Actual source code: ks-slice.c

slepc-3.10.1 2018-10-23
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2018, 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 eigensolver: "krylovschur"

 13:    Method: Krylov-Schur with spectrum slicing for symmetric eigenproblems

 15:    References:

 17:        [1] R.G. Grimes et al., "A shifted block Lanczos algorithm for
 18:            solving sparse symmetric generalized eigenproblems", SIAM J.
 19:            Matrix Anal. Appl. 15(1):228-272, 1994.

 21:        [2] C. Campos and J.E. Roman, "Spectrum slicing strategies based
 22:            on restarted Lanczos methods", Numer. Algor. 60(2):279-295,
 23:            2012.
 24: */

 26: #include <slepc/private/epsimpl.h>
 27: #include "krylovschur.h"

 29: static PetscBool  cited = PETSC_FALSE;
 30: static const char citation[] =
 31:   "@Article{slepc-slice,\n"
 32:   "   author = \"C. Campos and J. E. Roman\",\n"
 33:   "   title = \"Strategies for spectrum slicing based on restarted {Lanczos} methods\",\n"
 34:   "   journal = \"Numer. Algorithms\",\n"
 35:   "   volume = \"60\",\n"
 36:   "   number = \"2\",\n"
 37:   "   pages = \"279--295\",\n"
 38:   "   year = \"2012,\"\n"
 39:   "   doi = \"https://doi.org/10.1007/s11075-012-9564-z\"\n"
 40:   "}\n";

 42: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON

 44: static PetscErrorCode EPSSliceResetSR(EPS eps) {
 45:   PetscErrorCode  ierr;
 46:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
 47:   EPS_SR          sr=ctx->sr;
 48:   EPS_shift       s;

 51:   if (sr) {
 52:     if (ctx->npart>1) {
 53:       BVDestroy(&sr->V);
 54:       PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
 55:     }
 56:     /* Reviewing list of shifts to free memory */
 57:     s = sr->s0;
 58:     if (s) {
 59:       while (s->neighb[1]) {
 60:         s = s->neighb[1];
 61:         PetscFree(s->neighb[0]);
 62:       }
 63:       PetscFree(s);
 64:     }
 65:     PetscFree(sr);
 66:   }
 67:   ctx->sr = NULL;
 68:   return(0);
 69: }

 71: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
 72: {
 73:   PetscErrorCode  ierr;
 74:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

 77:   if (!ctx->global) return(0);
 78:   /* Destroy auxiliary EPS */
 79:   EPSSliceResetSR(ctx->eps);
 80:   EPSDestroy(&ctx->eps);
 81:   if (ctx->npart>1) {
 82:     PetscSubcommDestroy(&ctx->subc);
 83:     if (ctx->commset) {
 84:       MPI_Comm_free(&ctx->commrank);
 85:       ctx->commset = PETSC_FALSE;
 86:     }
 87:   }
 88:   PetscFree(ctx->subintervals);
 89:   PetscFree(ctx->nconv_loc);
 90:   EPSSliceResetSR(eps);
 91:   PetscFree(ctx->inertias);
 92:   PetscFree(ctx->shifts);
 93:   if (ctx->npart>1) {
 94:     ISDestroy(&ctx->isrow);
 95:     ISDestroy(&ctx->iscol);
 96:     MatDestroyMatrices(1,&ctx->submata);
 97:     MatDestroyMatrices(1,&ctx->submatb);
 98:   }
 99:   return(0);
100: }

102: /*
103:   EPSSliceAllocateSolution - Allocate memory storage for common variables such
104:   as eigenvalues and eigenvectors. The argument extra is used for methods
105:   that require a working basis slightly larger than ncv.
106: */
107: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
108: {
109:   PetscErrorCode     ierr;
110:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data;
111:   PetscReal          eta;
112:   PetscInt           k;
113:   PetscLogDouble     cnt;
114:   BVType             type;
115:   BVOrthogType       orthog_type;
116:   BVOrthogRefineType orthog_ref;
117:   BVOrthogBlockType  ob_type;
118:   Mat                matrix;
119:   Vec                t;
120:   EPS_SR             sr = ctx->sr;

123:   /* allocate space for eigenvalues and friends */
124:   k = PetscMax(1,sr->numEigs);
125:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
126:   PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
127:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
128:   PetscLogObjectMemory((PetscObject)eps,cnt);

130:   /* allocate sr->V and transfer options from eps->V */
131:   BVDestroy(&sr->V);
132:   BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
133:   PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
134:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
135:   if (!((PetscObject)(eps->V))->type_name) {
136:     BVSetType(sr->V,BVSVEC);
137:   } else {
138:     BVGetType(eps->V,&type);
139:     BVSetType(sr->V,type);
140:   }
141:   STMatCreateVecsEmpty(eps->st,&t,NULL);
142:   BVSetSizesFromVec(sr->V,t,k);
143:   VecDestroy(&t);
144:   EPS_SetInnerProduct(eps);
145:   BVGetMatrix(eps->V,&matrix,NULL);
146:   BVSetMatrix(sr->V,matrix,PETSC_FALSE);
147:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
148:   BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
149:   return(0);
150: }

152: static PetscErrorCode EPSSliceGetEPS(EPS eps)
153: {
154:   PetscErrorCode     ierr;
155:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
156:   BV                 V;
157:   BVType             type;
158:   PetscReal          eta;
159:   BVOrthogType       orthog_type;
160:   BVOrthogRefineType orthog_ref;
161:   BVOrthogBlockType  ob_type;
162:   Mat                A,B=NULL,Ar=NULL,Br=NULL;
163:   PetscInt           i;
164:   PetscReal          h,a,b,zero;
165:   PetscMPIInt        rank;
166:   EPS_SR             sr=ctx->sr;
167:   PC                 pc;
168:   PCType             pctype;
169:   KSP                ksp;
170:   KSPType            ksptype;
171:   STType             sttype;
172:   PetscObjectState   Astate,Bstate=0;
173:   PetscObjectId      Aid,Bid=0;
174:   MatSolverType      stype;

177:   EPSGetOperators(eps,&A,&B);
178:   if (ctx->npart==1) {
179:     if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
180:     EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
181:     EPSSetOperators(ctx->eps,A,B);
182:     a = eps->inta; b = eps->intb;
183:   } else {
184:     PetscObjectStateGet((PetscObject)A,&Astate);
185:     PetscObjectGetId((PetscObject)A,&Aid);
186:     if (B) {
187:       PetscObjectStateGet((PetscObject)B,&Bstate);
188:       PetscObjectGetId((PetscObject)B,&Bid);
189:     }
190:     if (!ctx->subc) {
191:       /* Create context for subcommunicators */
192:       PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
193:       PetscSubcommSetNumber(ctx->subc,ctx->npart);
194:       PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
195:       PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));

197:       /* Duplicate matrices */
198:       MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
199:       ctx->Astate = Astate;
200:       ctx->Aid = Aid;
201:       if (B) {
202:         MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
203:         ctx->Bstate = Bstate;
204:         ctx->Bid = Bid;
205:       }
206:     } else {
207:       if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
208:         EPSGetOperators(ctx->eps,&Ar,&Br);
209:         MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
210:         ctx->Astate = Astate;
211:         ctx->Aid = Aid;
212:         if (B) {
213:           MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
214:           ctx->Bstate = Bstate;
215:           ctx->Bid = Bid;
216:         }
217:         EPSSetOperators(ctx->eps,Ar,Br);
218:         MatDestroy(&Ar);
219:         MatDestroy(&Br);
220:       }
221:     }

223:     /* Determine subintervals */
224:     if (!ctx->subintset) { /* uniform distribution if no set by user */
225:       if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
226:       h = (eps->intb-eps->inta)/ctx->npart;
227:       a = eps->inta+ctx->subc->color*h;
228:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
229:       PetscFree(ctx->subintervals);
230:       PetscMalloc1(ctx->npart+1,&ctx->subintervals);
231:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
232:       ctx->subintervals[ctx->npart] = eps->intb;
233:     } else {
234:       a = ctx->subintervals[ctx->subc->color];
235:       b = ctx->subintervals[ctx->subc->color+1];
236:     }

238:     if (!ctx->eps) {
239:       /* Create auxiliary EPS */
240:       EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
241:       EPSSetOperators(ctx->eps,Ar,Br);
242:       MatDestroy(&Ar);
243:       MatDestroy(&Br);
244:     }

246:     /* Create subcommunicator grouping processes with same rank */
247:     if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
248:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
249:     MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
250:     ctx->commset = PETSC_TRUE;
251:   }
252:   EPSSetType(ctx->eps,((PetscObject)eps)->type_name);

254:   /* Transfer options for ST, KSP and PC */
255:   STGetType(eps->st,&sttype);
256:   STSetType(ctx->eps->st,sttype);
257:   STGetKSP(eps->st,&ksp);
258:   KSPGetType(ksp,&ksptype);
259:   KSPGetPC(ksp,&pc);
260:   PCGetType(pc,&pctype);
261:   PCFactorGetMatSolverType(pc,&stype);
262:   PCFactorGetZeroPivot(pc,&zero);
263:   STGetKSP(ctx->eps->st,&ksp);
264:   KSPSetType(ksp,ksptype);
265:   KSPGetPC(ksp,&pc);
266:   PCSetType(pc,pctype);
267:   PCFactorSetZeroPivot(pc,zero);
268:   if (stype) { PCFactorSetMatSolverType(pc,stype); }

270:   EPSSetConvergenceTest(ctx->eps,eps->conv);
271:   EPSSetInterval(ctx->eps,a,b);
272:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
273:   ctx_local->npart = ctx->npart;
274:   ctx_local->detect = ctx->detect;
275:   ctx_local->global = PETSC_FALSE;
276:   ctx_local->eps = eps;
277:   ctx_local->subc = ctx->subc;
278:   ctx_local->commrank = ctx->commrank;

280:   EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
281:   EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);

283:   /* transfer options from eps->V */
284:   EPSGetBV(ctx->eps,&V);
285:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
286:   if (!((PetscObject)(eps->V))->type_name) {
287:     BVSetType(V,BVSVEC);
288:   } else {
289:     BVGetType(eps->V,&type);
290:     BVSetType(V,type);
291:   }
292:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
293:   BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
294:   ctx->eps->which = eps->which;
295:   ctx->eps->max_it = eps->max_it;
296:   ctx->eps->tol = eps->tol;
297:   ctx->eps->purify = eps->purify;
298:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
299:   EPSSetProblemType(ctx->eps,eps->problem_type);
300:   EPSSetUp(ctx->eps);
301:   ctx->eps->nconv = 0;
302:   ctx->eps->its   = 0;
303:   for (i=0;i<ctx->eps->ncv;i++) {
304:     ctx->eps->eigr[i]   = 0.0;
305:     ctx->eps->eigi[i]   = 0.0;
306:     ctx->eps->errest[i] = 0.0;
307:   }
308:   return(0);
309: }

311: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
312: {
314:   KSP            ksp;
315:   PC             pc;
316:   Mat            F;
317:   PetscReal      nzshift;

320:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
321:     if (inertia) *inertia = eps->n;
322:   } else if (shift <= PETSC_MIN_REAL) {
323:     if (inertia) *inertia = 0;
324:     if (zeros) *zeros = 0;
325:   } else {
326:     /* If the shift is zero, perturb it to a very small positive value.
327:        The goal is that the nonzero pattern is the same in all cases and reuse
328:        the symbolic factorizations */
329:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
330:     STSetShift(eps->st,nzshift);
331:     STSetUp(eps->st);
332:     STGetKSP(eps->st,&ksp);
333:     KSPGetPC(ksp,&pc);
334:     PCFactorGetMatrix(pc,&F);
335:     MatGetInertia(F,inertia,zeros,NULL);
336:   }
337:   return(0);
338: }

340: /*
341:    Dummy backtransform operation
342:  */
343: static PetscErrorCode EPSBackTransform_Skip(EPS eps)
344: {
346:   return(0);
347: }

349: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
350: {
351:   PetscErrorCode  ierr;
352:   PetscBool       issinv;
353:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
354:   EPS_SR          sr,sr_loc,sr_glob;
355:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0,method;
356:   PetscMPIInt     nproc,rank=0,aux;
357:   PetscReal       r;
358:   MPI_Request     req;
359:   Mat             A,B=NULL;
360:   SlepcSC         sc;
361:   PetscInt        flg=0;
362:   DSParallelType  ptype;

365:   if (ctx->global) {
366:     if (eps->intb >= PETSC_MAX_REAL && eps->inta <= PETSC_MIN_REAL) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
367:     if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
368:     if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
369:     PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
370:     if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
371:     if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
372:     if (!eps->max_it) eps->max_it = 100;
373:     if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n);  /* nev not set, use default value */
374:     if (eps->n>10 && ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
375:   }
376:   eps->ops->backtransform = EPSBackTransform_Skip;

378:   /* create spectrum slicing context and initialize it */
379:   EPSSliceResetSR(eps);
380:   PetscNewLog(eps,&sr);
381:   ctx->sr = sr;
382:   sr->itsKs = 0;
383:   sr->nleap = 0;
384:   sr->nMAXCompl = eps->nev/4;
385:   sr->iterCompl = eps->max_it/4;
386:   sr->sPres = NULL;
387:   sr->nS = 0;

389:   if (ctx->npart==1 || ctx->global) {
390:     /* check presence of ends and finding direction */
391:     if ((eps->inta > PETSC_MIN_REAL && !(ctx->subintervals && ctx->subintervals[0]==ctx->subintervals[1])) || eps->intb >= PETSC_MAX_REAL) {
392:       sr->int0 = eps->inta;
393:       sr->int1 = eps->intb;
394:       sr->dir = 1;
395:       if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
396:         sr->hasEnd = PETSC_FALSE;
397:       } else sr->hasEnd = PETSC_TRUE;
398:     } else {
399:       sr->int0 = eps->intb;
400:       sr->int1 = eps->inta;
401:       sr->dir = -1;
402:       sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
403:     }
404:   }
405:   if (ctx->global) {
406:     /* prevent computation of factorization in global eps */
407:     STSetTransform(eps->st,PETSC_FALSE);
408:     EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
409:     /* create subintervals and initialize auxiliary eps for slicing runs */
410:     EPSSliceGetEPS(eps);
411:     sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
412:     if (ctx->npart>1) {
413:       if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
414:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
415:       if (!rank) {
416:         MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);
417:       }
418:       MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
419:       PetscFree(ctx->nconv_loc);
420:       PetscMalloc1(ctx->npart,&ctx->nconv_loc);
421:       MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
422:       if (sr->dir<0) off = 1;
423:       if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
424:         PetscMPIIntCast(sr_loc->numEigs,&aux);
425:         MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
426:         MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
427:       } else {
428:         MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
429:         if (!rank) {
430:           PetscMPIIntCast(sr_loc->numEigs,&aux);
431:           MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
432:           MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
433:         }
434:         PetscMPIIntCast(ctx->npart,&aux);
435:         MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
436:         MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
437:       }
438:       nEigs = 0;
439:       for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
440:     } else {
441:       nEigs = sr_loc->numEigs;
442:       sr->inertia0 = sr_loc->inertia0;
443:     }
444:     sr->inertia1 = sr->inertia0+sr->dir*nEigs;
445:     sr->numEigs = nEigs;
446:     eps->nev = nEigs;
447:     eps->ncv = nEigs;
448:     eps->mpd = nEigs;
449:   } else {
450:     ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
451:     sr_glob = ctx_glob->sr;
452:     if (ctx->npart>1) {
453:       sr->dir = sr_glob->dir;
454:       sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
455:       sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
456:       if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
457:       else sr->hasEnd = PETSC_TRUE;
458:     }

460:     /* compute inertia0 */
461:     EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
462:     PetscOptionsGetInt(NULL,NULL,"-eps_krylovschur_hiteigenvalue",&flg,NULL);
463:     if (zeros) { /* error in factorization */
464:       if (sr->int0==ctx->eps->inta || sr->int0==ctx->eps->intb) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
465:       else if(ctx_glob->subintset && !flg) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
466:       else {
467:         if (flg==1) { /* idle subgroup */
468:           sr->inertia0 = -1;
469:         } else { /* perturb shift */
470:           sr->int0 *= (1.0+SLICE_PTOL);
471:           EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
472:           if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
473:         }
474:       }
475:     }
476:     if (ctx->npart>1) {
477:       /* inertia1 is received from neighbour */
478:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
479:       if (!rank) {
480:         if ( sr->inertia0!=-1 && ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1)) ) { /* send inertia0 to neighbour0 */
481:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
482:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
483:         }
484:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
485:           MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
486:           MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
487:         }
488:         if ( sr->inertia0==-1 && !(sr->dir>0 && ctx->subc->color==ctx->npart-1) && !(sr->dir<0 && ctx->subc->color==0)) {
489:           sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
490:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
491:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
492:         }
493:       }
494:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
495:         MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
496:         MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
497:       } else sr_glob->inertia1 = sr->inertia1;
498:     }

500:     /* last process in eps comm computes inertia1 */
501:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
502:       EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
503:       if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
504:       if (!rank && sr->inertia0==-1) {
505:         sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
506:         MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
507:         MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
508:       }
509:       if (sr->hasEnd) {
510:         sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
511:         i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
512:       }
513:     }

515:     /* number of eigenvalues in interval */
516:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
517:     if (ctx->npart>1) {
518:       /* memory allocate for subinterval eigenpairs */
519:       EPSSliceAllocateSolution(eps,1);
520:     }
521:     dssz = eps->ncv+1;
522:     if (sr->numEigs>0) {
523:       DSGetSlepcSC(eps->ds,&sc);
524:       sc->rg            = NULL;
525:       sc->comparison    = SlepcCompareLargestMagnitude;
526:       sc->comparisonctx = NULL;
527:       sc->map           = NULL;
528:       sc->mapobj        = NULL;
529:     }
530:     DSGetParallel(ctx->eps->ds,&ptype);
531:     DSSetParallel(eps->ds,ptype);
532:     DSGetMethod(ctx->eps->ds,&method);
533:     DSSetMethod(eps->ds,method);
534:   }
535:   DSSetType(eps->ds,DSHEP);
536:   DSSetCompact(eps->ds,PETSC_TRUE);
537:   DSAllocate(eps->ds,dssz);
538:   /* keep state of subcomm matrices to check that the user does not modify them */
539:   EPSGetOperators(eps,&A,&B);
540:   PetscObjectStateGet((PetscObject)A,&ctx->Astate);
541:   PetscObjectGetId((PetscObject)A,&ctx->Aid);
542:   if (B) {
543:     PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
544:     PetscObjectGetId((PetscObject)B,&ctx->Bid);
545:   } else {
546:     ctx->Bstate=0;
547:     ctx->Bid=0;
548:   }
549:   return(0);
550: }

552: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
553: {
554:   PetscErrorCode  ierr;
555:   Vec             v,vg,v_loc;
556:   IS              is1,is2;
557:   VecScatter      vec_sc;
558:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
559:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
560:   PetscScalar     *array;
561:   EPS_SR          sr_loc;
562:   BV              V_loc;

565:   sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
566:   V_loc = sr_loc->V;

568:   /* Gather parallel eigenvectors */
569:   BVGetColumn(eps->V,0,&v);
570:   VecGetOwnershipRange(v,&n0,&m0);
571:   BVRestoreColumn(eps->V,0,&v);
572:   BVGetColumn(ctx->eps->V,0,&v);
573:   VecGetLocalSize(v,&nloc);
574:   BVRestoreColumn(ctx->eps->V,0,&v);
575:   PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
576:   VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
577:   idx = -1;
578:   for (si=0;si<ctx->npart;si++) {
579:     j = 0;
580:     for (i=n0;i<m0;i++) {
581:       idx1[j]   = i;
582:       idx2[j++] = i+eps->n*si;
583:     }
584:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
585:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
586:     BVGetColumn(eps->V,0,&v);
587:     VecScatterCreate(v,is1,vg,is2,&vec_sc);
588:     BVRestoreColumn(eps->V,0,&v);
589:     ISDestroy(&is1);
590:     ISDestroy(&is2);
591:     for (i=0;i<ctx->nconv_loc[si];i++) {
592:       BVGetColumn(eps->V,++idx,&v);
593:       if (ctx->subc->color==si) {
594:         BVGetColumn(V_loc,i,&v_loc);
595:         VecGetArray(v_loc,&array);
596:         VecPlaceArray(vg,array);
597:       }
598:       VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
599:       VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
600:       if (ctx->subc->color==si) {
601:         VecResetArray(vg);
602:         VecRestoreArray(v_loc,&array);
603:         BVRestoreColumn(V_loc,i,&v_loc);
604:       }
605:       BVRestoreColumn(eps->V,idx,&v);
606:     }
607:     VecScatterDestroy(&vec_sc);
608:   }
609:   PetscFree2(idx1,idx2);
610:   VecDestroy(&vg);
611:   return(0);
612: }

614: /*
615:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
616:  */
617: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
618: {
619:   PetscErrorCode  ierr;
620:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

623:   if (ctx->global && ctx->npart>1) {
624:     EPSComputeVectors(ctx->eps);
625:     EPSSliceGatherEigenVectors(eps);
626:   }
627:   return(0);
628: }

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

632: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
633: {
634:   PetscErrorCode  ierr;
635:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
636:   PetscInt        i=0,j,tmpi;
637:   PetscReal       v,tmpr;
638:   EPS_shift       s;

641:   if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
642:   if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
643:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
644:     *n = 2;
645:   } else {
646:     *n = 1;
647:     s = ctx->sr->s0;
648:     while (s) {
649:       (*n)++;
650:       s = s->neighb[1];
651:     }
652:   }
653:   PetscMalloc1(*n,shifts);
654:   PetscMalloc1(*n,inertias);
655:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
656:     (*shifts)[0]   = ctx->sr->int0;
657:     (*shifts)[1]   = ctx->sr->int1;
658:     (*inertias)[0] = ctx->sr->inertia0;
659:     (*inertias)[1] = ctx->sr->inertia1;
660:   } else {
661:     s = ctx->sr->s0;
662:     while (s) {
663:       (*shifts)[i]     = s->value;
664:       (*inertias)[i++] = s->inertia;
665:       s = s->neighb[1];
666:     }
667:     (*shifts)[i]   = ctx->sr->int1;
668:     (*inertias)[i] = ctx->sr->inertia1;
669:   }
670:   /* remove possible duplicate in last position */
671:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
672:   /* sort result */
673:   for (i=0;i<*n;i++) {
674:     v = (*shifts)[i];
675:     for (j=i+1;j<*n;j++) {
676:       if (v > (*shifts)[j]) {
677:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
678:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
679:         v = (*shifts)[i];
680:       }
681:     }
682:   }
683:   return(0);
684: }

686: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
687: {
688:   PetscErrorCode  ierr;
689:   PetscMPIInt     rank,nproc;
690:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
691:   PetscInt        i,idx,j;
692:   PetscInt        *perm_loc,off=0,*inertias_loc,ns;
693:   PetscScalar     *eigr_loc;
694:   EPS_SR          sr_loc;
695:   PetscReal       *shifts_loc;
696:   PetscMPIInt     *disp,*ns_loc,aux;

699:   eps->nconv = 0;
700:   for (i=0;i<ctx->npart;i++) eps->nconv += ctx->nconv_loc[i];
701:   sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;

703:   /* Gather the shifts used and the inertias computed */
704:   EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
705:   if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
706:   if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
707:     ns--;
708:     for (i=0;i<ns;i++) {
709:       inertias_loc[i] = inertias_loc[i+1];
710:       shifts_loc[i] = shifts_loc[i+1];
711:     }
712:   }
713:   PetscMalloc1(ctx->npart,&ns_loc);
714:   MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
715:   PetscMPIIntCast(ns,&aux);
716:   if (!rank) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank); }
717:   PetscMPIIntCast(ctx->npart,&aux);
718:   MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
719:   ctx->nshifts = 0;
720:   for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
721:   PetscFree(ctx->inertias);
722:   PetscFree(ctx->shifts);
723:   PetscMalloc1(ctx->nshifts,&ctx->inertias);
724:   PetscMalloc1(ctx->nshifts,&ctx->shifts);

726:   /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
727:   eigr_loc = sr_loc->eigr;
728:   perm_loc = sr_loc->perm;
729:   MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
730:   PetscMalloc1(ctx->npart,&disp);
731:   disp[0] = 0;
732:   for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
733:   if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
734:     PetscMPIIntCast(sr_loc->numEigs,&aux);
735:     MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
736:     MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
737:     for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
738:     PetscMPIIntCast(ns,&aux);
739:     MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
740:     MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
741:     MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
742:   } else { /* subcommunicators with different size */
743:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
744:     if (!rank) {
745:       PetscMPIIntCast(sr_loc->numEigs,&aux);
746:       MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
747:       MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
748:       for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
749:       PetscMPIIntCast(ns,&aux);
750:       MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
751:       MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
752:       MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
753:     }
754:     PetscMPIIntCast(eps->nconv,&aux);
755:     MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
756:     MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
757:     MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
758:     PetscMPIIntCast(ctx->nshifts,&aux);
759:     MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
760:     MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
761:   }
762:   /* Update global array eps->perm */
763:   idx = ctx->nconv_loc[0];
764:   for (i=1;i<ctx->npart;i++) {
765:     off += ctx->nconv_loc[i-1];
766:     for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
767:   }

769:   /* Gather parallel eigenvectors */
770:   PetscFree(ns_loc);
771:   PetscFree(disp);
772:   PetscFree(shifts_loc);
773:   PetscFree(inertias_loc);
774:   return(0);
775: }

777: /*
778:    Fills the fields of a shift structure
779: */
780: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
781: {
782:   PetscErrorCode  ierr;
783:   EPS_shift       s,*pending2;
784:   PetscInt        i;
785:   EPS_SR          sr;
786:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

789:   sr = ctx->sr;
790:   PetscNewLog(eps,&s);
791:   s->value = val;
792:   s->neighb[0] = neighb0;
793:   if (neighb0) neighb0->neighb[1] = s;
794:   s->neighb[1] = neighb1;
795:   if (neighb1) neighb1->neighb[0] = s;
796:   s->comp[0] = PETSC_FALSE;
797:   s->comp[1] = PETSC_FALSE;
798:   s->index = -1;
799:   s->neigs = 0;
800:   s->nconv[0] = s->nconv[1] = 0;
801:   s->nsch[0] = s->nsch[1]=0;
802:   /* Inserts in the stack of pending shifts */
803:   /* If needed, the array is resized */
804:   if (sr->nPend >= sr->maxPend) {
805:     sr->maxPend *= 2;
806:     PetscMalloc1(sr->maxPend,&pending2);
807:     PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
808:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
809:     PetscFree(sr->pending);
810:     sr->pending = pending2;
811:   }
812:   sr->pending[sr->nPend++]=s;
813:   return(0);
814: }

816: /* Prepare for Rational Krylov update */
817: static PetscErrorCode EPSPrepareRational(EPS eps)
818: {
819:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
820:   PetscErrorCode   ierr;
821:   PetscInt         dir,i,k,ld,nv;
822:   PetscScalar      *A;
823:   EPS_SR           sr = ctx->sr;
824:   Vec              v;

827:   DSGetLeadingDimension(eps->ds,&ld);
828:   dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
829:   dir*=sr->dir;
830:   k = 0;
831:   for (i=0;i<sr->nS;i++) {
832:     if (dir*PetscRealPart(sr->S[i])>0.0) {
833:       sr->S[k] = sr->S[i];
834:       sr->S[sr->nS+k] = sr->S[sr->nS+i];
835:       BVGetColumn(sr->Vnext,k,&v);
836:       BVCopyVec(eps->V,eps->nconv+i,v);
837:       BVRestoreColumn(sr->Vnext,k,&v);
838:       k++;
839:       if (k>=sr->nS/2)break;
840:     }
841:   }
842:   /* Copy to DS */
843:   DSGetArray(eps->ds,DS_MAT_A,&A);
844:   PetscMemzero(A,ld*ld*sizeof(PetscScalar));
845:   for (i=0;i<k;i++) {
846:     A[i*(1+ld)] = sr->S[i];
847:     A[k+i*ld] = sr->S[sr->nS+i];
848:   }
849:   sr->nS = k;
850:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
851:   DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
852:   DSSetDimensions(eps->ds,nv,0,0,k);
853:   /* Append u to V */
854:   BVGetColumn(sr->Vnext,sr->nS,&v);
855:   BVCopyVec(eps->V,sr->nv,v);
856:   BVRestoreColumn(sr->Vnext,sr->nS,&v);
857:   return(0);
858: }

860: /* Provides next shift to be computed */
861: static PetscErrorCode EPSExtractShift(EPS eps)
862: {
863:   PetscErrorCode   ierr;
864:   PetscInt         iner,zeros=0;
865:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
866:   EPS_SR           sr;
867:   PetscReal        newShift;
868:   EPS_shift        sPres;

871:   sr = ctx->sr;
872:   if (sr->nPend > 0) {
873:     sr->sPrev = sr->sPres;
874:     sr->sPres = sr->pending[--sr->nPend];
875:     sPres = sr->sPres;
876:     EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
877:     if (zeros) {
878:       newShift = sPres->value*(1.0+SLICE_PTOL);
879:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
880:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
881:       EPSSliceGetInertia(eps,newShift,&iner,&zeros);
882:       if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
883:       sPres->value = newShift;
884:     }
885:     sr->sPres->inertia = iner;
886:     eps->target = sr->sPres->value;
887:     eps->reason = EPS_CONVERGED_ITERATING;
888:     eps->its = 0;
889:   } else sr->sPres = NULL;
890:   return(0);
891: }

893: /*
894:    Symmetric KrylovSchur adapted to spectrum slicing:
895:    Allows searching an specific amount of eigenvalues in the subintervals left and right.
896:    Returns whether the search has succeeded
897: */
898: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
899: {
900:   PetscErrorCode  ierr;
901:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
902:   PetscInt        i,k,l,ld,nv,*iwork,j;
903:   Mat             U;
904:   PetscScalar     *Q,*A;
905:   PetscReal       *a,*b,beta;
906:   PetscBool       breakdown;
907:   PetscInt        count0,count1;
908:   PetscReal       lambda;
909:   EPS_shift       sPres;
910:   PetscBool       complIterating;
911:   PetscBool       sch0,sch1;
912:   PetscInt        iterCompl=0,n0,n1;
913:   EPS_SR          sr = ctx->sr;

916:   /* Spectrum slicing data */
917:   sPres = sr->sPres;
918:   complIterating =PETSC_FALSE;
919:   sch1 = sch0 = PETSC_TRUE;
920:   DSGetLeadingDimension(eps->ds,&ld);
921:   PetscMalloc1(2*ld,&iwork);
922:   count0=0;count1=0; /* Found on both sides */
923:   if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
924:     /* Rational Krylov */
925:     DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
926:     DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
927:     DSSetDimensions(eps->ds,l+1,0,0,0);
928:     BVSetActiveColumns(eps->V,0,l+1);
929:     DSGetMat(eps->ds,DS_MAT_Q,&U);
930:     BVMultInPlace(eps->V,U,0,l+1);
931:     MatDestroy(&U);
932:   } else {
933:     /* Get the starting Lanczos vector */
934:     EPSGetStartVector(eps,0,NULL);
935:     l = 0;
936:   }
937:   /* Restart loop */
938:   while (eps->reason == EPS_CONVERGED_ITERATING) {
939:     eps->its++; sr->itsKs++;
940:     /* Compute an nv-step Lanczos factorization */
941:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
942:     DSGetArrayReal(eps->ds,DS_MAT_T,&a);
943:     b = a + ld;
944:     EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
945:     sr->nv = nv;
946:     beta = b[nv-1];
947:     DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
948:     DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
949:     if (l==0) {
950:       DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
951:     } else {
952:       DSSetState(eps->ds,DS_STATE_RAW);
953:     }
954:     BVSetActiveColumns(eps->V,eps->nconv,nv);

956:     /* Solve projected problem and compute residual norm estimates */
957:     if (eps->its == 1 && l > 0) {/* After rational update */
958:       DSGetArray(eps->ds,DS_MAT_A,&A);
959:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
960:       b = a + ld;
961:       k = eps->nconv+l;
962:       A[k*ld+k-1] = A[(k-1)*ld+k];
963:       A[k*ld+k] = a[k];
964:       for (j=k+1; j< nv; j++) {
965:         A[j*ld+j] = a[j];
966:         A[j*ld+j-1] = b[j-1] ;
967:         A[(j-1)*ld+j] = b[j-1];
968:       }
969:       DSRestoreArray(eps->ds,DS_MAT_A,&A);
970:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
971:       DSSolve(eps->ds,eps->eigr,NULL);
972:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
973:       DSSetCompact(eps->ds,PETSC_TRUE);
974:     } else { /* Restart */
975:       DSSolve(eps->ds,eps->eigr,NULL);
976:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
977:     }
978:     DSSynchronize(eps->ds,eps->eigr,NULL);

980:     /* Residual */
981:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);
982:     /* Checking values obtained for completing */
983:     for (i=0;i<k;i++) {
984:       sr->back[i]=eps->eigr[i];
985:     }
986:     STBackTransform(eps->st,k,sr->back,eps->eigi);
987:     count0=count1=0;
988:     for (i=0;i<k;i++) {
989:       lambda = PetscRealPart(sr->back[i]);
990:       if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
991:       if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
992:     }
993:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
994:     else {
995:       /* Checks completion */
996:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
997:         eps->reason = EPS_CONVERGED_TOL;
998:       } else {
999:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
1000:         if (complIterating) {
1001:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
1002:         } else if (k >= eps->nev) {
1003:           n0 = sPres->nsch[0]-count0;
1004:           n1 = sPres->nsch[1]-count1;
1005:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
1006:             /* Iterating for completion*/
1007:             complIterating = PETSC_TRUE;
1008:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
1009:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
1010:             iterCompl = sr->iterCompl;
1011:           } else eps->reason = EPS_CONVERGED_TOL;
1012:         }
1013:       }
1014:     }
1015:     /* Update l */
1016:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
1017:     else l = nv-k;
1018:     if (breakdown) l=0;
1019:     if (!ctx->lock && l>0 && eps->reason == EPS_CONVERGED_ITERATING) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

1021:     if (eps->reason == EPS_CONVERGED_ITERATING) {
1022:       if (breakdown) {
1023:         /* Start a new Lanczos factorization */
1024:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
1025:         EPSGetStartVector(eps,k,&breakdown);
1026:         if (breakdown) {
1027:           eps->reason = EPS_DIVERGED_BREAKDOWN;
1028:           PetscInfo(eps,"Unable to generate more start vectors\n");
1029:         }
1030:       } else {
1031:         /* Prepare the Rayleigh quotient for restart */
1032:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
1033:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
1034:         b = a + ld;
1035:         for (i=k;i<k+l;i++) {
1036:           a[i] = PetscRealPart(eps->eigr[i]);
1037:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
1038:         }
1039:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
1040:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1041:       }
1042:     }
1043:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
1044:     DSGetMat(eps->ds,DS_MAT_Q,&U);
1045:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
1046:     MatDestroy(&U);

1048:     /* Normalize u and append it to V */
1049:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
1050:       BVCopyColumn(eps->V,nv,k+l);
1051:     }
1052:     eps->nconv = k;
1053:     if (eps->reason != EPS_CONVERGED_ITERATING) {
1054:       /* Store approximated values for next shift */
1055:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
1056:       sr->nS = l;
1057:       for (i=0;i<l;i++) {
1058:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
1059:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
1060:       }
1061:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1062:     }
1063:   }
1064:   /* Check for completion */
1065:   for (i=0;i< eps->nconv; i++) {
1066:     if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
1067:     else sPres->nconv[0]++;
1068:   }
1069:   sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
1070:   sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
1071:   if (count0 > sPres->nsch[0] || count1 > sPres->nsch[1]) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
1072:   PetscFree(iwork);
1073:   return(0);
1074: }

1076: /*
1077:   Obtains value of subsequent shift
1078: */
1079: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
1080: {
1081:   PetscReal       lambda,d_prev;
1082:   PetscInt        i,idxP;
1083:   EPS_SR          sr;
1084:   EPS_shift       sPres,s;
1085:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

1088:   sr = ctx->sr;
1089:   sPres = sr->sPres;
1090:   if (sPres->neighb[side]) {
1091:   /* Completing a previous interval */
1092:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
1093:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
1094:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
1095:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
1096:   } else { /* (Only for side=1). Creating a new interval. */
1097:     if (sPres->neigs==0) {/* No value has been accepted*/
1098:       if (sPres->neighb[0]) {
1099:         /* Multiplying by 10 the previous distance */
1100:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
1101:         sr->nleap++;
1102:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
1103:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
1104:       } else { /* First shift */
1105:         if (eps->nconv != 0) {
1106:           /* Unaccepted values give information for next shift */
1107:           idxP=0;/* Number of values left from shift */
1108:           for (i=0;i<eps->nconv;i++) {
1109:             lambda = PetscRealPart(eps->eigr[i]);
1110:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
1111:             else break;
1112:           }
1113:           /* Avoiding subtraction of eigenvalues (might be the same).*/
1114:           if (idxP>0) {
1115:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
1116:           } else {
1117:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
1118:           }
1119:           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
1120:         } else { /* No values found, no information for next shift */
1121:           SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
1122:         }
1123:       }
1124:     } else { /* Accepted values found */
1125:       sr->nleap = 0;
1126:       /* Average distance of values in previous subinterval */
1127:       s = sPres->neighb[0];
1128:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
1129:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
1130:       }
1131:       if (s) {
1132:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
1133:       } else { /* First shift. Average distance obtained with values in this shift */
1134:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
1135:         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(eps->tol)) {
1136:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
1137:         } else {
1138:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
1139:         }
1140:       }
1141:       /* Average distance is used for next shift by adding it to value on the right or to shift */
1142:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
1143:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
1144:       } else { /* Last accepted value is on the left of shift. Adding to shift */
1145:         *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
1146:       }
1147:     }
1148:     /* End of interval can not be surpassed */
1149:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
1150:   }/* of neighb[side]==null */
1151:   return(0);
1152: }

1154: /*
1155:   Function for sorting an array of real values
1156: */
1157: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
1158: {
1159:   PetscReal      re;
1160:   PetscInt       i,j,tmp;

1163:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
1164:   /* Insertion sort */
1165:   for (i=1;i<nr;i++) {
1166:     re = PetscRealPart(r[perm[i]]);
1167:     j = i-1;
1168:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
1169:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
1170:     }
1171:   }
1172:   return(0);
1173: }

1175: /* Stores the pairs obtained since the last shift in the global arrays */
1176: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
1177: {
1178:   PetscErrorCode  ierr;
1179:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1180:   PetscReal       lambda,err,norm;
1181:   PetscInt        i,count;
1182:   PetscBool       iscayley;
1183:   EPS_SR          sr = ctx->sr;
1184:   EPS_shift       sPres;
1185:   Vec             v,w;

1188:   sPres = sr->sPres;
1189:   sPres->index = sr->indexEig;
1190:   count = sr->indexEig;
1191:   /* Back-transform */
1192:   STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
1193:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
1194:   /* Sort eigenvalues */
1195:   sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
1196:   /* Values stored in global array */
1197:   for (i=0;i<eps->nconv;i++) {
1198:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
1199:     err = eps->errest[eps->perm[i]];

1201:     if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
1202:       if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
1203:       sr->eigr[count] = lambda;
1204:       sr->errest[count] = err;
1205:       /* Explicit purification */
1206:       BVGetColumn(eps->V,eps->perm[i],&w);
1207:       if (eps->purify) {
1208:         BVGetColumn(sr->V,count,&v);
1209:         STApply(eps->st,w,v);
1210:         BVRestoreColumn(sr->V,count,&v);
1211:       } else {
1212:         BVInsertVec(sr->V,count,w);
1213:       }
1214:       BVRestoreColumn(eps->V,eps->perm[i],&w);
1215:       BVNormColumn(sr->V,count,NORM_2,&norm);
1216:       BVScaleColumn(sr->V,count,1.0/norm);
1217:       count++;
1218:     }
1219:   }
1220:   sPres->neigs = count - sr->indexEig;
1221:   sr->indexEig = count;
1222:   /* Global ordering array updating */
1223:   sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
1224:   return(0);
1225: }

1227: static PetscErrorCode EPSLookForDeflation(EPS eps)
1228: {
1229:   PetscErrorCode  ierr;
1230:   PetscReal       val;
1231:   PetscInt        i,count0=0,count1=0;
1232:   EPS_shift       sPres;
1233:   PetscInt        ini,fin,k,idx0,idx1;
1234:   EPS_SR          sr;
1235:   Vec             v;
1236:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

1239:   sr = ctx->sr;
1240:   sPres = sr->sPres;

1242:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
1243:   else ini = 0;
1244:   fin = sr->indexEig;
1245:   /* Selection of ends for searching new values */
1246:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
1247:   else sPres->ext[0] = sPres->neighb[0]->value;
1248:   if (!sPres->neighb[1]) {
1249:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
1250:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
1251:   } else sPres->ext[1] = sPres->neighb[1]->value;
1252:   /* Selection of values between right and left ends */
1253:   for (i=ini;i<fin;i++) {
1254:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
1255:     /* Values to the right of left shift */
1256:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
1257:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
1258:       else count1++;
1259:     } else break;
1260:   }
1261:   /* The number of values on each side are found */
1262:   if (sPres->neighb[0]) {
1263:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
1264:     if (sPres->nsch[0]<0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
1265:   } else sPres->nsch[0] = 0;

1267:   if (sPres->neighb[1]) {
1268:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1269:     if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
1270:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

1272:   /* Completing vector of indexes for deflation */
1273:   idx0 = ini;
1274:   idx1 = ini+count0+count1;
1275:   k=0;
1276:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
1277:   BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
1278:   BVSetNumConstraints(sr->Vnext,k);
1279:   for (i=0;i<k;i++) {
1280:     BVGetColumn(sr->Vnext,-i-1,&v);
1281:     BVCopyVec(sr->V,sr->idxDef[i],v);
1282:     BVRestoreColumn(sr->Vnext,-i-1,&v);
1283:   }

1285:   /* For rational Krylov */
1286:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
1287:     EPSPrepareRational(eps);
1288:   }
1289:   eps->nconv = 0;
1290:   /* Get rid of temporary Vnext */
1291:   BVDestroy(&eps->V);
1292:   eps->V = sr->Vnext;
1293:   sr->Vnext = NULL;
1294:   return(0);
1295: }

1297: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
1298: {
1299:   PetscErrorCode   ierr;
1300:   PetscInt         i,lds,ti;
1301:   PetscReal        newS;
1302:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1303:   EPS_SR           sr=ctx->sr;
1304:   Mat              A,B=NULL;
1305:   PetscObjectState Astate,Bstate=0;
1306:   PetscObjectId    Aid,Bid=0;

1309:   PetscCitationsRegister(citation,&cited);
1310:   if (ctx->global) {
1311:     EPSSolve_KrylovSchur_Slice(ctx->eps);
1312:     ctx->eps->state = EPS_STATE_SOLVED;
1313:     eps->reason = EPS_CONVERGED_TOL;
1314:     if (ctx->npart>1) {
1315:       /* Gather solution from subsolvers */
1316:       EPSSliceGatherSolution(eps);
1317:     } else {
1318:       eps->nconv = sr->numEigs;
1319:       eps->its   = ctx->eps->its;
1320:       PetscFree(ctx->inertias);
1321:       PetscFree(ctx->shifts);
1322:       EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1323:     }
1324:   } else {
1325:     if (ctx->npart==1) {
1326:       sr->eigr   = ctx->eps->eigr;
1327:       sr->eigi   = ctx->eps->eigi;
1328:       sr->perm   = ctx->eps->perm;
1329:       sr->errest = ctx->eps->errest;
1330:       sr->V      = ctx->eps->V;
1331:     }
1332:     /* Check that the user did not modify subcomm matrices */
1333:     EPSGetOperators(eps,&A,&B);
1334:     PetscObjectStateGet((PetscObject)A,&Astate);
1335:     PetscObjectGetId((PetscObject)A,&Aid);
1336:     if (B) {
1337:       PetscObjectStateGet((PetscObject)B,&Bstate);
1338:       PetscObjectGetId((PetscObject)B,&Bid);
1339:     }
1340:     if (Astate!=ctx->Astate || (B && Bstate!=ctx->Bstate) || Aid!=ctx->Aid || (B && Bid!=ctx->Bid)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcomm matrices have been modified by user");
1341:     /* Only with eigenvalues present in the interval ...*/
1342:     if (sr->numEigs==0) {
1343:       eps->reason = EPS_CONVERGED_TOL;
1344:       return(0);
1345:     }
1346:     /* Array of pending shifts */
1347:     sr->maxPend = 100; /* Initial size */
1348:     sr->nPend = 0;
1349:     PetscMalloc1(sr->maxPend,&sr->pending);
1350:     PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
1351:     EPSCreateShift(eps,sr->int0,NULL,NULL);
1352:     /* extract first shift */
1353:     sr->sPrev = NULL;
1354:     sr->sPres = sr->pending[--sr->nPend];
1355:     sr->sPres->inertia = sr->inertia0;
1356:     eps->target = sr->sPres->value;
1357:     sr->s0 = sr->sPres;
1358:     sr->indexEig = 0;
1359:     /* Memory reservation for auxiliary variables */
1360:     lds = PetscMin(eps->mpd,eps->ncv);
1361:     PetscCalloc1(lds*lds,&sr->S);
1362:     PetscMalloc1(eps->ncv,&sr->back);
1363:     PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
1364:     for (i=0;i<sr->numEigs;i++) {
1365:       sr->eigr[i]   = 0.0;
1366:       sr->eigi[i]   = 0.0;
1367:       sr->errest[i] = 0.0;
1368:       sr->perm[i]   = i;
1369:     }
1370:     /* Vectors for deflation */
1371:     PetscMalloc1(sr->numEigs,&sr->idxDef);
1372:     PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
1373:     sr->indexEig = 0;
1374:     /* Main loop */
1375:     while (sr->sPres) {
1376:       /* Search for deflation */
1377:       EPSLookForDeflation(eps);
1378:       /* KrylovSchur */
1379:       EPSKrylovSchur_Slice(eps);

1381:       EPSStoreEigenpairs(eps);
1382:       /* Select new shift */
1383:       if (!sr->sPres->comp[1]) {
1384:         EPSGetNewShiftValue(eps,1,&newS);
1385:         EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
1386:       }
1387:       if (!sr->sPres->comp[0]) {
1388:         /* Completing earlier interval */
1389:         EPSGetNewShiftValue(eps,0,&newS);
1390:         EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
1391:       }
1392:       /* Preparing for a new search of values */
1393:       EPSExtractShift(eps);
1394:     }

1396:     /* Updating eps values prior to exit */
1397:     PetscFree(sr->S);
1398:     PetscFree(sr->idxDef);
1399:     PetscFree(sr->pending);
1400:     PetscFree(sr->back);
1401:     BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
1402:     BVSetNumConstraints(sr->Vnext,0);
1403:     BVDestroy(&eps->V);
1404:     eps->V      = sr->Vnext;
1405:     eps->nconv  = sr->indexEig;
1406:     eps->reason = EPS_CONVERGED_TOL;
1407:     eps->its    = sr->itsKs;
1408:     eps->nds    = 0;
1409:     if (sr->dir<0) {
1410:       for (i=0;i<eps->nconv/2;i++) {
1411:         ti = sr->perm[i]; sr->perm[i] = sr->perm[eps->nconv-1-i]; sr->perm[eps->nconv-1-i] = ti;
1412:       }
1413:     }
1414:   }
1415:   return(0);
1416: }