Actual source code: qslice.c

slepc-3.16.2 2022-02-01
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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,dot;
175:   PetscRandom    rand;
176:   PetscInt       nconv;
177:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
178:   PEP_SR         sr=ctx->sr;

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

231: /*
232:    Check eigenvalue type - used only in non-hyperbolic problems.
233:    All computed eigenvalues must have the same definite type (positive or negative).
234:    If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
235:    closest to shift and determine its type.
236:  */
237: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
238: {
240:   PEP            pep2;
241:   ST             st;
242:   PetscInt       nconv;
243:   PetscScalar    lambda;
244:   PetscReal      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:       VecDotRealPart(pep2->work[1],pep2->work[0],&dot);
277:       PetscInfo2(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(dot>0.0)?"positive":"negative");
278:       if (!sr->type) sr->type = (dot>0.0)?1:-1;
279:       else {
280:         if (sr->type*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;

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

322: PETSC_STATIC_INLINE PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
323: {

327:   MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
328:   MatAXPY(M,x,pep->A[1],str);
329:   MatAXPY(M,x*x,pep->A[2],str);
330:   return(0);
331: }

333: /*@
334:    PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
335:    is definite or not.

337:    Logically Collective on pep

339:    Input Parameter:
340: .  pep  - eigensolver context

342:    Output Parameters:
343: +  xi - first computed parameter
344: .  mu - second computed parameter
345: .  definite - flag indicating that the problem is definite
346: -  hyperbolic - flag indicating that the problem is hyperbolic

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

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

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

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

363:    Level: advanced
364: @*/
365: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
366: {
368:   PetscRandom    rand;
369:   Vec            u,w;
370:   PetscReal      d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
371:   PetscInt       k,its=10,hyp=0,check=0,nconv,inertia,n;
372:   Mat            M=NULL;
373:   MatStructure   str;
374:   EPS            eps;
375:   PetscBool      transform,ptypehyp;

378:   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");
379:   ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
380:   if (!pep->st) { PEPGetST(pep,&pep->st); }
381:   PEPSetDefaultST(pep);
382:   STSetMatrices(pep->st,pep->nmat,pep->A);
383:   MatGetSize(pep->A[0],&n,NULL);
384:   STGetTransform(pep->st,&transform);
385:   STSetTransform(pep->st,PETSC_FALSE);
386:   STSetUp(pep->st);
387:   MatCreateVecs(pep->A[0],&u,&w);
388:   PEPGetBV(pep,&pep->V);
389:   BVGetRandomContext(pep->V,&rand);
390:   VecSetRandom(u,rand);
391:   VecNormalize(u,NULL);
392:   PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
393:   if (d<0.0) check = -1;
394:   if (!check) {
395:     EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
396:     EPSSetProblemType(eps,EPS_HEP);
397:     EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
398:     EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
399:     MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
400:     STGetMatStructure(pep->st,&str);
401:   }
402:   for (k=0;k<its&&!check;k++) {
403:     PEPQSliceEvaluateQEP(pep,s,M,str);
404:     EPSSetOperators(eps,M,NULL);
405:     EPSSolve(eps);
406:     EPSGetConverged(eps,&nconv);
407:     if (!nconv) break;
408:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
409:     sp = s;
410:     PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
411:     if (d<0.0) {check = -1; break;}
412:     if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
413:     if (s>sp) {hyp = -1;}
414:     mut = 2*s-sp;
415:      PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
416:     if (inertia == n) {check = 1; break;}
417:   }
418:   for (;k<its&&!check;k++) {
419:     mut = (s-omg)/2;
420:      PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
421:     if (inertia == n) {check = 1; break;}
422:     if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
423:     PEPQSliceEvaluateQEP(pep,omg,M,str);
424:     EPSSetOperators(eps,M,NULL);
425:     EPSSolve(eps);
426:     EPSGetConverged(eps,&nconv);
427:     if (!nconv) break;
428:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
429:     omgp = omg;
430:     PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
431:     if (d<0.0) {check = -1; break;}
432:     if (omg<omgp) hyp = -1;
433:   }
434:   if (check==1) *xi = mut;
435:   if (hyp==-1 && ptypehyp) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Problem does not satisfy hyperbolic test; consider removing the hyperbolicity flag");
436:   if (check==1 && hyp==0) {
437:      PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
438:     if (inertia == 0) hyp = 1;
439:     else hyp = -1;
440:   }
441:   if (check==1 && hyp!=1) {
442:     check = 0;
443:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
444:     for (;k<its&&!check;k++) {
445:       PEPQSliceEvaluateQEP(pep,s,M,str);
446:       EPSSetOperators(eps,M,NULL);
447:       EPSSolve(eps);
448:       EPSGetConverged(eps,&nconv);
449:       if (!nconv) break;
450:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
451:       sp = s;
452:       PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
453:       if (d<0.0) {check = -1; break;}
454:       if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
455:       mut = 2*s-sp;
456:        PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
457:       if (inertia == 0) {check = 1; break;}
458:     }
459:     for (;k<its&&!check;k++) {
460:       mut = (s-omg)/2;
461:        PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
462:       if (inertia == 0) {check = 1; break;}
463:       if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
464:       PEPQSliceEvaluateQEP(pep,omg,M,str);
465:       EPSSetOperators(eps,M,NULL);
466:       EPSSolve(eps);
467:       EPSGetConverged(eps,&nconv);
468:       if (!nconv) break;
469:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
470:       PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
471:       if (d<0.0) {check = -1; break;}
472:     }
473:   }
474:   if (check==1) *mu = mut;
475:   *definite = check;
476:   *hyperbolic = hyp;
477:   if (M) { MatDestroy(&M); }
478:   VecDestroy(&u);
479:   VecDestroy(&w);
480:   EPSDestroy(&eps);
481:   STSetTransform(pep->st,transform);
482:   return(0);
483: }

485: /*
486:    Dummy backtransform operation
487:  */
488: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
489: {
491:   return(0);
492: }

494: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
495: {
497:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
498:   PEP_SR         sr;
499:   PetscInt       ld,i,zeros=0;
500:   SlepcSC        sc;
501:   PetscReal      r;

504:   PEPCheckSinvertCayley(pep);
505:   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()");
506:   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");
507:   PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
508:   if (pep->tol==PETSC_DEFAULT) {
509: #if defined(PETSC_USE_REAL_SINGLE)
510:     pep->tol = SLEPC_DEFAULT_TOL;
511: #else
512:     /* use tighter tolerance */
513:     pep->tol = SLEPC_DEFAULT_TOL*1e-2;
514: #endif
515:   }
516:   if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n);  /* nev not set, use default value */
517:   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");
518:   pep->ops->backtransform = PEPBackTransform_Skip;
519:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;

521:   /* create spectrum slicing context and initialize it */
522:   PEPQSliceResetSR(pep);
523:   PetscNewLog(pep,&sr);
524:   ctx->sr   = sr;
525:   sr->itsKs = 0;
526:   sr->nleap = 0;
527:   sr->sPres = NULL;

529:   if (pep->solvematcoeffs) { PetscFree(pep->solvematcoeffs); }
530:   PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
531:   if (!pep->st) { PEPGetST(pep,&pep->st); }
532:   STSetTransform(pep->st,PETSC_FALSE);
533:   STSetUp(pep->st);

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

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

552:   /* compute inertia0 */
553:   PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
554:   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");
555:   if (!ctx->hyperbolic && ctx->checket) {
556:     PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE);
557:   }

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

576:   if (sr->hasEnd) {
577:     sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
578:     i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
579:   }

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

603: /*
604:    Fills the fields of a shift structure
605: */
606: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
607: {
609:   PEP_shift      s,*pending2;
610:   PetscInt       i;
611:   PEP_SR         sr;
612:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

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

642: /* Provides next shift to be computed */
643: static PetscErrorCode PEPExtractShift(PEP pep)
644: {
646:   PetscInt       iner,zeros=0;
647:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
648:   PEP_SR         sr;
649:   PetscReal      newShift,aux;
650:   PEP_shift      sPres;

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

690: /*
691:   Obtains value of subsequent shift
692: */
693: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
694: {
695:   PetscReal lambda,d_prev;
696:   PetscInt  i,idxP;
697:   PEP_SR    sr;
698:   PEP_shift sPres,s;
699:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

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

773: /*
774:   Function for sorting an array of real values
775: */
776: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
777: {
778:   PetscReal re;
779:   PetscInt  i,j,tmp;

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

794: /* Stores the pairs obtained since the last shift in the global arrays */
795: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
796: {
798:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
799:   PetscReal      lambda,err,*errest;
800:   PetscInt       i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
801:   PetscBool      iscayley,divide=PETSC_FALSE;
802:   PEP_SR         sr = ctx->sr;
803:   PEP_shift      sPres;
804:   Vec            w,vomega;
805:   Mat            MS;
806:   BV             tV;
807:   PetscScalar    *S,*eigr,*tS,*omega;

810:   sPres = sr->sPres;
811:   sPres->index = sr->indexEig;

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

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

960: static PetscErrorCode PEPLookForDeflation(PEP pep)
961: {
962:   PetscReal val;
963:   PetscInt  i,count0=0,count1=0;
964:   PEP_shift sPres;
965:   PetscInt  ini,fin;
966:   PEP_SR    sr;
967:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

970:   sr = ctx->sr;
971:   sPres = sr->sPres;

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

998:   if (sPres->neighb[1]) {
999:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1000:     if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia");
1001:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

1003:   /* Completing vector of indexes for deflation */
1004:   for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
1005:   sr->ndef0 = count0;
1006:   for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
1007:   sr->ndef1 = count1;
1008:   return(0);
1009: }

1011: /*
1012:   Compute a run of Lanczos iterations
1013: */
1014: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
1015: {
1017:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
1018:   PetscInt       i,j,m=*M,l,lock;
1019:   PetscInt       lds,d,ld,offq,nqt,ldds;
1020:   Vec            v=t_[0],t=t_[1],q=t_[2];
1021:   PetscReal      norm,sym=0.0,fro=0.0,*f;
1022:   PetscScalar    *y,*S,sigma;
1023:   PetscBLASInt   j_,one=1;
1024:   PetscBool      lindep;
1025:   Mat            MS;

1028:   PetscMalloc1(*M,&y);
1029:   BVGetSizes(pep->V,NULL,NULL,&ld);
1030:   BVTensorGetDegree(ctx->V,&d);
1031:   BVGetActiveColumns(pep->V,&lock,&nqt);
1032:   lds = d*ld;
1033:   offq = ld;
1034:   DSGetLeadingDimension(pep->ds,&ldds);

1036:   *breakdown = PETSC_FALSE; /* ----- */
1037:   STGetShift(pep->st,&sigma);
1038:   DSGetDimensions(pep->ds,NULL,&l,NULL,NULL);
1039:   BVSetActiveColumns(ctx->V,0,m);
1040:   BVSetActiveColumns(pep->V,0,nqt);
1041:   for (j=k;j<m;j++) {
1042:     /* apply operator */
1043:     BVTensorGetFactors(ctx->V,NULL,&MS);
1044:     MatDenseGetArray(MS,&S);
1045:     BVGetColumn(pep->V,nqt,&t);
1046:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1047:     MatMult(pep->A[1],v,q);
1048:     MatMult(pep->A[2],v,t);
1049:     VecAXPY(q,sigma*pep->sfactor,t);
1050:     VecScale(q,pep->sfactor);
1051:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1052:     MatMult(pep->A[2],v,t);
1053:     VecAXPY(q,pep->sfactor*pep->sfactor,t);
1054:     STMatSolve(pep->st,q,t);
1055:     VecScale(t,-1.0);
1056:     BVRestoreColumn(pep->V,nqt,&t);

1058:     /* orthogonalize */
1059:     BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1060:     if (!lindep) {
1061:       *(S+(j+1)*lds+nqt) = norm;
1062:       BVScaleColumn(pep->V,nqt,1.0/norm);
1063:       nqt++;
1064:     }
1065:     for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1066:     BVSetActiveColumns(pep->V,0,nqt);
1067:     MatDenseRestoreArray(MS,&S);
1068:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1070:     /* level-2 orthogonalization */
1071:     BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1072:     a[j] = PetscRealPart(y[j]);
1073:     omega[j+1] = (norm > 0)?1.0:-1.0;
1074:     BVScaleColumn(ctx->V,j+1,1.0/norm);
1075:     b[j] = PetscAbsReal(norm);

1077:     /* check symmetry */
1078:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1079:     if (j==k) {
1080:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1081:       for (i=0;i<l;i++) y[i] = 0.0;
1082:     }
1083:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1084:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1085:     PetscBLASIntCast(j,&j_);
1086:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1087:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1088:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
1089:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1090:       *symmlost = PETSC_TRUE;
1091:       *M=j;
1092:       break;
1093:     }
1094:   }
1095:   BVSetActiveColumns(pep->V,lock,nqt);
1096:   BVSetActiveColumns(ctx->V,0,*M);
1097:   PetscFree(y);
1098:   return(0);
1099: }

1101: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1102: {
1104:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
1105:   PetscInt       j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1106:   PetscInt       nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1107:   PetscScalar    *om,sigma,*back,*S,*pQ;
1108:   PetscReal      beta,norm=1.0,*omega,*a,*b,eta,lambda;
1109:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1110:   Mat            MS,MQ;
1111:   Vec            v,vomega;
1112:   PEP_SR         sr;
1113:   BVOrthogType   otype;
1114:   BVOrthogBlockType obtype;

1117:   /* Resize if needed for deflating vectors  */
1118:   sr = ctx->sr;
1119:   sigma = sr->sPres->value;
1120:   k = sr->ndef0+sr->ndef1;
1121:   pep->ncv = ctx->ncv+k;
1122:   pep->nev = ctx->nev+k;
1123:   PEPAllocateSolution(pep,3);
1124:   BVDestroy(&ctx->V);
1125:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1126:   BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1127:   BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1128:   DSAllocate(pep->ds,pep->ncv+2);
1129:   PetscMalloc1(pep->ncv,&back);
1130:   DSGetLeadingDimension(pep->ds,&ldds);
1131:   BVSetMatrix(ctx->V,B,PETSC_TRUE);
1132:   if (ctx->lock) {
1133:     /* undocumented option to use a cheaper locking instead of the true locking */
1134:     PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1135:   } else SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
1136:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1137:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1138:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

1140:   /* Get the starting Arnoldi vector */
1141:   BVSetActiveColumns(pep->V,0,1);
1142:   BVTensorBuildFirstColumn(ctx->V,pep->nini);
1143:   BVSetActiveColumns(ctx->V,0,1);
1144:   if (k) {
1145:     /* Insert deflated vectors */
1146:     BVSetActiveColumns(pep->V,0,0);
1147:     idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1148:     for (j=0;j<k;j++) {
1149:       BVGetColumn(pep->V,j,&v);
1150:       BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1151:       BVRestoreColumn(pep->V,j,&v);
1152:     }
1153:     /* Update innerproduct matrix */
1154:     BVSetActiveColumns(ctx->V,0,0);
1155:     BVTensorGetFactors(ctx->V,NULL,&MS);
1156:     BVSetActiveColumns(pep->V,0,k);
1157:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1159:     BVGetSizes(pep->V,NULL,NULL,&ld);
1160:     BVTensorGetFactors(ctx->V,NULL,&MS);
1161:     MatDenseGetArray(MS,&S);
1162:     for (j=0;j<sr->ndef0;j++) {
1163:       PetscArrayzero(S+j*ld*deg,ld*deg);
1164:       PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
1165:       PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
1166:       pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1167:       pep->errest[j] = sr->errest[sr->idxDef0[j]];
1168:     }
1169:     for (j=0;j<sr->ndef1;j++) {
1170:       PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
1171:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
1172:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
1173:       pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1174:       pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1175:     }
1176:     MatDenseRestoreArray(MS,&S);
1177:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1178:     BVSetActiveColumns(ctx->V,0,k+1);
1179:     VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1180:     VecGetArray(vomega,&om);
1181:     for (j=0;j<k;j++) {
1182:       BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1183:       BVScaleColumn(ctx->V,j,1/norm);
1184:       om[j] = (norm>=0.0)?1.0:-1.0;
1185:     }
1186:     BVTensorGetFactors(ctx->V,NULL,&MS);
1187:     MatDenseGetArray(MS,&S);
1188:     for (j=0;j<deg;j++) {
1189:       BVSetRandomColumn(pep->V,k+j);
1190:       BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1191:       BVScaleColumn(pep->V,k+j,1.0/norm);
1192:       S[k*ld*deg+j*ld+k+j] = norm;
1193:     }
1194:     MatDenseRestoreArray(MS,&S);
1195:     BVSetActiveColumns(pep->V,0,k+deg);
1196:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1197:     BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1198:     BVScaleColumn(ctx->V,k,1.0/norm);
1199:     om[k] = (norm>=0.0)?1.0:-1.0;
1200:     VecRestoreArray(vomega,&om);
1201:     BVSetSignature(ctx->V,vomega);
1202:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1203:     VecGetArray(vomega,&om);
1204:     for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1205:     VecRestoreArray(vomega,&om);
1206:     VecDestroy(&vomega);
1207:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1208:     DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1209:     PetscArrayzero(pQ,ldds*k);
1210:     for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1211:     DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1212:   }
1213:   BVSetActiveColumns(ctx->V,0,k+1);
1214:   DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1215:   VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1216:   BVGetSignature(ctx->V,vomega);
1217:   VecGetArray(vomega,&om);
1218:   for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
1219:   VecRestoreArray(vomega,&om);
1220:   DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1221:   VecDestroy(&vomega);

1223:   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]);

1225:   /* Restart loop */
1226:   l = 0;
1227:   pep->nconv = k;
1228:   while (pep->reason == PEP_CONVERGED_ITERATING) {
1229:     pep->its++;
1230:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1231:     b = a+ldds;
1232:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

1234:     /* Compute an nv-step Lanczos factorization */
1235:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1236:     PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1237:     beta = b[nv-1];
1238:     if (symmlost && nv==pep->nconv+l) {
1239:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1240:       pep->nconv = nconv;
1241:       PetscInfo2(pep,"Symmetry lost in STOAR sigma=%g nconv=%D\n",(double)sr->sPres->value,nconv);
1242:       if (falselock || !ctx->lock) {
1243:         BVSetActiveColumns(ctx->V,0,pep->nconv);
1244:         BVTensorCompress(ctx->V,0);
1245:       }
1246:       break;
1247:     }
1248:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1249:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1250:     DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l);
1251:     if (l==0) {
1252:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1253:     } else {
1254:       DSSetState(pep->ds,DS_STATE_RAW);
1255:     }

1257:     /* Solve projected problem */
1258:     DSSolve(pep->ds,pep->eigr,pep->eigi);
1259:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1260:     DSUpdateExtraRow(pep->ds);
1261:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

1263:     /* Check convergence */
1264:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1265:     norm = 1.0;
1266:     DSGetDimensions(pep->ds,NULL,NULL,NULL,&t);
1267:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1268:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1269:     for (j=0;j<k;j++) back[j] = pep->eigr[j];
1270:     STBackTransform(pep->st,k,back,pep->eigi);
1271:     count0=count1=0;
1272:     for (j=0;j<k;j++) {
1273:       lambda = PetscRealPart(back[j]);
1274:       if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1275:       if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1276:     }
1277:     if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1278:     /* Update l */
1279:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1280:     else {
1281:       l = PetscMax(1,(PetscInt)((nv-k)/2));
1282:       l = PetscMin(l,t);
1283:       DSGetTruncateSize(pep->ds,k,t,&l);
1284:       if (!breakdown) {
1285:         /* Prepare the Rayleigh quotient for restart */
1286:         DSTruncate(pep->ds,k+l,PETSC_FALSE);
1287:       }
1288:     }
1289:     nconv = k;
1290:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1291:     if (l) { PetscInfo1(pep,"Preparing to restart keeping l=%D vectors\n",l); }

1293:     /* Update S */
1294:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1295:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1296:     MatDestroy(&MQ);

1298:     /* Copy last column of S */
1299:     BVCopyColumn(ctx->V,nv,k+l);
1300:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1301:     VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
1302:     VecGetArray(vomega,&om);
1303:     for (j=0;j<k+l;j++) om[j] = omega[j];
1304:     VecRestoreArray(vomega,&om);
1305:     BVSetActiveColumns(ctx->V,0,k+l);
1306:     BVSetSignature(ctx->V,vomega);
1307:     VecDestroy(&vomega);
1308:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);

1310:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1311:       /* stop if breakdown */
1312:       PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
1313:       pep->reason = PEP_DIVERGED_BREAKDOWN;
1314:     }
1315:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1316:     BVGetActiveColumns(pep->V,NULL,&nq);
1317:     if (k+l+deg<=nq) {
1318:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1319:       if (!falselock && ctx->lock) {
1320:         BVTensorCompress(ctx->V,k-pep->nconv);
1321:       } else {
1322:         BVTensorCompress(ctx->V,0);
1323:       }
1324:     }
1325:     pep->nconv = k;
1326:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1327:   }
1328:   sr->itsKs += pep->its;
1329:   if (pep->nconv>0) {
1330:     BVSetActiveColumns(ctx->V,0,pep->nconv);
1331:     BVGetActiveColumns(pep->V,NULL,&nq);
1332:     BVSetActiveColumns(pep->V,0,nq);
1333:     if (nq>pep->nconv) {
1334:       BVTensorCompress(ctx->V,pep->nconv);
1335:       BVSetActiveColumns(pep->V,0,pep->nconv);
1336:     }
1337:     for (j=0;j<pep->nconv;j++) {
1338:       pep->eigr[j] *= pep->sfactor;
1339:       pep->eigi[j] *= pep->sfactor;
1340:     }
1341:   }
1342:   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);
1343:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1344:   RGPopScale(pep->rg);

1346:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv<sr->ndef0+sr->ndef1) SETERRQ1(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1347:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1348:     if (++sr->symmlost>10) SETERRQ1(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1349:   } else sr->symmlost = 0;

1351:   DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
1352:   PetscFree(back);
1353:   return(0);
1354: }

1356: #define SWAP(a,b,t) {t=a;a=b;b=t;}

1358: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1359: {
1360:   PetscErrorCode  ierr;
1361:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1362:   PEP_SR          sr=ctx->sr;
1363:   PetscInt        i=0,j,tmpi;
1364:   PetscReal       v,tmpr;
1365:   PEP_shift       s;

1368:   if (!pep->state) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
1369:   if (!sr) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
1370:   if (!sr->s0) {  /* PEPSolve not called yet */
1371:     *n = 2;
1372:   } else {
1373:     *n = 1;
1374:     s = sr->s0;
1375:     while (s) {
1376:       (*n)++;
1377:       s = s->neighb[1];
1378:     }
1379:   }
1380:   PetscMalloc1(*n,shifts);
1381:   PetscMalloc1(*n,inertias);
1382:   if (!sr->s0) {  /* PEPSolve not called yet */
1383:     (*shifts)[0]   = sr->int0;
1384:     (*shifts)[1]   = sr->int1;
1385:     (*inertias)[0] = sr->inertia0;
1386:     (*inertias)[1] = sr->inertia1;
1387:   } else {
1388:     s = sr->s0;
1389:     while (s) {
1390:       (*shifts)[i]     = s->value;
1391:       (*inertias)[i++] = s->inertia;
1392:       s = s->neighb[1];
1393:     }
1394:     (*shifts)[i]   = sr->int1;
1395:     (*inertias)[i] = sr->inertia1;
1396:   }
1397:   /* remove possible duplicate in last position */
1398:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1399:   /* sort result */
1400:   for (i=0;i<*n;i++) {
1401:     v = (*shifts)[i];
1402:     for (j=i+1;j<*n;j++) {
1403:       if (v > (*shifts)[j]) {
1404:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
1405:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
1406:         v = (*shifts)[i];
1407:       }
1408:     }
1409:   }
1410:   return(0);
1411: }

1413: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1414: {
1416:   PetscInt       i,j,ti,deg=pep->nmat-1;
1417:   PetscReal      newS;
1418:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1419:   PEP_SR         sr=ctx->sr;
1420:   Mat            S,B;
1421:   PetscScalar    *pS;

1424:   PetscCitationsRegister(citation,&cited);

1426:   /* Only with eigenvalues present in the interval ...*/
1427:   if (sr->numEigs==0) {
1428:     pep->reason = PEP_CONVERGED_TOL;
1429:     return(0);
1430:   }

1432:   /* Inner product matrix */
1433:   PEPSTOARSetUpInnerMatrix(pep,&B);

1435:   /* Array of pending shifts */
1436:   sr->maxPend = 100; /* Initial size */
1437:   sr->nPend = 0;
1438:   PetscMalloc1(sr->maxPend,&sr->pending);
1439:   PetscLogObjectMemory((PetscObject)pep,sr->maxPend*sizeof(PEP_shift*));
1440:   PEPCreateShift(pep,sr->int0,NULL,NULL);
1441:   /* extract first shift */
1442:   sr->sPrev = NULL;
1443:   sr->sPres = sr->pending[--sr->nPend];
1444:   sr->sPres->inertia = sr->inertia0;
1445:   pep->target = sr->sPres->value;
1446:   sr->s0 = sr->sPres;
1447:   sr->indexEig = 0;

1449:   for (i=0;i<sr->numEigs;i++) {
1450:     sr->eigr[i]   = 0.0;
1451:     sr->eigi[i]   = 0.0;
1452:     sr->errest[i] = 0.0;
1453:     sr->perm[i]   = i;
1454:   }
1455:   /* Vectors for deflation */
1456:   PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1457:   PetscLogObjectMemory((PetscObject)pep,2*sr->numEigs*sizeof(PetscInt));
1458:   sr->indexEig = 0;
1459:   while (sr->sPres) {
1460:     /* Search for deflation */
1461:     PEPLookForDeflation(pep);
1462:     /* KrylovSchur */
1463:     PEPSTOAR_QSlice(pep,B);

1465:     PEPStoreEigenpairs(pep);
1466:     /* Select new shift */
1467:     if (!sr->sPres->comp[1]) {
1468:       PEPGetNewShiftValue(pep,1,&newS);
1469:       PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1470:     }
1471:     if (!sr->sPres->comp[0]) {
1472:       /* Completing earlier interval */
1473:       PEPGetNewShiftValue(pep,0,&newS);
1474:       PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1475:     }
1476:     /* Preparing for a new search of values */
1477:     PEPExtractShift(pep);
1478:   }

1480:   /* Updating pep values prior to exit */
1481:   PetscFree2(sr->idxDef0,sr->idxDef1);
1482:   PetscFree(sr->pending);
1483:   pep->nconv  = sr->indexEig;
1484:   pep->reason = PEP_CONVERGED_TOL;
1485:   pep->its    = sr->itsKs;
1486:   pep->nev    = sr->indexEig;
1487:   MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1488:   MatDenseGetArray(S,&pS);
1489:   for (i=0;i<pep->nconv;i++) {
1490:     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);
1491:   }
1492:   MatDenseRestoreArray(S,&pS);
1493:   BVSetActiveColumns(sr->V,0,pep->nconv);
1494:   BVMultInPlace(sr->V,S,0,pep->nconv);
1495:   MatDestroy(&S);
1496:   BVDestroy(&pep->V);
1497:   pep->V = sr->V;
1498:   PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1499:   pep->eigr   = sr->eigr;
1500:   pep->eigi   = sr->eigi;
1501:   pep->perm   = sr->perm;
1502:   pep->errest = sr->errest;
1503:   if (sr->dir<0) {
1504:     for (i=0;i<pep->nconv/2;i++) {
1505:       ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1506:     }
1507:   }
1508:   PetscFree(ctx->inertias);
1509:   PetscFree(ctx->shifts);
1510:   MatDestroy(&B);
1511:   PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1512:   return(0);
1513: }