Actual source code: ks-slice.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: SLEPc 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: /* Destroy auxiliary EPS */
85: EPSSliceResetSR(ctx->eps);
86: EPSDestroy(&ctx->eps);
87: if (ctx->npart>1) {
88: PetscSubcommDestroy(&ctx->subc);
89: if (ctx->commset) {
90: MPI_Comm_free(&ctx->commrank);
91: ctx->commset = PETSC_FALSE;
92: }
93: }
94: PetscFree(ctx->subintervals);
95: PetscFree(ctx->nconv_loc);
96: EPSSliceResetSR(eps);
97: PetscFree(ctx->inertias);
98: PetscFree(ctx->shifts);
99: if (ctx->npart>1) {
100: ISDestroy(&ctx->isrow);
101: ISDestroy(&ctx->iscol);
102: MatDestroyMatrices(1,&ctx->submata);
103: MatDestroyMatrices(1,&ctx->submatb);
104: }
105: return(0);
106: }
108: /*
109: EPSSliceAllocateSolution - Allocate memory storage for common variables such
110: as eigenvalues and eigenvectors. The argument extra is used for methods
111: that require a working basis slightly larger than ncv.
112: */
113: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
114: {
115: PetscErrorCode ierr;
116: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
117: PetscReal eta;
118: PetscInt k;
119: PetscLogDouble cnt;
120: BVType type;
121: BVOrthogType orthog_type;
122: BVOrthogRefineType orthog_ref;
123: BVOrthogBlockType ob_type;
124: Mat matrix;
125: Vec t;
126: EPS_SR sr = ctx->sr;
129: /* allocate space for eigenvalues and friends */
130: k = PetscMax(1,sr->numEigs);
131: PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
132: PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
133: cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
134: PetscLogObjectMemory((PetscObject)eps,cnt);
136: /* allocate sr->V and transfer options from eps->V */
137: BVDestroy(&sr->V);
138: BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
139: PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
140: if (!eps->V) { EPSGetBV(eps,&eps->V); }
141: if (!((PetscObject)(eps->V))->type_name) {
142: BVSetType(sr->V,BVSVEC);
143: } else {
144: BVGetType(eps->V,&type);
145: BVSetType(sr->V,type);
146: }
147: STMatCreateVecsEmpty(eps->st,&t,NULL);
148: BVSetSizesFromVec(sr->V,t,k);
149: VecDestroy(&t);
150: EPS_SetInnerProduct(eps);
151: BVGetMatrix(eps->V,&matrix,NULL);
152: BVSetMatrix(sr->V,matrix,PETSC_FALSE);
153: BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
154: BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
155: return(0);
156: }
158: static PetscErrorCode EPSSliceGetEPS(EPS eps)
159: {
160: PetscErrorCode ierr;
161: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
162: BV V;
163: BVType type;
164: PetscReal eta;
165: BVOrthogType orthog_type;
166: BVOrthogRefineType orthog_ref;
167: BVOrthogBlockType ob_type;
168: Mat A,B=NULL,Ar=NULL,Br=NULL;
169: PetscInt i;
170: PetscReal h,a,b,zero;
171: PetscMPIInt rank;
172: EPS_SR sr=ctx->sr;
173: PC pc;
174: PCType pctype;
175: KSP ksp;
176: KSPType ksptype;
177: STType sttype;
178: PetscObjectState Astate,Bstate=0;
179: PetscObjectId Aid,Bid=0;
180: MatSolverType stype;
183: EPSGetOperators(eps,&A,&B);
184: if (ctx->npart==1) {
185: if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
186: EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
187: EPSSetOperators(ctx->eps,A,B);
188: a = eps->inta; b = eps->intb;
189: } else {
190: PetscObjectStateGet((PetscObject)A,&Astate);
191: PetscObjectGetId((PetscObject)A,&Aid);
192: if (B) {
193: PetscObjectStateGet((PetscObject)B,&Bstate);
194: PetscObjectGetId((PetscObject)B,&Bid);
195: }
196: if (!ctx->subc) {
197: /* Create context for subcommunicators */
198: PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
199: PetscSubcommSetNumber(ctx->subc,ctx->npart);
200: PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
201: PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));
203: /* Duplicate matrices */
204: MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
205: ctx->Astate = Astate;
206: ctx->Aid = Aid;
207: if (B) {
208: MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
209: ctx->Bstate = Bstate;
210: ctx->Bid = Bid;
211: }
212: } else {
213: if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
214: EPSGetOperators(ctx->eps,&Ar,&Br);
215: MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
216: ctx->Astate = Astate;
217: ctx->Aid = Aid;
218: if (B) {
219: MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
220: ctx->Bstate = Bstate;
221: ctx->Bid = Bid;
222: }
223: EPSSetOperators(ctx->eps,Ar,Br);
224: MatDestroy(&Ar);
225: MatDestroy(&Br);
226: }
227: }
229: /* Determine subintervals */
230: if (!ctx->subintset) { /* uniform distribution if no set by user */
231: if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
232: h = (eps->intb-eps->inta)/ctx->npart;
233: a = eps->inta+ctx->subc->color*h;
234: b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
235: PetscFree(ctx->subintervals);
236: PetscMalloc1(ctx->npart+1,&ctx->subintervals);
237: for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
238: ctx->subintervals[ctx->npart] = eps->intb;
239: } else {
240: a = ctx->subintervals[ctx->subc->color];
241: b = ctx->subintervals[ctx->subc->color+1];
242: }
244: if (!ctx->eps) {
245: /* Create auxiliary EPS */
246: EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
247: EPSSetOperators(ctx->eps,Ar,Br);
248: MatDestroy(&Ar);
249: MatDestroy(&Br);
250: }
252: /* Create subcommunicator grouping processes with same rank */
253: if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
254: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
255: MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
256: ctx->commset = PETSC_TRUE;
257: }
258: EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
260: /* Transfer options for ST, KSP and PC */
261: STGetType(eps->st,&sttype);
262: STSetType(ctx->eps->st,sttype);
263: STGetKSP(eps->st,&ksp);
264: KSPGetType(ksp,&ksptype);
265: KSPGetPC(ksp,&pc);
266: PCGetType(pc,&pctype);
267: PCFactorGetMatSolverType(pc,&stype);
268: PCFactorGetZeroPivot(pc,&zero);
269: STGetKSP(ctx->eps->st,&ksp);
270: KSPSetType(ksp,ksptype);
271: KSPGetPC(ksp,&pc);
272: PCSetType(pc,pctype);
273: PCFactorSetZeroPivot(pc,zero);
274: if (stype) { PCFactorSetMatSolverType(pc,stype); }
276: EPSSetConvergenceTest(ctx->eps,eps->conv);
277: EPSSetInterval(ctx->eps,a,b);
278: ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
279: ctx_local->npart = ctx->npart;
280: ctx_local->detect = ctx->detect;
281: ctx_local->global = PETSC_FALSE;
282: ctx_local->eps = eps;
283: ctx_local->subc = ctx->subc;
284: ctx_local->commrank = ctx->commrank;
286: EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
287: EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);
289: /* transfer options from eps->V */
290: EPSGetBV(ctx->eps,&V);
291: if (!eps->V) { EPSGetBV(eps,&eps->V); }
292: if (!((PetscObject)(eps->V))->type_name) {
293: BVSetType(V,BVSVEC);
294: } else {
295: BVGetType(eps->V,&type);
296: BVSetType(V,type);
297: }
298: BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
299: BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
300: ctx->eps->which = eps->which;
301: ctx->eps->max_it = eps->max_it;
302: ctx->eps->tol = eps->tol;
303: ctx->eps->purify = eps->purify;
304: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
305: EPSSetProblemType(ctx->eps,eps->problem_type);
306: EPSSetUp(ctx->eps);
307: ctx->eps->nconv = 0;
308: ctx->eps->its = 0;
309: for (i=0;i<ctx->eps->ncv;i++) {
310: ctx->eps->eigr[i] = 0.0;
311: ctx->eps->eigi[i] = 0.0;
312: ctx->eps->errest[i] = 0.0;
313: }
314: return(0);
315: }
317: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
318: {
320: KSP ksp;
321: PC pc;
322: Mat F;
323: PetscReal nzshift;
326: if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
327: if (inertia) *inertia = eps->n;
328: } else if (shift <= PETSC_MIN_REAL) {
329: if (inertia) *inertia = 0;
330: if (zeros) *zeros = 0;
331: } else {
332: /* If the shift is zero, perturb it to a very small positive value.
333: The goal is that the nonzero pattern is the same in all cases and reuse
334: the symbolic factorizations */
335: nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
336: STSetShift(eps->st,nzshift);
337: STSetUp(eps->st);
338: STGetKSP(eps->st,&ksp);
339: KSPGetPC(ksp,&pc);
340: PCFactorGetMatrix(pc,&F);
341: MatGetInertia(F,inertia,zeros,NULL);
342: }
343: return(0);
344: }
346: /*
347: Dummy backtransform operation
348: */
349: static PetscErrorCode EPSBackTransform_Skip(EPS eps)
350: {
352: return(0);
353: }
355: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
356: {
357: PetscErrorCode ierr;
358: PetscBool issinv;
359: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
360: EPS_SR sr,sr_loc,sr_glob;
361: PetscInt nEigs,dssz=1,i,zeros=0,off=0,method;
362: PetscMPIInt nproc,rank=0,aux;
363: PetscReal r;
364: MPI_Request req;
365: Mat A,B=NULL;
366: SlepcSC sc;
367: PetscInt flg=0;
368: DSParallelType ptype;
371: if (ctx->global) {
372: 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");
373: if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
374: if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
375: PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
376: if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
377: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2; /* use tighter tolerance */
378: if (!eps->max_it) eps->max_it = 100;
379: if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n); /* nev not set, use default value */
380: 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");
381: }
382: eps->ops->backtransform = EPSBackTransform_Skip;
384: /* create spectrum slicing context and initialize it */
385: EPSSliceResetSR(eps);
386: PetscNewLog(eps,&sr);
387: ctx->sr = sr;
388: sr->itsKs = 0;
389: sr->nleap = 0;
390: sr->nMAXCompl = eps->nev/4;
391: sr->iterCompl = eps->max_it/4;
392: sr->sPres = NULL;
393: sr->nS = 0;
395: if (ctx->npart==1 || ctx->global) {
396: /* check presence of ends and finding direction */
397: if ((eps->inta > PETSC_MIN_REAL && !(ctx->subintervals && ctx->subintervals[0]==ctx->subintervals[1])) || eps->intb >= PETSC_MAX_REAL) {
398: sr->int0 = eps->inta;
399: sr->int1 = eps->intb;
400: sr->dir = 1;
401: if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
402: sr->hasEnd = PETSC_FALSE;
403: } else sr->hasEnd = PETSC_TRUE;
404: } else {
405: sr->int0 = eps->intb;
406: sr->int1 = eps->inta;
407: sr->dir = -1;
408: sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
409: }
410: }
411: if (ctx->global) {
412: /* prevent computation of factorization in global eps */
413: STSetTransform(eps->st,PETSC_FALSE);
414: EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
415: /* create subintervals and initialize auxiliary eps for slicing runs */
416: EPSSliceGetEPS(eps);
417: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
418: if (ctx->npart>1) {
419: if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
420: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
421: if (!rank) {
422: MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);
423: }
424: MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
425: PetscFree(ctx->nconv_loc);
426: PetscMalloc1(ctx->npart,&ctx->nconv_loc);
427: MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
428: if (sr->dir<0) off = 1;
429: if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
430: PetscMPIIntCast(sr_loc->numEigs,&aux);
431: MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
432: MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
433: } else {
434: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
435: if (!rank) {
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->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
439: }
440: PetscMPIIntCast(ctx->npart,&aux);
441: MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
442: MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
443: }
444: nEigs = 0;
445: for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
446: } else {
447: nEigs = sr_loc->numEigs;
448: sr->inertia0 = sr_loc->inertia0;
449: }
450: sr->inertia1 = sr->inertia0+sr->dir*nEigs;
451: sr->numEigs = nEigs;
452: eps->nev = nEigs;
453: eps->ncv = nEigs;
454: eps->mpd = nEigs;
455: } else {
456: ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
457: sr_glob = ctx_glob->sr;
458: if (ctx->npart>1) {
459: sr->dir = sr_glob->dir;
460: sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
461: sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
462: if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
463: else sr->hasEnd = PETSC_TRUE;
464: }
466: /* compute inertia0 */
467: EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
468: PetscOptionsGetInt(NULL,NULL,"-eps_krylovschur_hiteigenvalue",&flg,NULL);
469: if (zeros) { /* error in factorization */
470: 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");
471: else if(ctx_glob->subintset && !flg) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
472: else {
473: if (flg==1) { /* idle subgroup */
474: sr->inertia0 = -1;
475: } else { /* perturb shift */
476: sr->int0 *= (1.0+SLICE_PTOL);
477: EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
478: if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
479: }
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->inertia0!=-1 && ((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: if ( sr->inertia0==-1 && !(sr->dir>0 && ctx->subc->color==ctx->npart-1) && !(sr->dir<0 && ctx->subc->color==0)) {
495: sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
496: MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
497: MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
498: }
499: }
500: if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
501: MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
502: MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
503: } else sr_glob->inertia1 = sr->inertia1;
504: }
506: /* last process in eps comm computes inertia1 */
507: if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
508: EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
509: if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
510: if (!rank && sr->inertia0==-1) {
511: sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
512: MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
513: MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
514: }
515: if (sr->hasEnd) {
516: sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
517: i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
518: }
519: }
521: /* number of eigenvalues in interval */
522: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
523: if (ctx->npart>1) {
524: /* memory allocate for subinterval eigenpairs */
525: EPSSliceAllocateSolution(eps,1);
526: }
527: dssz = eps->ncv+1;
528: if (sr->numEigs>0) {
529: DSGetSlepcSC(eps->ds,&sc);
530: sc->rg = NULL;
531: sc->comparison = SlepcCompareLargestMagnitude;
532: sc->comparisonctx = NULL;
533: sc->map = NULL;
534: sc->mapobj = NULL;
535: }
536: DSGetParallel(ctx->eps->ds,&ptype);
537: DSSetParallel(eps->ds,ptype);
538: DSGetMethod(ctx->eps->ds,&method);
539: DSSetMethod(eps->ds,method);
540: }
541: DSSetType(eps->ds,DSHEP);
542: DSSetCompact(eps->ds,PETSC_TRUE);
543: DSAllocate(eps->ds,dssz);
544: /* keep state of subcomm matrices to check that the user does not modify them */
545: EPSGetOperators(eps,&A,&B);
546: PetscObjectStateGet((PetscObject)A,&ctx->Astate);
547: PetscObjectGetId((PetscObject)A,&ctx->Aid);
548: if (B) {
549: PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
550: PetscObjectGetId((PetscObject)B,&ctx->Bid);
551: } else {
552: ctx->Bstate=0;
553: ctx->Bid=0;
554: }
555: return(0);
556: }
558: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
559: {
560: PetscErrorCode ierr;
561: Vec v,vg,v_loc;
562: IS is1,is2;
563: VecScatter vec_sc;
564: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
565: PetscInt nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
566: PetscScalar *array;
567: EPS_SR sr_loc;
568: BV V_loc;
571: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
572: V_loc = sr_loc->V;
574: /* Gather parallel eigenvectors */
575: BVGetColumn(eps->V,0,&v);
576: VecGetOwnershipRange(v,&n0,&m0);
577: BVRestoreColumn(eps->V,0,&v);
578: BVGetColumn(ctx->eps->V,0,&v);
579: VecGetLocalSize(v,&nloc);
580: BVRestoreColumn(ctx->eps->V,0,&v);
581: PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
582: VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
583: idx = -1;
584: for (si=0;si<ctx->npart;si++) {
585: j = 0;
586: for (i=n0;i<m0;i++) {
587: idx1[j] = i;
588: idx2[j++] = i+eps->n*si;
589: }
590: ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
591: ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
592: BVGetColumn(eps->V,0,&v);
593: VecScatterCreate(v,is1,vg,is2,&vec_sc);
594: BVRestoreColumn(eps->V,0,&v);
595: ISDestroy(&is1);
596: ISDestroy(&is2);
597: for (i=0;i<ctx->nconv_loc[si];i++) {
598: BVGetColumn(eps->V,++idx,&v);
599: if (ctx->subc->color==si) {
600: BVGetColumn(V_loc,i,&v_loc);
601: VecGetArray(v_loc,&array);
602: VecPlaceArray(vg,array);
603: }
604: VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
605: VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
606: if (ctx->subc->color==si) {
607: VecResetArray(vg);
608: VecRestoreArray(v_loc,&array);
609: BVRestoreColumn(V_loc,i,&v_loc);
610: }
611: BVRestoreColumn(eps->V,idx,&v);
612: }
613: VecScatterDestroy(&vec_sc);
614: }
615: PetscFree2(idx1,idx2);
616: VecDestroy(&vg);
617: return(0);
618: }
620: /*
621: EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
622: */
623: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
624: {
625: PetscErrorCode ierr;
626: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
629: if (ctx->global && ctx->npart>1) {
630: EPSComputeVectors(ctx->eps);
631: EPSSliceGatherEigenVectors(eps);
632: }
633: return(0);
634: }
636: #define SWAP(a,b,t) {t=a;a=b;b=t;}
638: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
639: {
640: PetscErrorCode ierr;
641: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
642: PetscInt i=0,j,tmpi;
643: PetscReal v,tmpr;
644: EPS_shift s;
647: if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
648: if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
649: if (!ctx->sr->s0) { /* EPSSolve not called yet */
650: *n = 2;
651: } else {
652: *n = 1;
653: s = ctx->sr->s0;
654: while (s) {
655: (*n)++;
656: s = s->neighb[1];
657: }
658: }
659: PetscMalloc1(*n,shifts);
660: PetscMalloc1(*n,inertias);
661: if (!ctx->sr->s0) { /* EPSSolve not called yet */
662: (*shifts)[0] = ctx->sr->int0;
663: (*shifts)[1] = ctx->sr->int1;
664: (*inertias)[0] = ctx->sr->inertia0;
665: (*inertias)[1] = ctx->sr->inertia1;
666: } else {
667: s = ctx->sr->s0;
668: while (s) {
669: (*shifts)[i] = s->value;
670: (*inertias)[i++] = s->inertia;
671: s = s->neighb[1];
672: }
673: (*shifts)[i] = ctx->sr->int1;
674: (*inertias)[i] = ctx->sr->inertia1;
675: }
676: /* remove possible duplicate in last position */
677: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
678: /* sort result */
679: for (i=0;i<*n;i++) {
680: v = (*shifts)[i];
681: for (j=i+1;j<*n;j++) {
682: if (v > (*shifts)[j]) {
683: SWAP((*shifts)[i],(*shifts)[j],tmpr);
684: SWAP((*inertias)[i],(*inertias)[j],tmpi);
685: v = (*shifts)[i];
686: }
687: }
688: }
689: return(0);
690: }
692: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
693: {
694: PetscErrorCode ierr;
695: PetscMPIInt rank,nproc;
696: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
697: PetscInt i,idx,j;
698: PetscInt *perm_loc,off=0,*inertias_loc,ns;
699: PetscScalar *eigr_loc;
700: EPS_SR sr_loc;
701: PetscReal *shifts_loc;
702: PetscMPIInt *disp,*ns_loc,aux;
705: eps->nconv = 0;
706: for (i=0;i<ctx->npart;i++) eps->nconv += ctx->nconv_loc[i];
707: sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
709: /* Gather the shifts used and the inertias computed */
710: EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
711: if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
712: if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
713: ns--;
714: for (i=0;i<ns;i++) {
715: inertias_loc[i] = inertias_loc[i+1];
716: shifts_loc[i] = shifts_loc[i+1];
717: }
718: }
719: PetscMalloc1(ctx->npart,&ns_loc);
720: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
721: PetscMPIIntCast(ns,&aux);
722: if (!rank) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank); }
723: PetscMPIIntCast(ctx->npart,&aux);
724: MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
725: ctx->nshifts = 0;
726: for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
727: PetscFree(ctx->inertias);
728: PetscFree(ctx->shifts);
729: PetscMalloc1(ctx->nshifts,&ctx->inertias);
730: PetscMalloc1(ctx->nshifts,&ctx->shifts);
732: /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
733: eigr_loc = sr_loc->eigr;
734: perm_loc = sr_loc->perm;
735: MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
736: PetscMalloc1(ctx->npart,&disp);
737: disp[0] = 0;
738: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
739: if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
740: PetscMPIIntCast(sr_loc->numEigs,&aux);
741: MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
742: MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
743: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
744: PetscMPIIntCast(ns,&aux);
745: MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
746: MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
747: MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
748: } else { /* subcommunicators with different size */
749: MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
750: if (!rank) {
751: PetscMPIIntCast(sr_loc->numEigs,&aux);
752: MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
753: MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
754: for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
755: PetscMPIIntCast(ns,&aux);
756: MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
757: MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
758: MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
759: }
760: PetscMPIIntCast(eps->nconv,&aux);
761: MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
762: MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
763: MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
764: PetscMPIIntCast(ctx->nshifts,&aux);
765: MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
766: MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
767: }
768: /* Update global array eps->perm */
769: idx = ctx->nconv_loc[0];
770: for (i=1;i<ctx->npart;i++) {
771: off += ctx->nconv_loc[i-1];
772: for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
773: }
775: /* Gather parallel eigenvectors */
776: PetscFree(ns_loc);
777: PetscFree(disp);
778: PetscFree(shifts_loc);
779: PetscFree(inertias_loc);
780: return(0);
781: }
783: /*
784: Fills the fields of a shift structure
785: */
786: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
787: {
788: PetscErrorCode ierr;
789: EPS_shift s,*pending2;
790: PetscInt i;
791: EPS_SR sr;
792: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
795: sr = ctx->sr;
796: PetscNewLog(eps,&s);
797: s->value = val;
798: s->neighb[0] = neighb0;
799: if (neighb0) neighb0->neighb[1] = s;
800: s->neighb[1] = neighb1;
801: if (neighb1) neighb1->neighb[0] = s;
802: s->comp[0] = PETSC_FALSE;
803: s->comp[1] = PETSC_FALSE;
804: s->index = -1;
805: s->neigs = 0;
806: s->nconv[0] = s->nconv[1] = 0;
807: s->nsch[0] = s->nsch[1]=0;
808: /* Inserts in the stack of pending shifts */
809: /* If needed, the array is resized */
810: if (sr->nPend >= sr->maxPend) {
811: sr->maxPend *= 2;
812: PetscMalloc1(sr->maxPend,&pending2);
813: PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
814: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
815: PetscFree(sr->pending);
816: sr->pending = pending2;
817: }
818: sr->pending[sr->nPend++]=s;
819: return(0);
820: }
822: /* Prepare for Rational Krylov update */
823: static PetscErrorCode EPSPrepareRational(EPS eps)
824: {
825: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
826: PetscErrorCode ierr;
827: PetscInt dir,i,k,ld,nv;
828: PetscScalar *A;
829: EPS_SR sr = ctx->sr;
830: Vec v;
833: DSGetLeadingDimension(eps->ds,&ld);
834: dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
835: dir*=sr->dir;
836: k = 0;
837: for (i=0;i<sr->nS;i++) {
838: if (dir*PetscRealPart(sr->S[i])>0.0) {
839: sr->S[k] = sr->S[i];
840: sr->S[sr->nS+k] = sr->S[sr->nS+i];
841: BVGetColumn(sr->Vnext,k,&v);
842: BVCopyVec(eps->V,eps->nconv+i,v);
843: BVRestoreColumn(sr->Vnext,k,&v);
844: k++;
845: if (k>=sr->nS/2)break;
846: }
847: }
848: /* Copy to DS */
849: DSGetArray(eps->ds,DS_MAT_A,&A);
850: PetscMemzero(A,ld*ld*sizeof(PetscScalar));
851: for (i=0;i<k;i++) {
852: A[i*(1+ld)] = sr->S[i];
853: A[k+i*ld] = sr->S[sr->nS+i];
854: }
855: sr->nS = k;
856: DSRestoreArray(eps->ds,DS_MAT_A,&A);
857: DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
858: DSSetDimensions(eps->ds,nv,0,0,k);
859: /* Append u to V */
860: BVGetColumn(sr->Vnext,sr->nS,&v);
861: BVCopyVec(eps->V,sr->nv,v);
862: BVRestoreColumn(sr->Vnext,sr->nS,&v);
863: return(0);
864: }
866: /* Provides next shift to be computed */
867: static PetscErrorCode EPSExtractShift(EPS eps)
868: {
869: PetscErrorCode ierr;
870: PetscInt iner,zeros=0;
871: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
872: EPS_SR sr;
873: PetscReal newShift;
874: EPS_shift sPres;
877: sr = ctx->sr;
878: if (sr->nPend > 0) {
879: sr->sPrev = sr->sPres;
880: sr->sPres = sr->pending[--sr->nPend];
881: sPres = sr->sPres;
882: EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
883: if (zeros) {
884: newShift = sPres->value*(1.0+SLICE_PTOL);
885: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
886: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
887: EPSSliceGetInertia(eps,newShift,&iner,&zeros);
888: if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
889: sPres->value = newShift;
890: }
891: sr->sPres->inertia = iner;
892: eps->target = sr->sPres->value;
893: eps->reason = EPS_CONVERGED_ITERATING;
894: eps->its = 0;
895: } else sr->sPres = NULL;
896: return(0);
897: }
899: /*
900: Symmetric KrylovSchur adapted to spectrum slicing:
901: Allows searching an specific amount of eigenvalues in the subintervals left and right.
902: Returns whether the search has succeeded
903: */
904: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
905: {
906: PetscErrorCode ierr;
907: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
908: PetscInt i,k,l,ld,nv,*iwork,j;
909: Mat U;
910: PetscScalar *Q,*A;
911: PetscReal *a,*b,beta;
912: PetscBool breakdown;
913: PetscInt count0,count1;
914: PetscReal lambda;
915: EPS_shift sPres;
916: PetscBool complIterating;
917: PetscBool sch0,sch1;
918: PetscInt iterCompl=0,n0,n1;
919: EPS_SR sr = ctx->sr;
922: /* Spectrum slicing data */
923: sPres = sr->sPres;
924: complIterating =PETSC_FALSE;
925: sch1 = sch0 = PETSC_TRUE;
926: DSGetLeadingDimension(eps->ds,&ld);
927: PetscMalloc1(2*ld,&iwork);
928: count0=0;count1=0; /* Found on both sides */
929: if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
930: /* Rational Krylov */
931: DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
932: DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
933: DSSetDimensions(eps->ds,l+1,0,0,0);
934: BVSetActiveColumns(eps->V,0,l+1);
935: DSGetMat(eps->ds,DS_MAT_Q,&U);
936: BVMultInPlace(eps->V,U,0,l+1);
937: MatDestroy(&U);
938: } else {
939: /* Get the starting Lanczos vector */
940: EPSGetStartVector(eps,0,NULL);
941: l = 0;
942: }
943: /* Restart loop */
944: while (eps->reason == EPS_CONVERGED_ITERATING) {
945: eps->its++; sr->itsKs++;
946: /* Compute an nv-step Lanczos factorization */
947: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
948: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
949: b = a + ld;
950: EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
951: sr->nv = nv;
952: beta = b[nv-1];
953: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
954: DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
955: if (l==0) {
956: DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
957: } else {
958: DSSetState(eps->ds,DS_STATE_RAW);
959: }
960: BVSetActiveColumns(eps->V,eps->nconv,nv);
962: /* Solve projected problem and compute residual norm estimates */
963: if (eps->its == 1 && l > 0) {/* After rational update */
964: DSGetArray(eps->ds,DS_MAT_A,&A);
965: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
966: b = a + ld;
967: k = eps->nconv+l;
968: A[k*ld+k-1] = A[(k-1)*ld+k];
969: A[k*ld+k] = a[k];
970: for (j=k+1; j< nv; j++) {
971: A[j*ld+j] = a[j];
972: A[j*ld+j-1] = b[j-1] ;
973: A[(j-1)*ld+j] = b[j-1];
974: }
975: DSRestoreArray(eps->ds,DS_MAT_A,&A);
976: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
977: DSSolve(eps->ds,eps->eigr,NULL);
978: DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
979: DSSetCompact(eps->ds,PETSC_TRUE);
980: } else { /* Restart */
981: DSSolve(eps->ds,eps->eigr,NULL);
982: DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
983: }
984: DSSynchronize(eps->ds,eps->eigr,NULL);
986: /* Residual */
987: EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,0.0,1.0,&k);
988: /* Checking values obtained for completing */
989: for (i=0;i<k;i++) {
990: sr->back[i]=eps->eigr[i];
991: }
992: STBackTransform(eps->st,k,sr->back,eps->eigi);
993: count0=count1=0;
994: for (i=0;i<k;i++) {
995: lambda = PetscRealPart(sr->back[i]);
996: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
997: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
998: }
999: if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
1000: else {
1001: /* Checks completion */
1002: if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
1003: eps->reason = EPS_CONVERGED_TOL;
1004: } else {
1005: if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
1006: if (complIterating) {
1007: if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
1008: } else if (k >= eps->nev) {
1009: n0 = sPres->nsch[0]-count0;
1010: n1 = sPres->nsch[1]-count1;
1011: if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
1012: /* Iterating for completion*/
1013: complIterating = PETSC_TRUE;
1014: if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
1015: if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
1016: iterCompl = sr->iterCompl;
1017: } else eps->reason = EPS_CONVERGED_TOL;
1018: }
1019: }
1020: }
1021: /* Update l */
1022: if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
1023: else l = nv-k;
1024: if (breakdown) l=0;
1025: if (!ctx->lock && l>0 && eps->reason == EPS_CONVERGED_ITERATING) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1027: if (eps->reason == EPS_CONVERGED_ITERATING) {
1028: if (breakdown) {
1029: /* Start a new Lanczos factorization */
1030: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
1031: EPSGetStartVector(eps,k,&breakdown);
1032: if (breakdown) {
1033: eps->reason = EPS_DIVERGED_BREAKDOWN;
1034: PetscInfo(eps,"Unable to generate more start vectors\n");
1035: }
1036: } else {
1037: /* Prepare the Rayleigh quotient for restart */
1038: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
1039: DSGetArray(eps->ds,DS_MAT_Q,&Q);
1040: b = a + ld;
1041: for (i=k;i<k+l;i++) {
1042: a[i] = PetscRealPart(eps->eigr[i]);
1043: b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
1044: }
1045: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
1046: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1047: }
1048: }
1049: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
1050: DSGetMat(eps->ds,DS_MAT_Q,&U);
1051: BVMultInPlace(eps->V,U,eps->nconv,k+l);
1052: MatDestroy(&U);
1054: /* Normalize u and append it to V */
1055: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
1056: BVCopyColumn(eps->V,nv,k+l);
1057: }
1058: eps->nconv = k;
1059: if (eps->reason != EPS_CONVERGED_ITERATING) {
1060: /* Store approximated values for next shift */
1061: DSGetArray(eps->ds,DS_MAT_Q,&Q);
1062: sr->nS = l;
1063: for (i=0;i<l;i++) {
1064: sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
1065: sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
1066: }
1067: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
1068: }
1069: }
1070: /* Check for completion */
1071: for (i=0;i< eps->nconv; i++) {
1072: if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
1073: else sPres->nconv[0]++;
1074: }
1075: sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
1076: sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
1077: if (count0 > sPres->nsch[0] || count1 > sPres->nsch[1]) InertiaMismatch(eps,ctx->detect);
1078: PetscFree(iwork);
1079: return(0);
1080: }
1082: /*
1083: Obtains value of subsequent shift
1084: */
1085: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
1086: {
1087: PetscReal lambda,d_prev;
1088: PetscInt i,idxP;
1089: EPS_SR sr;
1090: EPS_shift sPres,s;
1091: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1094: sr = ctx->sr;
1095: sPres = sr->sPres;
1096: if (sPres->neighb[side]) {
1097: /* Completing a previous interval */
1098: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
1099: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
1100: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
1101: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
1102: } else { /* (Only for side=1). Creating a new interval. */
1103: if (sPres->neigs==0) {/* No value has been accepted*/
1104: if (sPres->neighb[0]) {
1105: /* Multiplying by 10 the previous distance */
1106: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
1107: sr->nleap++;
1108: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
1109: if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
1110: } else { /* First shift */
1111: if (eps->nconv != 0) {
1112: /* Unaccepted values give information for next shift */
1113: idxP=0;/* Number of values left from shift */
1114: for (i=0;i<eps->nconv;i++) {
1115: lambda = PetscRealPart(eps->eigr[i]);
1116: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
1117: else break;
1118: }
1119: /* Avoiding subtraction of eigenvalues (might be the same).*/
1120: if (idxP>0) {
1121: d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
1122: } else {
1123: d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
1124: }
1125: *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
1126: } else { /* No values found, no information for next shift */
1127: SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
1128: }
1129: }
1130: } else { /* Accepted values found */
1131: sr->nleap = 0;
1132: /* Average distance of values in previous subinterval */
1133: s = sPres->neighb[0];
1134: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
1135: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
1136: }
1137: if (s) {
1138: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
1139: } else { /* First shift. Average distance obtained with values in this shift */
1140: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
1141: 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)) {
1142: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
1143: } else {
1144: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
1145: }
1146: }
1147: /* Average distance is used for next shift by adding it to value on the right or to shift */
1148: if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
1149: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
1150: } else { /* Last accepted value is on the left of shift. Adding to shift */
1151: *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
1152: }
1153: }
1154: /* End of interval can not be surpassed */
1155: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
1156: }/* of neighb[side]==null */
1157: return(0);
1158: }
1160: /*
1161: Function for sorting an array of real values
1162: */
1163: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
1164: {
1165: PetscReal re;
1166: PetscInt i,j,tmp;
1169: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
1170: /* Insertion sort */
1171: for (i=1;i<nr;i++) {
1172: re = PetscRealPart(r[perm[i]]);
1173: j = i-1;
1174: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
1175: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
1176: }
1177: }
1178: return(0);
1179: }
1181: /* Stores the pairs obtained since the last shift in the global arrays */
1182: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
1183: {
1184: PetscErrorCode ierr;
1185: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1186: PetscReal lambda,err,norm;
1187: PetscInt i,count;
1188: PetscBool iscayley;
1189: EPS_SR sr = ctx->sr;
1190: EPS_shift sPres;
1191: Vec v,w;
1194: sPres = sr->sPres;
1195: sPres->index = sr->indexEig;
1196: count = sr->indexEig;
1197: /* Back-transform */
1198: STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
1199: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
1200: /* Sort eigenvalues */
1201: sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
1202: /* Values stored in global array */
1203: for (i=0;i<eps->nconv;i++) {
1204: lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
1205: err = eps->errest[eps->perm[i]];
1207: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
1208: if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
1209: sr->eigr[count] = lambda;
1210: sr->errest[count] = err;
1211: /* Explicit purification */
1212: BVGetColumn(eps->V,eps->perm[i],&w);
1213: if (eps->purify) {
1214: BVGetColumn(sr->V,count,&v);
1215: STApply(eps->st,w,v);
1216: BVRestoreColumn(sr->V,count,&v);
1217: } else {
1218: BVInsertVec(sr->V,count,w);
1219: }
1220: BVRestoreColumn(eps->V,eps->perm[i],&w);
1221: BVNormColumn(sr->V,count,NORM_2,&norm);
1222: BVScaleColumn(sr->V,count,1.0/norm);
1223: count++;
1224: }
1225: }
1226: sPres->neigs = count - sr->indexEig;
1227: sr->indexEig = count;
1228: /* Global ordering array updating */
1229: sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
1230: return(0);
1231: }
1233: static PetscErrorCode EPSLookForDeflation(EPS eps)
1234: {
1235: PetscErrorCode ierr;
1236: PetscReal val;
1237: PetscInt i,count0=0,count1=0;
1238: EPS_shift sPres;
1239: PetscInt ini,fin,k,idx0,idx1;
1240: EPS_SR sr;
1241: Vec v;
1242: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1245: sr = ctx->sr;
1246: sPres = sr->sPres;
1248: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
1249: else ini = 0;
1250: fin = sr->indexEig;
1251: /* Selection of ends for searching new values */
1252: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
1253: else sPres->ext[0] = sPres->neighb[0]->value;
1254: if (!sPres->neighb[1]) {
1255: if (sr->hasEnd) sPres->ext[1] = sr->int1;
1256: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
1257: } else sPres->ext[1] = sPres->neighb[1]->value;
1258: /* Selection of values between right and left ends */
1259: for (i=ini;i<fin;i++) {
1260: val=PetscRealPart(sr->eigr[sr->perm[i]]);
1261: /* Values to the right of left shift */
1262: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
1263: if ((sr->dir)*(val - sPres->value) < 0) count0++;
1264: else count1++;
1265: } else break;
1266: }
1267: /* The number of values on each side are found */
1268: if (sPres->neighb[0]) {
1269: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
1270: if (sPres->nsch[0]<0) InertiaMismatch(eps,ctx->detect);
1271: } else sPres->nsch[0] = 0;
1273: if (sPres->neighb[1]) {
1274: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1275: if (sPres->nsch[1]<0) InertiaMismatch(eps,ctx->detect);
1276: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
1278: /* Completing vector of indexes for deflation */
1279: idx0 = ini;
1280: idx1 = ini+count0+count1;
1281: k=0;
1282: for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
1283: BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
1284: BVSetNumConstraints(sr->Vnext,k);
1285: for (i=0;i<k;i++) {
1286: BVGetColumn(sr->Vnext,-i-1,&v);
1287: BVCopyVec(sr->V,sr->idxDef[i],v);
1288: BVRestoreColumn(sr->Vnext,-i-1,&v);
1289: }
1291: /* For rational Krylov */
1292: if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
1293: EPSPrepareRational(eps);
1294: }
1295: eps->nconv = 0;
1296: /* Get rid of temporary Vnext */
1297: BVDestroy(&eps->V);
1298: eps->V = sr->Vnext;
1299: sr->Vnext = NULL;
1300: return(0);
1301: }
1303: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
1304: {
1305: PetscErrorCode ierr;
1306: PetscInt i,lds,ti;
1307: PetscReal newS;
1308: EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
1309: EPS_SR sr=ctx->sr;
1310: Mat A,B=NULL;
1311: PetscObjectState Astate,Bstate=0;
1312: PetscObjectId Aid,Bid=0;
1315: PetscCitationsRegister(citation,&cited);
1316: if (ctx->global) {
1317: EPSSolve_KrylovSchur_Slice(ctx->eps);
1318: ctx->eps->state = EPS_STATE_SOLVED;
1319: eps->reason = EPS_CONVERGED_TOL;
1320: if (ctx->npart>1) {
1321: /* Gather solution from subsolvers */
1322: EPSSliceGatherSolution(eps);
1323: } else {
1324: eps->nconv = sr->numEigs;
1325: eps->its = ctx->eps->its;
1326: PetscFree(ctx->inertias);
1327: PetscFree(ctx->shifts);
1328: EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1329: }
1330: } else {
1331: if (ctx->npart==1) {
1332: sr->eigr = ctx->eps->eigr;
1333: sr->eigi = ctx->eps->eigi;
1334: sr->perm = ctx->eps->perm;
1335: sr->errest = ctx->eps->errest;
1336: sr->V = ctx->eps->V;
1337: }
1338: /* Check that the user did not modify subcomm matrices */
1339: EPSGetOperators(eps,&A,&B);
1340: PetscObjectStateGet((PetscObject)A,&Astate);
1341: PetscObjectGetId((PetscObject)A,&Aid);
1342: if (B) {
1343: PetscObjectStateGet((PetscObject)B,&Bstate);
1344: PetscObjectGetId((PetscObject)B,&Bid);
1345: }
1346: 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");
1347: /* Only with eigenvalues present in the interval ...*/
1348: if (sr->numEigs==0) {
1349: eps->reason = EPS_CONVERGED_TOL;
1350: return(0);
1351: }
1352: /* Array of pending shifts */
1353: sr->maxPend = 100; /* Initial size */
1354: sr->nPend = 0;
1355: PetscMalloc1(sr->maxPend,&sr->pending);
1356: PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
1357: EPSCreateShift(eps,sr->int0,NULL,NULL);
1358: /* extract first shift */
1359: sr->sPrev = NULL;
1360: sr->sPres = sr->pending[--sr->nPend];
1361: sr->sPres->inertia = sr->inertia0;
1362: eps->target = sr->sPres->value;
1363: sr->s0 = sr->sPres;
1364: sr->indexEig = 0;
1365: /* Memory reservation for auxiliary variables */
1366: lds = PetscMin(eps->mpd,eps->ncv);
1367: PetscCalloc1(lds*lds,&sr->S);
1368: PetscMalloc1(eps->ncv,&sr->back);
1369: PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
1370: for (i=0;i<sr->numEigs;i++) {
1371: sr->eigr[i] = 0.0;
1372: sr->eigi[i] = 0.0;
1373: sr->errest[i] = 0.0;
1374: sr->perm[i] = i;
1375: }
1376: /* Vectors for deflation */
1377: PetscMalloc1(sr->numEigs,&sr->idxDef);
1378: PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
1379: sr->indexEig = 0;
1380: /* Main loop */
1381: while (sr->sPres) {
1382: /* Search for deflation */
1383: EPSLookForDeflation(eps);
1384: /* KrylovSchur */
1385: EPSKrylovSchur_Slice(eps);
1387: EPSStoreEigenpairs(eps);
1388: /* Select new shift */
1389: if (!sr->sPres->comp[1]) {
1390: EPSGetNewShiftValue(eps,1,&newS);
1391: EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
1392: }
1393: if (!sr->sPres->comp[0]) {
1394: /* Completing earlier interval */
1395: EPSGetNewShiftValue(eps,0,&newS);
1396: EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
1397: }
1398: /* Preparing for a new search of values */
1399: EPSExtractShift(eps);
1400: }
1402: /* Updating eps values prior to exit */
1403: PetscFree(sr->S);
1404: PetscFree(sr->idxDef);
1405: PetscFree(sr->pending);
1406: PetscFree(sr->back);
1407: BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
1408: BVSetNumConstraints(sr->Vnext,0);
1409: BVDestroy(&eps->V);
1410: eps->V = sr->Vnext;
1411: eps->nconv = sr->indexEig;
1412: eps->reason = EPS_CONVERGED_TOL;
1413: eps->its = sr->itsKs;
1414: eps->nds = 0;
1415: if (sr->dir<0) {
1416: for (i=0;i<eps->nconv/2;i++) {
1417: ti = sr->perm[i]; sr->perm[i] = sr->perm[eps->nconv-1-i]; sr->perm[eps->nconv-1-i] = ti;
1418: }
1419: }
1420: }
1421: return(0);
1422: }