Actual source code: ks-slice.c
slepc-3.7.0 2016-05-16
1: /*
3: SLEPc eigensolver: "krylovschur"
5: Method: Krylov-Schur with spectrum slicing for symmetric eigenproblems
7: References:
9: [1] R.G. Grimes et al., "A shifted block Lanczos algorithm for
10: solving sparse symmetric generalized eigenproblems", SIAM J.
11: Matrix Anal. Appl. 15(1):228-272, 1994.
13: [2] C. Campos and J.E. Roman, "Spectrum slicing strategies based
14: on restarted Lanczos methods", Numer. Algor. 60(2):279-295,
15: 2012.
17: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
18: SLEPc - Scalable Library for Eigenvalue Problem Computations
19: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
21: This file is part of SLEPc.
23: SLEPc is free software: you can redistribute it and/or modify it under the
24: terms of version 3 of the GNU Lesser General Public License as published by
25: the Free Software Foundation.
27: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
28: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
29: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
30: more details.
32: You should have received a copy of the GNU Lesser General Public License
33: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
34: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: */
37: #include <slepc/private/epsimpl.h>
38: #include krylovschur.h
40: static PetscBool cited = PETSC_FALSE;
41: static const char citation[] =
42: "@Article{slepc-slice,\n"
43: " author = \"C. Campos and J. E. Roman\",\n"
44: " title = \"Strategies for spectrum slicing based on restarted {Lanczos} methods\",\n"
45: " journal = \"Numer. Algorithms\",\n"
46: " volume = \"60\",\n"
47: " number = \"2\",\n"
48: " pages = \"279--295\",\n"
49: " year = \"2012,\"\n"
50: " doi = \"http://dx.doi.org/10.1007/s11075-012-9564-z\"\n"
51: "}\n";
53: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON
57: static PetscErrorCode EPSSliceResetSR(EPS eps) {
58: PetscErrorCode ierr;
59: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
60: EPS_SR sr=ctx->sr;
61: EPS_shift s;
64: if (sr) {
65: if (ctx->npart>1) {
66: BVDestroy(&sr->V);
67: PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
68: }
69: /* Reviewing list of shifts to free memory */
70: s = sr->s0;
71: if (s) {
72: while (s->neighb[1]) {
73: s = s->neighb[1];
74: PetscFree(s->neighb[0]);
75: }
76: PetscFree(s);
77: }
78: PetscFree(sr);
79: }
80: ctx->sr = NULL;
81: return(0);
82: }
86: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
87: {
88: PetscErrorCode ierr;
89: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
92: if (!ctx->global) return(0);
93: /* Destroy auxiliary EPS */
94: EPSSliceResetSR(ctx->eps);
95: EPSDestroy(&ctx->eps);
96: if (ctx->npart>1) {
97: PetscSubcommDestroy(&ctx->subc);
98: if (ctx->commset) {
99: MPI_Comm_free(&ctx->commrank);
100: ctx->commset = PETSC_FALSE;
101: }
102: }
103: PetscFree(ctx->subintervals);
104: PetscFree(ctx->nconv_loc);
105: EPSSliceResetSR(eps);
106: PetscFree(ctx->inertias);
107: PetscFree(ctx->shifts);
108: if (ctx->npart>1) {
109: ISDestroy(&ctx->isrow);
110: ISDestroy(&ctx->iscol);
111: MatDestroyMatrices(1,&ctx->submata);
112: MatDestroyMatrices(1,&ctx->submatb);
113: }
114: return(0);
115: }
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: STMatCreateVecs(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: }
171: static PetscErrorCode EPSSliceGetEPS(EPS eps)
172: {
173: PetscErrorCode ierr;
174: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
175: BV V;
176: BVType type;
177: PetscReal eta;
178: BVOrthogType orthog_type;
179: BVOrthogRefineType orthog_ref;
180: BVOrthogBlockType ob_type;
181: Mat A,B=NULL,Ar,Br=NULL;
182: PetscInt i;
183: PetscReal h,a,b;
184: PetscMPIInt rank;
185: EPS_SR sr=ctx->sr;
186: PC pc;
187: PCType pctype;
188: KSP ksp;
189: KSPType ksptype;
190: STType sttype;
191: PetscObjectState Astate,Bstate=0;
192: PetscObjectId Aid,Bid=0;
193: const MatSolverPackage stype;
196: EPSGetOperators(eps,&A,&B);
197: if (ctx->npart==1) {
198: if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
199: EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
200: EPSSetOperators(ctx->eps,A,B);
201: a = eps->inta; b = eps->intb;
202: } else {
203: PetscObjectStateGet((PetscObject)A,&Astate);
204: PetscObjectGetId((PetscObject)A,&Aid);
205: if (B) {
206: PetscObjectStateGet((PetscObject)B,&Bstate);
207: PetscObjectGetId((PetscObject)B,&Bid);
208: }
209: if (!ctx->subc) {
210: /* Create context for subcommunicators */
211: PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
212: PetscSubcommSetNumber(ctx->subc,ctx->npart);
213: PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
214: PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));
216: /* Duplicate matrices */
217: MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
218: ctx->Astate = Astate;
219: ctx->Aid = Aid;
220: if (B) {
221: MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
222: ctx->Bstate = Bstate;
223: ctx->Bid = Bid;
224: }
225: } else {
226: if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
227: EPSGetOperators(ctx->eps,&Ar,&Br);
228: MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
229: ctx->Astate = Astate;
230: ctx->Aid = Aid;
231: if (B) {
232: MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
233: ctx->Bstate = Bstate;
234: ctx->Bid = Bid;
235: }
236: EPSSetOperators(ctx->eps,Ar,Br);
237: MatDestroy(&Ar);
238: MatDestroy(&Br);
239: }
240: }
242: /* Determine subintervals */
243: if (!ctx->subintset) { /* uniform distribution if no set by user */
244: if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
245: h = (eps->intb-eps->inta)/ctx->npart;
246: a = eps->inta+ctx->subc->color*h;
247: b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
248: PetscFree(ctx->subintervals);
249: PetscMalloc1(ctx->npart+1,&ctx->subintervals);
250: for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
251: ctx->subintervals[ctx->npart] = eps->intb;
252: } else {
253: a = ctx->subintervals[ctx->subc->color];
254: b = ctx->subintervals[ctx->subc->color+1];
255: }
257: if (!ctx->eps) {
258: /* Create auxiliary EPS */
259: EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
260: EPSSetOperators(ctx->eps,Ar,Br);
261: MatDestroy(&Ar);
262: MatDestroy(&Br);
263: }
265: /* Create subcommunicator grouping processes with same rank */
266: if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
267: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
268: MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
269: ctx->commset = PETSC_TRUE;
270: }
271: EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
273: /* Transfer options for ST, KSP and PC */
274: STGetType(eps->st,&sttype);
275: STSetType(ctx->eps->st,sttype);
276: STGetKSP(eps->st,&ksp);
277: KSPGetType(ksp,&ksptype);
278: KSPGetPC(ksp,&pc);
279: PCGetType(pc,&pctype);
280: PCFactorGetMatSolverPackage(pc,&stype);
281: STGetKSP(ctx->eps->st,&ksp);
282: KSPSetType(ksp,ksptype);
283: KSPGetPC(ksp,&pc);
284: PCSetType(pc,pctype);
285: if (stype) { PCFactorSetMatSolverPackage(pc,stype); }
287: EPSSetConvergenceTest(ctx->eps,eps->conv);
288: EPSSetInterval(ctx->eps,a,b);
289: ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
290: ctx_local->npart = ctx->npart;
291: ctx_local->detect = ctx->detect;
292: ctx_local->global = PETSC_FALSE;
293: ctx_local->eps = eps;
294: ctx_local->subc = ctx->subc;
295: ctx_local->commrank = ctx->commrank;
297: EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
298: EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);
300: /* transfer options from eps->V */
301: EPSGetBV(ctx->eps,&V);
302: if (!eps->V) { EPSGetBV(eps,&eps->V); }
303: if (!((PetscObject)(eps->V))->type_name) {
304: BVSetType(V,BVSVEC);
305: } else {
306: BVGetType(eps->V,&type);
307: BVSetType(V,type);
308: }
309: BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
310: BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
311: ctx->eps->which = eps->which;
312: ctx->eps->max_it = eps->max_it;
313: ctx->eps->tol = eps->tol;
314: ctx->eps->purify = eps->purify;
315: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
316: EPSSetProblemType(ctx->eps,eps->problem_type);
317: EPSSetUp(ctx->eps);
318: ctx->eps->nconv = 0;
319: ctx->eps->its = 0;
320: for (i=0;i<ctx->eps->ncv;i++) {
321: ctx->eps->eigr[i] = 0.0;
322: ctx->eps->eigi[i] = 0.0;
323: ctx->eps->errest[i] = 0.0;
324: }
325: return(0);
326: }
330: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
331: {
333: KSP ksp;
334: PC pc;
335: Mat F;
336: PetscReal nzshift;
339: if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
340: if (inertia) *inertia = eps->n;
341: } else if (shift <= PETSC_MIN_REAL) {
342: if (inertia) *inertia = 0;
343: if (zeros) *zeros = 0;
344: } else {
345: /* If the shift is zero, perturb it to a very small positive value.
346: The goal is that the nonzero pattern is the same in all cases and reuse
347: the symbolic factorizations */
348: nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
349: STSetShift(eps->st,nzshift);
350: STSetUp(eps->st);
351: STGetKSP(eps->st,&ksp);
352: KSPGetPC(ksp,&pc);
353: PCFactorGetMatrix(pc,&F);
354: MatGetInertia(F,inertia,zeros,NULL);
355: }
356: return(0);
357: }
361: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
362: {
363: PetscErrorCode ierr;
364: PetscBool issinv;
365: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
366: EPS_SR sr,sr_loc,sr_glob;
367: PetscInt nEigs,dssz=1,i,zeros=0,off=0;
368: PetscMPIInt nproc,rank,aux;
369: MPI_Request req;
370: Mat A,B=NULL;
373: if (ctx->global) {
374: if (eps->inta==0.0 && eps->intb==0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Must define a computational interval when using EPS_ALL");
375: 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");
376: if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
377: if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
378: if (!((PetscObject)(eps->st))->type_name) { /* default to shift-and-invert */
379: STSetType(eps->st,STSINVERT);
380: }
381: PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
382: if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
383: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2; /* use tighter tolerance */
384: if (!eps->max_it) eps->max_it = 100;
385: if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n); /* nev not set, use default value */
386: 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");
387: }
388: eps->ops->backtransform = NULL;
390: /* create spectrum slicing context and initialize it */
391: EPSSliceResetSR(eps);
392: PetscNewLog(eps,&sr);
393: ctx->sr = sr;
394: sr->itsKs = 0;
395: sr->nleap = 0;
396: sr->nMAXCompl = eps->nev/4;
397: sr->iterCompl = eps->max_it/4;
398: sr->sPres = NULL;
399: sr->nS = 0;
401: if (ctx->npart==1 || ctx->global) {
402: /* check presence of ends and finding direction */
403: if ((eps->inta > PETSC_MIN_REAL && eps->inta != 0.0) || eps->intb >= PETSC_MAX_REAL) {
404: sr->int0 = eps->inta;
405: sr->int1 = eps->intb;
406: sr->dir = 1;
407: if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
408: sr->hasEnd = PETSC_FALSE;
409: } else sr->hasEnd = PETSC_TRUE;
410: } else {
411: sr->int0 = eps->intb;
412: sr->int1 = eps->inta;
413: sr->dir = -1;
414: sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
415: }
416: }
417: if (ctx->global) {
418: /* prevent computation of factorization in global eps */
419: STSetTransform(eps->st,PETSC_FALSE);
420: EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
421: /* create subintervals and initialize auxiliary eps for slicing runs */
422: EPSSliceGetEPS(eps);
423: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
424: if (ctx->npart>1) {
425: if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
426: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
427: if (rank==0) {
428: MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);
429: }
430: MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
431: PetscFree(ctx->nconv_loc);
432: PetscMalloc1(ctx->npart,&ctx->nconv_loc);
433: MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
434: if (sr->dir<0) off = 1;
435: if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
436: PetscMPIIntCast(sr_loc->numEigs,&aux);
437: MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
438: MPI_Allgather(&sr_loc->int0,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
439: } else {
440: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
441: if (!rank) {
442: PetscMPIIntCast(sr_loc->numEigs,&aux);
443: MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
444: MPI_Allgather(&sr_loc->int0,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
445: }
446: PetscMPIIntCast(ctx->npart,&aux);
447: MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
448: MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
449: }
450: nEigs = 0;
451: for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
452: } else {
453: nEigs = sr_loc->numEigs;
454: sr->inertia0 = sr_loc->inertia0;
455: }
456: sr->inertia1 = sr->inertia0+sr->dir*nEigs;
457: sr->numEigs = nEigs;
458: eps->nev = nEigs;
459: eps->ncv = nEigs;
460: eps->mpd = nEigs;
461: } else {
462: ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
463: sr_glob = ctx_glob->sr;
464: if (ctx->npart>1) {
465: sr->dir = sr_glob->dir;
466: sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
467: sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
468: if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
469: else sr->hasEnd = PETSC_TRUE;
470: }
472: /* compute inertia0 */
473: EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
474: if (zeros) { /* error in factorization */
475: if (ctx->npart==1 || ctx_glob->subintset || ((sr->dir>0 && ctx->subc->color==0) || (sr->dir<0 && ctx->subc->color==ctx->npart-1))) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
476: else { /* perturb shift */
477: sr->int0 *= (1.0+SLICE_PTOL);
478: EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
479: if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
480: }
481: }
482: if (ctx->npart>1) {
483: /* inertia1 is received from neighbour */
484: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
485: if (!rank) {
486: if ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1)) { /* send inertia0 to neighbour0 */
487: MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
488: MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
489: }
490: if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
491: MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
492: MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
493: }
494: }
495: if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
496: MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
497: MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
498: } else sr_glob->inertia1 = sr->inertia1;
499: }
501: /* last process in eps comm computes inertia1 */
502: if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
503: EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
504: if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
505: }
507: /* number of eigenvalues in interval */
508: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
509: if (ctx->npart>1) {
510: /* memory allocate for subinterval eigenpairs */
511: EPSSliceAllocateSolution(eps,1);
512: }
513: dssz = eps->ncv+1;
514: }
515: DSSetType(eps->ds,DSHEP);
516: DSSetCompact(eps->ds,PETSC_TRUE);
517: DSAllocate(eps->ds,dssz);
518: /* keep state of subcomm matrices to check that the user does not modify them */
519: EPSGetOperators(eps,&A,&B);
520: PetscObjectStateGet((PetscObject)A,&ctx->Astate);
521: PetscObjectGetId((PetscObject)A,&ctx->Aid);
522: if (B) {
523: PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
524: PetscObjectGetId((PetscObject)B,&ctx->Bid);
525: } else {
526: ctx->Bstate=0;
527: ctx->Bid=0;
528: }
529: return(0);
530: }
534: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
535: {
536: PetscErrorCode ierr;
537: Vec v,vg,v_loc;
538: IS is1,is2;
539: VecScatter vec_sc;
540: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
541: PetscInt nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
542: PetscScalar *array;
543: EPS_SR sr_loc;
544: BV V_loc;
547: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
548: V_loc = sr_loc->V;
550: /* Gather parallel eigenvectors */
551: BVGetColumn(eps->V,0,&v);
552: VecGetOwnershipRange(v,&n0,&m0);
553: BVRestoreColumn(eps->V,0,&v);
554: BVGetColumn(ctx->eps->V,0,&v);
555: VecGetLocalSize(v,&nloc);
556: BVRestoreColumn(ctx->eps->V,0,&v);
557: PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
558: VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
559: idx = -1;
560: for (si=0;si<ctx->npart;si++) {
561: j = 0;
562: for (i=n0;i<m0;i++) {
563: idx1[j] = i;
564: idx2[j++] = i+eps->n*si;
565: }
566: ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
567: ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
568: BVGetColumn(eps->V,0,&v);
569: VecScatterCreate(v,is1,vg,is2,&vec_sc);
570: BVRestoreColumn(eps->V,0,&v);
571: ISDestroy(&is1);
572: ISDestroy(&is2);
573: for (i=0;i<ctx->nconv_loc[si];i++) {
574: BVGetColumn(eps->V,++idx,&v);
575: if (ctx->subc->color==si) {
576: BVGetColumn(V_loc,i,&v_loc);
577: VecGetArray(v_loc,&array);
578: VecPlaceArray(vg,array);
579: }
580: VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
581: VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
582: if (ctx->subc->color==si) {
583: VecResetArray(vg);
584: VecRestoreArray(v_loc,&array);
585: BVRestoreColumn(V_loc,i,&v_loc);
586: }
587: BVRestoreColumn(eps->V,idx,&v);
588: }
589: VecScatterDestroy(&vec_sc);
590: }
591: PetscFree2(idx1,idx2);
592: VecDestroy(&vg);
593: return(0);
594: }
598: /*
599: EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
600: */
601: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
602: {
603: PetscErrorCode ierr;
604: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
607: if (ctx->global && ctx->npart>1) {
608: EPSComputeVectors(ctx->eps);
609: EPSSliceGatherEigenVectors(eps);
610: }
611: return(0);
612: }
614: #define SWAP(a,b,t) {t=a;a=b;b=t;}
618: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
619: {
620: PetscErrorCode ierr;
621: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
622: PetscInt i=0,j,tmpi;
623: PetscReal v,tmpr;
624: EPS_shift s;
627: if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
628: if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
629: if (!ctx->sr->s0) { /* EPSSolve not called yet */
630: *n = 2;
631: } else {
632: *n = 1;
633: s = ctx->sr->s0;
634: while (s) {
635: (*n)++;
636: s = s->neighb[1];
637: }
638: }
639: PetscMalloc1(*n,shifts);
640: PetscMalloc1(*n,inertias);
641: if (!ctx->sr->s0) { /* EPSSolve not called yet */
642: (*shifts)[0] = ctx->sr->int0;
643: (*shifts)[1] = ctx->sr->int1;
644: (*inertias)[0] = ctx->sr->inertia0;
645: (*inertias)[1] = ctx->sr->inertia1;
646: } else {
647: s = ctx->sr->s0;
648: while (s) {
649: (*shifts)[i] = s->value;
650: (*inertias)[i++] = s->inertia;
651: s = s->neighb[1];
652: }
653: (*shifts)[i] = ctx->sr->int1;
654: (*inertias)[i] = ctx->sr->inertia1;
655: }
656: /* remove possible duplicate in last position */
657: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
658: /* sort result */
659: for (i=0;i<*n;i++) {
660: v = (*shifts)[i];
661: for (j=i+1;j<*n;j++) {
662: if (v > (*shifts)[j]) {
663: SWAP((*shifts)[i],(*shifts)[j],tmpr);
664: SWAP((*inertias)[i],(*inertias)[j],tmpi);
665: v = (*shifts)[i];
666: }
667: }
668: }
669: return(0);
670: }
674: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
675: {
676: PetscErrorCode ierr;
677: PetscMPIInt rank,nproc;
678: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
679: PetscInt i,idx,j;
680: PetscInt *perm_loc,off=0,*inertias_loc,ns;
681: PetscScalar *eigr_loc;
682: EPS_SR sr_loc;
683: PetscReal *shifts_loc;
684: PetscMPIInt *disp,*ns_loc,aux;
687: eps->nconv = 0;
688: for (i=0;i<ctx->npart;i++) eps->nconv += ctx->nconv_loc[i];
689: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
691: /* Gather the shifts used and the inertias computed */
692: EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
693: if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
694: if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
695: ns--;
696: for (i=0;i<ns;i++) {
697: inertias_loc[i] = inertias_loc[i+1];
698: shifts_loc[i] = shifts_loc[i+1];
699: }
700: }
701: PetscMalloc1(ctx->npart,&ns_loc);
702: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
703: PetscMPIIntCast(ns,&aux);
704: if (rank==0) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank); }
705: PetscMPIIntCast(ctx->npart,&aux);
706: MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
707: ctx->nshifts = 0;
708: for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
709: PetscFree(ctx->inertias);
710: PetscFree(ctx->shifts);
711: PetscMalloc1(ctx->nshifts,&ctx->inertias);
712: PetscMalloc1(ctx->nshifts,&ctx->shifts);
714: /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
715: eigr_loc = sr_loc->eigr;
716: perm_loc = sr_loc->perm;
717: MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
718: PetscMalloc1(ctx->npart,&disp);
719: disp[0] = 0;
720: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
721: if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
722: PetscMPIIntCast(sr_loc->numEigs,&aux);
723: MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
724: MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
725: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
726: PetscMPIIntCast(ns,&aux);
727: MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
728: MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
729: MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
730: } else { /* subcommunicators with different size */
731: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
732: if (rank==0) {
733: PetscMPIIntCast(sr_loc->numEigs,&aux);
734: MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
735: MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
736: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
737: PetscMPIIntCast(ns,&aux);
738: MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
739: MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
740: MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
741: }
742: PetscMPIIntCast(eps->nconv,&aux);
743: MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
744: MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
745: MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
746: PetscMPIIntCast(ctx->nshifts,&aux);
747: MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
748: MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
749: }
750: /* Update global array eps->perm */
751: idx = ctx->nconv_loc[0];
752: for (i=1;i<ctx->npart;i++) {
753: off += ctx->nconv_loc[i-1];
754: for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
755: }
757: /* Gather parallel eigenvectors */
758: PetscFree(ns_loc);
759: PetscFree(disp);
760: PetscFree(shifts_loc);
761: PetscFree(inertias_loc);
762: return(0);
763: }
765: /*
766: Fills the fields of a shift structure
767: */
770: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
771: {
772: PetscErrorCode ierr;
773: EPS_shift s,*pending2;
774: PetscInt i;
775: EPS_SR sr;
776: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
779: sr = ctx->sr;
780: PetscNewLog(eps,&s);
781: s->value = val;
782: s->neighb[0] = neighb0;
783: if (neighb0) neighb0->neighb[1] = s;
784: s->neighb[1] = neighb1;
785: if (neighb1) neighb1->neighb[0] = s;
786: s->comp[0] = PETSC_FALSE;
787: s->comp[1] = PETSC_FALSE;
788: s->index = -1;
789: s->neigs = 0;
790: s->nconv[0] = s->nconv[1] = 0;
791: s->nsch[0] = s->nsch[1]=0;
792: /* Inserts in the stack of pending shifts */
793: /* If needed, the array is resized */
794: if (sr->nPend >= sr->maxPend) {
795: sr->maxPend *= 2;
796: PetscMalloc1(sr->maxPend,&pending2);
797: PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
798: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
799: PetscFree(sr->pending);
800: sr->pending = pending2;
801: }
802: sr->pending[sr->nPend++]=s;
803: return(0);
804: }
806: /* Prepare for Rational Krylov update */
809: static PetscErrorCode EPSPrepareRational(EPS eps)
810: {
811: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
812: PetscErrorCode ierr;
813: PetscInt dir,i,k,ld,nv;
814: PetscScalar *A;
815: EPS_SR sr = ctx->sr;
816: Vec v;
819: DSGetLeadingDimension(eps->ds,&ld);
820: dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
821: dir*=sr->dir;
822: k = 0;
823: for (i=0;i<sr->nS;i++) {
824: if (dir*PetscRealPart(sr->S[i])>0.0) {
825: sr->S[k] = sr->S[i];
826: sr->S[sr->nS+k] = sr->S[sr->nS+i];
827: BVGetColumn(sr->Vnext,k,&v);
828: BVCopyVec(eps->V,eps->nconv+i,v);
829: BVRestoreColumn(sr->Vnext,k,&v);
830: k++;
831: if (k>=sr->nS/2)break;
832: }
833: }
834: /* Copy to DS */
835: DSGetArray(eps->ds,DS_MAT_A,&A);
836: PetscMemzero(A,ld*ld*sizeof(PetscScalar));
837: for (i=0;i<k;i++) {
838: A[i*(1+ld)] = sr->S[i];
839: A[k+i*ld] = sr->S[sr->nS+i];
840: }
841: sr->nS = k;
842: DSRestoreArray(eps->ds,DS_MAT_A,&A);
843: DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
844: DSSetDimensions(eps->ds,nv,0,0,k);
845: /* Append u to V */
846: BVGetColumn(sr->Vnext,sr->nS,&v);
847: BVCopyVec(eps->V,sr->nv,v);
848: BVRestoreColumn(sr->Vnext,sr->nS,&v);
849: return(0);
850: }
852: /* Provides next shift to be computed */
855: static PetscErrorCode EPSExtractShift(EPS eps)
856: {
857: PetscErrorCode ierr;
858: PetscInt iner,zeros=0;
859: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
860: EPS_SR sr;
861: PetscReal newShift;
862: EPS_shift sPres;
865: sr = ctx->sr;
866: if (sr->nPend > 0) {
867: sr->sPrev = sr->sPres;
868: sr->sPres = sr->pending[--sr->nPend];
869: sPres = sr->sPres;
870: EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
871: if (zeros) {
872: newShift = sPres->value*(1.0+SLICE_PTOL);
873: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
874: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
875: EPSSliceGetInertia(eps,newShift,&iner,&zeros);
876: if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
877: sPres->value = newShift;
878: }
879: sr->sPres->inertia = iner;
880: eps->target = sr->sPres->value;
881: eps->reason = EPS_CONVERGED_ITERATING;
882: eps->its = 0;
883: } else sr->sPres = NULL;
884: return(0);
885: }
887: /*
888: Symmetric KrylovSchur adapted to spectrum slicing:
889: Allows searching an specific amount of eigenvalues in the subintervals left and right.
890: Returns whether the search has succeeded
891: */
894: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
895: {
896: PetscErrorCode ierr;
897: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
898: PetscInt i,conv,k,l,ld,nv,*iwork,j,p;
899: Mat U;
900: PetscScalar *Q,*A,rtmp;
901: PetscReal *a,*b,beta;
902: PetscBool breakdown;
903: PetscInt count0,count1;
904: PetscReal lambda;
905: EPS_shift sPres;
906: PetscBool complIterating;
907: PetscBool sch0,sch1;
908: PetscInt iterCompl=0,n0,n1;
909: EPS_SR sr = ctx->sr;
912: /* Spectrum slicing data */
913: sPres = sr->sPres;
914: complIterating =PETSC_FALSE;
915: sch1 = sch0 = PETSC_TRUE;
916: DSGetLeadingDimension(eps->ds,&ld);
917: PetscMalloc1(2*ld,&iwork);
918: count0=0;count1=0; /* Found on both sides */
919: if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
920: /* Rational Krylov */
921: DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
922: DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
923: DSSetDimensions(eps->ds,l+1,0,0,0);
924: BVSetActiveColumns(eps->V,0,l+1);
925: DSGetMat(eps->ds,DS_MAT_Q,&U);
926: BVMultInPlace(eps->V,U,0,l+1);
927: MatDestroy(&U);
928: } else {
929: /* Get the starting Lanczos vector */
930: EPSGetStartVector(eps,0,NULL);
931: l = 0;
932: }
933: /* Restart loop */
934: while (eps->reason == EPS_CONVERGED_ITERATING) {
935: eps->its++; sr->itsKs++;
936: /* Compute an nv-step Lanczos factorization */
937: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
938: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
939: b = a + ld;
940: EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
941: sr->nv = nv;
942: beta = b[nv-1];
943: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
944: DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
945: if (l==0) {
946: DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
947: } else {
948: DSSetState(eps->ds,DS_STATE_RAW);
949: }
950: BVSetActiveColumns(eps->V,eps->nconv,nv);
952: /* Solve projected problem and compute residual norm estimates */
953: if (eps->its == 1 && l > 0) {/* After rational update */
954: DSGetArray(eps->ds,DS_MAT_A,&A);
955: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
956: b = a + ld;
957: k = eps->nconv+l;
958: A[k*ld+k-1] = A[(k-1)*ld+k];
959: A[k*ld+k] = a[k];
960: for (j=k+1; j< nv; j++) {
961: A[j*ld+j] = a[j];
962: A[j*ld+j-1] = b[j-1] ;
963: A[(j-1)*ld+j] = b[j-1];
964: }
965: DSRestoreArray(eps->ds,DS_MAT_A,&A);
966: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
967: DSSolve(eps->ds,eps->eigr,NULL);
968: DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
969: DSSetCompact(eps->ds,PETSC_TRUE);
970: } else { /* Restart */
971: DSSolve(eps->ds,eps->eigr,NULL);
972: DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
973: }
974: /* Residual */
975: EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);
977: if (ctx->lock) {
978: /* Check convergence */
979: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
980: b = a + ld;
981: conv = 0;
982: j = k = eps->nconv;
983: for (i=eps->nconv;i<nv;i++) if (eps->errest[i] < eps->tol) conv++;
984: for (i=eps->nconv;i<nv;i++) {
985: if (eps->errest[i] < eps->tol) {
986: iwork[j++]=i;
987: } else iwork[conv+k++]=i;
988: }
989: for (i=eps->nconv;i<nv;i++) {
990: a[i]=PetscRealPart(eps->eigr[i]);
991: b[i]=eps->errest[i];
992: }
993: for (i=eps->nconv;i<nv;i++) {
994: eps->eigr[i] = a[iwork[i]];
995: eps->errest[i] = b[iwork[i]];
996: }
997: for (i=eps->nconv;i<nv;i++) {
998: a[i]=PetscRealPart(eps->eigr[i]);
999: b[i]=eps->errest[i];
1000: }
1001: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
1002: DSGetArray(eps->ds,DS_MAT_Q,&Q);
1003: for (i=eps->nconv;i<nv;i++) {
1004: p=iwork[i];
1005: if (p!=i) {
1006: j=i+1;
1007: while (iwork[j]!=i) j++;
1008: iwork[j]=p;iwork[i]=i;
1009: for (k=0;k<nv;k++) {
1010: rtmp=Q[k+p*ld];Q[k+p*ld]=Q[k+i*ld];Q[k+i*ld]=rtmp;
1011: }
1012: }
1013: }
1014: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1015: k=eps->nconv+conv;
1016: }
1018: /* Checking values obtained for completing */
1019: for (i=0;i<k;i++) {
1020: sr->back[i]=eps->eigr[i];
1021: }
1022: STBackTransform(eps->st,k,sr->back,eps->eigi);
1023: count0=count1=0;
1024: for (i=0;i<k;i++) {
1025: lambda = PetscRealPart(sr->back[i]);
1026: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
1027: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
1028: }
1029: if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
1030: else {
1031: /* Checks completion */
1032: if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
1033: eps->reason = EPS_CONVERGED_TOL;
1034: } else {
1035: if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
1036: if (complIterating) {
1037: if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
1038: } else if (k >= eps->nev) {
1039: n0 = sPres->nsch[0]-count0;
1040: n1 = sPres->nsch[1]-count1;
1041: if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
1042: /* Iterating for completion*/
1043: complIterating = PETSC_TRUE;
1044: if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
1045: if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
1046: iterCompl = sr->iterCompl;
1047: } else eps->reason = EPS_CONVERGED_TOL;
1048: }
1049: }
1050: }
1051: /* Update l */
1052: if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
1053: else l = 0;
1054: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1055: if (breakdown) l=0;
1057: if (eps->reason == EPS_CONVERGED_ITERATING) {
1058: if (breakdown) {
1059: /* Start a new Lanczos factorization */
1060: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
1061: EPSGetStartVector(eps,k,&breakdown);
1062: if (breakdown) {
1063: eps->reason = EPS_DIVERGED_BREAKDOWN;
1064: PetscInfo(eps,"Unable to generate more start vectors\n");
1065: }
1066: } else {
1067: /* Prepare the Rayleigh quotient for restart */
1068: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
1069: DSGetArray(eps->ds,DS_MAT_Q,&Q);
1070: b = a + ld;
1071: for (i=k;i<k+l;i++) {
1072: a[i] = PetscRealPart(eps->eigr[i]);
1073: b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
1074: }
1075: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
1076: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1077: }
1078: }
1079: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
1080: DSGetMat(eps->ds,DS_MAT_Q,&U);
1081: BVMultInPlace(eps->V,U,eps->nconv,k+l);
1082: MatDestroy(&U);
1084: /* Normalize u and append it to V */
1085: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
1086: BVCopyColumn(eps->V,nv,k+l);
1087: }
1088: eps->nconv = k;
1089: if (eps->reason != EPS_CONVERGED_ITERATING) {
1090: /* Store approximated values for next shift */
1091: DSGetArray(eps->ds,DS_MAT_Q,&Q);
1092: sr->nS = l;
1093: for (i=0;i<l;i++) {
1094: sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
1095: sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
1096: }
1097: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1098: }
1099: }
1100: /* Check for completion */
1101: for (i=0;i< eps->nconv; i++) {
1102: if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
1103: else sPres->nconv[0]++;
1104: }
1105: sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
1106: sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
1107: 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()");
1108: PetscFree(iwork);
1109: return(0);
1110: }
1112: /*
1113: Obtains value of subsequent shift
1114: */
1117: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
1118: {
1119: PetscReal lambda,d_prev;
1120: PetscInt i,idxP;
1121: EPS_SR sr;
1122: EPS_shift sPres,s;
1123: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1126: sr = ctx->sr;
1127: sPres = sr->sPres;
1128: if (sPres->neighb[side]) {
1129: /* Completing a previous interval */
1130: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
1131: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
1132: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
1133: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
1134: } else { /* (Only for side=1). Creating a new interval. */
1135: if (sPres->neigs==0) {/* No value has been accepted*/
1136: if (sPres->neighb[0]) {
1137: /* Multiplying by 10 the previous distance */
1138: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
1139: sr->nleap++;
1140: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
1141: if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
1142: } else { /* First shift */
1143: if (eps->nconv != 0) {
1144: /* Unaccepted values give information for next shift */
1145: idxP=0;/* Number of values left from shift */
1146: for (i=0;i<eps->nconv;i++) {
1147: lambda = PetscRealPart(sr->eigr[i]);
1148: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
1149: else break;
1150: }
1151: /* Avoiding subtraction of eigenvalues (might be the same).*/
1152: if (idxP>0) {
1153: d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[0]))/(idxP+0.3);
1154: } else {
1155: d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[eps->nconv-1]))/(eps->nconv+0.3);
1156: }
1157: *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
1158: } else { /* No values found, no information for next shift */
1159: SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
1160: }
1161: }
1162: } else { /* Accepted values found */
1163: sr->nleap = 0;
1164: /* Average distance of values in previous subinterval */
1165: s = sPres->neighb[0];
1166: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
1167: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
1168: }
1169: if (s) {
1170: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
1171: } else { /* First shift. Average distance obtained with values in this shift */
1172: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
1173: 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)) {
1174: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
1175: } else {
1176: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
1177: }
1178: }
1179: /* Average distance is used for next shift by adding it to value on the right or to shift */
1180: if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
1181: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
1182: } else { /* Last accepted value is on the left of shift. Adding to shift */
1183: *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
1184: }
1185: }
1186: /* End of interval can not be surpassed */
1187: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
1188: }/* of neighb[side]==null */
1189: return(0);
1190: }
1192: /*
1193: Function for sorting an array of real values
1194: */
1197: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
1198: {
1199: PetscReal re;
1200: PetscInt i,j,tmp;
1203: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
1204: /* Insertion sort */
1205: for (i=1;i<nr;i++) {
1206: re = PetscRealPart(r[perm[i]]);
1207: j = i-1;
1208: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
1209: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
1210: }
1211: }
1212: return(0);
1213: }
1215: /* Stores the pairs obtained since the last shift in the global arrays */
1218: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
1219: {
1220: PetscErrorCode ierr;
1221: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1222: PetscReal lambda,err,norm;
1223: PetscInt i,count;
1224: PetscBool iscayley;
1225: EPS_SR sr = ctx->sr;
1226: EPS_shift sPres;
1227: Vec v,w;
1230: sPres = sr->sPres;
1231: sPres->index = sr->indexEig;
1232: count = sr->indexEig;
1233: /* Back-transform */
1234: STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
1235: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
1236: /* Sort eigenvalues */
1237: sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
1238: /* Values stored in global array */
1239: for (i=0;i<eps->nconv;i++) {
1240: lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
1241: err = eps->errest[eps->perm[i]];
1243: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
1244: if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
1245: sr->eigr[count] = lambda;
1246: sr->errest[count] = err;
1247: /* Explicit purification */
1248: if (eps->purify) {
1249: BVGetColumn(sr->V,count,&v);
1250: BVGetColumn(eps->V,eps->perm[i],&w);
1251: STApply(eps->st,w,v);
1252: BVRestoreColumn(sr->V,count,&v);
1253: BVRestoreColumn(eps->V,eps->perm[i],&w);
1254: BVNormColumn(sr->V,count,NORM_2,&norm);
1255: BVScaleColumn(sr->V,count,1.0/norm);
1256: } else {
1257: BVGetColumn(eps->V,eps->perm[i],&w);
1258: BVInsertVec(sr->V,count,w);
1259: BVRestoreColumn(eps->V,eps->perm[i],&w);
1260: BVNormColumn(sr->V,count,NORM_2,&norm);
1261: BVScaleColumn(sr->V,count,1.0/norm);
1262: }
1263: count++;
1264: }
1265: }
1266: sPres->neigs = count - sr->indexEig;
1267: sr->indexEig = count;
1268: /* Global ordering array updating */
1269: sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
1270: return(0);
1271: }
1275: static PetscErrorCode EPSLookForDeflation(EPS eps)
1276: {
1277: PetscErrorCode ierr;
1278: PetscReal val;
1279: PetscInt i,count0=0,count1=0;
1280: EPS_shift sPres;
1281: PetscInt ini,fin,k,idx0,idx1;
1282: EPS_SR sr;
1283: Vec v;
1284: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1287: sr = ctx->sr;
1288: sPres = sr->sPres;
1290: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
1291: else ini = 0;
1292: fin = sr->indexEig;
1293: /* Selection of ends for searching new values */
1294: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
1295: else sPres->ext[0] = sPres->neighb[0]->value;
1296: if (!sPres->neighb[1]) {
1297: if (sr->hasEnd) sPres->ext[1] = sr->int1;
1298: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
1299: } else sPres->ext[1] = sPres->neighb[1]->value;
1300: /* Selection of values between right and left ends */
1301: for (i=ini;i<fin;i++) {
1302: val=PetscRealPart(sr->eigr[sr->perm[i]]);
1303: /* Values to the right of left shift */
1304: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
1305: if ((sr->dir)*(val - sPres->value) < 0) count0++;
1306: else count1++;
1307: } else break;
1308: }
1309: /* The number of values on each side are found */
1310: if (sPres->neighb[0]) {
1311: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
1312: if (sPres->nsch[0]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
1313: } else sPres->nsch[0] = 0;
1315: if (sPres->neighb[1]) {
1316: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1317: if (sPres->nsch[1]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
1318: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
1320: /* Completing vector of indexes for deflation */
1321: idx0 = ini;
1322: idx1 = ini+count0+count1;
1323: k=0;
1324: for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
1325: BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
1326: BVSetNumConstraints(sr->Vnext,k);
1327: for (i=0;i<k;i++) {
1328: BVGetColumn(sr->Vnext,-i-1,&v);
1329: BVCopyVec(sr->V,sr->idxDef[i],v);
1330: BVRestoreColumn(sr->Vnext,-i-1,&v);
1331: }
1333: /* For rational Krylov */
1334: if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
1335: EPSPrepareRational(eps);
1336: }
1337: eps->nconv = 0;
1338: /* Get rid of temporary Vnext */
1339: BVDestroy(&eps->V);
1340: eps->V = sr->Vnext;
1341: sr->Vnext = NULL;
1342: return(0);
1343: }
1347: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
1348: {
1349: PetscErrorCode ierr;
1350: PetscInt i,lds;
1351: PetscReal newS;
1352: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1353: EPS_SR sr=ctx->sr;
1354: Mat A,B=NULL;
1355: PetscObjectState Astate,Bstate=0;
1356: PetscObjectId Aid,Bid=0;
1359: PetscCitationsRegister(citation,&cited);
1360: if (ctx->global) {
1361: EPSSolve_KrylovSchur_Slice(ctx->eps);
1362: ctx->eps->state = EPS_STATE_SOLVED;
1363: eps->reason = EPS_CONVERGED_TOL;
1364: if (ctx->npart>1) {
1365: /* Gather solution from subsolvers */
1366: EPSSliceGatherSolution(eps);
1367: } else {
1368: eps->nconv = sr->numEigs;
1369: eps->its = ctx->eps->its;
1370: PetscFree(ctx->inertias);
1371: PetscFree(ctx->shifts);
1372: EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1373: }
1374: } else {
1375: if (ctx->npart==1) {
1376: sr->eigr = ctx->eps->eigr;
1377: sr->eigi = ctx->eps->eigi;
1378: sr->perm = ctx->eps->perm;
1379: sr->errest = ctx->eps->errest;
1380: sr->V = ctx->eps->V;
1381: }
1382: /* Check that the user did not modify subcomm matrices */
1383: EPSGetOperators(eps,&A,&B);
1384: PetscObjectStateGet((PetscObject)A,&Astate);
1385: PetscObjectGetId((PetscObject)A,&Aid);
1386: if (B) {
1387: PetscObjectStateGet((PetscObject)B,&Bstate);
1388: PetscObjectGetId((PetscObject)B,&Bid);
1389: }
1390: 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");
1391: /* Only with eigenvalues present in the interval ...*/
1392: if (sr->numEigs==0) {
1393: eps->reason = EPS_CONVERGED_TOL;
1394: return(0);
1395: }
1396: /* Array of pending shifts */
1397: sr->maxPend = 100; /* Initial size */
1398: sr->nPend = 0;
1399: PetscMalloc1(sr->maxPend,&sr->pending);
1400: PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
1401: EPSCreateShift(eps,sr->int0,NULL,NULL);
1402: /* extract first shift */
1403: sr->sPrev = NULL;
1404: sr->sPres = sr->pending[--sr->nPend];
1405: sr->sPres->inertia = sr->inertia0;
1406: eps->target = sr->sPres->value;
1407: sr->s0 = sr->sPres;
1408: sr->indexEig = 0;
1409: /* Memory reservation for auxiliary variables */
1410: lds = PetscMin(eps->mpd,eps->ncv);
1411: PetscCalloc1(lds*lds,&sr->S);
1412: PetscMalloc1(eps->ncv,&sr->back);
1413: PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
1414: for (i=0;i<sr->numEigs;i++) {
1415: sr->eigr[i] = 0.0;
1416: sr->eigi[i] = 0.0;
1417: sr->errest[i] = 0.0;
1418: sr->perm[i] = i;
1419: }
1420: /* Vectors for deflation */
1421: PetscMalloc1(sr->numEigs,&sr->idxDef);
1422: PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
1423: sr->indexEig = 0;
1424: /* Main loop */
1425: while (sr->sPres) {
1426: /* Search for deflation */
1427: EPSLookForDeflation(eps);
1428: /* KrylovSchur */
1429: EPSKrylovSchur_Slice(eps);
1431: EPSStoreEigenpairs(eps);
1432: /* Select new shift */
1433: if (!sr->sPres->comp[1]) {
1434: EPSGetNewShiftValue(eps,1,&newS);
1435: EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
1436: }
1437: if (!sr->sPres->comp[0]) {
1438: /* Completing earlier interval */
1439: EPSGetNewShiftValue(eps,0,&newS);
1440: EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
1441: }
1442: /* Preparing for a new search of values */
1443: EPSExtractShift(eps);
1444: }
1446: /* Updating eps values prior to exit */
1447: PetscFree(sr->S);
1448: PetscFree(sr->idxDef);
1449: PetscFree(sr->pending);
1450: PetscFree(sr->back);
1451: BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
1452: BVSetNumConstraints(sr->Vnext,0);
1453: BVDestroy(&eps->V);
1454: eps->V = sr->Vnext;
1455: eps->nconv = sr->indexEig;
1456: eps->reason = EPS_CONVERGED_TOL;
1457: eps->its = sr->itsKs;
1458: eps->nds = 0;
1459: }
1460: return(0);
1461: }