Date: 2021-02-01T14:42:12+00:00

Actual source code: qslice.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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: {
     48:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
     49:   PEP_SR         sr=ctx->sr;
     50:   PEP_shift      s;
     51:   PetscInt       i;

     54:   if (sr) {
     55:     /* Reviewing list of shifts to free memory */
     56:     s = sr->s0;
     57:     if (s) {
     58:       while (s->neighb[1]) {
     59:         s = s->neighb[1];
     60:         PetscFree(s->neighb[0]);
     61:       }
     62:       PetscFree(s);
     63:     }
     64:     PetscFree(sr->S);
     65:     for (i=0;i<pep->nconv;i++) {PetscFree(sr->qinfo[i].q);}
     66:     PetscFree(sr->qinfo);
     67:     for (i=0;i<3;i++) {VecDestroy(&sr->v[i]);}
     68:     EPSDestroy(&sr->eps);
     69:     PetscFree(sr);
     70:   }
     71:   ctx->sr = NULL;
     72:   return(0);
     73: }

     75: PetscErrorCode PEPReset_STOAR_QSlice(PEP pep)
     76: {
     78:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

     81:   PEPQSliceResetSR(pep);
     82:   PetscFree(ctx->inertias);
     83:   PetscFree(ctx->shifts);
     84:   return(0);
     85: }

     87: /*
     88:   PEPQSliceAllocateSolution - Allocate memory storage for common variables such
     89:   as eigenvalues and eigenvectors.
     90: */
     91: static PetscErrorCode PEPQSliceAllocateSolution(PEP pep)
     92: {
     94:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
     95:   PetscInt       k;
     96:   PetscLogDouble cnt;
     97:   BVType         type;
     98:   Vec            t;
     99:   PEP_SR         sr = ctx->sr;

    102:   /* allocate space for eigenvalues and friends */
    103:   k = PetscMax(1,sr->numEigs);
    104:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
    105:   PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
    106:   PetscFree(sr->qinfo);
    107:   PetscCalloc1(k,&sr->qinfo);
    108:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
    109:   PetscLogObjectMemory((PetscObject)pep,cnt);

    111:   /* allocate sr->V and transfer options from pep->V */
    112:   BVDestroy(&sr->V);
    113:   BVCreate(PetscObjectComm((PetscObject)pep),&sr->V);
    114:   PetscLogObjectParent((PetscObject)pep,(PetscObject)sr->V);
    115:   if (!pep->V) { PEPGetBV(pep,&pep->V); }
    116:   if (!((PetscObject)(pep->V))->type_name) {
    117:     BVSetType(sr->V,BVSVEC);
    118:   } else {
    119:     BVGetType(pep->V,&type);
    120:     BVSetType(sr->V,type);
    121:   }
    122:   STMatCreateVecsEmpty(pep->st,&t,NULL);
    123:   BVSetSizesFromVec(sr->V,t,k+1);
    124:   VecDestroy(&t);
    125:   sr->ld = k;
    126:   PetscFree(sr->S);
    127:   PetscMalloc1((k+1)*sr->ld*(pep->nmat-1),&sr->S);
    128:   return(0);
    129: }

    131: /* Convergence test to compute positive Ritz values */
    132: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    133: {
    135:   *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
    136:   return(0);
    137: }

    139: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    140: {
    141:   KSP            ksp,kspr;
    142:   PC             pc;
    143:   Mat            F;
    144:   PetscBool      flg;

    148:   if (!pep->solvematcoeffs) {
    149:     PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
    150:   }
    151:   if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
    152:     pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
    153:   } else {
    154:     PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL);
    155:   }
    156:   STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
    157:   STGetKSP(pep->st,&ksp);
    158:   KSPGetPC(ksp,&pc);
    159:   PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
    160:   if (flg) {
    161:     PCRedundantGetKSP(pc,&kspr);
    162:     KSPGetPC(kspr,&pc);
    163:   }
    164:   PCFactorGetMatrix(pc,&F);
    165:   MatGetInertia(F,inertia,zeros,NULL);
    166:   return(0);
    167: }

    169: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
    170: {
    172:   KSP            ksp;
    173:   Mat            P;
    174:   PetscReal      nzshift=0.0;
    175:   PetscScalar    dot;
    176:   PetscRandom    rand;
    177:   PetscInt       nconv;
    178:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    179:   PEP_SR         sr=ctx->sr;

    182:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    183:     *inertia = 0;
    184:   } else if (shift <= PETSC_MIN_REAL) {
    185:     *inertia = 0;
    186:     if (zeros) *zeros = 0;
    187:   } else {
    188:     /* If the shift is zero, perturb it to a very small positive value.
    189:        The goal is that the nonzero pattern is the same in all cases and reuse
    190:        the symbolic factorizations */
    191:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
    192:     PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
    193:     STSetShift(pep->st,nzshift);
    194:   }
    195:   if (!correction) {
    196:     if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
    197:     else if (shift>PETSC_MIN_REAL) {
    198:       STGetKSP(pep->st,&ksp);
    199:       KSPGetOperators(ksp,&P,NULL);
    200:       if (*inertia!=pep->n && !sr->v[0]) {
    201:         MatCreateVecs(P,&sr->v[0],NULL);
    202:         VecDuplicate(sr->v[0],&sr->v[1]);
    203:         VecDuplicate(sr->v[0],&sr->v[2]);
    204:         BVGetRandomContext(pep->V,&rand);
    205:         VecSetRandom(sr->v[0],rand);
    206:       }
    207:       if (*inertia<pep->n && *inertia>0) {
    208:         if (!sr->eps) {
    209:           EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
    210:           EPSSetProblemType(sr->eps,EPS_HEP);
    211:           EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
    212:         }
    213:         EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
    214:         EPSSetOperators(sr->eps,P,NULL);
    215:         EPSSolve(sr->eps);
    216:         EPSGetConverged(sr->eps,&nconv);
    217:         if (!nconv) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",nzshift);
    218:         EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
    219:       }
    220:       if (*inertia!=pep->n) {
    221:         MatMult(pep->A[1],sr->v[0],sr->v[1]);
    222:         MatMult(pep->A[2],sr->v[0],sr->v[2]);
    223:         VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
    224:         VecDot(sr->v[1],sr->v[0],&dot);
    225:         if (PetscRealPart(dot)>0.0) *inertia = 2*pep->n-*inertia;
    226:       }
    227:     }
    228:   } else if (correction<0) *inertia = 2*pep->n-*inertia;
    229:   return(0);
    230: }

    232: /*
    233:    Check eigenvalue type - used only in non-hyperbolic problems.
    234:    All computed eigenvalues must have the same definite type (positive or negative).
    235:    If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
    236:    closest to shift and determine its type.
    237:  */
    238: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
    239: {
    241:   PEP            pep2;
    242:   ST             st;
    243:   PetscInt       nconv;
    244:   PetscScalar    lambda,dot;
    245:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    246:   PEP_SR         sr=ctx->sr;

    249:   if (!ini) {
    250:     if (-(omega/(shift*ctx->alpha+ctx->beta))*sr->type<0) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)shift);
    251:   } else {
    252:     PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
    253:     PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
    254:     PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
    255:     PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
    256:     PEPSetType(pep2,PEPTOAR);
    257:     PEPSetOperators(pep2,pep->nmat,pep->A);
    258:     PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
    259:     PEPGetRG(pep2,&pep2->rg);
    260:     RGSetType(pep2->rg,RGINTERVAL);
    261: #if defined(PETSC_USE_COMPLEX)
    262:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
    263: #else
    264:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
    265: #endif
    266:     pep2->target = shift;
    267:     st = pep2->st;
    268:     pep2->st = pep->st;
    269:     PEPSolve(pep2);
    270:     PEPGetConverged(pep2,&nconv);
    271:     if (nconv) {
    272:       PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
    273:       MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
    274:       MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
    275:       VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
    276:       VecDot(pep2->work[1],pep2->work[0],&dot);
    277:       PetscInfo2(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(PetscRealPart(dot)>0.0)?"positive":"negative");
    278:       if (!sr->type) sr->type = (PetscRealPart(dot)>0.0)?1:-1;
    279:       else {
    280:         if (sr->type*PetscRealPart(dot)<0.0) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)PetscRealPart(lambda));
    281:       }
    282:     }
    283:     pep2->st = st;
    284:     PEPDestroy(&pep2);
    285:   }
    286:   return(0);
    287: }

    289: PETSC_STATIC_INLINE PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
    290: {
    291:   PetscReal      ap,bp,cp,dis;
    292:   PetscScalar    ts;

    296:   MatMult(pep->A[0],u,w);
    297:   VecDot(w,u,&ts);
    298:   cp = PetscRealPart(ts);
    299:   MatMult(pep->A[1],u,w);
    300:   VecDot(w,u,&ts);
    301:   bp = PetscRealPart(ts);
    302:   MatMult(pep->A[2],u,w);
    303:   VecDot(w,u,&ts);
    304:   ap = PetscRealPart(ts);
    305:   dis = bp*bp-4*ap*cp;
    306:   if (dis>=0.0 && smas) {
    307:     if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
    308:     else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
    309:     else {
    310:       if (bp >0) *smas = -cp/bp;
    311:       else *smas = PETSC_MAX_REAL;
    312:     }
    313:   }
    314:   if (dis>=0.0 && smenos) {
    315:     if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
    316:     else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
    317:     else {
    318:       if (bp<0) *smenos = -cp/bp;
    319:       else *smenos = PETSC_MAX_REAL;
    320:     }
    321:   }
    322:   if (d) *d = dis;
    323:   return(0);
    324: }

    326: PETSC_STATIC_INLINE PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
    327: {

    331:   MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
    332:   MatAXPY(M,x,pep->A[1],str);
    333:   MatAXPY(M,x*x,pep->A[2],str);
    334:   return(0);
    335: }

    337: /*@
    338:    PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
    339:    is definite or not.

    341:    Logically Collective on pep

    343:    Input Parameter:
    344: .  pep  - eigensolver context

    346:    Output Parameters:
    347: +  xi - first computed parameter
    348: .  mu - second computed parameter
    349: .  definite - flag indicating that the problem is definite
    350: -  hyperbolic - flag indicating that the problem is hyperbolic

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

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

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

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

    367:    Level: advanced
    368: @*/
    369: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
    370: {
    372:   PetscRandom    rand;
    373:   Vec            u,w;
    374:   PetscReal      d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
    375:   PetscInt       k,its=10,hyp=0,check=0,nconv,inertia,n;
    376:   Mat            M=NULL;
    377:   MatStructure   str;
    378:   EPS            eps;
    379:   PetscBool      transform,ptypehyp;

    382:   if (pep->problem_type!=PEP_HERMITIAN && pep->problem_type!=PEP_HYPERBOLIC) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only available for Hermitian (or hyperbolic) problems");
    383:   ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
    384:   if (!pep->st) { PEPGetST(pep,&pep->st); }
    385:   PEPSetDefaultST(pep);
    386:   STSetMatrices(pep->st,pep->nmat,pep->A);
    387:   MatGetSize(pep->A[0],&n,NULL);
    388:   STGetTransform(pep->st,&transform);
    389:   STSetTransform(pep->st,PETSC_FALSE);
    390:   STSetUp(pep->st);
    391:   MatCreateVecs(pep->A[0],&u,&w);
    392:   PEPGetBV(pep,&pep->V);
    393:   BVGetRandomContext(pep->V,&rand);
    394:   VecSetRandom(u,rand);
    395:   VecNormalize(u,NULL);
    396:   PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
    397:   if (d<0.0) check = -1;
    398:   if (!check) {
    399:     EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
    400:     EPSSetProblemType(eps,EPS_HEP);
    401:     EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
    402:     EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
    403:     MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
    404:     STGetMatStructure(pep->st,&str);
    405:   }
    406:   for (k=0;k<its&&!check;k++) {
    407:     PEPQSliceEvaluateQEP(pep,s,M,str);
    408:     EPSSetOperators(eps,M,NULL);
    409:     EPSSolve(eps);
    410:     EPSGetConverged(eps,&nconv);
    411:     if (!nconv) break;
    412:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    413:     sp = s;
    414:     PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
    415:     if (d<0.0) {check = -1; break;}
    416:     if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
    417:     if (s>sp) {hyp = -1;}
    418:     mut = 2*s-sp;
    419:      PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    420:     if (inertia == n) {check = 1; break;}
    421:   }
    422:   for (;k<its&&!check;k++) {
    423:     mut = (s-omg)/2;
    424:      PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    425:     if (inertia == n) {check = 1; break;}
    426:     if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
    427:     PEPQSliceEvaluateQEP(pep,omg,M,str);
    428:     EPSSetOperators(eps,M,NULL);
    429:     EPSSolve(eps);
    430:     EPSGetConverged(eps,&nconv);
    431:     if (!nconv) break;
    432:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    433:     omgp = omg;
    434:     PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
    435:     if (d<0.0) {check = -1; break;}
    436:     if (omg<omgp) hyp = -1;
    437:   }
    438:   if (check==1) *xi = mut;
    439:   if (hyp==-1 && ptypehyp) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem does not satisfy hyperbolic test; consider removing the hyperbolicity flag");
    440:   if (check==1 && hyp==0) {
    441:      PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
    442:     if (inertia == 0) hyp = 1;
    443:     else hyp = -1;
    444:   }
    445:   if (check==1 && hyp!=1) {
    446:     check = 0;
    447:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
    448:     for (;k<its&&!check;k++) {
    449:       PEPQSliceEvaluateQEP(pep,s,M,str);
    450:       EPSSetOperators(eps,M,NULL);
    451:       EPSSolve(eps);
    452:       EPSGetConverged(eps,&nconv);
    453:       if (!nconv) break;
    454:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    455:       sp = s;
    456:       PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
    457:       if (d<0.0) {check = -1; break;}
    458:       if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
    459:       mut = 2*s-sp;
    460:        PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    461:       if (inertia == 0) {check = 1; break;}
    462:     }
    463:     for (;k<its&&!check;k++) {
    464:       mut = (s-omg)/2;
    465:        PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
    466:       if (inertia == 0) {check = 1; break;}
    467:       if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
    468:       PEPQSliceEvaluateQEP(pep,omg,M,str);
    469:       EPSSetOperators(eps,M,NULL);
    470:       EPSSolve(eps);
    471:       EPSGetConverged(eps,&nconv);
    472:       if (!nconv) break;
    473:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
    474:       PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
    475:       if (d<0.0) {check = -1; break;}
    476:     }
    477:   }
    478:   if (check==1) *mu = mut;
    479:   *definite = check;
    480:   *hyperbolic = hyp;
    481:   if (M) { MatDestroy(&M); }
    482:   VecDestroy(&u);
    483:   VecDestroy(&w);
    484:   EPSDestroy(&eps);
    485:   STSetTransform(pep->st,transform);
    486:   return(0);
    487: }

    489: /*
    490:    Dummy backtransform operation
    491:  */
    492: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
    493: {
    495:   return(0);
    496: }

    498: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
    499: {
    501:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    502:   PEP_SR         sr;
    503:   PetscInt       ld,i,zeros=0;
    504:   SlepcSC        sc;
    505:   PetscReal      r;

    508:   PEPCheckSinvertCayley(pep);
    509:   if (pep->inta==pep->intb) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues unless you provide a computational interval with PEPSetInterval()");
    510:   if (pep->intb >= PETSC_MAX_REAL && pep->inta <= PETSC_MIN_REAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
    511:   PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
    512:   if (pep->tol==PETSC_DEFAULT) {
    513: #if defined(PETSC_USE_REAL_SINGLE)
    514:     pep->tol = SLEPC_DEFAULT_TOL;
    515: #else
    516:     /* use tighter tolerance */
    517:     pep->tol = SLEPC_DEFAULT_TOL*1e-2;
    518: #endif
    519:   }
    520:   if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n);  /* nev not set, use default value */
    521:   if (pep->n>10 && ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
    522:   pep->ops->backtransform = PEPBackTransform_Skip;
    523:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;

    525:   /* create spectrum slicing context and initialize it */
    526:   PEPQSliceResetSR(pep);
    527:   PetscNewLog(pep,&sr);
    528:   ctx->sr   = sr;
    529:   sr->itsKs = 0;
    530:   sr->nleap = 0;
    531:   sr->sPres = NULL;

    533:   if (pep->solvematcoeffs) { PetscFree(pep->solvematcoeffs); }
    534:   PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
    535:   if (!pep->st) { PEPGetST(pep,&pep->st); }
    536:   STSetTransform(pep->st,PETSC_FALSE);
    537:   STSetUp(pep->st);

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

    541:   /* check presence of ends and finding direction */
    542:   if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
    543:     sr->int0 = pep->inta;
    544:     sr->int1 = pep->intb;
    545:     sr->dir = 1;
    546:     if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
    547:       sr->hasEnd = PETSC_FALSE;
    548:     } else sr->hasEnd = PETSC_TRUE;
    549:   } else {
    550:     sr->int0 = pep->intb;
    551:     sr->int1 = pep->inta;
    552:     sr->dir = -1;
    553:     sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
    554:   }

    556:   /* compute inertia0 */
    557:   PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
    558:   if (zeros && (sr->int0==pep->inta || sr->int0==pep->intb)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
    559:   if (!ctx->hyperbolic && ctx->checket) {
    560:     PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE);
    561:   }

    563:   /* compute inertia1 */
    564:   PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
    565:   if (zeros) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    566:   if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
    567:     PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE);
    568:     if (!sr->type && (sr->inertia1-sr->inertia0)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"No information of eigenvalue type in Interval");
    569:     if (sr->type && !(sr->inertia1-sr->inertia0)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected");
    570:     if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
    571:       sr->intcorr = -1;
    572:       sr->inertia0 = 2*pep->n-sr->inertia0;
    573:       sr->inertia1 = 2*pep->n-sr->inertia1;
    574:     } else sr->intcorr = 1;
    575:   } else {
    576:     if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
    577:     else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
    578:   }

    580:   if (sr->hasEnd) {
    581:     sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
    582:     i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
    583:   }

    585:   /* number of eigenvalues in interval */
    586:   sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    587:   PetscInfo3(pep,"QSlice setup: allocating for %D eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb);
    588:   if (sr->numEigs) {
    589:     PEPQSliceAllocateSolution(pep);
    590:     PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd);
    591:     pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
    592:     ld   = ctx->ncv+2;
    593:     DSSetType(pep->ds,DSGHIEP);
    594:     DSSetCompact(pep->ds,PETSC_TRUE);
    595:     DSAllocate(pep->ds,ld);
    596:     DSGetSlepcSC(pep->ds,&sc);
    597:     sc->rg            = NULL;
    598:     sc->comparison    = SlepcCompareLargestMagnitude;
    599:     sc->comparisonctx = NULL;
    600:     sc->map           = NULL;
    601:     sc->mapobj        = NULL;
    602:   }
    603:   return(0);
    604: }

    606: /*
    607:    Fills the fields of a shift structure
    608: */
    609: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
    610: {
    612:   PEP_shift      s,*pending2;
    613:   PetscInt       i;
    614:   PEP_SR         sr;
    615:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

    618:   sr = ctx->sr;
    619:   PetscNewLog(pep,&s);
    620:   s->value = val;
    621:   s->neighb[0] = neighb0;
    622:   if (neighb0) neighb0->neighb[1] = s;
    623:   s->neighb[1] = neighb1;
    624:   if (neighb1) neighb1->neighb[0] = s;
    625:   s->comp[0] = PETSC_FALSE;
    626:   s->comp[1] = PETSC_FALSE;
    627:   s->index = -1;
    628:   s->neigs = 0;
    629:   s->nconv[0] = s->nconv[1] = 0;
    630:   s->nsch[0] = s->nsch[1]=0;
    631:   /* Inserts in the stack of pending shifts */
    632:   /* If needed, the array is resized */
    633:   if (sr->nPend >= sr->maxPend) {
    634:     sr->maxPend *= 2;
    635:     PetscMalloc1(sr->maxPend,&pending2);
    636:     PetscLogObjectMemory((PetscObject)pep,sizeof(PEP_shift));
    637:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
    638:     PetscFree(sr->pending);
    639:     sr->pending = pending2;
    640:   }
    641:   sr->pending[sr->nPend++]=s;
    642:   return(0);
    643: }

    645: /* Provides next shift to be computed */
    646: static PetscErrorCode PEPExtractShift(PEP pep)
    647: {
    649:   PetscInt       iner,zeros=0;
    650:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    651:   PEP_SR         sr;
    652:   PetscReal      newShift,aux;
    653:   PEP_shift      sPres;

    656:   sr = ctx->sr;
    657:   if (sr->nPend > 0) {
    658:     if (sr->dirch) {
    659:       aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
    660:       iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
    661:       sr->dir *= -1;
    662:       PetscFree(sr->s0->neighb[1]);
    663:       PetscFree(sr->s0);
    664:       sr->nPend--;
    665:       PEPCreateShift(pep,sr->int0,NULL,NULL);
    666:       sr->sPrev = NULL;
    667:       sr->sPres = sr->pending[--sr->nPend];
    668:       pep->target = sr->sPres->value;
    669:       sr->s0 = sr->sPres;
    670:       pep->reason = PEP_CONVERGED_ITERATING;
    671:     } else {
    672:       sr->sPrev = sr->sPres;
    673:       sr->sPres = sr->pending[--sr->nPend];
    674:     }
    675:     sPres = sr->sPres;
    676:     PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
    677:     if (zeros) {
    678:       newShift = sPres->value*(1.0+SLICE_PTOL);
    679:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    680:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    681:       PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
    682:       if (zeros) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
    683:       sPres->value = newShift;
    684:     }
    685:     sr->sPres->inertia = iner;
    686:     pep->target = sr->sPres->value;
    687:     pep->reason = PEP_CONVERGED_ITERATING;
    688:     pep->its = 0;
    689:   } else sr->sPres = NULL;
    690:   return(0);
    691: }

    693: /*
    694:   Obtains value of subsequent shift
    695: */
    696: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
    697: {
    698:   PetscReal lambda,d_prev;
    699:   PetscInt  i,idxP;
    700:   PEP_SR    sr;
    701:   PEP_shift sPres,s;
    702:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

    705:   sr = ctx->sr;
    706:   sPres = sr->sPres;
    707:   if (sPres->neighb[side]) {
    708:   /* Completing a previous interval */
    709:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
    710:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
    711:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
    712:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
    713:   } else { /* (Only for side=1). Creating a new interval. */
    714:     if (sPres->neigs==0) {/* No value has been accepted*/
    715:       if (sPres->neighb[0]) {
    716:         /* Multiplying by 10 the previous distance */
    717:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    718:         sr->nleap++;
    719:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    720:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unable to compute the wanted eigenvalues with open interval");
    721:       } else { /* First shift */
    722:         if (pep->nconv != 0) {
    723:           /* Unaccepted values give information for next shift */
    724:           idxP=0;/* Number of values left from shift */
    725:           for (i=0;i<pep->nconv;i++) {
    726:             lambda = PetscRealPart(pep->eigr[i]);
    727:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
    728:             else break;
    729:           }
    730:           /* Avoiding subtraction of eigenvalues (might be the same).*/
    731:           if (idxP>0) {
    732:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
    733:           } else {
    734:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
    735:           }
    736:           *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
    737:           sr->dirch = PETSC_FALSE;
    738:         } else { /* No values found, no information for next shift */
    739:           if (!sr->dirch) {
    740:             sr->dirch = PETSC_TRUE;
    741:             *newS = sr->int1;
    742:           } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"First shift renders no information");
    743:         }
    744:       }
    745:     } else { /* Accepted values found */
    746:       sr->dirch = PETSC_FALSE;
    747:       sr->nleap = 0;
    748:       /* Average distance of values in previous subinterval */
    749:       s = sPres->neighb[0];
    750:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    751:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    752:       }
    753:       if (s) {
    754:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    755:       } else { /* First shift. Average distance obtained with values in this shift */
    756:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    757:         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)) {
    758:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    759:         } else {
    760:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    761:         }
    762:       }
    763:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    764:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    765:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
    766:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    767:         *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
    768:       }
    769:     }
    770:     /* End of interval can not be surpassed */
    771:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
    772:   }/* of neighb[side]==null */
    773:   return(0);
    774: }

    776: /*
    777:   Function for sorting an array of real values
    778: */
    779: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    780: {
    781:   PetscReal re;
    782:   PetscInt  i,j,tmp;

    785:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    786:   /* Insertion sort */
    787:   for (i=1;i<nr;i++) {
    788:     re = PetscRealPart(r[perm[i]]);
    789:     j = i-1;
    790:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    791:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    792:     }
    793:   }
    794:   return(0);
    795: }

    797: /* Stores the pairs obtained since the last shift in the global arrays */
    798: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
    799: {
    801:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    802:   PetscReal      lambda,err,*errest;
    803:   PetscInt       i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
    804:   PetscBool      iscayley,divide=PETSC_FALSE;
    805:   PEP_SR         sr = ctx->sr;
    806:   PEP_shift      sPres;
    807:   Vec            w,vomega;
    808:   Mat            MS;
    809:   BV             tV;
    810:   PetscScalar    *S,*eigr,*tS,*omega;

    813:   sPres = sr->sPres;
    814:   sPres->index = sr->indexEig;

    816:   if (nconv>sr->ndef0+sr->ndef1) {
    817:     /* Back-transform */
    818:     STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
    819:     for (i=0;i<nconv;i++) {
    820: #if defined(PETSC_USE_COMPLEX)
    821:       if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
    822: #else
    823:       if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
    824: #endif
    825:     }
    826:     PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
    827:     /* Sort eigenvalues */
    828:     sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
    829:     VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
    830:     BVGetSignature(ctx->V,vomega);
    831:     VecGetArray(vomega,&omega);
    832:     BVGetSizes(pep->V,NULL,NULL,&ld);
    833:     BVTensorGetFactors(ctx->V,NULL,&MS);
    834:     MatDenseGetArray(MS,&S);
    835:     /* Values stored in global array */
    836:     PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
    837:     ndef = sr->ndef0+sr->ndef1;
    838:     for (i=0;i<nconv;i++) {
    839:       lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
    840:       err = pep->errest[pep->perm[i]];
    841:       if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    842:         if (sr->indexEig+count-ndef>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unexpected error in Spectrum Slicing");
    843:         PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
    844:         eigr[count] = lambda;
    845:         errest[count] = err;
    846:         if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
    847:         if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
    848:         PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
    849:         PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
    850:         count++;
    851:       }
    852:     }
    853:     VecRestoreArray(vomega,&omega);
    854:     VecDestroy(&vomega);
    855:     for (i=0;i<count;i++) {
    856:       PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
    857:       PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
    858:     }
    859:     MatDenseRestoreArray(MS,&S);
    860:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    861:     BVSetActiveColumns(ctx->V,0,count);
    862:     BVTensorCompress(ctx->V,count);
    863:     if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
    864:       divide = PETSC_TRUE;
    865:       BVTensorGetFactors(ctx->V,NULL,&MS);
    866:       MatDenseGetArray(MS,&S);
    867:       PetscArrayzero(tS,nconv*nconv*d);
    868:       for (i=0;i<count;i++) {
    869:         PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
    870:         PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
    871:       }
    872:       MatDenseRestoreArray(MS,&S);
    873:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    874:       BVSetActiveColumns(pep->V,0,count);
    875:       BVDuplicateResize(pep->V,count,&tV);
    876:       BVCopy(pep->V,tV);
    877:     }
    878:     if (sr->sPres->nconv[0]) {
    879:       if (divide) {
    880:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
    881:         BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
    882:       }
    883:       for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
    884:       for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
    885:       BVTensorGetFactors(ctx->V,NULL,&MS);
    886:       MatDenseGetArray(MS,&S);
    887:       for (i=0;i<sr->sPres->nconv[0];i++) {
    888:         sr->eigr[aux[i]] = eigr[i];
    889:         sr->errest[aux[i]] = errest[i];
    890:         BVGetColumn(pep->V,i,&w);
    891:         BVInsertVec(sr->V,aux[i],w);
    892:         BVRestoreColumn(pep->V,i,&w);
    893:         idx = sr->ld*d*aux[i];
    894:         PetscArrayzero(sr->S+idx,sr->ld*d);
    895:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
    896:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
    897:         PetscFree(sr->qinfo[aux[i]].q);
    898:         PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
    899:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
    900:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
    901:       }
    902:       MatDenseRestoreArray(MS,&S);
    903:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    904:     }

    906:     if (sr->sPres->nconv[1]) {
    907:       if (divide) {
    908:         BVTensorGetFactors(ctx->V,NULL,&MS);
    909:         MatDenseGetArray(MS,&S);
    910:         for (i=0;i<sr->sPres->nconv[1];i++) {
    911:           PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
    912:           PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
    913:         }
    914:         MatDenseRestoreArray(MS,&S);
    915:         BVTensorRestoreFactors(ctx->V,NULL,&MS);
    916:         BVSetActiveColumns(pep->V,0,count);
    917:         BVCopy(tV,pep->V);
    918:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
    919:         BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
    920:       }
    921:       for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
    922:       for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
    923:       BVTensorGetFactors(ctx->V,NULL,&MS);
    924:       MatDenseGetArray(MS,&S);
    925:       for (i=0;i<sr->sPres->nconv[1];i++) {
    926:         sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
    927:         sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
    928:         BVGetColumn(pep->V,i,&w);
    929:         BVInsertVec(sr->V,aux[i],w);
    930:         BVRestoreColumn(pep->V,i,&w);
    931:         idx = sr->ld*d*aux[i];
    932:         PetscArrayzero(sr->S+idx,sr->ld*d);
    933:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
    934:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
    935:         PetscFree(sr->qinfo[aux[i]].q);
    936:         PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
    937:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
    938:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
    939:       }
    940:       MatDenseRestoreArray(MS,&S);
    941:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
    942:     }
    943:     sPres->neigs = count-sr->ndef0-sr->ndef1;
    944:     sr->indexEig += sPres->neigs;
    945:     sPres->nconv[0]-= sr->ndef0;
    946:     sPres->nconv[1]-= sr->ndef1;
    947:     PetscFree4(eigr,errest,tS,aux);
    948:   } else {
    949:     sPres->neigs = 0;
    950:     sPres->nconv[0]= 0;
    951:     sPres->nconv[1]= 0;
    952:   }
    953:   /* Global ordering array updating */
    954:   sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
    955:   /* Check for completion */
    956:   sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
    957:   sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
    958:   if (sPres->nconv[0] > sPres->nsch[0] || sPres->nconv[1] > sPres->nsch[1]) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
    959:   if (divide) { BVDestroy(&tV); }
    960:   return(0);
    961: }

    963: static PetscErrorCode PEPLookForDeflation(PEP pep)
    964: {
    965:   PetscReal val;
    966:   PetscInt  i,count0=0,count1=0;
    967:   PEP_shift sPres;
    968:   PetscInt  ini,fin;
    969:   PEP_SR    sr;
    970:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

    973:   sr = ctx->sr;
    974:   sPres = sr->sPres;

    976:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    977:   else ini = 0;
    978:   fin = sr->indexEig;
    979:   /* Selection of ends for searching new values */
    980:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    981:   else sPres->ext[0] = sPres->neighb[0]->value;
    982:   if (!sPres->neighb[1]) {
    983:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    984:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    985:   } else sPres->ext[1] = sPres->neighb[1]->value;
    986:   /* Selection of values between right and left ends */
    987:   for (i=ini;i<fin;i++) {
    988:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    989:     /* Values to the right of left shift */
    990:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
    991:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
    992:       else count1++;
    993:     } else break;
    994:   }
    995:   /* The number of values on each side are found */
    996:   if (sPres->neighb[0]) {
    997:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    998:     if (sPres->nsch[0]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
    999:   } else sPres->nsch[0] = 0;

    1001:   if (sPres->neighb[1]) {
    1002:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    1003:     if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
    1004:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    1006:   /* Completing vector of indexes for deflation */
    1007:   for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
    1008:   sr->ndef0 = count0;
    1009:   for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
    1010:   sr->ndef1 = count1;
    1011:   return(0);
    1012: }

    1014: /*
    1015:   Compute a run of Lanczos iterations
    1016: */
    1017: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
    1018: {
    1020:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
    1021:   PetscInt       i,j,m=*M,l,lock;
    1022:   PetscInt       lds,d,ld,offq,nqt,ldds;
    1023:   Vec            v=t_[0],t=t_[1],q=t_[2];
    1024:   PetscReal      norm,sym=0.0,fro=0.0,*f;
    1025:   PetscScalar    *y,*S,sigma;
    1026:   PetscBLASInt   j_,one=1;
    1027:   PetscBool      lindep;
    1028:   Mat            MS;

    1031:   PetscMalloc1(*M,&y);
    1032:   BVGetSizes(pep->V,NULL,NULL,&ld);
    1033:   BVTensorGetDegree(ctx->V,&d);
    1034:   BVGetActiveColumns(pep->V,&lock,&nqt);
    1035:   lds = d*ld;
    1036:   offq = ld;
    1037:   DSGetLeadingDimension(pep->ds,&ldds);

    1039:   *breakdown = PETSC_FALSE; /* ----- */
    1040:   STGetShift(pep->st,&sigma);
    1041:   DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
    1042:   BVSetActiveColumns(ctx->V,0,m);
    1043:   BVSetActiveColumns(pep->V,0,nqt);
    1044:   for (j=k;j<m;j++) {
    1045:     /* apply operator */
    1046:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1047:     MatDenseGetArray(MS,&S);
    1048:     BVGetColumn(pep->V,nqt,&t);
    1049:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
    1050:     MatMult(pep->A[1],v,q);
    1051:     MatMult(pep->A[2],v,t);
    1052:     VecAXPY(q,sigma*pep->sfactor,t);
    1053:     VecScale(q,pep->sfactor);
    1054:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
    1055:     MatMult(pep->A[2],v,t);
    1056:     VecAXPY(q,pep->sfactor*pep->sfactor,t);
    1057:     STMatSolve(pep->st,q,t);
    1058:     VecScale(t,-1.0);
    1059:     BVRestoreColumn(pep->V,nqt,&t);

    1061:     /* orthogonalize */
    1062:     BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
    1063:     if (!lindep) {
    1064:       *(S+(j+1)*lds+nqt) = norm;
    1065:       BVScaleColumn(pep->V,nqt,1.0/norm);
    1066:       nqt++;
    1067:     }
    1068:     for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
    1069:     BVSetActiveColumns(pep->V,0,nqt);
    1070:     MatDenseRestoreArray(MS,&S);
    1071:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

    1073:     /* level-2 orthogonalization */
    1074:     BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
    1075:     a[j] = PetscRealPart(y[j]);
    1076:     omega[j+1] = (norm > 0)?1.0:-1.0;
    1077:     BVScaleColumn(ctx->V,j+1,1.0/norm);
    1078:     b[j] = PetscAbsReal(norm);

    1080:     /* check symmetry */
    1081:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
    1082:     if (j==k) {
    1083:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
    1084:       for (i=0;i<l;i++) y[i] = 0.0;
    1085:     }
    1086:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
    1087:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
    1088:     PetscBLASIntCast(j,&j_);
    1089:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
    1090:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
    1091:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
    1092:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
    1093:       *symmlost = PETSC_TRUE;
    1094:       *M=j;
    1095:       break;
    1096:     }
    1097:   }
    1098:   BVSetActiveColumns(pep->V,lock,nqt);
    1099:   BVSetActiveColumns(ctx->V,0,*M);
    1100:   PetscFree(y);
    1101:   return(0);
    1102: }

    1104: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
    1105: {
    1107:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
    1108:   PetscInt       j,k,l,nv=0,ld,ldds,t,nq=0,idx;
    1109:   PetscInt       nconv=0,deg=pep->nmat-1,count0=0,count1=0;
    1110:   PetscScalar    *Q,*om,sigma,*back,*S,*pQ;
    1111:   PetscReal      beta,norm=1.0,*omega,*a,*b,*r,eta,lambda;
    1112:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
    1113:   Mat            MS,MQ;
    1114:   Vec            v,vomega;
    1115:   PEP_SR         sr;
    1116:   BVOrthogType   otype;
    1117:   BVOrthogBlockType obtype;

    1120:   /* Resize if needed for deflating vectors  */
    1121:   sr = ctx->sr;
    1122:   sigma = sr->sPres->value;
    1123:   k = sr->ndef0+sr->ndef1;
    1124:   pep->ncv = ctx->ncv+k;
    1125:   pep->nev = ctx->nev+k;
    1126:   PEPAllocateSolution(pep,3);
    1127:   BVDestroy(&ctx->V);
    1128:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
    1129:   BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
    1130:   BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
    1131:   DSAllocate(pep->ds,pep->ncv+2);
    1132:   PetscMalloc1(pep->ncv,&back);
    1133:   DSGetLeadingDimension(pep->ds,&ldds);
    1134:   BVSetMatrix(ctx->V,B,PETSC_TRUE);
    1135:   if (ctx->lock) {
    1136:     /* undocumented option to use a cheaper locking instead of the true locking */
    1137:     PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
    1138:   } else SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
    1139:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
    1140:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
    1141:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

    1143:   /* Get the starting Arnoldi vector */
    1144:   BVSetActiveColumns(pep->V,0,1);
    1145:   BVTensorBuildFirstColumn(ctx->V,pep->nini);
    1146:   BVSetActiveColumns(ctx->V,0,1);
    1147:   if (k) {
    1148:     /* Insert deflated vectors */
    1149:     BVSetActiveColumns(pep->V,0,0);
    1150:     idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
    1151:     for (j=0;j<k;j++) {
    1152:       BVGetColumn(pep->V,j,&v);
    1153:       BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
    1154:       BVRestoreColumn(pep->V,j,&v);
    1155:     }
    1156:     /* Update innerproduct matrix */
    1157:     BVSetActiveColumns(ctx->V,0,0);
    1158:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1159:     BVSetActiveColumns(pep->V,0,k);
    1160:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

    1162:     BVGetSizes(pep->V,NULL,NULL,&ld);
    1163:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1164:     MatDenseGetArray(MS,&S);
    1165:     for (j=0;j<sr->ndef0;j++) {
    1166:       PetscArrayzero(S+j*ld*deg,ld*deg);
    1167:       PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
    1168:       PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
    1169:       pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
    1170:       pep->errest[j] = sr->errest[sr->idxDef0[j]];
    1171:     }
    1172:     for (j=0;j<sr->ndef1;j++) {
    1173:       PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
    1174:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
    1175:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
    1176:       pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
    1177:       pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
    1178:     }
    1179:     MatDenseRestoreArray(MS,&S);
    1180:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1181:     BVSetActiveColumns(ctx->V,0,k+1);
    1182:     VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
    1183:     VecGetArray(vomega,&om);
    1184:     for (j=0;j<k;j++) {
    1185:       BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
    1186:       BVScaleColumn(ctx->V,j,1/norm);
    1187:       om[j] = (norm>=0.0)?1.0:-1.0;
    1188:     }
    1189:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1190:     MatDenseGetArray(MS,&S);
    1191:     for (j=0;j<deg;j++) {
    1192:       BVSetRandomColumn(pep->V,k+j);
    1193:       BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
    1194:       BVScaleColumn(pep->V,k+j,1.0/norm);
    1195:       S[k*ld*deg+j*ld+k+j] = norm;
    1196:     }
    1197:     MatDenseRestoreArray(MS,&S);
    1198:     BVSetActiveColumns(pep->V,0,k+deg);
    1199:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1200:     BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
    1201:     BVScaleColumn(ctx->V,k,1.0/norm);
    1202:     om[k] = (norm>=0.0)?1.0:-1.0;
    1203:     VecRestoreArray(vomega,&om);
    1204:     BVSetSignature(ctx->V,vomega);
    1205:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
    1206:     VecGetArray(vomega,&om);
    1207:     for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
    1208:     VecRestoreArray(vomega,&om);
    1209:     VecDestroy(&vomega);
    1210:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
    1211:     DSGetArray(pep->ds,DS_MAT_Q,&pQ);
    1212:     PetscArrayzero(pQ,ldds*k);
    1213:     for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
    1214:     DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
    1215:   }
    1216:   BVSetActiveColumns(ctx->V,0,k+1);
    1217:   DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
    1218:   VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
    1219:   BVGetSignature(ctx->V,vomega);
    1220:   VecGetArray(vomega,&om);
    1221:   for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
    1222:   VecRestoreArray(vomega,&om);
    1223:   DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
    1224:   VecDestroy(&vomega);

    1226:   PetscInfo7(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%D right=%D, searching: left=%D right=%D\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]);

    1228:   /* Restart loop */
    1229:   l = 0;
    1230:   pep->nconv = k;
    1231:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    1232:     pep->its++;
    1233:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
    1234:     b = a+ldds;
    1235:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

    1237:     /* Compute an nv-step Lanczos factorization */
    1238:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
    1239:     PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
    1240:     beta = b[nv-1];
    1241:     if (symmlost && nv==pep->nconv+l) {
    1242:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
    1243:       pep->nconv = nconv;
    1244:       PetscInfo2(pep,"Symmetry lost in STOAR sigma=%g nconv=%D\n",(double)sr->sPres->value,nconv);
    1245:       if (falselock || !ctx->lock) {
    1246:         BVSetActiveColumns(ctx->V,0,pep->nconv);
    1247:         BVTensorCompress(ctx->V,0);
    1248:       }
    1249:       break;
    1250:     }
    1251:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
    1252:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
    1253:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
    1254:     if (l==0) {
    1255:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
    1256:     } else {
    1257:       DSSetState(pep->ds,DS_STATE_RAW);
    1258:     }

    1260:     /* Solve projected problem */
    1261:     DSSolve(pep->ds,pep->eigr,pep->eigi);
    1262:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
    1263:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

    1265:     /* Check convergence */
    1266:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
    1267:     norm = 1.0;
    1268:     DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
    1269:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
    1270:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
    1271:     for (j=0;j<k;j++) back[j] = pep->eigr[j];
    1272:     STBackTransform(pep->st,k,back,pep->eigi);
    1273:     count0=count1=0;
    1274:     for (j=0;j<k;j++) {
    1275:       lambda = PetscRealPart(back[j]);
    1276:       if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
    1277:       if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
    1278:     }
    1279:     if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
    1280:     /* Update l */
    1281:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
    1282:     else {
    1283:       l = PetscMax(1,(PetscInt)((nv-k)/2));
    1284:       l = PetscMin(l,t);
    1285:       if (!breakdown) {
    1286:         DSGetArrayReal(pep->ds,DS_MAT_T,&a);
    1287:         if (*(a+ldds+k+l-1)!=0) {
    1288:           if (k+l<nv-1) l = l+1;
    1289:           else l = l-1;
    1290:         }
    1291:         /* Prepare the Rayleigh quotient for restart */
    1292:         DSGetArray(pep->ds,DS_MAT_Q,&Q);
    1293:         DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
    1294:         r = a + 2*ldds;
    1295:         for (j=k;j<k+l;j++) {
    1296:           r[j] = PetscRealPart(Q[nv-1+j*ldds]*beta);
    1297:         }
    1298:         b = a+ldds;
    1299:         b[k+l-1] = r[k+l-1];
    1300:         omega[k+l] = omega[nv];
    1301:         DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
    1302:         DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
    1303:         DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
    1304:       }
    1305:     }
    1306:     nconv = k;
    1307:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

    1309:     /* Update S */
    1310:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
    1311:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
    1312:     MatDestroy(&MQ);

    1314:     /* Copy last column of S */
    1315:     BVCopyColumn(ctx->V,nv,k+l);
    1316:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
    1317:     VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
    1318:     VecGetArray(vomega,&om);
    1319:     for (j=0;j<k+l;j++) om[j] = omega[j];
    1320:     VecRestoreArray(vomega,&om);
    1321:     BVSetActiveColumns(ctx->V,0,k+l);
    1322:     BVSetSignature(ctx->V,vomega);
    1323:     VecDestroy(&vomega);
    1324:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);

    1326:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
    1327:       /* stop if breakdown */
    1328:       PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
    1329:       pep->reason = PEP_DIVERGED_BREAKDOWN;
    1330:     }
    1331:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
    1332:     BVGetActiveColumns(pep->V,NULL,&nq);
    1333:     if (k+l+deg<=nq) {
    1334:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
    1335:       if (!falselock && ctx->lock) {
    1336:         BVTensorCompress(ctx->V,k-pep->nconv);
    1337:       } else {
    1338:         BVTensorCompress(ctx->V,0);
    1339:       }
    1340:     }
    1341:     pep->nconv = k;
    1342:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
    1343:   }
    1344:   sr->itsKs += pep->its;
    1345:   if (pep->nconv>0) {
    1346:     BVSetActiveColumns(ctx->V,0,pep->nconv);
    1347:     BVGetActiveColumns(pep->V,NULL,&nq);
    1348:     BVSetActiveColumns(pep->V,0,nq);
    1349:     if (nq>pep->nconv) {
    1350:       BVTensorCompress(ctx->V,pep->nconv);
    1351:       BVSetActiveColumns(pep->V,0,pep->nconv);
    1352:     }
    1353:     for (j=0;j<pep->nconv;j++) {
    1354:       pep->eigr[j] *= pep->sfactor;
    1355:       pep->eigi[j] *= pep->sfactor;
    1356:     }
    1357:   }
    1358:   PetscInfo4(pep,"Finished STOAR: nconv=%D (deflated=%D, left=%D, right=%D)\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1);
    1359:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
    1360:   RGPopScale(pep->rg);

    1362:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv<sr->ndef0+sr->ndef1) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
    1363:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
    1364:     if (++sr->symmlost>10) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
    1365:   } else sr->symmlost = 0;

    1367:   /* truncate Schur decomposition and change the state to raw so that
    1368:      DSVectors() computes eigenvectors from scratch */
    1369:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
    1370:   DSSetState(pep->ds,DS_STATE_RAW);
    1371:   PetscFree(back);
    1372:   return(0);
    1373: }

    1375: #define SWAP(a,b,t) {t=a;a=b;b=t;}

    1377: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    1378: {
    1379:   PetscErrorCode  ierr;
    1380:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    1381:   PEP_SR          sr=ctx->sr;
    1382:   PetscInt        i=0,j,tmpi;
    1383:   PetscReal       v,tmpr;
    1384:   PEP_shift       s;

    1387:   if (!pep->state) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
    1388:   if (!sr) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
    1389:   if (!sr->s0) {  /* PEPSolve not called yet */
    1390:     *n = 2;
    1391:   } else {
    1392:     *n = 1;
    1393:     s = sr->s0;
    1394:     while (s) {
    1395:       (*n)++;
    1396:       s = s->neighb[1];
    1397:     }
    1398:   }
    1399:   PetscMalloc1(*n,shifts);
    1400:   PetscMalloc1(*n,inertias);
    1401:   if (!sr->s0) {  /* PEPSolve not called yet */
    1402:     (*shifts)[0]   = sr->int0;
    1403:     (*shifts)[1]   = sr->int1;
    1404:     (*inertias)[0] = sr->inertia0;
    1405:     (*inertias)[1] = sr->inertia1;
    1406:   } else {
    1407:     s = sr->s0;
    1408:     while (s) {
    1409:       (*shifts)[i]     = s->value;
    1410:       (*inertias)[i++] = s->inertia;
    1411:       s = s->neighb[1];
    1412:     }
    1413:     (*shifts)[i]   = sr->int1;
    1414:     (*inertias)[i] = sr->inertia1;
    1415:   }
    1416:   /* remove possible duplicate in last position */
    1417:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    1418:   /* sort result */
    1419:   for (i=0;i<*n;i++) {
    1420:     v = (*shifts)[i];
    1421:     for (j=i+1;j<*n;j++) {
    1422:       if (v > (*shifts)[j]) {
    1423:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    1424:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    1425:         v = (*shifts)[i];
    1426:       }
    1427:     }
    1428:   }
    1429:   return(0);
    1430: }

    1432: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
    1433: {
    1435:   PetscInt       i,j,ti,deg=pep->nmat-1;
    1436:   PetscReal      newS;
    1437:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
    1438:   PEP_SR         sr=ctx->sr;
    1439:   Mat            S,B;
    1440:   PetscScalar    *pS;

    1443:   PetscCitationsRegister(citation,&cited);

    1445:   /* Only with eigenvalues present in the interval ...*/
    1446:   if (sr->numEigs==0) {
    1447:     pep->reason = PEP_CONVERGED_TOL;
    1448:     return(0);
    1449:   }

    1451:   /* Inner product matrix */
    1452:   PEPSTOARSetUpInnerMatrix(pep,&B);

    1454:   /* Array of pending shifts */
    1455:   sr->maxPend = 100; /* Initial size */
    1456:   sr->nPend = 0;
    1457:   PetscMalloc1(sr->maxPend,&sr->pending);
    1458:   PetscLogObjectMemory((PetscObject)pep,(sr->maxPend)*sizeof(PEP_shift));
    1459:   PEPCreateShift(pep,sr->int0,NULL,NULL);
    1460:   /* extract first shift */
    1461:   sr->sPrev = NULL;
    1462:   sr->sPres = sr->pending[--sr->nPend];
    1463:   sr->sPres->inertia = sr->inertia0;
    1464:   pep->target = sr->sPres->value;
    1465:   sr->s0 = sr->sPres;
    1466:   sr->indexEig = 0;

    1468:   /* Memory reservation for auxiliary variables */
    1469:   PetscLogObjectMemory((PetscObject)pep,(sr->numEigs+2*pep->ncv)*sizeof(PetscScalar));
    1470:   for (i=0;i<sr->numEigs;i++) {
    1471:     sr->eigr[i]   = 0.0;
    1472:     sr->eigi[i]   = 0.0;
    1473:     sr->errest[i] = 0.0;
    1474:     sr->perm[i]   = i;
    1475:   }
    1476:   /* Vectors for deflation */
    1477:   PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
    1478:   PetscLogObjectMemory((PetscObject)pep,sr->numEigs*sizeof(PetscInt));
    1479:   sr->indexEig = 0;
    1480:   while (sr->sPres) {
    1481:     /* Search for deflation */
    1482:     PEPLookForDeflation(pep);
    1483:     /* KrylovSchur */
    1484:     PEPSTOAR_QSlice(pep,B);

    1486:     PEPStoreEigenpairs(pep);
    1487:     /* Select new shift */
    1488:     if (!sr->sPres->comp[1]) {
    1489:       PEPGetNewShiftValue(pep,1,&newS);
    1490:       PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
    1491:     }
    1492:     if (!sr->sPres->comp[0]) {
    1493:       /* Completing earlier interval */
    1494:       PEPGetNewShiftValue(pep,0,&newS);
    1495:       PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
    1496:     }
    1497:     /* Preparing for a new search of values */
    1498:     PEPExtractShift(pep);
    1499:   }

    1501:   /* Updating pep values prior to exit */
    1502:   PetscFree2(sr->idxDef0,sr->idxDef1);
    1503:   PetscFree(sr->pending);
    1504:   pep->nconv  = sr->indexEig;
    1505:   pep->reason = PEP_CONVERGED_TOL;
    1506:   pep->its    = sr->itsKs;
    1507:   pep->nev    = sr->indexEig;
    1508:   MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
    1509:   MatDenseGetArray(S,&pS);
    1510:   for (i=0;i<pep->nconv;i++) {
    1511:     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);
    1512:   }
    1513:   MatDenseRestoreArray(S,&pS);
    1514:   BVSetActiveColumns(sr->V,0,pep->nconv);
    1515:   BVMultInPlace(sr->V,S,0,pep->nconv);
    1516:   MatDestroy(&S);
    1517:   BVDestroy(&pep->V);
    1518:   pep->V = sr->V;
    1519:   PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
    1520:   pep->eigr   = sr->eigr;
    1521:   pep->eigi   = sr->eigi;
    1522:   pep->perm   = sr->perm;
    1523:   pep->errest = sr->errest;
    1524:   if (sr->dir<0) {
    1525:     for (i=0;i<pep->nconv/2;i++) {
    1526:       ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
    1527:     }
    1528:   }
    1529:   PetscFree(ctx->inertias);
    1530:   PetscFree(ctx->shifts);
    1531:   MatDestroy(&B);
    1532:   PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
    1533:   return(0);
    1534: }