Actual source code: qslice.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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", submitted,
 23:            2019.
 24: */

 26: #include <slepc/private/pepimpl.h>         /*I "slepcpep.h" I*/
 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 = \"In preparation\",\n"
 36:   "   volume = \"xx\",\n"
 37:   "   number = \"x\",\n"
 38:   "   pages = \"xx--xx\",\n"
 39:   "   year = \"2018,\"\n"
 40:   "   doi = \"https://doi.org/10.1007/xxx\"\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:   STSetUp(pep->st);
157:   STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
158:   STGetKSP(pep->st,&ksp);
159:   KSPGetPC(ksp,&pc);
160:   PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
161:   if (flg) {
162:     PCRedundantGetKSP(pc,&kspr);
163:     KSPGetPC(kspr,&pc);
164:   }
165:   PCFactorGetMatrix(pc,&F);
166:   MatGetInertia(F,inertia,zeros,NULL);
167:   return(0);
168: }

170: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
171: {
173:   KSP            ksp;
174:   Mat            P;
175:   PetscReal      nzshift=0.0;
176:   PetscScalar    dot;
177:   PetscRandom    rand;
178:   PetscInt       nconv;
179:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
180:   PEP_SR         sr=ctx->sr;

183:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
184:     *inertia = 0;
185:   } else if (shift <= PETSC_MIN_REAL) {
186:     *inertia = 0;
187:     if (zeros) *zeros = 0;
188:   } else {
189:     /* If the shift is zero, perturb it to a very small positive value.
190:        The goal is that the nonzero pattern is the same in all cases and reuse
191:        the symbolic factorizations */
192:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
193:     PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
194:     STSetShift(pep->st,nzshift);
195:   }
196:   if (!correction) {
197:     if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
198:     else if (shift>PETSC_MIN_REAL) {
199:       STGetKSP(pep->st,&ksp);
200:       KSPGetOperators(ksp,&P,NULL);
201:       if (*inertia!=pep->n && !sr->v[0]) {
202:         MatCreateVecs(P,&sr->v[0],NULL);
203:         VecDuplicate(sr->v[0],&sr->v[1]);
204:         VecDuplicate(sr->v[0],&sr->v[2]);
205:         BVGetRandomContext(pep->V,&rand);
206:         VecSetRandom(sr->v[0],rand);
207:       }
208:       if (*inertia<pep->n && *inertia>0) {
209:         if (!sr->eps) {
210:           EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
211:           EPSSetProblemType(sr->eps,EPS_HEP);
212:           EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
213:         }
214:         EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
215:         EPSSetOperators(sr->eps,P,NULL);
216:         EPSSolve(sr->eps);
217:         EPSGetConverged(sr->eps,&nconv);
218:         if (!nconv) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",nzshift);
219:         EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
220:       }
221:       if (*inertia!=pep->n) {
222:         MatMult(pep->A[1],sr->v[0],sr->v[1]);
223:         MatMult(pep->A[2],sr->v[0],sr->v[2]);
224:         VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
225:         VecDot(sr->v[1],sr->v[0],&dot);
226:         if (PetscRealPart(dot)>0.0) *inertia = 2*pep->n-*inertia;
227:       }
228:     }
229:   } else if (correction<0) *inertia = 2*pep->n-*inertia;
230:   return(0);
231: }

233: /*
234:    Check eigenvalue type - used only in non-hyperbolic problems.
235:    All computed eigenvalues must have the same definite type (positive or negative).
236:    If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
237:    closest to shift and determine its type.
238:  */
239: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
240: {
242:   PEP            pep2;
243:   ST             st;
244:   PetscInt       nconv;
245:   PetscScalar    lambda,dot;
246:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
247:   PEP_SR         sr=ctx->sr;

250:   if (!ini) {
251:     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);
252:   } else {
253:     PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
254:     PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
255:     PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
256:     PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
257:     PEPSetType(pep2,PEPTOAR);
258:     PEPSetOperators(pep2,pep->nmat,pep->A);
259:     PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
260:     PEPGetRG(pep2,&pep2->rg);
261:     RGSetType(pep2->rg,RGINTERVAL);
262: #if defined(PETSC_USE_COMPLEX)
263:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
264: #else
265:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
266: #endif
267:     pep2->target = shift;
268:     st = pep2->st;
269:     pep2->st = pep->st;
270:     PEPSolve(pep2);
271:     PEPGetConverged(pep2,&nconv);
272:     if (nconv) {
273:       PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
274:       MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
275:       MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
276:       VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
277:       VecDot(pep2->work[1],pep2->work[0],&dot);
278:       PetscInfo2(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(PetscRealPart(dot)>0.0)?"positive":"negative");
279:       if (!sr->type) sr->type = (PetscRealPart(dot)>0.0)?1:-1;
280:       else {
281:         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));
282:       }
283:     }
284:     pep2->st = st;
285:     PEPDestroy(&pep2);
286:   }
287:   return(0);
288: }

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

297:   MatMult(pep->A[0],u,w);
298:   VecDot(w,u,&ts);
299:   cp = PetscRealPart(ts);
300:   MatMult(pep->A[1],u,w);
301:   VecDot(w,u,&ts);
302:   bp = PetscRealPart(ts);
303:   MatMult(pep->A[2],u,w);
304:   VecDot(w,u,&ts);
305:   ap = PetscRealPart(ts);
306:   if (d) *d = bp*bp-4*ap*cp;
307:   if (*d>=0.0 && smas) {
308:     if (ap>0) *smas = (-bp+PetscSqrtReal(*d))/(2*ap);
309:     else if (ap<0) *smas = (-bp-PetscSqrtReal(*d))/(2*ap);
310:     else {
311:       if (bp >0) *smas = -cp/bp;
312:       else *smas = PETSC_MAX_REAL;
313:     }
314:   }
315:   if (*d>=0.0 && smenos) {
316:     if (ap>0) *smenos = (-bp-PetscSqrtReal(*d))/(2*ap);
317:     else if (ap<0) *smenos = (-bp+PetscSqrtReal(*d))/(2*ap);
318:     else {
319:       if (bp<0) *smenos = -cp/bp;
320:       else *smenos = PETSC_MAX_REAL;
321:     }
322:   }
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,s,sp,mut=0.0,omg,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:       omgp = omg;
475:       PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
476:       if (d<0.0) {check = -1; break;}
477:     }
478:   }
479:   if (check==1) *mu = mut;
480:   *definite = check;
481:   *hyperbolic = hyp;
482:   if (M) { MatDestroy(&M); }
483:   VecDestroy(&u);
484:   VecDestroy(&w);
485:   EPSDestroy(&eps);
486:   STSetTransform(pep->st,transform);
487:   return(0);
488: }

490: /*
491:    Dummy backtransform operation
492:  */
493: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
494: {
496:   return(0);
497: }

499: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
500: {
502:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
503:   PEP_SR         sr;
504:   PetscInt       ld,i,zeros=0;
505:   SlepcSC        sc;
506:   PetscBool      issinv;
507:   PetscReal      r;

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:   PetscObjectTypeCompareAny((PetscObject)pep->st,&issinv,STSINVERT,STCAYLEY,"");
512:   if (!issinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
513:   if (pep->tol==PETSC_DEFAULT) pep->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
514:   if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n);  /* nev not set, use default value */
515:   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");
516:   pep->ops->backtransform = PEPBackTransform_Skip;
517:   if (!pep->max_it) pep->max_it = 100;

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

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

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

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

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

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

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

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

600: /*
601:    Fills the fields of a shift structure
602: */
603: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
604: {
606:   PEP_shift      s,*pending2;
607:   PetscInt       i;
608:   PEP_SR         sr;
609:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;

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

639: /* Provides next shift to be computed */
640: static PetscErrorCode PEPExtractShift(PEP pep)
641: {
643:   PetscInt       iner,zeros=0;
644:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
645:   PEP_SR         sr;
646:   PetscReal      newShift,aux;
647:   PEP_shift      sPres;

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

687: /*
688:   Obtains value of subsequent shift
689: */
690: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
691: {
692:   PetscReal lambda,d_prev;
693:   PetscInt  i,idxP;
694:   PEP_SR    sr;
695:   PEP_shift sPres,s;
696:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

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

770: /*
771:   Function for sorting an array of real values
772: */
773: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
774: {
775:   PetscReal re;
776:   PetscInt  i,j,tmp;

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

791: /* Stores the pairs obtained since the last shift in the global arrays */
792: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
793: {
795:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
796:   PetscReal      lambda,err,*errest;
797:   PetscInt       i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
798:   PetscBool      iscayley,divide=PETSC_FALSE;
799:   PEP_SR         sr = ctx->sr;
800:   PEP_shift      sPres;
801:   Vec            w,vomega;
802:   Mat            MS;
803:   BV             tV;
804:   PetscScalar    *S,*eigr,*tS,*omega;

807:   sPres = sr->sPres;
808:   sPres->index = sr->indexEig;

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

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

957: static PetscErrorCode PEPLookForDeflation(PEP pep)
958: {
959:   PetscReal val;
960:   PetscInt  i,count0=0,count1=0;
961:   PEP_shift sPres;
962:   PetscInt  ini,fin;
963:   PEP_SR    sr;
964:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

967:   sr = ctx->sr;
968:   sPres = sr->sPres;

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

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

1000:   /* Completing vector of indexes for deflation */
1001:   for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
1002:   sr->ndef0 = count0;
1003:   for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
1004:   sr->ndef1 = count1;
1005:   return(0);
1006: }

1008: /*
1009:   Compute a run of Lanczos iterations
1010: */
1011: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
1012: {
1014:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
1015:   PetscInt       i,j,m=*M,l,lock;
1016:   PetscInt       lds,d,ld,offq,nqt,ldds;
1017:   Vec            v=t_[0],t=t_[1],q=t_[2];
1018:   PetscReal      norm,sym=0.0,fro=0.0,*f;
1019:   PetscScalar    *y,*S,sigma;
1020:   PetscBLASInt   j_,one=1;
1021:   PetscBool      lindep;
1022:   Mat            MS;

1025:   PetscMalloc1(*M,&y);
1026:   BVGetSizes(pep->V,NULL,NULL,&ld);
1027:   BVTensorGetDegree(ctx->V,&d);
1028:   BVGetActiveColumns(pep->V,&lock,&nqt);
1029:   lds = d*ld;
1030:   offq = ld;
1031:   DSGetLeadingDimension(pep->ds,&ldds);

1033:   *breakdown = PETSC_FALSE; /* ----- */
1034:   STGetShift(pep->st,&sigma);
1035:   DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
1036:   BVSetActiveColumns(ctx->V,0,m);
1037:   BVSetActiveColumns(pep->V,0,nqt);
1038:   for (j=k;j<m;j++) {
1039:     /* apply operator */
1040:     BVTensorGetFactors(ctx->V,NULL,&MS);
1041:     MatDenseGetArray(MS,&S);
1042:     BVGetColumn(pep->V,nqt,&t);
1043:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1044:     MatMult(pep->A[1],v,q);
1045:     MatMult(pep->A[2],v,t);
1046:     VecAXPY(q,sigma*pep->sfactor,t);
1047:     VecScale(q,pep->sfactor);
1048:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1049:     MatMult(pep->A[2],v,t);
1050:     VecAXPY(q,pep->sfactor*pep->sfactor,t);
1051:     STMatSolve(pep->st,q,t);
1052:     VecScale(t,-1.0);
1053:     BVRestoreColumn(pep->V,nqt,&t);

1055:     /* orthogonalize */
1056:     BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1057:     if (!lindep) {
1058:       *(S+(j+1)*lds+nqt) = norm;
1059:       BVScaleColumn(pep->V,nqt,1.0/norm);
1060:       nqt++;
1061:     }
1062:     for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1063:     BVSetActiveColumns(pep->V,0,nqt);
1064:     MatDenseRestoreArray(MS,&S);
1065:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1067:     /* level-2 orthogonalization */
1068:     BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1069:     a[j] = PetscRealPart(y[j]);
1070:     omega[j+1] = (norm > 0)?1.0:-1.0;
1071:     BVScaleColumn(ctx->V,j+1,1.0/norm);
1072:     b[j] = PetscAbsReal(norm);

1074:     /* check symmetry */
1075:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1076:     if (j==k) {
1077:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1078:       for (i=0;i<l;i++) y[i] = 0.0;
1079:     }
1080:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1081:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1082:     PetscBLASIntCast(j,&j_);
1083:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1084:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1085:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
1086:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1087:       *symmlost = PETSC_TRUE;
1088:       *M=j;
1089:       break;
1090:     }
1091:   }
1092:   BVSetActiveColumns(pep->V,lock,nqt);
1093:   BVSetActiveColumns(ctx->V,0,*M);
1094:   PetscFree(y);
1095:   return(0);
1096: }

1098: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1099: {
1101:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
1102:   PetscInt       j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1103:   PetscInt       nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1104:   PetscScalar    *Q,*om,sigma,*back,*S,*pQ;
1105:   PetscReal      beta,norm=1.0,*omega,*a,*b,*r,eta,lambda;
1106:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1107:   Mat            MS,MQ;
1108:   Vec            v,vomega;
1109:   PEP_SR         sr;
1110:   BVOrthogType   otype;
1111:   BVOrthogBlockType obtype;

1114:   PetscCitationsRegister(citation,&cited);

1116:   /* Resize if needed for deflating vectors  */
1117:   sr = ctx->sr;
1118:   sigma = sr->sPres->value;
1119:   k = sr->ndef0+sr->ndef1;
1120:   pep->ncv = ctx->ncv+k;
1121:   pep->nev = ctx->nev+k;
1122:   PEPAllocateSolution(pep,3);
1123:   BVDestroy(&ctx->V);
1124:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1125:   BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1126:   BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1127:   DSAllocate(pep->ds,pep->ncv+2);
1128:   PetscMalloc1(pep->ncv,&back);
1129:   DSGetLeadingDimension(pep->ds,&ldds);
1130:   BVSetMatrix(ctx->V,B,PETSC_TRUE);
1131:   if (ctx->lock) {
1132:     PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1133:   } else SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
1134:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1135:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1136:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

1138:   /* Get the starting Arnoldi vector */
1139:   BVSetActiveColumns(pep->V,0,1);
1140:   BVTensorBuildFirstColumn(ctx->V,pep->nini);
1141:   BVSetActiveColumns(ctx->V,0,1);
1142:   if (k) {
1143:     /* Insert deflated vectors */
1144:     BVSetActiveColumns(pep->V,0,0);
1145:     idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1146:     for (j=0;j<k;j++) {
1147:       BVGetColumn(pep->V,j,&v);
1148:       BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1149:       BVRestoreColumn(pep->V,j,&v);
1150:     }
1151:     /* Update innerproduct matrix */
1152:     BVSetActiveColumns(ctx->V,0,0);
1153:     BVTensorGetFactors(ctx->V,NULL,&MS);
1154:     BVSetActiveColumns(pep->V,0,k);
1155:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1157:     BVGetSizes(pep->V,NULL,NULL,&ld);
1158:     BVTensorGetFactors(ctx->V,NULL,&MS);
1159:     MatDenseGetArray(MS,&S);
1160:     for (j=0;j<sr->ndef0;j++) {
1161:       PetscMemzero(S+j*ld*deg,ld*deg*sizeof(PetscScalar));
1162:       PetscMemcpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k*sizeof(PetscScalar));
1163:       PetscMemcpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k*sizeof(PetscScalar));
1164:       pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1165:       pep->errest[j] = sr->errest[sr->idxDef0[j]];
1166:     }
1167:     for (j=0;j<sr->ndef1;j++) {
1168:       PetscMemzero(S+(j+sr->ndef0)*ld*deg,ld*deg*sizeof(PetscScalar));
1169:       PetscMemcpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k*sizeof(PetscScalar));
1170:       PetscMemcpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k*sizeof(PetscScalar));
1171:       pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1172:       pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1173:     }
1174:     MatDenseRestoreArray(MS,&S);
1175:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1176:     BVSetActiveColumns(ctx->V,0,k+1);
1177:     VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1178:     VecGetArray(vomega,&om);
1179:     for (j=0;j<k;j++) {
1180:       BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1181:       BVScaleColumn(ctx->V,j,1/norm);
1182:       om[j] = (norm>=0.0)?1.0:-1.0;
1183:     }
1184:     BVTensorGetFactors(ctx->V,NULL,&MS);
1185:     MatDenseGetArray(MS,&S);
1186:     for (j=0;j<deg;j++) {
1187:       BVSetRandomColumn(pep->V,k+j);
1188:       BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1189:       BVScaleColumn(pep->V,k+j,1.0/norm);
1190:       S[k*ld*deg+j*ld+k+j] = norm;
1191:     }
1192:     MatDenseRestoreArray(MS,&S);
1193:     BVSetActiveColumns(pep->V,0,k+deg);
1194:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1195:     BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1196:     BVScaleColumn(ctx->V,k,1.0/norm);
1197:     om[k] = (norm>=0.0)?1.0:-1.0;
1198:     VecRestoreArray(vomega,&om);
1199:     BVSetSignature(ctx->V,vomega);
1200:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1201:     VecGetArray(vomega,&om);
1202:     for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1203:     VecRestoreArray(vomega,&om);
1204:     VecDestroy(&vomega);
1205:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1206:     DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1207:     PetscMemzero(pQ,ldds*k*sizeof(PetscScalar));
1208:     for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1209:     DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1210:   }
1211:   BVSetActiveColumns(ctx->V,0,k+1);
1212:   DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1213:   VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1214:   BVGetSignature(ctx->V,vomega);
1215:   VecGetArray(vomega,&om);
1216:   for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
1217:   VecRestoreArray(vomega,&om);
1218:   DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1219:   VecDestroy(&vomega);

1221:   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]);

1223:   /* Restart loop */
1224:   l = 0;
1225:   pep->nconv = k;
1226:   while (pep->reason == PEP_CONVERGED_ITERATING) {
1227:     pep->its++;
1228:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1229:     b = a+ldds;
1230:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

1232:     /* Compute an nv-step Lanczos factorization */
1233:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1234:     PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1235:     beta = b[nv-1];
1236:     if (symmlost && nv==pep->nconv+l) {
1237:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1238:       pep->nconv = nconv;
1239:       PetscInfo2(pep,"Symmetry lost in STOAR sigma=%g nconv=%D\n",(double)sr->sPres->value,nconv);
1240:       if (falselock || !ctx->lock) {
1241:         BVSetActiveColumns(ctx->V,0,pep->nconv);
1242:         BVTensorCompress(ctx->V,0);
1243:       }
1244:       break;
1245:     }
1246:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1247:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1248:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
1249:     if (l==0) {
1250:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1251:     } else {
1252:       DSSetState(pep->ds,DS_STATE_RAW);
1253:     }

1255:     /* Solve projected problem */
1256:     DSSolve(pep->ds,pep->eigr,pep->eigi);
1257:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1258:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

1260:     /* Check convergence */
1261:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1262:     norm = 1.0;
1263:     DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
1264:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1265:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1266:     for (j=0;j<k;j++) back[j] = pep->eigr[j];
1267:     STBackTransform(pep->st,k,back,pep->eigi);
1268:     count0=count1=0;
1269:     for (j=0;j<k;j++) {
1270:       lambda = PetscRealPart(back[j]);
1271:       if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1272:       if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1273:     }
1274:     if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1275:     /* Update l */
1276:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1277:     else {
1278:       l = PetscMax(1,(PetscInt)((nv-k)/2));
1279:       l = PetscMin(l,t);
1280:       if (!breakdown) {
1281:         DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1282:         if (*(a+ldds+k+l-1)!=0) {
1283:           if (k+l<nv-1) l = l+1;
1284:           else l = l-1;
1285:         }
1286:         /* Prepare the Rayleigh quotient for restart */
1287:         DSGetArray(pep->ds,DS_MAT_Q,&Q);
1288:         DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1289:         r = a + 2*ldds;
1290:         for (j=k;j<k+l;j++) {
1291:           r[j] = PetscRealPart(Q[nv-1+j*ldds]*beta);
1292:         }
1293:         b = a+ldds;
1294:         b[k+l-1] = r[k+l-1];
1295:         omega[k+l] = omega[nv];
1296:         DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
1297:         DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1298:         DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1299:       }
1300:     }
1301:     nconv = k;
1302:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

1304:     /* Update S */
1305:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1306:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1307:     MatDestroy(&MQ);

1309:     /* Copy last column of S */
1310:     BVCopyColumn(ctx->V,nv,k+l);
1311:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1312:     VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
1313:     VecGetArray(vomega,&om);
1314:     for (j=0;j<k+l;j++) om[j] = omega[j];
1315:     VecRestoreArray(vomega,&om);
1316:     BVSetActiveColumns(ctx->V,0,k+l);
1317:     BVSetSignature(ctx->V,vomega);
1318:     VecDestroy(&vomega);
1319:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);

1321:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1322:       /* stop if breakdown */
1323:       PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
1324:       pep->reason = PEP_DIVERGED_BREAKDOWN;
1325:     }
1326:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1327:     BVGetActiveColumns(pep->V,NULL,&nq);
1328:     if (k+l+deg<=nq) {
1329:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1330:       if (!falselock && ctx->lock) {
1331:         BVTensorCompress(ctx->V,k-pep->nconv);
1332:       } else {
1333:         BVTensorCompress(ctx->V,0);
1334:       }
1335:     }
1336:     pep->nconv = k;
1337:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1338:   }
1339:   sr->itsKs += pep->its;
1340:   if (pep->nconv>0) {
1341:     BVSetActiveColumns(ctx->V,0,pep->nconv);
1342:     BVGetActiveColumns(pep->V,NULL,&nq);
1343:     BVSetActiveColumns(pep->V,0,nq);
1344:     if (nq>pep->nconv) {
1345:       BVTensorCompress(ctx->V,pep->nconv);
1346:       BVSetActiveColumns(pep->V,0,pep->nconv);
1347:     }
1348:     for (j=0;j<pep->nconv;j++) {
1349:       pep->eigr[j] *= pep->sfactor;
1350:       pep->eigi[j] *= pep->sfactor;
1351:     }
1352:   }
1353:   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);
1354:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1355:   RGPopScale(pep->rg);

1357:   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);
1358:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1359:     if (++sr->symmlost>10) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1360:   } else sr->symmlost = 0;

1362:   /* truncate Schur decomposition and change the state to raw so that
1363:      DSVectors() computes eigenvectors from scratch */
1364:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
1365:   DSSetState(pep->ds,DS_STATE_RAW);
1366:   PetscFree(back);
1367:   return(0);
1368: }

1370: #define SWAP(a,b,t) {t=a;a=b;b=t;}

1372: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1373: {
1374:   PetscErrorCode  ierr;
1375:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1376:   PEP_SR          sr=ctx->sr;
1377:   PetscInt        i=0,j,tmpi;
1378:   PetscReal       v,tmpr;
1379:   PEP_shift       s;

1382:   if (!pep->state) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
1383:   if (!sr) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
1384:   if (!sr->s0) {  /* PEPSolve not called yet */
1385:     *n = 2;
1386:   } else {
1387:     *n = 1;
1388:     s = sr->s0;
1389:     while (s) {
1390:       (*n)++;
1391:       s = s->neighb[1];
1392:     }
1393:   }
1394:   PetscMalloc1(*n,shifts);
1395:   PetscMalloc1(*n,inertias);
1396:   if (!sr->s0) {  /* PEPSolve not called yet */
1397:     (*shifts)[0]   = sr->int0;
1398:     (*shifts)[1]   = sr->int1;
1399:     (*inertias)[0] = sr->inertia0;
1400:     (*inertias)[1] = sr->inertia1;
1401:   } else {
1402:     s = sr->s0;
1403:     while (s) {
1404:       (*shifts)[i]     = s->value;
1405:       (*inertias)[i++] = s->inertia;
1406:       s = s->neighb[1];
1407:     }
1408:     (*shifts)[i]   = sr->int1;
1409:     (*inertias)[i] = sr->inertia1;
1410:   }
1411:   /* remove possible duplicate in last position */
1412:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1413:   /* sort result */
1414:   for (i=0;i<*n;i++) {
1415:     v = (*shifts)[i];
1416:     for (j=i+1;j<*n;j++) {
1417:       if (v > (*shifts)[j]) {
1418:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
1419:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
1420:         v = (*shifts)[i];
1421:       }
1422:     }
1423:   }
1424:   return(0);
1425: }

1427: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1428: {
1430:   PetscInt       i,j,ti,deg=pep->nmat-1;
1431:   PetscReal      newS;
1432:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1433:   PEP_SR         sr=ctx->sr;
1434:   Mat            S,B;
1435:   PetscScalar    *pS;

1438:   /* Only with eigenvalues present in the interval ...*/
1439:   if (sr->numEigs==0) {
1440:     pep->reason = PEP_CONVERGED_TOL;
1441:     return(0);
1442:   }

1444:   /* Inner product matrix */
1445:   PEPSTOARSetUpInnerMatrix(pep,&B);

1447:   /* Array of pending shifts */
1448:   sr->maxPend = 100; /* Initial size */
1449:   sr->nPend = 0;
1450:   PetscMalloc1(sr->maxPend,&sr->pending);
1451:   PetscLogObjectMemory((PetscObject)pep,(sr->maxPend)*sizeof(PEP_shift));
1452:   PEPCreateShift(pep,sr->int0,NULL,NULL);
1453:   /* extract first shift */
1454:   sr->sPrev = NULL;
1455:   sr->sPres = sr->pending[--sr->nPend];
1456:   sr->sPres->inertia = sr->inertia0;
1457:   pep->target = sr->sPres->value;
1458:   sr->s0 = sr->sPres;
1459:   sr->indexEig = 0;

1461:   /* Memory reservation for auxiliary variables */
1462:   PetscLogObjectMemory((PetscObject)pep,(sr->numEigs+2*pep->ncv)*sizeof(PetscScalar));
1463:   for (i=0;i<sr->numEigs;i++) {
1464:     sr->eigr[i]   = 0.0;
1465:     sr->eigi[i]   = 0.0;
1466:     sr->errest[i] = 0.0;
1467:     sr->perm[i]   = i;
1468:   }
1469:   /* Vectors for deflation */
1470:   PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1471:   PetscLogObjectMemory((PetscObject)pep,sr->numEigs*sizeof(PetscInt));
1472:   sr->indexEig = 0;
1473:   while (sr->sPres) {
1474:     /* Search for deflation */
1475:     PEPLookForDeflation(pep);
1476:     /* KrylovSchur */
1477:     PEPSTOAR_QSlice(pep,B);

1479:     PEPStoreEigenpairs(pep);
1480:     /* Select new shift */
1481:     if (!sr->sPres->comp[1]) {
1482:       PEPGetNewShiftValue(pep,1,&newS);
1483:       PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1484:     }
1485:     if (!sr->sPres->comp[0]) {
1486:       /* Completing earlier interval */
1487:       PEPGetNewShiftValue(pep,0,&newS);
1488:       PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1489:     }
1490:     /* Preparing for a new search of values */
1491:     PEPExtractShift(pep);
1492:   }

1494:   /* Updating pep values prior to exit */
1495:   PetscFree2(sr->idxDef0,sr->idxDef1);
1496:   PetscFree(sr->pending);
1497:   pep->nconv  = sr->indexEig;
1498:   pep->reason = PEP_CONVERGED_TOL;
1499:   pep->its    = sr->itsKs;
1500:   pep->nev    = sr->indexEig;
1501:   MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1502:   MatDenseGetArray(S,&pS);
1503:   for (i=0;i<pep->nconv;i++) {
1504:     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);
1505:   }
1506:   MatDenseRestoreArray(S,&pS);
1507:   BVSetActiveColumns(sr->V,0,pep->nconv);
1508:   BVMultInPlace(sr->V,S,0,pep->nconv);
1509:   MatDestroy(&S);
1510:   BVDestroy(&pep->V);
1511:   pep->V = sr->V;
1512:   PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1513:   pep->eigr   = sr->eigr;
1514:   pep->eigi   = sr->eigi;
1515:   pep->perm   = sr->perm;
1516:   pep->errest = sr->errest;
1517:   if (sr->dir<0) {
1518:     for (i=0;i<pep->nconv/2;i++) {
1519:       ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1520:     }
1521:   }
1522:   PetscFree(ctx->inertias);
1523:   PetscFree(ctx->shifts);
1524:   MatDestroy(&B);
1525:   PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1526:   return(0);
1527: }