Actual source code: ks-slice.c

slepc-3.15.2 2021-09-20
Report Typos and Errors
  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */
 10: /*
 11:    SLEPc 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: #define InertiaMismatch(h,d) \
 45:   do { \
 46:     SETERRQ1(PetscObjectComm((PetscObject)h),1,"Mismatch between number of values found and information from inertia%s",d?"":", consider using EPSKrylovSchurSetDetectZeros()"); \
 47:   } while (0)

 49: static PetscErrorCode EPSSliceResetSR(EPS eps)
 50: {
 51:   PetscErrorCode  ierr;
 52:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
 53:   EPS_SR          sr=ctx->sr;
 54:   EPS_shift       s;

 57:   if (sr) {
 58:     if (ctx->npart>1) {
 59:       BVDestroy(&sr->V);
 60:       PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
 61:     }
 62:     /* Reviewing list of shifts to free memory */
 63:     s = sr->s0;
 64:     if (s) {
 65:       while (s->neighb[1]) {
 66:         s = s->neighb[1];
 67:         PetscFree(s->neighb[0]);
 68:       }
 69:       PetscFree(s);
 70:     }
 71:     PetscFree(sr);
 72:   }
 73:   ctx->sr = NULL;
 74:   return(0);
 75: }

 77: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
 78: {
 79:   PetscErrorCode  ierr;
 80:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

 83:   if (!ctx->global) return(0);
 84:   /* Reset auxiliary EPS */
 85:   EPSSliceResetSR(ctx->eps);
 86:   EPSReset(ctx->eps);
 87:   EPSSliceResetSR(eps);
 88:   PetscFree(ctx->inertias);
 89:   PetscFree(ctx->shifts);
 90:   return(0);
 91: }

 93: PetscErrorCode EPSDestroy_KrylovSchur_Slice(EPS eps)
 94: {
 95:   PetscErrorCode  ierr;
 96:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

 99:   if (!ctx->global) return(0);
100:   /* Destroy auxiliary EPS */
101:   EPSReset_KrylovSchur_Slice(eps);
102:   EPSDestroy(&ctx->eps);
103:   if (ctx->npart>1) {
104:     PetscSubcommDestroy(&ctx->subc);
105:     if (ctx->commset) {
106:       MPI_Comm_free(&ctx->commrank);CHKERRMPI(ierr);
107:       ctx->commset = PETSC_FALSE;
108:     }
109:     ISDestroy(&ctx->isrow);
110:     ISDestroy(&ctx->iscol);
111:     MatDestroyMatrices(1,&ctx->submata);
112:     MatDestroyMatrices(1,&ctx->submatb);
113:   }
114:   PetscFree(ctx->subintervals);
115:   PetscFree(ctx->nconv_loc);
116:   return(0);
117: }

119: /*
120:   EPSSliceAllocateSolution - Allocate memory storage for common variables such
121:   as eigenvalues and eigenvectors. The argument extra is used for methods
122:   that require a working basis slightly larger than ncv.
123: */
124: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
125: {
126:   PetscErrorCode     ierr;
127:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data;
128:   PetscReal          eta;
129:   PetscInt           k;
130:   PetscLogDouble     cnt;
131:   BVType             type;
132:   BVOrthogType       orthog_type;
133:   BVOrthogRefineType orthog_ref;
134:   BVOrthogBlockType  ob_type;
135:   Mat                matrix;
136:   Vec                t;
137:   EPS_SR             sr = ctx->sr;

140:   /* allocate space for eigenvalues and friends */
141:   k = PetscMax(1,sr->numEigs);
142:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
143:   PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
144:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
145:   PetscLogObjectMemory((PetscObject)eps,cnt);

147:   /* allocate sr->V and transfer options from eps->V */
148:   BVDestroy(&sr->V);
149:   BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
150:   PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
151:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
152:   if (!((PetscObject)(eps->V))->type_name) {
153:     BVSetType(sr->V,BVSVEC);
154:   } else {
155:     BVGetType(eps->V,&type);
156:     BVSetType(sr->V,type);
157:   }
158:   STMatCreateVecsEmpty(eps->st,&t,NULL);
159:   BVSetSizesFromVec(sr->V,t,k);
160:   VecDestroy(&t);
161:   EPS_SetInnerProduct(eps);
162:   BVGetMatrix(eps->V,&matrix,NULL);
163:   BVSetMatrix(sr->V,matrix,PETSC_FALSE);
164:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
165:   BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
166:   return(0);
167: }

169: static PetscErrorCode EPSSliceGetEPS(EPS eps)
170: {
171:   PetscErrorCode     ierr;
172:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
173:   BV                 V;
174:   BVType             type;
175:   PetscReal          eta;
176:   BVOrthogType       orthog_type;
177:   BVOrthogRefineType orthog_ref;
178:   BVOrthogBlockType  ob_type;
179:   PetscInt           i;
180:   PetscReal          h,a,b;
181:   PetscRandom        rand;
182:   EPS_SR             sr=ctx->sr;

185:   if (!ctx->eps) { EPSKrylovSchurGetChildEPS(eps,&ctx->eps); }

187:   /* Determine subintervals */
188:   if (ctx->npart==1) {
189:     a = eps->inta; b = eps->intb;
190:   } else {
191:     if (!ctx->subintset) { /* uniform distribution if no set by user */
192:       if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
193:       h = (eps->intb-eps->inta)/ctx->npart;
194:       a = eps->inta+ctx->subc->color*h;
195:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
196:       PetscFree(ctx->subintervals);
197:       PetscMalloc1(ctx->npart+1,&ctx->subintervals);
198:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
199:       ctx->subintervals[ctx->npart] = eps->intb;
200:     } else {
201:       a = ctx->subintervals[ctx->subc->color];
202:       b = ctx->subintervals[ctx->subc->color+1];
203:     }
204:   }
205:   EPSSetInterval(ctx->eps,a,b);
206:   EPSSetConvergenceTest(ctx->eps,eps->conv);
207:   EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
208:   EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);

210:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
211:   ctx_local->detect = ctx->detect;

213:   /* transfer options from eps->V */
214:   EPSGetBV(ctx->eps,&V);
215:   BVGetRandomContext(V,&rand);  /* make sure the random context is available when duplicating */
216:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
217:   if (!((PetscObject)(eps->V))->type_name) {
218:     BVSetType(V,BVSVEC);
219:   } else {
220:     BVGetType(eps->V,&type);
221:     BVSetType(V,type);
222:   }
223:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
224:   BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);

226:   ctx->eps->which = eps->which;
227:   ctx->eps->max_it = eps->max_it;
228:   ctx->eps->tol = eps->tol;
229:   ctx->eps->purify = eps->purify;
230:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
231:   EPSSetProblemType(ctx->eps,eps->problem_type);
232:   EPSSetUp(ctx->eps);
233:   ctx->eps->nconv = 0;
234:   ctx->eps->its   = 0;
235:   for (i=0;i<ctx->eps->ncv;i++) {
236:     ctx->eps->eigr[i]   = 0.0;
237:     ctx->eps->eigi[i]   = 0.0;
238:     ctx->eps->errest[i] = 0.0;
239:   }
240:   return(0);
241: }

243: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
244: {
246:   KSP            ksp,kspr;
247:   PC             pc;
248:   Mat            F;
249:   PetscReal      nzshift=shift;
250:   PetscBool      flg;

253:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
254:     if (inertia) *inertia = eps->n;
255:   } else if (shift <= PETSC_MIN_REAL) {
256:     if (inertia) *inertia = 0;
257:     if (zeros) *zeros = 0;
258:   } else {
259:     /* If the shift is zero, perturb it to a very small positive value.
260:        The goal is that the nonzero pattern is the same in all cases and reuse
261:        the symbolic factorizations */
262:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
263:     STSetShift(eps->st,nzshift);
264:     STGetKSP(eps->st,&ksp);
265:     KSPGetPC(ksp,&pc);
266:     PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
267:     if (flg) {
268:       PCRedundantGetKSP(pc,&kspr);
269:       KSPGetPC(kspr,&pc);
270:     }
271:     PCFactorGetMatrix(pc,&F);
272:     MatGetInertia(F,inertia,zeros,NULL);
273:   }
274:   if (inertia) { PetscInfo2(eps,"Computed inertia at shift %g: %D\n",(double)nzshift,*inertia); }
275:   return(0);
276: }

278: /*
279:    Dummy backtransform operation
280:  */
281: static PetscErrorCode EPSBackTransform_Skip(EPS eps)
282: {
284:   return(0);
285: }

287: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
288: {
289:   PetscErrorCode  ierr;
290:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
291:   EPS_SR          sr,sr_loc,sr_glob;
292:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0,method,hiteig=0;
293:   PetscMPIInt     nproc,rank=0,aux;
294:   PetscReal       r;
295:   MPI_Request     req;
296:   Mat             A,B=NULL;
297:   DSParallelType  ptype;

300:   if (ctx->global) {
301:     EPSCheckHermitianDefiniteCondition(eps,PETSC_TRUE," with spectrum slicing");
302:     EPSCheckSinvertCayleyCondition(eps,PETSC_TRUE," with spectrum slicing");
303:     if (eps->inta==eps->intb) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues unless you provide a computational interval with EPSSetInterval()");
304:     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");
305:     EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_STOPPING,PETSC_TRUE," with spectrum slicing");
306:     EPSCheckIgnoredCondition(eps,EPS_FEATURE_BALANCE,PETSC_TRUE," with spectrum slicing");
307:     if (eps->tol==PETSC_DEFAULT) {
308:  #if defined(PETSC_USE_REAL_SINGLE)
309:       eps->tol = SLEPC_DEFAULT_TOL;
310: #else
311:       /* use tighter tolerance */
312:       eps->tol = SLEPC_DEFAULT_TOL*1e-2;
313: #endif
314:     }
315:     if (eps->max_it==PETSC_DEFAULT) eps->max_it = 100;
316:     if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n);  /* nev not set, use default value */
317:     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");
318:   }
319:   eps->ops->backtransform = EPSBackTransform_Skip;

321:   /* create spectrum slicing context and initialize it */
322:   EPSSliceResetSR(eps);
323:   PetscNewLog(eps,&sr);
324:   ctx->sr = sr;
325:   sr->itsKs = 0;
326:   sr->nleap = 0;
327:   sr->nMAXCompl = eps->nev/4;
328:   sr->iterCompl = eps->max_it/4;
329:   sr->sPres = NULL;
330:   sr->nS = 0;

332:   if (ctx->npart==1 || ctx->global) {
333:     /* check presence of ends and finding direction */
334:     if ((eps->inta > PETSC_MIN_REAL && !(ctx->subintervals && ctx->subintervals[0]==ctx->subintervals[1])) || eps->intb >= PETSC_MAX_REAL) {
335:       sr->int0 = eps->inta;
336:       sr->int1 = eps->intb;
337:       sr->dir = 1;
338:       if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
339:         sr->hasEnd = PETSC_FALSE;
340:       } else sr->hasEnd = PETSC_TRUE;
341:     } else {
342:       sr->int0 = eps->intb;
343:       sr->int1 = eps->inta;
344:       sr->dir = -1;
345:       sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
346:     }
347:   }
348:   if (ctx->global) {
349:     EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
350:     /* create subintervals and initialize auxiliary eps for slicing runs */
351:     EPSKrylovSchurGetChildEPS(eps,&ctx->eps);
352:     /* prevent computation of factorization in global eps */
353:     STSetTransform(eps->st,PETSC_FALSE);
354:     EPSSliceGetEPS(eps);
355:     sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
356:     if (ctx->npart>1) {
357:       if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
358:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);CHKERRMPI(ierr);
359:       if (!rank) {
360:         MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);CHKERRMPI(ierr);
361:       }
362:       MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
363:       PetscFree(ctx->nconv_loc);
364:       PetscMalloc1(ctx->npart,&ctx->nconv_loc);
365:       MPI_Comm_size(((PetscObject)eps)->comm,&nproc);CHKERRMPI(ierr);
366:       if (sr->dir<0) off = 1;
367:       if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
368:         PetscMPIIntCast(sr_loc->numEigs,&aux);
369:         MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);CHKERRMPI(ierr);
370:         MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);CHKERRMPI(ierr);
371:       } else {
372:         MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);CHKERRMPI(ierr);
373:         if (!rank) {
374:           PetscMPIIntCast(sr_loc->numEigs,&aux);
375:           MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);CHKERRMPI(ierr);
376:           MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);CHKERRMPI(ierr);
377:         }
378:         PetscMPIIntCast(ctx->npart,&aux);
379:         MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
380:         MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
381:       }
382:       nEigs = 0;
383:       for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
384:     } else {
385:       nEigs = sr_loc->numEigs;
386:       sr->inertia0 = sr_loc->inertia0;
387:       sr->dir = sr_loc->dir;
388:     }
389:     sr->inertia1 = sr->inertia0+sr->dir*nEigs;
390:     sr->numEigs = nEigs;
391:     eps->nev = nEigs;
392:     eps->ncv = nEigs;
393:     eps->mpd = nEigs;
394:   } else {
395:     ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
396:     sr_glob = ctx_glob->sr;
397:     if (ctx->npart>1) {
398:       sr->dir = sr_glob->dir;
399:       sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
400:       sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
401:       if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
402:       else sr->hasEnd = PETSC_TRUE;
403:     }
404:     /* sets first shift */
405:     STSetShift(eps->st,(sr->int0==0.0)?10.0/PETSC_MAX_REAL:sr->int0);
406:     STSetUp(eps->st);

408:     /* compute inertia0 */
409:     EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
410:     /* undocumented option to control what to do when an eigenvalue is found:
411:        - error out if it's the endpoint of the user-provided interval (or sub-interval)
412:        - if it's an endpoint computed internally:
413:           + if hiteig=0 error out
414:           + else if hiteig=1 the subgroup that hit the eigenvalue does nothing
415:           + otherwise the subgroup that hit the eigenvalue perturbs the shift and recomputes inertia
416:     */
417:     PetscOptionsGetInt(NULL,NULL,"-eps_krylovschur_hiteigenvalue",&hiteig,NULL);
418:     if (zeros) { /* error in factorization */
419:       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");
420:       else if (ctx_glob->subintset && !hiteig) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
421:       else {
422:         if (hiteig==1) { /* idle subgroup */
423:           sr->inertia0 = -1;
424:         } else { /* perturb shift */
425:           sr->int0 *= (1.0+SLICE_PTOL);
426:           EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
427:           if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
428:         }
429:       }
430:     }
431:     if (ctx->npart>1) {
432:       /* inertia1 is received from neighbour */
433:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);CHKERRMPI(ierr);
434:       if (!rank) {
435:         if (sr->inertia0!=-1 && ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1))) { /* send inertia0 to neighbour0 */
436:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
437:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
438:         }
439:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
440:           MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);CHKERRMPI(ierr);
441:           MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);CHKERRMPI(ierr);
442:         }
443:         if (sr->inertia0==-1 && !(sr->dir>0 && ctx->subc->color==ctx->npart-1) && !(sr->dir<0 && ctx->subc->color==0)) {
444:           sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
445:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
446:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
447:         }
448:       }
449:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
450:         MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
451:         MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
452:       } else sr_glob->inertia1 = sr->inertia1;
453:     }

455:     /* last process in eps comm computes inertia1 */
456:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
457:       EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
458:       if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
459:       if (!rank && sr->inertia0==-1) {
460:         sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
461:         MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
462:         MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);CHKERRMPI(ierr);
463:       }
464:       if (sr->hasEnd) {
465:         sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
466:         i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
467:       }
468:     }

470:     /* number of eigenvalues in interval */
471:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
472:     if (ctx->npart>1) {
473:       /* memory allocate for subinterval eigenpairs */
474:       EPSSliceAllocateSolution(eps,1);
475:     }
476:     dssz = eps->ncv+1;
477:     DSGetParallel(ctx->eps->ds,&ptype);
478:     DSSetParallel(eps->ds,ptype);
479:     DSGetMethod(ctx->eps->ds,&method);
480:     DSSetMethod(eps->ds,method);
481:   }
482:   DSSetType(eps->ds,DSHEP);
483:   DSSetCompact(eps->ds,PETSC_TRUE);
484:   DSAllocate(eps->ds,dssz);
485:   /* keep state of subcomm matrices to check that the user does not modify them */
486:   EPSGetOperators(eps,&A,&B);
487:   PetscObjectStateGet((PetscObject)A,&ctx->Astate);
488:   PetscObjectGetId((PetscObject)A,&ctx->Aid);
489:   if (B) {
490:     PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
491:     PetscObjectGetId((PetscObject)B,&ctx->Bid);
492:   } else {
493:     ctx->Bstate=0;
494:     ctx->Bid=0;
495:   }
496:   return(0);
497: }

499: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
500: {
501:   PetscErrorCode  ierr;
502:   Vec             v,vg,v_loc;
503:   IS              is1,is2;
504:   VecScatter      vec_sc;
505:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
506:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
507:   PetscScalar     *array;
508:   EPS_SR          sr_loc;
509:   BV              V_loc;

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

515:   /* Gather parallel eigenvectors */
516:   BVGetColumn(eps->V,0,&v);
517:   VecGetOwnershipRange(v,&n0,&m0);
518:   BVRestoreColumn(eps->V,0,&v);
519:   BVGetColumn(ctx->eps->V,0,&v);
520:   VecGetLocalSize(v,&nloc);
521:   BVRestoreColumn(ctx->eps->V,0,&v);
522:   PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
523:   VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
524:   idx = -1;
525:   for (si=0;si<ctx->npart;si++) {
526:     j = 0;
527:     for (i=n0;i<m0;i++) {
528:       idx1[j]   = i;
529:       idx2[j++] = i+eps->n*si;
530:     }
531:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
532:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
533:     BVGetColumn(eps->V,0,&v);
534:     VecScatterCreate(v,is1,vg,is2,&vec_sc);
535:     BVRestoreColumn(eps->V,0,&v);
536:     ISDestroy(&is1);
537:     ISDestroy(&is2);
538:     for (i=0;i<ctx->nconv_loc[si];i++) {
539:       BVGetColumn(eps->V,++idx,&v);
540:       if (ctx->subc->color==si) {
541:         BVGetColumn(V_loc,i,&v_loc);
542:         VecGetArray(v_loc,&array);
543:         VecPlaceArray(vg,array);
544:       }
545:       VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
546:       VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
547:       if (ctx->subc->color==si) {
548:         VecResetArray(vg);
549:         VecRestoreArray(v_loc,&array);
550:         BVRestoreColumn(V_loc,i,&v_loc);
551:       }
552:       BVRestoreColumn(eps->V,idx,&v);
553:     }
554:     VecScatterDestroy(&vec_sc);
555:   }
556:   PetscFree2(idx1,idx2);
557:   VecDestroy(&vg);
558:   return(0);
559: }

561: /*
562:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
563:  */
564: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
565: {
566:   PetscErrorCode  ierr;
567:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

570:   if (ctx->global && ctx->npart>1) {
571:     EPSComputeVectors(ctx->eps);
572:     EPSSliceGatherEigenVectors(eps);
573:   }
574:   return(0);
575: }

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

579: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
580: {
581:   PetscErrorCode  ierr;
582:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
583:   PetscInt        i=0,j,tmpi;
584:   PetscReal       v,tmpr;
585:   EPS_shift       s;

588:   if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
589:   if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
590:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
591:     *n = 2;
592:   } else {
593:     *n = 1;
594:     s = ctx->sr->s0;
595:     while (s) {
596:       (*n)++;
597:       s = s->neighb[1];
598:     }
599:   }
600:   PetscMalloc1(*n,shifts);
601:   PetscMalloc1(*n,inertias);
602:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
603:     (*shifts)[0]   = ctx->sr->int0;
604:     (*shifts)[1]   = ctx->sr->int1;
605:     (*inertias)[0] = ctx->sr->inertia0;
606:     (*inertias)[1] = ctx->sr->inertia1;
607:   } else {
608:     s = ctx->sr->s0;
609:     while (s) {
610:       (*shifts)[i]     = s->value;
611:       (*inertias)[i++] = s->inertia;
612:       s = s->neighb[1];
613:     }
614:     (*shifts)[i]   = ctx->sr->int1;
615:     (*inertias)[i] = ctx->sr->inertia1;
616:   }
617:   /* remove possible duplicate in last position */
618:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
619:   /* sort result */
620:   for (i=0;i<*n;i++) {
621:     v = (*shifts)[i];
622:     for (j=i+1;j<*n;j++) {
623:       if (v > (*shifts)[j]) {
624:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
625:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
626:         v = (*shifts)[i];
627:       }
628:     }
629:   }
630:   return(0);
631: }

633: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
634: {
635:   PetscErrorCode  ierr;
636:   PetscMPIInt     rank,nproc;
637:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
638:   PetscInt        i,idx,j;
639:   PetscInt        *perm_loc,off=0,*inertias_loc,ns;
640:   PetscScalar     *eigr_loc;
641:   EPS_SR          sr_loc;
642:   PetscReal       *shifts_loc;
643:   PetscMPIInt     *disp,*ns_loc,aux;

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

650:   /* Gather the shifts used and the inertias computed */
651:   EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
652:   if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
653:   if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
654:     ns--;
655:     for (i=0;i<ns;i++) {
656:       inertias_loc[i] = inertias_loc[i+1];
657:       shifts_loc[i] = shifts_loc[i+1];
658:     }
659:   }
660:   PetscMalloc1(ctx->npart,&ns_loc);
661:   MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);CHKERRMPI(ierr);
662:   PetscMPIIntCast(ns,&aux);
663:   if (!rank) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank);CHKERRMPI(ierr); }
664:   PetscMPIIntCast(ctx->npart,&aux);
665:   MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
666:   ctx->nshifts = 0;
667:   for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
668:   PetscFree(ctx->inertias);
669:   PetscFree(ctx->shifts);
670:   PetscMalloc1(ctx->nshifts,&ctx->inertias);
671:   PetscMalloc1(ctx->nshifts,&ctx->shifts);

673:   /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
674:   eigr_loc = sr_loc->eigr;
675:   perm_loc = sr_loc->perm;
676:   MPI_Comm_size(((PetscObject)eps)->comm,&nproc);CHKERRMPI(ierr);
677:   PetscMalloc1(ctx->npart,&disp);
678:   disp[0] = 0;
679:   for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
680:   if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
681:     PetscMPIIntCast(sr_loc->numEigs,&aux);
682:     MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank);CHKERRMPI(ierr); /* eigenvalues */
683:     MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank);CHKERRMPI(ierr); /* perm */
684:     for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
685:     PetscMPIIntCast(ns,&aux);
686:     MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank);CHKERRMPI(ierr); /* shifts */
687:     MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank);CHKERRMPI(ierr); /* inertias */
688:     MPIU_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
689:   } else { /* subcommunicators with different size */
690:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);CHKERRMPI(ierr);
691:     if (!rank) {
692:       PetscMPIIntCast(sr_loc->numEigs,&aux);
693:       MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank);CHKERRMPI(ierr); /* eigenvalues */
694:       MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank);CHKERRMPI(ierr); /* perm */
695:       for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
696:       PetscMPIIntCast(ns,&aux);
697:       MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank);CHKERRMPI(ierr); /* shifts */
698:       MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank);CHKERRMPI(ierr); /* inertias */
699:       MPIU_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
700:     }
701:     PetscMPIIntCast(eps->nconv,&aux);
702:     MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
703:     MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
704:     MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
705:     PetscMPIIntCast(ctx->nshifts,&aux);
706:     MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
707:     MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));CHKERRMPI(ierr);
708:   }
709:   /* Update global array eps->perm */
710:   idx = ctx->nconv_loc[0];
711:   for (i=1;i<ctx->npart;i++) {
712:     off += ctx->nconv_loc[i-1];
713:     for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
714:   }

716:   /* Gather parallel eigenvectors */
717:   PetscFree(ns_loc);
718:   PetscFree(disp);
719:   PetscFree(shifts_loc);
720:   PetscFree(inertias_loc);
721:   return(0);
722: }

724: /*
725:    Fills the fields of a shift structure
726: */
727: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
728: {
729:   PetscErrorCode  ierr;
730:   EPS_shift       s,*pending2;
731:   PetscInt        i;
732:   EPS_SR          sr;
733:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

736:   sr = ctx->sr;
737:   if ((neighb0 && val==neighb0->value) || (neighb1 && val==neighb1->value)) {
738:     sr->nPend++;
739:     return(0);
740:   }
741:   PetscNewLog(eps,&s);
742:   s->value = val;
743:   s->neighb[0] = neighb0;
744:   if (neighb0) neighb0->neighb[1] = s;
745:   s->neighb[1] = neighb1;
746:   if (neighb1) neighb1->neighb[0] = s;
747:   s->comp[0] = PETSC_FALSE;
748:   s->comp[1] = PETSC_FALSE;
749:   s->index = -1;
750:   s->neigs = 0;
751:   s->nconv[0] = s->nconv[1] = 0;
752:   s->nsch[0] = s->nsch[1]=0;
753:   /* Inserts in the stack of pending shifts */
754:   /* If needed, the array is resized */
755:   if (sr->nPend >= sr->maxPend) {
756:     sr->maxPend *= 2;
757:     PetscMalloc1(sr->maxPend,&pending2);
758:     PetscLogObjectMemory((PetscObject)eps,sr->maxPend*sizeof(EPS_shift*));
759:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
760:     PetscFree(sr->pending);
761:     sr->pending = pending2;
762:   }
763:   sr->pending[sr->nPend++]=s;
764:   return(0);
765: }

767: /* Prepare for Rational Krylov update */
768: static PetscErrorCode EPSPrepareRational(EPS eps)
769: {
770:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
771:   PetscErrorCode  ierr;
772:   PetscInt        dir,i,k,ld,nv;
773:   PetscScalar     *A;
774:   EPS_SR          sr = ctx->sr;
775:   Vec             v;

778:   DSGetLeadingDimension(eps->ds,&ld);
779:   dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
780:   dir*=sr->dir;
781:   k = 0;
782:   for (i=0;i<sr->nS;i++) {
783:     if (dir*PetscRealPart(sr->S[i])>0.0) {
784:       sr->S[k] = sr->S[i];
785:       sr->S[sr->nS+k] = sr->S[sr->nS+i];
786:       BVGetColumn(sr->Vnext,k,&v);
787:       BVCopyVec(eps->V,eps->nconv+i,v);
788:       BVRestoreColumn(sr->Vnext,k,&v);
789:       k++;
790:       if (k>=sr->nS/2)break;
791:     }
792:   }
793:   /* Copy to DS */
794:   DSGetArray(eps->ds,DS_MAT_A,&A);
795:   PetscArrayzero(A,ld*ld);
796:   for (i=0;i<k;i++) {
797:     A[i*(1+ld)] = sr->S[i];
798:     A[k+i*ld] = sr->S[sr->nS+i];
799:   }
800:   sr->nS = k;
801:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
802:   DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
803:   DSSetDimensions(eps->ds,nv,0,0,k);
804:   /* Append u to V */
805:   BVGetColumn(sr->Vnext,sr->nS,&v);
806:   BVCopyVec(eps->V,sr->nv,v);
807:   BVRestoreColumn(sr->Vnext,sr->nS,&v);
808:   return(0);
809: }

811: /* Provides next shift to be computed */
812: static PetscErrorCode EPSExtractShift(EPS eps)
813: {
814:   PetscErrorCode  ierr;
815:   PetscInt        iner,zeros=0;
816:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
817:   EPS_SR          sr;
818:   PetscReal       newShift,diam,ptol;
819:   EPS_shift       sPres;

822:   sr = ctx->sr;
823:   if (sr->nPend > 0) {
824:     if (sr->sPres==sr->pending[sr->nPend-1]) {
825:       eps->reason = EPS_CONVERGED_ITERATING;
826:       eps->its = 0;
827:       sr->nPend--;
828:       sr->sPres->rep = PETSC_TRUE;
829:       return(0);
830:     }
831:     sr->sPrev = sr->sPres;
832:     sr->sPres = sr->pending[--sr->nPend];
833:     sPres = sr->sPres;
834:     EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
835:     if (zeros) {
836:       diam = PetscMin(PetscAbsReal(sPres->neighb[0]->value-sPres->value),PetscAbsReal(sPres->neighb[1]->value-sPres->value));
837:       ptol = PetscMin(SLICE_PTOL,diam/2);
838:       newShift = sPres->value*(1.0+ptol);
839:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
840:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
841:       EPSSliceGetInertia(eps,newShift,&iner,&zeros);
842:       if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
843:       sPres->value = newShift;
844:     }
845:     sr->sPres->inertia = iner;
846:     eps->target = sr->sPres->value;
847:     eps->reason = EPS_CONVERGED_ITERATING;
848:     eps->its = 0;
849:   } else sr->sPres = NULL;
850:   return(0);
851: }

853: /*
854:    Symmetric KrylovSchur adapted to spectrum slicing:
855:    Allows searching an specific amount of eigenvalues in the subintervals left and right.
856:    Returns whether the search has succeeded
857: */
858: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
859: {
860:   PetscErrorCode  ierr;
861:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
862:   PetscInt        i,k,l,ld,nv,*iwork,j,count0,count1,iterCompl=0,n0,n1;
863:   Mat             U,Op;
864:   PetscScalar     *Q,*A;
865:   PetscReal       *a,*b,beta,lambda;
866:   EPS_shift       sPres;
867:   PetscBool       breakdown,complIterating,sch0,sch1;
868:   EPS_SR          sr = ctx->sr;
869:   char            messg[100];

872:   /* Spectrum slicing data */
873:   sPres = sr->sPres;
874:   complIterating =PETSC_FALSE;
875:   sch1 = sch0 = PETSC_TRUE;
876:   DSGetLeadingDimension(eps->ds,&ld);
877:   PetscMalloc1(2*ld,&iwork);
878:   count0=0;count1=0; /* Found on both sides */
879:   if (!sPres->rep && sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
880:     /* Rational Krylov */
881:     DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
882:     DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
883:     DSSetDimensions(eps->ds,l+1,0,0,0);
884:     BVSetActiveColumns(eps->V,0,l+1);
885:     DSGetMat(eps->ds,DS_MAT_Q,&U);
886:     BVMultInPlace(eps->V,U,0,l+1);
887:     MatDestroy(&U);
888:   } else {
889:     /* Get the starting Lanczos vector */
890:     EPSGetStartVector(eps,0,NULL);
891:     l = 0;
892:   }
893:   /* Restart loop */
894:   while (eps->reason == EPS_CONVERGED_ITERATING) {
895:     eps->its++; sr->itsKs++;
896:     /* Compute an nv-step Lanczos factorization */
897:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
898:     DSGetArrayReal(eps->ds,DS_MAT_T,&a);
899:     b = a + ld;
900:     STGetOperator(eps->st,&Op);
901:     BVMatLanczos(eps->V,Op,a,b,eps->nconv+l,&nv,&breakdown);
902:     STRestoreOperator(eps->st,&Op);
903:     sr->nv = nv;
904:     beta = b[nv-1];
905:     DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
906:     DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
907:     if (l==0) {
908:       DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
909:     } else {
910:       DSSetState(eps->ds,DS_STATE_RAW);
911:     }
912:     BVSetActiveColumns(eps->V,eps->nconv,nv);

914:     /* Solve projected problem and compute residual norm estimates */
915:     if (eps->its == 1 && l > 0) {/* After rational update */
916:       DSGetArray(eps->ds,DS_MAT_A,&A);
917:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
918:       b = a + ld;
919:       k = eps->nconv+l;
920:       A[k*ld+k-1] = A[(k-1)*ld+k];
921:       A[k*ld+k] = a[k];
922:       for (j=k+1; j< nv; j++) {
923:         A[j*ld+j] = a[j];
924:         A[j*ld+j-1] = b[j-1] ;
925:         A[(j-1)*ld+j] = b[j-1];
926:       }
927:       DSRestoreArray(eps->ds,DS_MAT_A,&A);
928:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
929:       DSSolve(eps->ds,eps->eigr,NULL);
930:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
931:       DSSetCompact(eps->ds,PETSC_TRUE);
932:     } else { /* Restart */
933:       DSSolve(eps->ds,eps->eigr,NULL);
934:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
935:     }
936:     DSSynchronize(eps->ds,eps->eigr,NULL);

938:     /* Residual */
939:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,0.0,1.0,&k);
940:     /* Checking values obtained for completing */
941:     for (i=0;i<k;i++) {
942:       sr->back[i]=eps->eigr[i];
943:     }
944:     STBackTransform(eps->st,k,sr->back,eps->eigi);
945:     count0=count1=0;
946:     for (i=0;i<k;i++) {
947:       lambda = PetscRealPart(sr->back[i]);
948:       if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
949:       if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
950:     }
951:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
952:     else {
953:       /* Checks completion */
954:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
955:         eps->reason = EPS_CONVERGED_TOL;
956:       } else {
957:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
958:         if (complIterating) {
959:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
960:         } else if (k >= eps->nev) {
961:           n0 = sPres->nsch[0]-count0;
962:           n1 = sPres->nsch[1]-count1;
963:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
964:             /* Iterating for completion*/
965:             complIterating = PETSC_TRUE;
966:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
967:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
968:             iterCompl = sr->iterCompl;
969:           } else eps->reason = EPS_CONVERGED_TOL;
970:         }
971:       }
972:     }
973:     /* Update l */
974:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
975:     else l = nv-k;
976:     if (breakdown) l=0;
977:     if (!ctx->lock && l>0 && eps->reason == EPS_CONVERGED_ITERATING) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

979:     if (eps->reason == EPS_CONVERGED_ITERATING) {
980:       if (breakdown) {
981:         /* Start a new Lanczos factorization */
982:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
983:         EPSGetStartVector(eps,k,&breakdown);
984:         if (breakdown) {
985:           eps->reason = EPS_DIVERGED_BREAKDOWN;
986:           PetscInfo(eps,"Unable to generate more start vectors\n");
987:         }
988:       } else {
989:         /* Prepare the Rayleigh quotient for restart */
990:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
991:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
992:         b = a + ld;
993:         for (i=k;i<k+l;i++) {
994:           a[i] = PetscRealPart(eps->eigr[i]);
995:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
996:         }
997:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
998:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
999:       }
1000:     }
1001:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
1002:     DSGetMat(eps->ds,DS_MAT_Q,&U);
1003:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
1004:     MatDestroy(&U);

1006:     /* Normalize u and append it to V */
1007:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
1008:       BVCopyColumn(eps->V,nv,k+l);
1009:     }
1010:     eps->nconv = k;
1011:     if (eps->reason != EPS_CONVERGED_ITERATING) {
1012:       /* Store approximated values for next shift */
1013:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
1014:       sr->nS = l;
1015:       for (i=0;i<l;i++) {
1016:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
1017:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
1018:       }
1019:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1020:     }
1021:   }
1022:   /* Check for completion */
1023:   for (i=0;i< eps->nconv; i++) {
1024:     if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
1025:     else sPres->nconv[0]++;
1026:   }
1027:   sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
1028:   sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
1029:   PetscSNPrintf(messg,sizeof(messg),"Lanczos: %D evals in [%g,%g]%s and %D evals in [%g,%g]%s\n",count0,(double)(sr->dir==1)?sPres->ext[0]:sPres->value,(double)(sr->dir==1)?sPres->value:sPres->ext[0],(sPres->comp[0])?"*":"",count1,(double)(sr->dir==1)?sPres->value:sPres->ext[1],(double)(sr->dir==1)?sPres->ext[1]:sPres->value,(sPres->comp[1])?"*":"");
1030:   PetscInfo(eps,messg);
1031:   if (count0 > sPres->nsch[0] || count1 > sPres->nsch[1]) InertiaMismatch(eps,ctx->detect);
1032:   PetscFree(iwork);
1033:   return(0);
1034: }

1036: /*
1037:   Obtains value of subsequent shift
1038: */
1039: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
1040: {
1041:   PetscReal       lambda,d_prev;
1042:   PetscInt        i,idxP;
1043:   EPS_SR          sr;
1044:   EPS_shift       sPres,s;
1045:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

1048:   sr = ctx->sr;
1049:   sPres = sr->sPres;
1050:   if (sPres->neighb[side]) {
1051:     /* Completing a previous interval */
1052:     *newS = (sPres->value + sPres->neighb[side]->value)/2;
1053:     if (PetscAbsReal(sPres->value - *newS)/PetscAbsReal(sPres->value)<=100*PETSC_SQRT_MACHINE_EPSILON) *newS = sPres->value;
1054:   } else { /* (Only for side=1). Creating a new interval. */
1055:     if (sPres->neigs==0) {/* No value has been accepted*/
1056:       if (sPres->neighb[0]) {
1057:         /* Multiplying by 10 the previous distance */
1058:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
1059:         sr->nleap++;
1060:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
1061:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
1062:       } else { /* First shift */
1063:         if (eps->nconv != 0) {
1064:           /* Unaccepted values give information for next shift */
1065:           idxP=0;/* Number of values left from shift */
1066:           for (i=0;i<eps->nconv;i++) {
1067:             lambda = PetscRealPart(eps->eigr[i]);
1068:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
1069:             else break;
1070:           }
1071:           /* Avoiding subtraction of eigenvalues (might be the same).*/
1072:           if (idxP>0) {
1073:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
1074:           } else {
1075:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
1076:           }
1077:           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
1078:         } else { /* No values found, no information for next shift */
1079:           SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
1080:         }
1081:       }
1082:     } else { /* Accepted values found */
1083:       sr->nleap = 0;
1084:       /* Average distance of values in previous subinterval */
1085:       s = sPres->neighb[0];
1086:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
1087:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
1088:       }
1089:       if (s) {
1090:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
1091:       } else { /* First shift. Average distance obtained with values in this shift */
1092:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
1093:         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)) {
1094:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
1095:         } else {
1096:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
1097:         }
1098:       }
1099:       /* Average distance is used for next shift by adding it to value on the right or to shift */
1100:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
1101:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
1102:       } else { /* Last accepted value is on the left of shift. Adding to shift */
1103:         *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
1104:       }
1105:     }
1106:     /* End of interval can not be surpassed */
1107:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
1108:   }/* of neighb[side]==null */
1109:   return(0);
1110: }

1112: /*
1113:   Function for sorting an array of real values
1114: */
1115: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
1116: {
1117:   PetscReal re;
1118:   PetscInt  i,j,tmp;

1121:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
1122:   /* Insertion sort */
1123:   for (i=1;i<nr;i++) {
1124:     re = PetscRealPart(r[perm[i]]);
1125:     j = i-1;
1126:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
1127:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
1128:     }
1129:   }
1130:   return(0);
1131: }

1133: /* Stores the pairs obtained since the last shift in the global arrays */
1134: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
1135: {
1136:   PetscErrorCode  ierr;
1137:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1138:   PetscReal       lambda,err,norm;
1139:   PetscInt        i,count;
1140:   PetscBool       iscayley;
1141:   EPS_SR          sr = ctx->sr;
1142:   EPS_shift       sPres;
1143:   Vec             v,w;

1146:   sPres = sr->sPres;
1147:   sPres->index = sr->indexEig;
1148:   count = sr->indexEig;
1149:   /* Back-transform */
1150:   STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
1151:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
1152:   /* Sort eigenvalues */
1153:   sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
1154:   /* Values stored in global array */
1155:   for (i=0;i<eps->nconv;i++) {
1156:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
1157:     err = eps->errest[eps->perm[i]];

1159:     if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
1160:       if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
1161:       sr->eigr[count] = lambda;
1162:       sr->errest[count] = err;
1163:       /* Explicit purification */
1164:       BVGetColumn(eps->V,eps->perm[i],&w);
1165:       if (eps->purify) {
1166:         BVGetColumn(sr->V,count,&v);
1167:         STApply(eps->st,w,v);
1168:         BVRestoreColumn(sr->V,count,&v);
1169:       } else {
1170:         BVInsertVec(sr->V,count,w);
1171:       }
1172:       BVRestoreColumn(eps->V,eps->perm[i],&w);
1173:       BVNormColumn(sr->V,count,NORM_2,&norm);
1174:       BVScaleColumn(sr->V,count,1.0/norm);
1175:       count++;
1176:     }
1177:   }
1178:   sPres->neigs = count - sr->indexEig;
1179:   sr->indexEig = count;
1180:   /* Global ordering array updating */
1181:   sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
1182:   return(0);
1183: }

1185: static PetscErrorCode EPSLookForDeflation(EPS eps)
1186: {
1187:   PetscErrorCode  ierr;
1188:   PetscReal       val;
1189:   PetscInt        i,count0=0,count1=0;
1190:   EPS_shift       sPres;
1191:   PetscInt        ini,fin,k,idx0,idx1;
1192:   EPS_SR          sr;
1193:   Vec             v;
1194:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

1197:   sr = ctx->sr;
1198:   sPres = sr->sPres;

1200:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
1201:   else ini = 0;
1202:   fin = sr->indexEig;
1203:   /* Selection of ends for searching new values */
1204:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
1205:   else sPres->ext[0] = sPres->neighb[0]->value;
1206:   if (!sPres->neighb[1]) {
1207:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
1208:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
1209:   } else sPres->ext[1] = sPres->neighb[1]->value;
1210:   /* Selection of values between right and left ends */
1211:   for (i=ini;i<fin;i++) {
1212:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
1213:     /* Values to the right of left shift */
1214:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
1215:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
1216:       else count1++;
1217:     } else break;
1218:   }
1219:   /* The number of values on each side are found */
1220:   if (sPres->neighb[0]) {
1221:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
1222:     if (sPres->nsch[0]<0) InertiaMismatch(eps,ctx->detect);
1223:   } else sPres->nsch[0] = 0;

1225:   if (sPres->neighb[1]) {
1226:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1227:     if (sPres->nsch[1]<0) InertiaMismatch(eps,ctx->detect);
1228:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

1230:   /* Completing vector of indexes for deflation */
1231:   idx0 = ini;
1232:   idx1 = ini+count0+count1;
1233:   k=0;
1234:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
1235:   BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
1236:   BVSetNumConstraints(sr->Vnext,k);
1237:   for (i=0;i<k;i++) {
1238:     BVGetColumn(sr->Vnext,-i-1,&v);
1239:     BVCopyVec(sr->V,sr->idxDef[i],v);
1240:     BVRestoreColumn(sr->Vnext,-i-1,&v);
1241:   }

1243:   /* For rational Krylov */
1244:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
1245:     EPSPrepareRational(eps);
1246:   }
1247:   eps->nconv = 0;
1248:   /* Get rid of temporary Vnext */
1249:   BVDestroy(&eps->V);
1250:   eps->V = sr->Vnext;
1251:   sr->Vnext = NULL;
1252:   return(0);
1253: }

1255: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
1256: {
1257:   PetscErrorCode   ierr;
1258:   PetscInt         i,lds,ti;
1259:   PetscReal        newS;
1260:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1261:   EPS_SR           sr=ctx->sr;
1262:   Mat              A,B=NULL;
1263:   PetscObjectState Astate,Bstate=0;
1264:   PetscObjectId    Aid,Bid=0;

1267:   PetscCitationsRegister(citation,&cited);
1268:   if (ctx->global) {
1269:     EPSSolve_KrylovSchur_Slice(ctx->eps);
1270:     ctx->eps->state = EPS_STATE_SOLVED;
1271:     eps->reason = EPS_CONVERGED_TOL;
1272:     if (ctx->npart>1) {
1273:       /* Gather solution from subsolvers */
1274:       EPSSliceGatherSolution(eps);
1275:     } else {
1276:       eps->nconv = sr->numEigs;
1277:       eps->its   = ctx->eps->its;
1278:       PetscFree(ctx->inertias);
1279:       PetscFree(ctx->shifts);
1280:       EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1281:     }
1282:   } else {
1283:     if (ctx->npart==1) {
1284:       sr->eigr   = ctx->eps->eigr;
1285:       sr->eigi   = ctx->eps->eigi;
1286:       sr->perm   = ctx->eps->perm;
1287:       sr->errest = ctx->eps->errest;
1288:       sr->V      = ctx->eps->V;
1289:     }
1290:     /* Check that the user did not modify subcomm matrices */
1291:     EPSGetOperators(eps,&A,&B);
1292:     PetscObjectStateGet((PetscObject)A,&Astate);
1293:     PetscObjectGetId((PetscObject)A,&Aid);
1294:     if (B) {
1295:       PetscObjectStateGet((PetscObject)B,&Bstate);
1296:       PetscObjectGetId((PetscObject)B,&Bid);
1297:     }
1298:     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");
1299:     /* Only with eigenvalues present in the interval ...*/
1300:     if (sr->numEigs==0) {
1301:       eps->reason = EPS_CONVERGED_TOL;
1302:       return(0);
1303:     }
1304:     /* Array of pending shifts */
1305:     sr->maxPend = 100; /* Initial size */
1306:     sr->nPend = 0;
1307:     PetscMalloc1(sr->maxPend,&sr->pending);
1308:     PetscLogObjectMemory((PetscObject)eps,sr->maxPend*sizeof(EPS_shift*));
1309:     EPSCreateShift(eps,sr->int0,NULL,NULL);
1310:     /* extract first shift */
1311:     sr->sPrev = NULL;
1312:     sr->sPres = sr->pending[--sr->nPend];
1313:     sr->sPres->inertia = sr->inertia0;
1314:     eps->target = sr->sPres->value;
1315:     sr->s0 = sr->sPres;
1316:     sr->indexEig = 0;
1317:     /* Memory reservation for auxiliary variables */
1318:     lds = PetscMin(eps->mpd,eps->ncv);
1319:     PetscCalloc1(lds*lds,&sr->S);
1320:     PetscMalloc1(eps->ncv,&sr->back);
1321:     PetscLogObjectMemory((PetscObject)eps,(lds*lds+eps->ncv)*sizeof(PetscScalar));
1322:     for (i=0;i<sr->numEigs;i++) {
1323:       sr->eigr[i]   = 0.0;
1324:       sr->eigi[i]   = 0.0;
1325:       sr->errest[i] = 0.0;
1326:       sr->perm[i]   = i;
1327:     }
1328:     /* Vectors for deflation */
1329:     PetscMalloc1(sr->numEigs,&sr->idxDef);
1330:     PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
1331:     sr->indexEig = 0;
1332:     /* Main loop */
1333:     while (sr->sPres) {
1334:       /* Search for deflation */
1335:       EPSLookForDeflation(eps);
1336:       /* KrylovSchur */
1337:       EPSKrylovSchur_Slice(eps);

1339:       EPSStoreEigenpairs(eps);
1340:       /* Select new shift */
1341:       if (!sr->sPres->comp[1]) {
1342:         EPSGetNewShiftValue(eps,1,&newS);
1343:         EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
1344:       }
1345:       if (!sr->sPres->comp[0]) {
1346:         /* Completing earlier interval */
1347:         EPSGetNewShiftValue(eps,0,&newS);
1348:         EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
1349:       }
1350:       /* Preparing for a new search of values */
1351:       EPSExtractShift(eps);
1352:     }

1354:     /* Updating eps values prior to exit */
1355:     PetscFree(sr->S);
1356:     PetscFree(sr->idxDef);
1357:     PetscFree(sr->pending);
1358:     PetscFree(sr->back);
1359:     BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
1360:     BVSetNumConstraints(sr->Vnext,0);
1361:     BVDestroy(&eps->V);
1362:     eps->V      = sr->Vnext;
1363:     eps->nconv  = sr->indexEig;
1364:     eps->reason = EPS_CONVERGED_TOL;
1365:     eps->its    = sr->itsKs;
1366:     eps->nds    = 0;
1367:     if (sr->dir<0) {
1368:       for (i=0;i<eps->nconv/2;i++) {
1369:         ti = sr->perm[i]; sr->perm[i] = sr->perm[eps->nconv-1-i]; sr->perm[eps->nconv-1-i] = ti;
1370:       }
1371:     }
1372:   }
1373:   return(0);
1374: }