Actual source code: qslice.c

slepc-3.17.0 2022-03-31
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

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

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

 15:    Algorithm:

 17:        Symmetric Two-Level Orthogonal Arnoldi.

 19:    References:

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

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

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

 43: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON

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

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

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

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

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

 96:   /* allocate space for eigenvalues and friends */
 97:   k = PetscMax(1,sr->numEigs);
 98:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
 99:   PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
100:   PetscFree(sr->qinfo);
101:   PetscCalloc1(k,&sr->qinfo);
102:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
103:   PetscLogObjectMemory((PetscObject)pep,cnt);

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

124: /* Convergence test to compute positive Ritz values */
125: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
126: {
127:   *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
128:   PetscFunctionReturn(0);
129: }

131: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
132: {
133:   KSP            ksp,kspr;
134:   PC             pc;
135:   Mat            F;
136:   PetscBool      flg;

138:   if (!pep->solvematcoeffs) PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
139:   if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
140:     pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
141:   } else PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL);
142:   STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
143:   STGetKSP(pep->st,&ksp);
144:   KSPGetPC(ksp,&pc);
145:   PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
146:   if (flg) {
147:     PCRedundantGetKSP(pc,&kspr);
148:     KSPGetPC(kspr,&pc);
149:   }
150:   PCFactorGetMatrix(pc,&F);
151:   MatGetInertia(F,inertia,zeros,NULL);
152:   PetscFunctionReturn(0);
153: }

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

165:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
166:     *inertia = 0;
167:   } else if (shift <= PETSC_MIN_REAL) {
168:     *inertia = 0;
169:     if (zeros) *zeros = 0;
170:   } else {
171:     /* If the shift is zero, perturb it to a very small positive value.
172:        The goal is that the nonzero pattern is the same in all cases and reuse
173:        the symbolic factorizations */
174:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
175:     PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
176:     STSetShift(pep->st,nzshift);
177:   }
178:   if (!correction) {
179:     if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
180:     else if (shift>PETSC_MIN_REAL) {
181:       STGetKSP(pep->st,&ksp);
182:       KSPGetOperators(ksp,&P,NULL);
183:       if (*inertia!=pep->n && !sr->v[0]) {
184:         MatCreateVecs(P,&sr->v[0],NULL);
185:         VecDuplicate(sr->v[0],&sr->v[1]);
186:         VecDuplicate(sr->v[0],&sr->v[2]);
187:         BVGetRandomContext(pep->V,&rand);
188:         VecSetRandom(sr->v[0],rand);
189:       }
190:       if (*inertia<pep->n && *inertia>0) {
191:         if (!sr->eps) {
192:           EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
193:           EPSSetProblemType(sr->eps,EPS_HEP);
194:           EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
195:         }
196:         EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
197:         EPSSetOperators(sr->eps,P,NULL);
198:         EPSSolve(sr->eps);
199:         EPSGetConverged(sr->eps,&nconv);
201:         EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
202:       }
203:       if (*inertia!=pep->n) {
204:         MatMult(pep->A[1],sr->v[0],sr->v[1]);
205:         MatMult(pep->A[2],sr->v[0],sr->v[2]);
206:         VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
207:         VecDotRealPart(sr->v[1],sr->v[0],&dot);
208:         if (dot>0.0) *inertia = 2*pep->n-*inertia;
209:       }
210:     }
211:   } else if (correction<0) *inertia = 2*pep->n-*inertia;
212:   PetscFunctionReturn(0);
213: }

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

231:   if (!ini) {
233:   } else {
234:     PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
235:     PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
236:     PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
237:     PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
238:     PEPSetType(pep2,PEPTOAR);
239:     PEPSetOperators(pep2,pep->nmat,pep->A);
240:     PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
241:     PEPGetRG(pep2,&pep2->rg);
242:     RGSetType(pep2->rg,RGINTERVAL);
243: #if defined(PETSC_USE_COMPLEX)
244:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
245: #else
246:     RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
247: #endif
248:     pep2->target = shift;
249:     st = pep2->st;
250:     pep2->st = pep->st;
251:     PEPSolve(pep2);
252:     PEPGetConverged(pep2,&nconv);
253:     if (nconv) {
254:       PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
255:       MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
256:       MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
257:       VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
258:       VecDotRealPart(pep2->work[1],pep2->work[0],&dot);
259:       PetscInfo(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(dot>0.0)?"positive":"negative");
260:       if (!sr->type) sr->type = (dot>0.0)?1:-1;
262:     }
263:     pep2->st = st;
264:     PEPDestroy(&pep2);
265:   }
266:   PetscFunctionReturn(0);
267: }

269: static inline PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
270: {
271:   PetscReal      ap,bp,cp,dis;

273:   MatMult(pep->A[0],u,w);
274:   VecDotRealPart(w,u,&cp);
275:   MatMult(pep->A[1],u,w);
276:   VecDotRealPart(w,u,&bp);
277:   MatMult(pep->A[2],u,w);
278:   VecDotRealPart(w,u,&ap);
279:   dis = bp*bp-4*ap*cp;
280:   if (dis>=0.0 && smas) {
281:     if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
282:     else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
283:     else {
284:       if (bp >0) *smas = -cp/bp;
285:       else *smas = PETSC_MAX_REAL;
286:     }
287:   }
288:   if (dis>=0.0 && smenos) {
289:     if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
290:     else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
291:     else {
292:       if (bp<0) *smenos = -cp/bp;
293:       else *smenos = PETSC_MAX_REAL;
294:     }
295:   }
296:   if (d) *d = dis;
297:   PetscFunctionReturn(0);
298: }

300: static inline PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
301: {
302:   MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
303:   MatAXPY(M,x,pep->A[1],str);
304:   MatAXPY(M,x*x,pep->A[2],str);
305:   PetscFunctionReturn(0);
306: }

308: /*@
309:    PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
310:    is definite or not.

312:    Logically Collective on pep

314:    Input Parameter:
315: .  pep  - eigensolver context

317:    Output Parameters:
318: +  xi - first computed parameter
319: .  mu - second computed parameter
320: .  definite - flag indicating that the problem is definite
321: -  hyperbolic - flag indicating that the problem is hyperbolic

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

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

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

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

338:    Level: advanced

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

354:   ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
355:   if (!pep->st) PEPGetST(pep,&pep->st);
356:   PEPSetDefaultST(pep);
357:   STSetMatrices(pep->st,pep->nmat,pep->A);
358:   MatGetSize(pep->A[0],&n,NULL);
359:   STGetTransform(pep->st,&transform);
360:   STSetTransform(pep->st,PETSC_FALSE);
361:   STSetUp(pep->st);
362:   MatCreateVecs(pep->A[0],&u,&w);
363:   PEPGetBV(pep,&pep->V);
364:   BVGetRandomContext(pep->V,&rand);
365:   VecSetRandom(u,rand);
366:   VecNormalize(u,NULL);
367:   PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
368:   if (d<0.0) check = -1;
369:   if (!check) {
370:     EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
371:     EPSSetProblemType(eps,EPS_HEP);
372:     EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
373:     EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
374:     MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
375:     STGetMatStructure(pep->st,&str);
376:   }
377:   for (k=0;k<its&&!check;k++) {
378:     PEPQSliceEvaluateQEP(pep,s,M,str);
379:     EPSSetOperators(eps,M,NULL);
380:     EPSSolve(eps);
381:     EPSGetConverged(eps,&nconv);
382:     if (!nconv) break;
383:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
384:     sp = s;
385:     PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
386:     if (d<0.0) {check = -1; break;}
387:     if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
388:     if (s>sp) {hyp = -1;}
389:     mut = 2*s-sp;
390:     PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
391:     if (inertia == n) {check = 1; break;}
392:   }
393:   for (;k<its&&!check;k++) {
394:     mut = (s-omg)/2;
395:     PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
396:     if (inertia == n) {check = 1; break;}
397:     if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
398:     PEPQSliceEvaluateQEP(pep,omg,M,str);
399:     EPSSetOperators(eps,M,NULL);
400:     EPSSolve(eps);
401:     EPSGetConverged(eps,&nconv);
402:     if (!nconv) break;
403:     EPSGetEigenpair(eps,0,NULL,NULL,u,w);
404:     omgp = omg;
405:     PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
406:     if (d<0.0) {check = -1; break;}
407:     if (omg<omgp) hyp = -1;
408:   }
409:   if (check==1) *xi = mut;
411:   if (check==1 && hyp==0) {
412:     PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
413:     if (inertia == 0) hyp = 1;
414:     else hyp = -1;
415:   }
416:   if (check==1 && hyp!=1) {
417:     check = 0;
418:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
419:     for (;k<its&&!check;k++) {
420:       PEPQSliceEvaluateQEP(pep,s,M,str);
421:       EPSSetOperators(eps,M,NULL);
422:       EPSSolve(eps);
423:       EPSGetConverged(eps,&nconv);
424:       if (!nconv) break;
425:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
426:       sp = s;
427:       PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
428:       if (d<0.0) {check = -1; break;}
429:       if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
430:       mut = 2*s-sp;
431:       PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
432:       if (inertia == 0) {check = 1; break;}
433:     }
434:     for (;k<its&&!check;k++) {
435:       mut = (s-omg)/2;
436:       PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
437:       if (inertia == 0) {check = 1; break;}
438:       if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
439:       PEPQSliceEvaluateQEP(pep,omg,M,str);
440:       EPSSetOperators(eps,M,NULL);
441:       EPSSolve(eps);
442:       EPSGetConverged(eps,&nconv);
443:       if (!nconv) break;
444:       EPSGetEigenpair(eps,0,NULL,NULL,u,w);
445:       PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
446:       if (d<0.0) {check = -1; break;}
447:     }
448:   }
449:   if (check==1) *mu = mut;
450:   *definite = check;
451:   *hyperbolic = hyp;
452:   if (M) MatDestroy(&M);
453:   VecDestroy(&u);
454:   VecDestroy(&w);
455:   EPSDestroy(&eps);
456:   STSetTransform(pep->st,transform);
457:   PetscFunctionReturn(0);
458: }

460: /*
461:    Dummy backtransform operation
462:  */
463: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
464: {
465:   PetscFunctionReturn(0);
466: }

468: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
469: {
470:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
471:   PEP_SR         sr;
472:   PetscInt       ld,i,zeros=0;
473:   SlepcSC        sc;
474:   PetscReal      r;

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

493:   /* create spectrum slicing context and initialize it */
494:   PEPQSliceResetSR(pep);
495:   PetscNewLog(pep,&sr);
496:   ctx->sr   = sr;
497:   sr->itsKs = 0;
498:   sr->nleap = 0;
499:   sr->sPres = NULL;

501:   if (pep->solvematcoeffs) PetscFree(pep->solvematcoeffs);
502:   PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
503:   if (!pep->st) PEPGetST(pep,&pep->st);
504:   STSetTransform(pep->st,PETSC_FALSE);
505:   STSetUp(pep->st);

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

509:   /* check presence of ends and finding direction */
510:   if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
511:     sr->int0 = pep->inta;
512:     sr->int1 = pep->intb;
513:     sr->dir = 1;
514:     if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
515:       sr->hasEnd = PETSC_FALSE;
516:     } else sr->hasEnd = PETSC_TRUE;
517:   } else {
518:     sr->int0 = pep->intb;
519:     sr->int1 = pep->inta;
520:     sr->dir = -1;
521:     sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
522:   }

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

529:   /* compute inertia1 */
530:   PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
532:   if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
533:     PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE);
536:     if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
537:       sr->intcorr = -1;
538:       sr->inertia0 = 2*pep->n-sr->inertia0;
539:       sr->inertia1 = 2*pep->n-sr->inertia1;
540:     } else sr->intcorr = 1;
541:   } else {
542:     if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
543:     else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
544:   }

546:   if (sr->hasEnd) {
547:     sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
548:     i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
549:   }

551:   /* number of eigenvalues in interval */
552:   sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
553:   PetscInfo(pep,"QSlice setup: allocating for %" PetscInt_FMT " eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb);
554:   if (sr->numEigs) {
555:     PEPQSliceAllocateSolution(pep);
556:     PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd);
557:     pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
558:     ld   = ctx->ncv+2;
559:     DSSetType(pep->ds,DSGHIEP);
560:     DSSetCompact(pep->ds,PETSC_TRUE);
561:     DSSetExtraRow(pep->ds,PETSC_TRUE);
562:     DSAllocate(pep->ds,ld);
563:     DSGetSlepcSC(pep->ds,&sc);
564:     sc->rg            = NULL;
565:     sc->comparison    = SlepcCompareLargestMagnitude;
566:     sc->comparisonctx = NULL;
567:     sc->map           = NULL;
568:     sc->mapobj        = NULL;
569:   } else {pep->ncv = 0; pep->nev = 0; pep->mpd = 0;}
570:   PetscFunctionReturn(0);
571: }

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

583:   sr = ctx->sr;
584:   PetscNewLog(pep,&s);
585:   s->value = val;
586:   s->neighb[0] = neighb0;
587:   if (neighb0) neighb0->neighb[1] = s;
588:   s->neighb[1] = neighb1;
589:   if (neighb1) neighb1->neighb[0] = s;
590:   s->comp[0] = PETSC_FALSE;
591:   s->comp[1] = PETSC_FALSE;
592:   s->index = -1;
593:   s->neigs = 0;
594:   s->nconv[0] = s->nconv[1] = 0;
595:   s->nsch[0] = s->nsch[1]=0;
596:   /* Inserts in the stack of pending shifts */
597:   /* If needed, the array is resized */
598:   if (sr->nPend >= sr->maxPend) {
599:     sr->maxPend *= 2;
600:     PetscMalloc1(sr->maxPend,&pending2);
601:     PetscLogObjectMemory((PetscObject)pep,sr->maxPend*sizeof(PEP_shift*));
602:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
603:     PetscFree(sr->pending);
604:     sr->pending = pending2;
605:   }
606:   sr->pending[sr->nPend++]=s;
607:   PetscFunctionReturn(0);
608: }

610: /* Provides next shift to be computed */
611: static PetscErrorCode PEPExtractShift(PEP pep)
612: {
613:   PetscInt       iner,zeros=0;
614:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
615:   PEP_SR         sr;
616:   PetscReal      newShift,aux;
617:   PEP_shift      sPres;

619:   sr = ctx->sr;
620:   if (sr->nPend > 0) {
621:     if (sr->dirch) {
622:       aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
623:       iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
624:       sr->dir *= -1;
625:       PetscFree(sr->s0->neighb[1]);
626:       PetscFree(sr->s0);
627:       sr->nPend--;
628:       PEPCreateShift(pep,sr->int0,NULL,NULL);
629:       sr->sPrev = NULL;
630:       sr->sPres = sr->pending[--sr->nPend];
631:       pep->target = sr->sPres->value;
632:       sr->s0 = sr->sPres;
633:       pep->reason = PEP_CONVERGED_ITERATING;
634:     } else {
635:       sr->sPrev = sr->sPres;
636:       sr->sPres = sr->pending[--sr->nPend];
637:     }
638:     sPres = sr->sPres;
639:     PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
640:     if (zeros) {
641:       newShift = sPres->value*(1.0+SLICE_PTOL);
642:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
643:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
644:       PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
646:       sPres->value = newShift;
647:     }
648:     sr->sPres->inertia = iner;
649:     pep->target = sr->sPres->value;
650:     pep->reason = PEP_CONVERGED_ITERATING;
651:     pep->its = 0;
652:   } else sr->sPres = NULL;
653:   PetscFunctionReturn(0);
654: }

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

667:   sr = ctx->sr;
668:   sPres = sr->sPres;
669:   if (sPres->neighb[side]) {
670:   /* Completing a previous interval */
671:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
672:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
673:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
674:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
675:   } else { /* (Only for side=1). Creating a new interval. */
676:     if (sPres->neigs==0) {/* No value has been accepted*/
677:       if (sPres->neighb[0]) {
678:         /* Multiplying by 10 the previous distance */
679:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
680:         sr->nleap++;
681:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
683:       } else { /* First shift */
684:         if (pep->nconv != 0) {
685:           /* Unaccepted values give information for next shift */
686:           idxP=0;/* Number of values left from shift */
687:           for (i=0;i<pep->nconv;i++) {
688:             lambda = PetscRealPart(pep->eigr[i]);
689:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
690:             else break;
691:           }
692:           /* Avoiding subtraction of eigenvalues (might be the same).*/
693:           if (idxP>0) {
694:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
695:           } else {
696:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
697:           }
698:           *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
699:           sr->dirch = PETSC_FALSE;
700:         } else { /* No values found, no information for next shift */
702:           sr->dirch = PETSC_TRUE;
703:           *newS = sr->int1;
704:         }
705:       }
706:     } else { /* Accepted values found */
707:       sr->dirch = PETSC_FALSE;
708:       sr->nleap = 0;
709:       /* Average distance of values in previous subinterval */
710:       s = sPres->neighb[0];
711:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
712:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
713:       }
714:       if (s) {
715:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
716:       } else { /* First shift. Average distance obtained with values in this shift */
717:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
718:         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)) {
719:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
720:         } else {
721:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
722:         }
723:       }
724:       /* Average distance is used for next shift by adding it to value on the right or to shift */
725:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
726:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
727:       } else { /* Last accepted value is on the left of shift. Adding to shift */
728:         *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
729:       }
730:     }
731:     /* End of interval can not be surpassed */
732:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
733:   }/* of neighb[side]==null */
734:   PetscFunctionReturn(0);
735: }

737: /*
738:   Function for sorting an array of real values
739: */
740: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
741: {
742:   PetscReal re;
743:   PetscInt  i,j,tmp;

745:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
746:   /* Insertion sort */
747:   for (i=1;i<nr;i++) {
748:     re = PetscRealPart(r[perm[i]]);
749:     j = i-1;
750:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
751:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
752:     }
753:   }
754:   PetscFunctionReturn(0);
755: }

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

771:   sPres = sr->sPres;
772:   sPres->index = sr->indexEig;

774:   if (nconv>sr->ndef0+sr->ndef1) {
775:     /* Back-transform */
776:     STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
777:     for (i=0;i<nconv;i++) {
778: #if defined(PETSC_USE_COMPLEX)
779:       if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
780: #else
781:       if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
782: #endif
783:     }
784:     PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
785:     /* Sort eigenvalues */
786:     sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
787:     VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
788:     BVGetSignature(ctx->V,vomega);
789:     VecGetArray(vomega,&omega);
790:     BVGetSizes(pep->V,NULL,NULL,&ld);
791:     BVTensorGetFactors(ctx->V,NULL,&MS);
792:     MatDenseGetArray(MS,&S);
793:     /* Values stored in global array */
794:     PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
795:     ndef = sr->ndef0+sr->ndef1;
796:     for (i=0;i<nconv;i++) {
797:       lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
798:       err = pep->errest[pep->perm[i]];
799:       if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
801:         PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
802:         eigr[count] = lambda;
803:         errest[count] = err;
804:         if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
805:         if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
806:         PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
807:         PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
808:         count++;
809:       }
810:     }
811:     VecRestoreArray(vomega,&omega);
812:     VecDestroy(&vomega);
813:     for (i=0;i<count;i++) {
814:       PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
815:       PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
816:     }
817:     MatDenseRestoreArray(MS,&S);
818:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
819:     BVSetActiveColumns(ctx->V,0,count);
820:     BVTensorCompress(ctx->V,count);
821:     if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
822:       divide = PETSC_TRUE;
823:       BVTensorGetFactors(ctx->V,NULL,&MS);
824:       MatDenseGetArray(MS,&S);
825:       PetscArrayzero(tS,nconv*nconv*d);
826:       for (i=0;i<count;i++) {
827:         PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
828:         PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
829:       }
830:       MatDenseRestoreArray(MS,&S);
831:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
832:       BVSetActiveColumns(pep->V,0,count);
833:       BVDuplicateResize(pep->V,count,&tV);
834:       BVCopy(pep->V,tV);
835:     }
836:     if (sr->sPres->nconv[0]) {
837:       if (divide) {
838:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
839:         BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
840:       }
841:       for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
842:       for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
843:       BVTensorGetFactors(ctx->V,NULL,&MS);
844:       MatDenseGetArray(MS,&S);
845:       for (i=0;i<sr->sPres->nconv[0];i++) {
846:         sr->eigr[aux[i]] = eigr[i];
847:         sr->errest[aux[i]] = errest[i];
848:         BVGetColumn(pep->V,i,&w);
849:         BVInsertVec(sr->V,aux[i],w);
850:         BVRestoreColumn(pep->V,i,&w);
851:         idx = sr->ld*d*aux[i];
852:         PetscArrayzero(sr->S+idx,sr->ld*d);
853:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
854:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
855:         PetscFree(sr->qinfo[aux[i]].q);
856:         PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
857:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
858:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
859:       }
860:       MatDenseRestoreArray(MS,&S);
861:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
862:     }

864:     if (sr->sPres->nconv[1]) {
865:       if (divide) {
866:         BVTensorGetFactors(ctx->V,NULL,&MS);
867:         MatDenseGetArray(MS,&S);
868:         for (i=0;i<sr->sPres->nconv[1];i++) {
869:           PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
870:           PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
871:         }
872:         MatDenseRestoreArray(MS,&S);
873:         BVTensorRestoreFactors(ctx->V,NULL,&MS);
874:         BVSetActiveColumns(pep->V,0,count);
875:         BVCopy(tV,pep->V);
876:         BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
877:         BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
878:       }
879:       for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
880:       for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
881:       BVTensorGetFactors(ctx->V,NULL,&MS);
882:       MatDenseGetArray(MS,&S);
883:       for (i=0;i<sr->sPres->nconv[1];i++) {
884:         sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
885:         sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
886:         BVGetColumn(pep->V,i,&w);
887:         BVInsertVec(sr->V,aux[i],w);
888:         BVRestoreColumn(pep->V,i,&w);
889:         idx = sr->ld*d*aux[i];
890:         PetscArrayzero(sr->S+idx,sr->ld*d);
891:         PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
892:         PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
893:         PetscFree(sr->qinfo[aux[i]].q);
894:         PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
895:         PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
896:         sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
897:       }
898:       MatDenseRestoreArray(MS,&S);
899:       BVTensorRestoreFactors(ctx->V,NULL,&MS);
900:     }
901:     sPres->neigs = count-sr->ndef0-sr->ndef1;
902:     sr->indexEig += sPres->neigs;
903:     sPres->nconv[0]-= sr->ndef0;
904:     sPres->nconv[1]-= sr->ndef1;
905:     PetscFree4(eigr,errest,tS,aux);
906:   } else {
907:     sPres->neigs = 0;
908:     sPres->nconv[0]= 0;
909:     sPres->nconv[1]= 0;
910:   }
911:   /* Global ordering array updating */
912:   sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
913:   /* Check for completion */
914:   sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
915:   sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
917:   if (divide) BVDestroy(&tV);
918:   PetscFunctionReturn(0);
919: }

921: static PetscErrorCode PEPLookForDeflation(PEP pep)
922: {
923:   PetscReal val;
924:   PetscInt  i,count0=0,count1=0;
925:   PEP_shift sPres;
926:   PetscInt  ini,fin;
927:   PEP_SR    sr;
928:   PEP_STOAR *ctx=(PEP_STOAR*)pep->data;

930:   sr = ctx->sr;
931:   sPres = sr->sPres;

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

958:   if (sPres->neighb[1]) {
959:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
961:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

963:   /* Completing vector of indexes for deflation */
964:   for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
965:   sr->ndef0 = count0;
966:   for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
967:   sr->ndef1 = count1;
968:   PetscFunctionReturn(0);
969: }

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

986:   PetscMalloc1(*M,&y);
987:   BVGetSizes(pep->V,NULL,NULL,&ld);
988:   BVTensorGetDegree(ctx->V,&d);
989:   BVGetActiveColumns(pep->V,&lock,&nqt);
990:   lds = d*ld;
991:   offq = ld;
992:   DSGetLeadingDimension(pep->ds,&ldds);

994:   *breakdown = PETSC_FALSE; /* ----- */
995:   STGetShift(pep->st,&sigma);
996:   DSGetDimensions(pep->ds,NULL,&l,NULL,NULL);
997:   BVSetActiveColumns(ctx->V,0,m);
998:   BVSetActiveColumns(pep->V,0,nqt);
999:   for (j=k;j<m;j++) {
1000:     /* apply operator */
1001:     BVTensorGetFactors(ctx->V,NULL,&MS);
1002:     MatDenseGetArray(MS,&S);
1003:     BVGetColumn(pep->V,nqt,&t);
1004:     BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1005:     MatMult(pep->A[1],v,q);
1006:     MatMult(pep->A[2],v,t);
1007:     VecAXPY(q,sigma*pep->sfactor,t);
1008:     VecScale(q,pep->sfactor);
1009:     BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1010:     MatMult(pep->A[2],v,t);
1011:     VecAXPY(q,pep->sfactor*pep->sfactor,t);
1012:     STMatSolve(pep->st,q,t);
1013:     VecScale(t,-1.0);
1014:     BVRestoreColumn(pep->V,nqt,&t);

1016:     /* orthogonalize */
1017:     BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1018:     if (!lindep) {
1019:       *(S+(j+1)*lds+nqt) = norm;
1020:       BVScaleColumn(pep->V,nqt,1.0/norm);
1021:       nqt++;
1022:     }
1023:     for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1024:     BVSetActiveColumns(pep->V,0,nqt);
1025:     MatDenseRestoreArray(MS,&S);
1026:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1028:     /* level-2 orthogonalization */
1029:     BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1030:     a[j] = PetscRealPart(y[j]);
1031:     omega[j+1] = (norm > 0)?1.0:-1.0;
1032:     BVScaleColumn(ctx->V,j+1,1.0/norm);
1033:     b[j] = PetscAbsReal(norm);

1035:     /* check symmetry */
1036:     DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1037:     if (j==k) {
1038:       for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1039:       for (i=0;i<l;i++) y[i] = 0.0;
1040:     }
1041:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1042:     if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1043:     PetscBLASIntCast(j,&j_);
1044:     sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1045:     fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1046:     if (j>0) fro = SlepcAbs(fro,b[j-1]);
1047:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1048:       *symmlost = PETSC_TRUE;
1049:       *M=j;
1050:       break;
1051:     }
1052:   }
1053:   BVSetActiveColumns(pep->V,lock,nqt);
1054:   BVSetActiveColumns(ctx->V,0,*M);
1055:   PetscFree(y);
1056:   PetscFunctionReturn(0);
1057: }

1059: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1060: {
1061:   PEP_STOAR      *ctx = (PEP_STOAR*)pep->data;
1062:   PetscInt       j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1063:   PetscInt       nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1064:   PetscScalar    *om,sigma,*back,*S,*pQ;
1065:   PetscReal      beta,norm=1.0,*omega,*a,*b,eta,lambda;
1066:   PetscBool      breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1067:   Mat            MS,MQ;
1068:   Vec            v,vomega;
1069:   PEP_SR         sr;
1070:   BVOrthogType   otype;
1071:   BVOrthogBlockType obtype;

1073:   /* Resize if needed for deflating vectors  */
1074:   sr = ctx->sr;
1075:   sigma = sr->sPres->value;
1076:   k = sr->ndef0+sr->ndef1;
1077:   pep->ncv = ctx->ncv+k;
1078:   pep->nev = ctx->nev+k;
1079:   PEPAllocateSolution(pep,3);
1080:   BVDestroy(&ctx->V);
1081:   BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1082:   BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1083:   BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1084:   DSAllocate(pep->ds,pep->ncv+2);
1085:   PetscMalloc1(pep->ncv,&back);
1086:   DSGetLeadingDimension(pep->ds,&ldds);
1087:   BVSetMatrix(ctx->V,B,PETSC_TRUE);
1089:   /* undocumented option to use a cheaper locking instead of the true locking */
1090:   PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1091:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1092:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1093:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

1095:   /* Get the starting Arnoldi vector */
1096:   BVSetActiveColumns(pep->V,0,1);
1097:   BVTensorBuildFirstColumn(ctx->V,pep->nini);
1098:   BVSetActiveColumns(ctx->V,0,1);
1099:   if (k) {
1100:     /* Insert deflated vectors */
1101:     BVSetActiveColumns(pep->V,0,0);
1102:     idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1103:     for (j=0;j<k;j++) {
1104:       BVGetColumn(pep->V,j,&v);
1105:       BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1106:       BVRestoreColumn(pep->V,j,&v);
1107:     }
1108:     /* Update innerproduct matrix */
1109:     BVSetActiveColumns(ctx->V,0,0);
1110:     BVTensorGetFactors(ctx->V,NULL,&MS);
1111:     BVSetActiveColumns(pep->V,0,k);
1112:     BVTensorRestoreFactors(ctx->V,NULL,&MS);

1114:     BVGetSizes(pep->V,NULL,NULL,&ld);
1115:     BVTensorGetFactors(ctx->V,NULL,&MS);
1116:     MatDenseGetArray(MS,&S);
1117:     for (j=0;j<sr->ndef0;j++) {
1118:       PetscArrayzero(S+j*ld*deg,ld*deg);
1119:       PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
1120:       PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
1121:       pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1122:       pep->errest[j] = sr->errest[sr->idxDef0[j]];
1123:     }
1124:     for (j=0;j<sr->ndef1;j++) {
1125:       PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
1126:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
1127:       PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
1128:       pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1129:       pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1130:     }
1131:     MatDenseRestoreArray(MS,&S);
1132:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1133:     BVSetActiveColumns(ctx->V,0,k+1);
1134:     VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1135:     VecGetArray(vomega,&om);
1136:     for (j=0;j<k;j++) {
1137:       BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1138:       BVScaleColumn(ctx->V,j,1/norm);
1139:       om[j] = (norm>=0.0)?1.0:-1.0;
1140:     }
1141:     BVTensorGetFactors(ctx->V,NULL,&MS);
1142:     MatDenseGetArray(MS,&S);
1143:     for (j=0;j<deg;j++) {
1144:       BVSetRandomColumn(pep->V,k+j);
1145:       BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1146:       BVScaleColumn(pep->V,k+j,1.0/norm);
1147:       S[k*ld*deg+j*ld+k+j] = norm;
1148:     }
1149:     MatDenseRestoreArray(MS,&S);
1150:     BVSetActiveColumns(pep->V,0,k+deg);
1151:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
1152:     BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1153:     BVScaleColumn(ctx->V,k,1.0/norm);
1154:     om[k] = (norm>=0.0)?1.0:-1.0;
1155:     VecRestoreArray(vomega,&om);
1156:     BVSetSignature(ctx->V,vomega);
1157:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1158:     VecGetArray(vomega,&om);
1159:     for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1160:     VecRestoreArray(vomega,&om);
1161:     VecDestroy(&vomega);
1162:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1163:     DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1164:     PetscArrayzero(pQ,ldds*k);
1165:     for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1166:     DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1167:   }
1168:   BVSetActiveColumns(ctx->V,0,k+1);
1169:   DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1170:   VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1171:   BVGetSignature(ctx->V,vomega);
1172:   VecGetArray(vomega,&om);
1173:   for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
1174:   VecRestoreArray(vomega,&om);
1175:   DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1176:   VecDestroy(&vomega);

1178:   PetscInfo(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%" PetscInt_FMT " right=%" PetscInt_FMT ", searching: left=%" PetscInt_FMT " right=%" PetscInt_FMT "\n",(double)sr->sPres->value,(double)(sr->sPres->neighb[0]?sr->sPres->neighb[0]->value:sr->int0),(double)(sr->sPres->neighb[1]?sr->sPres->neighb[1]->value:sr->int1),sr->ndef0,sr->ndef1,sr->sPres->nsch[0],sr->sPres->nsch[1]);

1180:   /* Restart loop */
1181:   l = 0;
1182:   pep->nconv = k;
1183:   while (pep->reason == PEP_CONVERGED_ITERATING) {
1184:     pep->its++;
1185:     DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1186:     b = a+ldds;
1187:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);

1189:     /* Compute an nv-step Lanczos factorization */
1190:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1191:     PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1192:     beta = b[nv-1];
1193:     if (symmlost && nv==pep->nconv+l) {
1194:       pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1195:       pep->nconv = nconv;
1196:       PetscInfo(pep,"Symmetry lost in STOAR sigma=%g nconv=%" PetscInt_FMT "\n",(double)sr->sPres->value,nconv);
1197:       if (falselock || !ctx->lock) {
1198:         BVSetActiveColumns(ctx->V,0,pep->nconv);
1199:         BVTensorCompress(ctx->V,0);
1200:       }
1201:       break;
1202:     }
1203:     DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1204:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1205:     DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l);
1206:     if (l==0) DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1207:     else DSSetState(pep->ds,DS_STATE_RAW);

1209:     /* Solve projected problem */
1210:     DSSolve(pep->ds,pep->eigr,pep->eigi);
1211:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1212:     DSUpdateExtraRow(pep->ds);
1213:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

1215:     /* Check convergence */
1216:     /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1217:     norm = 1.0;
1218:     DSGetDimensions(pep->ds,NULL,NULL,NULL,&t);
1219:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1220:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1221:     for (j=0;j<k;j++) back[j] = pep->eigr[j];
1222:     STBackTransform(pep->st,k,back,pep->eigi);
1223:     count0=count1=0;
1224:     for (j=0;j<k;j++) {
1225:       lambda = PetscRealPart(back[j]);
1226:       if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1227:       if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1228:     }
1229:     if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1230:     /* Update l */
1231:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1232:     else {
1233:       l = PetscMax(1,(PetscInt)((nv-k)/2));
1234:       l = PetscMin(l,t);
1235:       DSGetTruncateSize(pep->ds,k,t,&l);
1236:       if (!breakdown) {
1237:         /* Prepare the Rayleigh quotient for restart */
1238:         DSTruncate(pep->ds,k+l,PETSC_FALSE);
1239:       }
1240:     }
1241:     nconv = k;
1242:     if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1243:     if (l) PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);

1245:     /* Update S */
1246:     DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1247:     BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1248:     MatDestroy(&MQ);

1250:     /* Copy last column of S */
1251:     BVCopyColumn(ctx->V,nv,k+l);
1252:     DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1253:     VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
1254:     VecGetArray(vomega,&om);
1255:     for (j=0;j<k+l;j++) om[j] = omega[j];
1256:     VecRestoreArray(vomega,&om);
1257:     BVSetActiveColumns(ctx->V,0,k+l);
1258:     BVSetSignature(ctx->V,vomega);
1259:     VecDestroy(&vomega);
1260:     DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);

1262:     if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1263:       /* stop if breakdown */
1264:       PetscInfo(pep,"Breakdown TOAR method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta);
1265:       pep->reason = PEP_DIVERGED_BREAKDOWN;
1266:     }
1267:     if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1268:     BVGetActiveColumns(pep->V,NULL,&nq);
1269:     if (k+l+deg<=nq) {
1270:       BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1271:       if (!falselock && ctx->lock) BVTensorCompress(ctx->V,k-pep->nconv);
1272:       else BVTensorCompress(ctx->V,0);
1273:     }
1274:     pep->nconv = k;
1275:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1276:   }
1277:   sr->itsKs += pep->its;
1278:   if (pep->nconv>0) {
1279:     BVSetActiveColumns(ctx->V,0,pep->nconv);
1280:     BVGetActiveColumns(pep->V,NULL,&nq);
1281:     BVSetActiveColumns(pep->V,0,nq);
1282:     if (nq>pep->nconv) {
1283:       BVTensorCompress(ctx->V,pep->nconv);
1284:       BVSetActiveColumns(pep->V,0,pep->nconv);
1285:     }
1286:     for (j=0;j<pep->nconv;j++) {
1287:       pep->eigr[j] *= pep->sfactor;
1288:       pep->eigi[j] *= pep->sfactor;
1289:     }
1290:   }
1291:   PetscInfo(pep,"Finished STOAR: nconv=%" PetscInt_FMT " (deflated=%" PetscInt_FMT ", left=%" PetscInt_FMT ", right=%" PetscInt_FMT ")\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1);
1292:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1293:   RGPopScale(pep->rg);

1296:   if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1298:   } else sr->symmlost = 0;

1300:   DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
1301:   PetscFree(back);
1302:   PetscFunctionReturn(0);
1303: }

1305: #define SWAP(a,b,t) {t=a;a=b;b=t;}

1307: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1308: {
1309:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1310:   PEP_SR          sr=ctx->sr;
1311:   PetscInt        i=0,j,tmpi;
1312:   PetscReal       v,tmpr;
1313:   PEP_shift       s;

1317:   if (!sr->s0) {  /* PEPSolve not called yet */
1318:     *n = 2;
1319:   } else {
1320:     *n = 1;
1321:     s = sr->s0;
1322:     while (s) {
1323:       (*n)++;
1324:       s = s->neighb[1];
1325:     }
1326:   }
1327:   PetscMalloc1(*n,shifts);
1328:   PetscMalloc1(*n,inertias);
1329:   if (!sr->s0) {  /* PEPSolve not called yet */
1330:     (*shifts)[0]   = sr->int0;
1331:     (*shifts)[1]   = sr->int1;
1332:     (*inertias)[0] = sr->inertia0;
1333:     (*inertias)[1] = sr->inertia1;
1334:   } else {
1335:     s = sr->s0;
1336:     while (s) {
1337:       (*shifts)[i]     = s->value;
1338:       (*inertias)[i++] = s->inertia;
1339:       s = s->neighb[1];
1340:     }
1341:     (*shifts)[i]   = sr->int1;
1342:     (*inertias)[i] = sr->inertia1;
1343:   }
1344:   /* remove possible duplicate in last position */
1345:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1346:   /* sort result */
1347:   for (i=0;i<*n;i++) {
1348:     v = (*shifts)[i];
1349:     for (j=i+1;j<*n;j++) {
1350:       if (v > (*shifts)[j]) {
1351:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
1352:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
1353:         v = (*shifts)[i];
1354:       }
1355:     }
1356:   }
1357:   PetscFunctionReturn(0);
1358: }

1360: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1361: {
1362:   PetscInt       i,j,ti,deg=pep->nmat-1;
1363:   PetscReal      newS;
1364:   PEP_STOAR      *ctx=(PEP_STOAR*)pep->data;
1365:   PEP_SR         sr=ctx->sr;
1366:   Mat            S,B;
1367:   PetscScalar    *pS;

1369:   PetscCitationsRegister(citation,&cited);

1371:   /* Only with eigenvalues present in the interval ...*/
1372:   if (sr->numEigs==0) {
1373:     pep->reason = PEP_CONVERGED_TOL;
1374:     PetscFunctionReturn(0);
1375:   }

1377:   /* Inner product matrix */
1378:   PEPSTOARSetUpInnerMatrix(pep,&B);

1380:   /* Array of pending shifts */
1381:   sr->maxPend = 100; /* Initial size */
1382:   sr->nPend = 0;
1383:   PetscMalloc1(sr->maxPend,&sr->pending);
1384:   PetscLogObjectMemory((PetscObject)pep,sr->maxPend*sizeof(PEP_shift*));
1385:   PEPCreateShift(pep,sr->int0,NULL,NULL);
1386:   /* extract first shift */
1387:   sr->sPrev = NULL;
1388:   sr->sPres = sr->pending[--sr->nPend];
1389:   sr->sPres->inertia = sr->inertia0;
1390:   pep->target = sr->sPres->value;
1391:   sr->s0 = sr->sPres;
1392:   sr->indexEig = 0;

1394:   for (i=0;i<sr->numEigs;i++) {
1395:     sr->eigr[i]   = 0.0;
1396:     sr->eigi[i]   = 0.0;
1397:     sr->errest[i] = 0.0;
1398:     sr->perm[i]   = i;
1399:   }
1400:   /* Vectors for deflation */
1401:   PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1402:   PetscLogObjectMemory((PetscObject)pep,2*sr->numEigs*sizeof(PetscInt));
1403:   sr->indexEig = 0;
1404:   while (sr->sPres) {
1405:     /* Search for deflation */
1406:     PEPLookForDeflation(pep);
1407:     /* KrylovSchur */
1408:     PEPSTOAR_QSlice(pep,B);

1410:     PEPStoreEigenpairs(pep);
1411:     /* Select new shift */
1412:     if (!sr->sPres->comp[1]) {
1413:       PEPGetNewShiftValue(pep,1,&newS);
1414:       PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1415:     }
1416:     if (!sr->sPres->comp[0]) {
1417:       /* Completing earlier interval */
1418:       PEPGetNewShiftValue(pep,0,&newS);
1419:       PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1420:     }
1421:     /* Preparing for a new search of values */
1422:     PEPExtractShift(pep);
1423:   }

1425:   /* Updating pep values prior to exit */
1426:   PetscFree2(sr->idxDef0,sr->idxDef1);
1427:   PetscFree(sr->pending);
1428:   pep->nconv  = sr->indexEig;
1429:   pep->reason = PEP_CONVERGED_TOL;
1430:   pep->its    = sr->itsKs;
1431:   pep->nev    = sr->indexEig;
1432:   MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1433:   MatDenseGetArray(S,&pS);
1434:   for (i=0;i<pep->nconv;i++) {
1435:     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);
1436:   }
1437:   MatDenseRestoreArray(S,&pS);
1438:   BVSetActiveColumns(sr->V,0,pep->nconv);
1439:   BVMultInPlace(sr->V,S,0,pep->nconv);
1440:   MatDestroy(&S);
1441:   BVDestroy(&pep->V);
1442:   pep->V = sr->V;
1443:   PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1444:   pep->eigr   = sr->eigr;
1445:   pep->eigi   = sr->eigi;
1446:   pep->perm   = sr->perm;
1447:   pep->errest = sr->errest;
1448:   if (sr->dir<0) {
1449:     for (i=0;i<pep->nconv/2;i++) {
1450:       ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1451:     }
1452:   }
1453:   PetscFree(ctx->inertias);
1454:   PetscFree(ctx->shifts);
1455:   MatDestroy(&B);
1456:   PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1457:   PetscFunctionReturn(0);
1458: }