;
    926:   sPres = sr->sPres;

    928:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    929:   else ini = 0;
    930:   fin = sr->indexEig;
    931:   /* Selection of ends for searching new values */
    932:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    933:   else sPres->ext[0] = sPres->neighb[0]->value;
    934:   if (!sPres->neighb[1]) {
    935:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    936:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    937:   } else sPres->ext[1] = sPres->neighb[1]->value;
    938:   /* Selection of values between right and left ends */
    939:   for (i=ini;i<fin;i++) {
    940:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    941:     /* Values to the right of left shift */
    942:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
    943:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
    944:       else count1++;
    945:     } else break;
    946:   }
    947:   /* The number of values on each side are found */
    948:   if (sPres->neighb[0]) {
    949:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    951:   } else sPres->nsch[0] = 0;

    953:   if (sPres->neighb[1]) {
    954:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    956:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    958:   /* Completing vector of indexes for deflation */
    959:   for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
    960:   sr->ndef0 = count0;
    961:   for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
    962:   sr->ndef1 = count1;
    963:   return 0;
    964: }

    966: /*
    967:   Compute a run of Lanczos iterations
    968: */
    969: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
    970: {
    971:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
    972:   PetscInt       i,j,m=*M,l,lock;
    973:   PetscInt       lds,d,ld,offq,nqt,ldds;
    974:   Vec            v=t_[0],t=t_[1],q=t_[2];
    975:   PetscReal      norm,sym=0.0,fro=0.0,*f;
    976:   PetscScalar    *y,*S,sigma;
    977:   PetscBLASInt   j_,one=1;
    978:   PetscBool      lindep;
    979:   Mat            MS;

    981:   PetscMalloc1(*M,&y);
    982:   BVGetSizes(pep->V,NULL,NULL,&ld);
    983:   BVTensorGetDegree(ctx->V,&d);
    984:   BVGetActiveColumns(pep->V,&lock,&nqt);
    985:   lds = d*ld;
    986:   offq = ld;
    987:   DSGetLeadingDimension(pep->ds,&ldds);

    989:   *breakdown = PETSC_FALSE; /* ----- */
    990:   STGetShift(pep->st,&sigma);
    991:   DSGetDimensions(pep->ds,NULL,&l,NULL,NULL);
    992:   BVSetActiveColumns(ctx->V,0,m);
    993:   BVSetActiveColumns(pep->V,0,nqt);
    994:   for (j=k;j<m;j++) {
    995:     /* apply operator */
    996:     BVTensorGetFactors(ctx->V,NULL,&MS);
    997:     MatDenseGetArray(MS,&S);
    998:     BVGetColumn(pep->V,nqt,&t);
    999:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
    1000:     MatMult(pep->A[1],v,q);
    1001:     MatMult(pep->A[2],v,t);
    1002:     VecAXPY(q,sigma*pep->sfactor,t);
    1003:     VecScale(q,pep->sfactor);
    1004:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
    1005:     MatMult(pep->A[2],v,t);
    1006:     VecAXPY(q,pep->sfactor*pep->sfactor,t);
    1007:     STMatSolve(pep->st,q,t);
    1008:     VecScale(t,-1.0);
    1009:     BVRestoreColumn(pep->V,nqt,&t);

    1011:     /* orthogonalize */
    1012:     BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
    1013:     if (!lindep) {
    1014:       *(S+(j+1)*lds+nqt) = norm;
    1015:       BVScaleColumn(pep->V,nqt,1.0/norm);
    1016:       nqt++;
    1017:     }
    1018:     for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
    1019:     BVSetActiveColumns(pep->V,0,nqt);
    1020:     MatDenseRestoreArray(MS,&S);
    1021:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

    1023:     /* level-2 orthogonalization */
    1024:     BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
    1025:     a[j] = PetscRealPart(y[j]);
    1026:     omega[j+1] = (norm > 0)?1.0:-1.0;
    1027:     BVScaleColumn(ctx->V,j+1,1.0/norm);
    1028:     b[j] = PetscAbsReal(norm);

    1030:     /* check symmetry */
    1031:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
    1032:     if (j==k) {
    1033:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
    1034:       for (i=0;i<l;i++) y[i] = 0.0;
    1035:     }
    1036:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
    1037:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
    1038:     PetscBLASIntCast(j,&j_);
    1039:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
    1040:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
    1041:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
    1042:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
    1043:       *symmlost = PETSC_TRUE;
    1044:       *M=j;
    1045:       break;
    1046:     }
    1047:   }
    1048:   BVSetActiveColumns(pep->V,lock,nqt);
    1049:   BVSetActiveColumns(ctx->V,0,*M);
    1050:   PetscFree(y);
    1051:   return 0;
    1052: }

    1054: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
    1055: {
    1056:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
    1057:   PetscInt       j,k,l,nv=0,ld,ldds,t,nq=0,idx;
    1058:   PetscInt       nconv=0,deg=pep->nmat-1,count0=0,count1=0;
    1059:   PetscScalar    *om,sigma,*back,*S,*pQ;
    1060:   PetscReal      beta,norm=1.0,*omega,*a,*b,eta,lambda;
    1061:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
    1062:   Mat            MS,MQ,D;
    1063:   Vec            v,vomega;
    1064:   PEP_SR         sr;
    1065:   BVOrthogType   otype;
    1066:   BVOrthogBlockType obtype;

    1068:   /* Resize if needed for deflating vectors  */
    1069:   sr = ctx->sr;
    1070:   sigma = sr->sPres->value;
    1071:   k = sr->ndef0+sr->ndef1;
    1072:   pep->ncv = ctx->ncv+k;
    1073:   pep->nev = ctx->nev+k;
    1074:   PEPAllocateSolution(pep,3);
    1075:   BVDestroy(&ctx->V);
    1076:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
    1077:   BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
    1078:   BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
    1079:   DSAllocate(pep->ds,pep->ncv+2);
    1080:   PetscMalloc1(pep->ncv,&back);
    1081:   DSGetLeadingDimension(pep->ds,&ldds);
    1082:   BVSetMatrix(ctx->V,B,PETSC_TRUE);
    1084:   /* undocumented option to use a cheaper locking instead of the true locking */
    1085:   PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
    1086:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
    1087:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
    1088:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

    1090:   /* Get the starting Arnoldi vector */
    1091:   BVSetActiveColumns(pep->V,0,1);
    1092:   BVTensorBuildFirstColumn(ctx->V,pep->nini);
    1093:   BVSetActiveColumns(ctx->V,0,1);
    1094:   if (k) {
    1095:     /* Insert deflated vectors */
    1096:     BVSetActiveColumns(pep->V,0,0);
    1097:     idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
    1098:     for (j=0;j<k;j++) {
    1099:       BVGetColumn(pep->V,j,&v);
    1100:       BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
    1101:       BVRestoreColumn(pep->V,j,&v);
    1102:     }
    1103:     /* Update innerproduct matrix */
    1104:     BVSetActiveColumns(ctx->V,0,0);
    1105:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1106:     BVSetActiveColumns(pep->V,0,k);
    1107:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

    1109:     BVGetSizes(pep->V,NULL,NULL,&ld);
    1110:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1111:     MatDenseGetArray(MS,&S);
    1112:     for (j=0;j<sr->ndef0;j++) {
    1113:       PetscArrayzero(S+j*ld*deg,ld*deg);
    1114:       PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
    1115:       PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
    1116:       pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
    1117:       pep->errest[j] = sr->errest[sr->idxDef0[j]];
    1118:     }
    1119:     for (j=0;j<sr->ndef1;j++) {
    1120:       PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
    1121:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
    1122:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
    1123:       pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
    1124:       pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
    1125:     }
    1126:     MatDenseRestoreArray(MS,&S);
    1127:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1128:     BVSetActiveColumns(ctx->V,0,k+1);
    1129:     VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
    1130:     VecGetArray(vomega,&om);
    1131:     for (j=0;j<k;j++) {
    1132:       BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
    1133:       BVScaleColumn(ctx->V,j,1/norm);
    1134:       om[j] = (norm>=0.0)?1.0:-1.0;
    1135:     }
    1136:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1137:     MatDenseGetArray(MS,&S);
    1138:     for (j=0;j<deg;j++) {
    1139:       BVSetRandomColumn(pep->V,k+j);
    1140:       BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
    1141:       BVScaleColumn(pep->V,k+j,1.0/norm);
    1142:       S[k*ld*deg+j*ld+k+j] = norm;
    1143:     }
    1144:     MatDenseRestoreArray(MS,&S);
    1145:     BVSetActiveColumns(pep->V,0,k+deg);
    1146:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1147:     BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
    1148:     BVScaleColumn(ctx->V,k,1.0/norm);
    1149:     om[k] = (norm>=0.0)?1.0:-1.0;
    1150:     VecRestoreArray(vomega,&om);
    1151:     BVSetSignature(ctx->V,vomega);
    1152:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
    1153:     VecGetArray(vomega,&om);
    1154:     for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
    1155:     VecRestoreArray(vomega,&om);
    1156:     VecDestroy(&vomega);
    1157:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
    1158:     DSGetArray(pep->ds,DS_MAT_Q,&pQ);
    1159:     PetscArrayzero(pQ,ldds*k);
    1160:     for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
    1161:     DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
    1162:   }
    1163:   BVSetActiveColumns(ctx->V,0,k+1);
    1164:   DSSetDimensions(pep->ds,k+1,PETSC_DEFAULT,PETSC_DEFAULT);
    1165:   DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
    1166:   BVGetSignature(ctx->V,vomega);
    1167:   DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);

    1169:   PetscInfo(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%" PetscInt_FMT " right=%" PetscInt_FMT ", searching: left=%" PetscInt_FMT " right=%" PetscInt_FMT "\n",(double)sr->sPres->value,(double)(sr->sPres->neighb[0]?sr->sPres->neighb[0]->value:sr->int0),(double)(sr->sPres->neighb[1]?sr->sPres->neighb[1]->value:sr->int1),sr->ndef0,sr->ndef1,sr->sPres->nsch[0],sr->sPres->nsch[1]);

    1171:   /* Restart loop */
    1172:   l = 0;
    1173:   pep->nconv = k;
    1174:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    1175:     pep->its++;
    1176:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
    1177:     b = a+ldds;
    1178:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

    1180:     /* Compute an nv-step Lanczos factorization */
    1181:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
    1182:     PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
    1183:     beta = b[nv-1];
    1184:     if (symmlost && nv==pep->nconv+l) {
    1185:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
    1186:       pep->nconv = nconv;
    1187:       PetscInfo(pep,"Symmetry lost in STOAR sigma=%g nconv=%" PetscInt_FMT "\n",(double)sr->sPres->value,nconv);
    1188:       if (falselock || !ctx->lock) {
    1189:         BVSetActiveColumns(ctx->V,0,pep->nconv);
    1190:         BVTensorCompress(ctx->V,0);
    1191:       }
    1192:       break;
    1193:     }
    1194:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
    1195:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
    1196:     DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l);
    1197:     if (l==0) DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
    1198:     else DSSetState(pep->ds,DS_STATE_RAW);

    1200:     /* Solve projected problem */
    1201:     DSSolve(pep->ds,pep->eigr,pep->eigi);
    1202:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
    1203:     DSUpdateExtraRow(pep->ds);
    1204:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

    1206:     /* Check convergence */
    1207:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
    1208:     norm = 1.0;
    1209:     DSGetDimensions(pep->ds,NULL,NULL,NULL,&t);
    1210:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
    1211:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
    1212:     for (j=0;j<k;j++) back[j] = pep->eigr[j];
    1213:     STBackTransform(pep->st,k,back,pep->eigi);
    1214:     count0=count1=0;
    1215:     for (j=0;j<k;j++) {
    1216:       lambda = PetscRealPart(back[j]);
    1217:       if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
    1218:       if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
    1219:     }
    1220:     if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
    1221:     /* Update l */
    1222:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
    1223:     else {
    1224:       l = PetscMax(1,(PetscInt)((nv-k)/2));
    1225:       l = PetscMin(l,t);
    1226:       DSGetTruncateSize(pep->ds,k,t,&l);
    1227:       if (!breakdown) {
    1228:         /* Prepare the Rayleigh quotient for restart */
    1229:         DSTruncate(pep->ds,k+l,PETSC_FALSE);
    1230:       }
    1231:     }
    1232:     nconv = k;
    1233:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
    1234:     if (l) PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);

    1236:     /* Update S */
    1237:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
    1238:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
    1239:     DSRestoreMat(pep->ds,DS_MAT_Q,&MQ);

    1241:     /* Copy last column of S */
    1242:     BVCopyColumn(ctx->V,nv,k+l);
    1243:     BVSetActiveColumns(ctx->V,0,k+l);
    1244:     if (k+l) {
    1245:       DSSetDimensions(pep->ds,k+l,PETSC_DEFAULT,PETSC_DEFAULT);
    1246:       DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
    1247:       BVSetSignature(ctx->V,vomega);
    1248:       DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
    1249:     }

    1251:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
    1252:       /* stop if breakdown */
    1253:       PetscInfo(pep,"Breakdown TOAR method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta);
    1254:       pep->reason = PEP_DIVERGED_BREAKDOWN;
    1255:     }
    1256:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
    1257:     BVGetActiveColumns(pep->V,NULL,&nq);
    1258:     if (k+l+deg<=nq) {
    1259:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
    1260:       if (!falselock && ctx->lock) BVTensorCompress(ctx->V,k-pep->nconv);
    1261:       else BVTensorCompress(ctx->V,0);
    1262:     }
    1263:     pep->nconv = k;
    1264:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
    1265:   }
    1266:   sr->itsKs += pep->its;
    1267:   if (pep->nconv>0) {
    1268:     BVSetActiveColumns(ctx->V,0,pep->nconv);
    1269:     BVGetActiveColumns(pep->V,NULL,&nq);
    1270:     BVSetActiveColumns(pep->V,0,nq);
    1271:     if (nq>pep->nconv) {
    1272:       BVTensorCompress(ctx->V,pep->nconv);
    1273:       BVSetActiveColumns(pep->V,0,pep->nconv);
    1274:     }
    1275:     for (j=0;j<pep->nconv;j++) {
    1276:       pep->eigr[j] *= pep->sfactor;
    1277:       pep->eigi[j] *= pep->sfactor;
    1278:     }
    1279:   }
    1280:   PetscInfo(pep,"Finished STOAR: nconv=%" PetscInt_FMT " (deflated=%" PetscInt_FMT ", left=%" PetscInt_FMT ", right=%" PetscInt_FMT ")\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1);
    1281:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
    1282:   RGPopScale(pep->rg);

    1285:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
    1287:   } else sr->symmlost = 0;

    1289:   DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
    1290:   PetscFree(back);
    1291:   return 0;
    1292: }

    1294: #define SWAP(a,b,t) {t=a;a=b;b=t;}

    1296: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    1297: {
    1298:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    1299:   PEP_SR          sr=ctx->sr;
    1300:   PetscInt        i=0,j,tmpi;
    1301:   PetscReal       v,tmpr;
    1302:   PEP_shift       s;

    1306:   if (!sr->s0) {  /* PEPSolve not called yet */
    1307:     *n = 2;
    1308:   } else {
    1309:     *n = 1;
    1310:     s = sr->s0;
    1311:     while (s) {
    1312:       (*n)++;
    1313:       s = s->neighb[1];
    1314:     }
    1315:   }
    1316:   PetscMalloc1(*n,shifts);
    1317:   PetscMalloc1(*n,inertias);
    1318:   if (!sr->s0) {  /* PEPSolve not called yet */
    1319:     (*shifts)[0]   = sr->int0;
    1320:     (*shifts)[1]   = sr->int1;
    1321:     (*inertias)[0] = sr->inertia0;
    1322:     (*inertias)[1] = sr->inertia1;
    1323:   } else {
    1324:     s = sr->s0;
    1325:     while (s) {
    1326:       (*shifts)[i]     = s->value;
    1327:       (*inertias)[i++] = s->inertia;
    1328:       s = s->neighb[1];
    1329:     }
    1330:     (*shifts)[i]   = sr->int1;
    1331:     (*inertias)[i] = sr->inertia1;
    1332:   }
    1333:   /* remove possible duplicate in last position */
    1334:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    1335:   /* sort result */
    1336:   for (i=0;i<*n;i++) {
    1337:     v = (*shifts)[i];
    1338:     for (j=i+1;j<*n;j++) {
    1339:       if (v > (*shifts)[j]) {
    1340:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    1341:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    1342:         v = (*shifts)[i];
    1343:       }
    1344:     }
    1345:   }
    1346:   return 0;
    1347: }

    1349: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
    1350: {
    1351:   PetscInt       i,j,ti,deg=pep->nmat-1;
    1352:   PetscReal      newS;
    1353:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    1354:   PEP_SR         sr=ctx->sr;
    1355:   Mat            S,B;
    1356:   PetscScalar    *pS;

    1358:   PetscCitationsRegister(citation,&cited);

    1360:   /* Only with eigenvalues present in the interval ...*/
    1361:   if (sr->numEigs==0) {
    1362:     pep->reason = PEP_CONVERGED_TOL;
    1363:     return 0;
    1364:   }

    1366:   /* Inner product matrix */
    1367:   PEPSTOARSetUpInnerMatrix(pep,&B);

    1369:   /* Array of pending shifts */
    1370:   sr->maxPend = 100; /* Initial size */
    1371:   sr->nPend = 0;
    1372:   PetscMalloc1(sr->maxPend,&sr->pending);
    1373:   PEPCreateShift(pep,sr->int0,NULL,NULL);
    1374:   /* extract first shift */
    1375:   sr->sPrev = NULL;
    1376:   sr->sPres = sr->pending[--sr->nPend];
    1377:   sr->sPres->inertia = sr->inertia0;
    1378:   pep->target = sr->sPres->value;
    1379:   sr->s0 = sr->sPres;
    1380:   sr->indexEig = 0;

    1382:   for (i=0;i<sr->numEigs;i++) {
    1383:     sr->eigr[i]   = 0.0;
    1384:     sr->eigi[i]   = 0.0;
    1385:     sr->errest[i] = 0.0;
    1386:     sr->perm[i]   = i;
    1387:   }
    1388:   /* Vectors for deflation */
    1389:   PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
    1390:   sr->indexEig = 0;
    1391:   while (sr->sPres) {
    1392:     /* Search for deflation */
    1393:     PEPLookForDeflation(pep);
    1394:     /* KrylovSchur */
    1395:     PEPSTOAR_QSlice(pep,B);

    1397:     PEPStoreEigenpairs(pep);
    1398:     /* Select new shift */
    1399:     if (!sr->sPres->comp[1]) {
    1400:       PEPGetNewShiftValue(pep,1,&newS);
    1401:       PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
    1402:     }
    1403:     if (!sr->sPres->comp[0]) {
    1404:       /* Completing earlier interval */
    1405:       PEPGetNewShiftValue(pep,0,&newS);
    1406:       PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
    1407:     }
    1408:     /* Preparing for a new search of values */
    1409:     PEPExtractShift(pep);
    1410:   }

    1412:   /* Updating pep values prior to exit */
    1413:   PetscFree2(sr->idxDef0,sr->idxDef1);
    1414:   PetscFree(sr->pending);
    1415:   pep->nconv  = sr->indexEig;
    1416:   pep->reason = PEP_CONVERGED_TOL;
    1417:   pep->its    = sr->itsKs;
    1418:   pep->nev    = sr->indexEig;
    1419:   MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
    1420:   MatDenseGetArray(S,&pS);
    1421:   for (i=0;i<pep->nconv;i++) {
    1422:     for (j=0;j<sr->qinfo[i].nq;j++) pS[i*pep->nconv+sr->qinfo[i].q[j]] = *(sr->S+i*sr->ld*deg+j);
    1423:   }
    1424:   MatDenseRestoreArray(S,&pS);
    1425:   BVSetActiveColumns(sr->V,0,pep->nconv);
    1426:   BVMultInPlace(sr->V,S,0,pep->nconv);
    1427:   MatDestroy(&S);
    1428:   BVDestroy(&pep->V);
    1429:   pep->V = sr->V;
    1430:   PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
    1431:   pep->eigr   = sr->eigr;
    1432:   pep->eigi   = sr->eigi;
    1433:   pep->perm   = sr->perm;
    1434:   pep->errest = sr->errest;
    1435:   if (sr->dir<0) {
    1436:     for (i=0;i<pep->nconv/2;i++) {
    1437:       ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
    1438:     }
    1439:   }
    1440:   PetscFree(ctx->inertias);
    1441:   PetscFree(ctx->shifts);
    1442:   MatDestroy(&B);
    1443:   PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
    1444:   return 0;
    1445: }