Actual source code: ks-slice.c
slepc-3.5.1 2014-09-01
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) 2002-2014, 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
42: /*
43: EPSAllocateSolutionSlice - Allocate memory storage for common variables such
44: as eigenvalues and eigenvectors. The argument extra is used for methods
45: that require a working basis slightly larger than ncv.
46: */
47: PetscErrorCode EPSAllocateSolutionSlice(EPS eps,PetscInt extra)
48: {
50: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
51: PetscInt requested;
52: PetscReal eta;
53: PetscLogDouble cnt;
54: BVType type;
55: BVOrthogType orthog_type;
56: BVOrthogRefineType orthog_ref;
57: Mat matrix;
58: Vec t;
59: EPS_SR sr = ctx->sr;
62: requested = ctx->ncv + extra;
64: /* allocate space for eigenvalues and friends */
65: PetscMalloc4(requested,&sr->eigr,requested,&sr->eigi,requested,&sr->errest,requested,&sr->perm);
66: cnt = 2*requested*sizeof(PetscScalar) + 2*requested*sizeof(PetscReal) + requested*sizeof(PetscInt);
67: PetscLogObjectMemory((PetscObject)eps,cnt);
69: /* allocate sr->V and transfer options from eps->V */
70: BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
71: PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
72: if (!((PetscObject)(eps->V))->type_name) {
73: BVSetType(sr->V,BVSVEC);
74: } else {
75: BVGetType(eps->V,&type);
76: BVSetType(sr->V,type);
77: }
78: STMatGetVecs(eps->st,&t,NULL);
79: BVSetSizesFromVec(sr->V,t,requested);
80: VecDestroy(&t);
81: EPS_SetInnerProduct(eps);
82: BVGetMatrix(eps->V,&matrix,NULL);
83: BVSetMatrix(sr->V,matrix,PETSC_FALSE);
84: BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta);
85: BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta);
86: return(0);
87: }
91: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
92: {
93: PetscErrorCode ierr;
94: PetscBool issinv;
95: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
96: EPS_SR sr;
97: KSP ksp;
98: PC pc;
99: Mat F;
102: 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");
103: if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
104: if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
105: if (!((PetscObject)(eps->st))->type_name) { /* default to shift-and-invert */
106: STSetType(eps->st,STSINVERT);
107: }
108: PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
109: if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
110: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2; /* use tighter tolerance */
111: if (!eps->max_it) eps->max_it = 100;
112: if (ctx->nev==1) ctx->nev = 40; /* nev not set, use default value */
113: if (ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
114: eps->ops->backtransform = NULL;
116: /* create spectrum slicing context and initialize it */
117: EPSReset_KrylovSchur(eps);
118: PetscNewLog(eps,&sr);
119: ctx->sr = sr;
120: sr->itsKs = 0;
121: sr->nleap = 0;
122: sr->nMAXCompl = ctx->nev/4;
123: sr->iterCompl = eps->max_it/4;
124: sr->sPres = NULL;
125: sr->nS = 0;
127: /* check presence of ends and finding direction */
128: if ((eps->inta > PETSC_MIN_REAL && eps->inta != 0.0) || eps->intb >= PETSC_MAX_REAL) {
129: sr->int0 = eps->inta;
130: sr->int1 = eps->intb;
131: sr->dir = 1;
132: if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
133: sr->hasEnd = PETSC_FALSE;
134: sr->inertia1 = eps->n;
135: } else sr->hasEnd = PETSC_TRUE;
136: } else {
137: sr->int0 = eps->intb;
138: sr->int1 = eps->inta;
139: sr->dir = -1;
140: if (eps->inta <= PETSC_MIN_REAL) { /* Left-open interval */
141: sr->hasEnd = PETSC_FALSE;
142: sr->inertia1 = 0;
143: }
144: }
146: if (eps->intb >= PETSC_MAX_REAL) { /* right-open interval */
147: if (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");
148: STSetShift(eps->st,eps->inta);
149: } else {
150: STSetShift(eps->st,eps->intb);
151: }
152: STSetUp(eps->st);
153: STGetKSP(eps->st,&ksp);
154: KSPGetPC(ksp,&pc);
156: /* compute inertia1 if necessary */
157: if (sr->hasEnd) {
158: PCFactorGetMatrix(pc,&F);
159: MatGetInertia(F,&sr->inertia1,NULL,NULL);
160: }
162: /* compute inertia0 */
163: STSetShift(eps->st,sr->int0);
164: PCFactorGetMatrix(pc,&F);
165: MatGetInertia(F,&sr->inertia0,NULL,NULL);
167: /* number of eigenvalues in interval */
168: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
169: eps->nev = sr->numEigs;
170: eps->ncv = sr->numEigs;
171: eps->mpd = sr->numEigs;
172: EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
174: /* allocate solution for subsolves */
175: if (sr->numEigs) {
176: EPSAllocateSolutionSlice(eps,1);
177: }
178: return(0);
179: }
181: /*
182: Fills the fields of a shift structure
183: */
186: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
187: {
188: PetscErrorCode ierr;
189: EPS_shift s,*pending2;
190: PetscInt i;
191: EPS_SR sr;
192: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
195: sr = ctx->sr;
196: PetscNewLog(eps,&s);
197: s->value = val;
198: s->neighb[0] = neighb0;
199: if (neighb0) neighb0->neighb[1] = s;
200: s->neighb[1] = neighb1;
201: if (neighb1) neighb1->neighb[0] = s;
202: s->comp[0] = PETSC_FALSE;
203: s->comp[1] = PETSC_FALSE;
204: s->index = -1;
205: s->neigs = 0;
206: s->nconv[0] = s->nconv[1] = 0;
207: s->nsch[0] = s->nsch[1]=0;
208: /* Inserts in the stack of pending shifts */
209: /* If needed, the array is resized */
210: if (sr->nPend >= sr->maxPend) {
211: sr->maxPend *= 2;
212: PetscMalloc1(sr->maxPend,&pending2);
213: PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
214: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
215: PetscFree(sr->pending);
216: sr->pending = pending2;
217: }
218: sr->pending[sr->nPend++]=s;
219: return(0);
220: }
222: /* Prepare for Rational Krylov update */
225: static PetscErrorCode EPSPrepareRational(EPS eps)
226: {
227: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
228: PetscErrorCode ierr;
229: PetscInt dir,i,k,ld,nv;
230: PetscScalar *A;
231: EPS_SR sr = ctx->sr;
232: Vec v;
235: DSGetLeadingDimension(eps->ds,&ld);
236: dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
237: dir*=sr->dir;
238: k = 0;
239: for (i=0;i<sr->nS;i++) {
240: if (dir*PetscRealPart(sr->S[i])>0.0) {
241: sr->S[k] = sr->S[i];
242: sr->S[sr->nS+k] = sr->S[sr->nS+i];
243: BVGetColumn(sr->Vnext,k,&v);
244: BVCopyVec(sr->V,eps->nconv+i,v);
245: BVRestoreColumn(sr->Vnext,k,&v);
246: k++;
247: if (k>=sr->nS/2)break;
248: }
249: }
250: /* Copy to DS */
251: DSGetArray(eps->ds,DS_MAT_A,&A);
252: PetscMemzero(A,ld*ld*sizeof(PetscScalar));
253: for (i=0;i<k;i++) {
254: A[i*(1+ld)] = sr->S[i];
255: A[k+i*ld] = sr->S[sr->nS+i];
256: }
257: sr->nS = k;
258: DSRestoreArray(eps->ds,DS_MAT_A,&A);
259: DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
260: DSSetDimensions(eps->ds,nv,0,0,k);
261: /* Append u to V */
262: BVGetColumn(sr->Vnext,sr->nS,&v);
263: BVCopyVec(sr->V,sr->nv,v);
264: BVRestoreColumn(sr->Vnext,sr->nS,&v);
265: return(0);
266: }
268: /* Provides next shift to be computed */
271: static PetscErrorCode EPSExtractShift(EPS eps)
272: {
273: PetscErrorCode ierr;
274: PetscInt iner;
275: Mat F;
276: PC pc;
277: KSP ksp;
278: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
279: EPS_SR sr;
282: sr = ctx->sr;
283: if (sr->nPend > 0) {
284: sr->sPrev = sr->sPres;
285: sr->sPres = sr->pending[--sr->nPend];
286: STSetShift(eps->st,sr->sPres->value);
287: STGetKSP(eps->st,&ksp);
288: KSPGetPC(ksp,&pc);
289: PCFactorGetMatrix(pc,&F);
290: MatGetInertia(F,&iner,NULL,NULL);
291: sr->sPres->inertia = iner;
292: eps->target = sr->sPres->value;
293: eps->reason = EPS_CONVERGED_ITERATING;
294: eps->its = 0;
295: } else sr->sPres = NULL;
296: return(0);
297: }
299: /*
300: Symmetric KrylovSchur adapted to spectrum slicing:
301: Allows searching an specific amount of eigenvalues in the subintervals left and right.
302: Returns whether the search has succeeded
303: */
306: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
307: {
308: PetscErrorCode ierr;
309: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
310: PetscInt i,conv,k,l,ld,nv,*iwork,j,p;
311: Mat U;
312: PetscScalar *Q,*A,rtmp,*eigrsave,*eigisave;
313: PetscReal *a,*b,beta,*errestsave;
314: PetscBool breakdown;
315: PetscInt count0,count1;
316: PetscReal lambda;
317: EPS_shift sPres;
318: PetscBool complIterating;
319: PetscBool sch0,sch1;
320: PetscInt iterCompl=0,n0,n1;
321: EPS_SR sr = ctx->sr;
322: BV bvsave;
325: bvsave = eps->V; /* temporarily swap basis vectors */
326: eps->V = sr->V;
327: eigrsave = eps->eigr;
328: eps->eigr = sr->eigr;
329: eigisave = eps->eigi;
330: eps->eigi = sr->eigi;
331: errestsave = eps->errest;
332: eps->errest = sr->errest;
333: /* Spectrum slicing data */
334: sPres = sr->sPres;
335: complIterating =PETSC_FALSE;
336: sch1 = sch0 = PETSC_TRUE;
337: DSGetLeadingDimension(eps->ds,&ld);
338: PetscMalloc1(2*ld,&iwork);
339: count0=0;count1=0; /* Found on both sides */
340: if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
341: /* Rational Krylov */
342: DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
343: DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
344: DSSetDimensions(eps->ds,l+1,0,0,0);
345: BVSetActiveColumns(sr->V,0,l+1);
346: DSGetMat(eps->ds,DS_MAT_Q,&U);
347: BVMultInPlace(sr->V,U,0,l+1);
348: MatDestroy(&U);
349: } else {
350: /* Get the starting Lanczos vector */
351: EPSGetStartVector(eps,0,NULL);
352: l = 0;
353: }
354: /* Restart loop */
355: while (eps->reason == EPS_CONVERGED_ITERATING) {
356: eps->its++; sr->itsKs++;
357: /* Compute an nv-step Lanczos factorization */
358: nv = PetscMin(eps->nconv+ctx->mpd,ctx->ncv);
359: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
360: b = a + ld;
361: EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
362: sr->nv = nv;
363: beta = b[nv-1];
364: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
365: DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
366: if (l==0) {
367: DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
368: } else {
369: DSSetState(eps->ds,DS_STATE_RAW);
370: }
371: BVSetActiveColumns(sr->V,eps->nconv,nv);
373: /* Solve projected problem and compute residual norm estimates */
374: if (eps->its == 1 && l > 0) {/* After rational update */
375: DSGetArray(eps->ds,DS_MAT_A,&A);
376: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
377: b = a + ld;
378: k = eps->nconv+l;
379: A[k*ld+k-1] = A[(k-1)*ld+k];
380: A[k*ld+k] = a[k];
381: for (j=k+1; j< nv; j++) {
382: A[j*ld+j] = a[j];
383: A[j*ld+j-1] = b[j-1] ;
384: A[(j-1)*ld+j] = b[j-1];
385: }
386: DSRestoreArray(eps->ds,DS_MAT_A,&A);
387: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
388: DSSolve(eps->ds,sr->eigr,NULL);
389: DSSort(eps->ds,sr->eigr,NULL,NULL,NULL,NULL);
390: DSSetCompact(eps->ds,PETSC_TRUE);
391: } else { /* Restart */
392: DSSolve(eps->ds,sr->eigr,NULL);
393: DSSort(eps->ds,sr->eigr,NULL,NULL,NULL,NULL);
394: }
395: /* Residual */
396: EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);
398: /* Check convergence */
399: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
400: b = a + ld;
401: conv = 0;
402: j = k = eps->nconv;
403: for (i=eps->nconv;i<nv;i++) if (sr->errest[i] < eps->tol) conv++;
404: for (i=eps->nconv;i<nv;i++) {
405: if (sr->errest[i] < eps->tol) {
406: iwork[j++]=i;
407: } else iwork[conv+k++]=i;
408: }
409: for (i=eps->nconv;i<nv;i++) {
410: a[i]=PetscRealPart(sr->eigr[i]);
411: b[i]=sr->errest[i];
412: }
413: for (i=eps->nconv;i<nv;i++) {
414: sr->eigr[i] = a[iwork[i]];
415: sr->errest[i] = b[iwork[i]];
416: }
417: for (i=eps->nconv;i<nv;i++) {
418: a[i]=PetscRealPart(sr->eigr[i]);
419: b[i]=sr->errest[i];
420: }
421: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
422: DSGetArray(eps->ds,DS_MAT_Q,&Q);
423: for (i=eps->nconv;i<nv;i++) {
424: p=iwork[i];
425: if (p!=i) {
426: j=i+1;
427: while (iwork[j]!=i) j++;
428: iwork[j]=p;iwork[i]=i;
429: for (k=0;k<nv;k++) {
430: rtmp=Q[k+p*ld];Q[k+p*ld]=Q[k+i*ld];Q[k+i*ld]=rtmp;
431: }
432: }
433: }
434: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
435: k=eps->nconv+conv;
437: /* Checking values obtained for completing */
438: for (i=0;i<k;i++) {
439: sr->back[i]=sr->eigr[i];
440: }
441: STBackTransform(eps->st,k,sr->back,sr->eigi);
442: count0=count1=0;
443: for (i=0;i<k;i++) {
444: lambda = PetscRealPart(sr->back[i]);
445: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
446: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
447: }
448: if (k>ctx->nev && ctx->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
449: else {
450: /* Checks completion */
451: if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
452: eps->reason = EPS_CONVERGED_TOL;
453: } else {
454: if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
455: if (complIterating) {
456: if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
457: } else if (k >= ctx->nev) {
458: n0 = sPres->nsch[0]-count0;
459: n1 = sPres->nsch[1]-count1;
460: if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
461: /* Iterating for completion*/
462: complIterating = PETSC_TRUE;
463: if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
464: if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
465: iterCompl = sr->iterCompl;
466: } else eps->reason = EPS_CONVERGED_TOL;
467: }
468: }
469: }
470: /* Update l */
471: if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
472: else l = nv-k;
473: if (breakdown) l=0;
475: if (eps->reason == EPS_CONVERGED_ITERATING) {
476: if (breakdown) {
477: /* Start a new Lanczos factorization */
478: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
479: EPSGetStartVector(eps,k,&breakdown);
480: if (breakdown) {
481: eps->reason = EPS_DIVERGED_BREAKDOWN;
482: PetscInfo(eps,"Unable to generate more start vectors\n");
483: }
484: } else {
485: /* Prepare the Rayleigh quotient for restart */
486: DSGetArrayReal(eps->ds,DS_MAT_T,&a);
487: DSGetArray(eps->ds,DS_MAT_Q,&Q);
488: b = a + ld;
489: for (i=k;i<k+l;i++) {
490: a[i] = PetscRealPart(sr->eigr[i]);
491: b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
492: }
493: DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
494: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
495: }
496: }
497: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
498: DSGetMat(eps->ds,DS_MAT_Q,&U);
499: BVMultInPlace(eps->V,U,eps->nconv,k+l);
500: MatDestroy(&U);
502: /* Normalize u and append it to V */
503: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
504: BVCopyColumn(sr->V,nv,k+l);
505: }
506: /* Monitor */
507: eps->nconv = k;
508: EPSMonitor(eps,ctx->sr->itsKs,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
509: if (eps->reason != EPS_CONVERGED_ITERATING) {
510: /* Store approximated values for next shift */
511: DSGetArray(eps->ds,DS_MAT_Q,&Q);
512: sr->nS = l;
513: for (i=0;i<l;i++) {
514: sr->S[i] = sr->eigr[i+k];/* Diagonal elements */
515: sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
516: }
517: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
518: }
519: }
520: /* Check for completion */
521: for (i=0;i< eps->nconv; i++) {
522: if ((sr->dir)*PetscRealPart(sr->eigr[i])>0) sPres->nconv[1]++;
523: else sPres->nconv[0]++;
524: }
525: sPres->comp[0] = (count0 >= sPres->nsch[0])?PETSC_TRUE:PETSC_FALSE;
526: sPres->comp[1] = (count1 >= sPres->nsch[1])?PETSC_TRUE:PETSC_FALSE;
527: if (count0 > sPres->nsch[0] || count1 > sPres->nsch[1])SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing!\nMismatch between number of values found and information from inertia");
528: PetscFree(iwork);
529: eps->V = bvsave; /* restore basis */
530: eps->eigr = eigrsave;
531: eps->eigi = eigisave;
532: eps->errest = errestsave;
533: return(0);
534: }
536: /*
537: Obtains value of subsequent shift
538: */
541: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
542: {
543: PetscReal lambda,d_prev;
544: PetscInt i,idxP;
545: EPS_SR sr;
546: EPS_shift sPres,s;
547: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
550: sr = ctx->sr;
551: sPres = sr->sPres;
552: if (sPres->neighb[side]) {
553: /* Completing a previous interval */
554: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
555: if (side) *newS = (sPres->value + PetscRealPart(eps->eigr[eps->perm[sr->indexEig-1]]))/2;
556: else *newS = (sPres->value + PetscRealPart(eps->eigr[eps->perm[0]]))/2;
557: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
558: } else { /* (Only for side=1). Creating a new interval. */
559: if (sPres->neigs==0) {/* No value has been accepted*/
560: if (sPres->neighb[0]) {
561: /* Multiplying by 10 the previous distance */
562: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
563: sr->nleap++;
564: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
565: if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
566: } else { /* First shift */
567: if (eps->nconv != 0) {
568: /* Unaccepted values give information for next shift */
569: idxP=0;/* Number of values left from shift */
570: for (i=0;i<eps->nconv;i++) {
571: lambda = PetscRealPart(sr->eigr[i]);
572: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
573: else break;
574: }
575: /* Avoiding subtraction of eigenvalues (might be the same).*/
576: if (idxP>0) {
577: d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[0]))/(idxP+0.3);
578: } else {
579: d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[eps->nconv-1]))/(eps->nconv+0.3);
580: }
581: *newS = sPres->value + ((sr->dir)*d_prev*ctx->nev)/2;
582: } else { /* No values found, no information for next shift */
583: SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
584: }
585: }
586: } else { /* Accepted values found */
587: sr->nleap = 0;
588: /* Average distance of values in previous subinterval */
589: s = sPres->neighb[0];
590: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
591: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
592: }
593: if (s) {
594: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
595: } else { /* First shift. Average distance obtained with values in this shift */
596: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
597: if ((sr->dir)*(PetscRealPart(eps->eigr[0])-sPres->value)>0 && PetscAbsReal((PetscRealPart(eps->eigr[sr->indexEig-1]) - PetscRealPart(eps->eigr[0]))/PetscRealPart(eps->eigr[0])) > PetscSqrtReal(eps->tol)) {
598: d_prev = PetscAbsReal((PetscRealPart(eps->eigr[sr->indexEig-1]) - PetscRealPart(eps->eigr[0])))/(sPres->neigs+0.3);
599: } else {
600: d_prev = PetscAbsReal(PetscRealPart(eps->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
601: }
602: }
603: /* Average distance is used for next shift by adding it to value on the right or to shift */
604: if ((sr->dir)*(PetscRealPart(eps->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
605: *newS = PetscRealPart(eps->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(ctx->nev))/2;
606: } else { /* Last accepted value is on the left of shift. Adding to shift */
607: *newS = sPres->value + ((sr->dir)*d_prev*(ctx->nev))/2;
608: }
609: }
610: /* End of interval can not be surpassed */
611: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
612: }/* of neighb[side]==null */
613: return(0);
614: }
616: /*
617: Function for sorting an array of real values
618: */
621: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
622: {
623: PetscReal re;
624: PetscInt i,j,tmp;
627: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
628: /* Insertion sort */
629: for (i=1;i<nr;i++) {
630: re = PetscRealPart(r[perm[i]]);
631: j = i-1;
632: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
633: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
634: }
635: }
636: return(0);
637: }
639: /* Stores the pairs obtained since the last shift in the global arrays */
642: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
643: {
644: PetscErrorCode ierr;
645: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
646: PetscReal lambda,err,norm;
647: PetscInt i,count;
648: PetscBool iscayley;
649: EPS_SR sr = ctx->sr;
650: EPS_shift sPres;
651: Vec v,w;
652:
654: sPres = sr->sPres;
655: sPres->index = sr->indexEig;
656: count = sr->indexEig;
657: /* Back-transform */
658: STBackTransform(eps->st,eps->nconv,sr->eigr,sr->eigi);
659: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
660: /* Sort eigenvalues */
661: sortRealEigenvalues(sr->eigr,sr->perm,eps->nconv,PETSC_FALSE,sr->dir);
662: /* Values stored in global array */
663: for (i=0;i<eps->nconv;i++) {
664: lambda = PetscRealPart(sr->eigr[sr->perm[i]]);
665: err = sr->errest[sr->perm[i]];
667: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
668: if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
669: eps->eigr[count] = lambda;
670: eps->errest[count] = err;
671: /* Explicit purification */
672: BVGetColumn(eps->V,count,&v);
673: BVGetColumn(sr->V,sr->perm[i],&w);
674: STApply(eps->st,w,v);
675: BVRestoreColumn(eps->V,count,&v);
676: BVRestoreColumn(sr->V,sr->perm[i],&w);
677: BVNormColumn(eps->V,count,NORM_2,&norm);
678: BVScaleColumn(eps->V,count,1.0/norm);
679: count++;
680: }
681: }
682: sPres->neigs = count - sr->indexEig;
683: sr->indexEig = count;
684: /* Global ordering array updating */
685: sortRealEigenvalues(eps->eigr,eps->perm,count,PETSC_TRUE,sr->dir);
686: return(0);
687: }
691: static PetscErrorCode EPSLookForDeflation(EPS eps)
692: {
693: PetscErrorCode ierr;
694: PetscReal val;
695: PetscInt i,count0=0,count1=0;
696: EPS_shift sPres;
697: PetscInt ini,fin,k,idx0,idx1;
698: EPS_SR sr;
699: Vec v;
700: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
703: sr = ctx->sr;
704: sPres = sr->sPres;
706: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
707: else ini = 0;
708: fin = sr->indexEig;
709: /* Selection of ends for searching new values */
710: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
711: else sPres->ext[0] = sPres->neighb[0]->value;
712: if (!sPres->neighb[1]) {
713: if (sr->hasEnd) sPres->ext[1] = sr->int1;
714: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
715: } else sPres->ext[1] = sPres->neighb[1]->value;
716: /* Selection of values between right and left ends */
717: for (i=ini;i<fin;i++) {
718: val=PetscRealPart(eps->eigr[eps->perm[i]]);
719: /* Values to the right of left shift */
720: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
721: if ((sr->dir)*(val - sPres->value) < 0) count0++;
722: else count1++;
723: } else break;
724: }
725: /* The number of values on each side are found */
726: if (sPres->neighb[0]) {
727: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
728: if (sPres->nsch[0]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing!\nMismatch between number of values found and information from inertia");
729: } else sPres->nsch[0] = 0;
731: if (sPres->neighb[1]) {
732: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
733: if (sPres->nsch[1]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing!\nMismatch between number of values found and information from inertia");
734: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
736: /* Completing vector of indexes for deflation */
737: idx0 = ini;
738: idx1 = ini+count0+count1;
739: k=0;
740: for (i=idx0;i<idx1;i++) sr->idxDef[k++]=eps->perm[i];
741: BVDuplicateResize(sr->V,k+ctx->ncv+1,&sr->Vnext);
742: BVSetNumConstraints(sr->Vnext,k);
743: for (i=0;i<k;i++) {
744: BVGetColumn(sr->Vnext,-i-1,&v);
745: BVCopyVec(eps->V,sr->idxDef[i],v);
746: BVRestoreColumn(sr->Vnext,-i-1,&v);
747: }
749: /* For rational Krylov */
750: if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
751: EPSPrepareRational(eps);
752: }
753: eps->nconv = 0;
754: /* Get rid of temporary Vnext */
755: BVDestroy(&sr->V);
756: sr->V = sr->Vnext;
757: sr->Vnext = NULL;
758: return(0);
759: }
763: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
764: {
765: PetscErrorCode ierr;
766: PetscInt i,lds;
767: PetscReal newS;
768: EPS_SR sr;
769: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
772: sr = ctx->sr;
773: /* Only with eigenvalues present in the interval ...*/
774: if (sr->numEigs==0) {
775: eps->reason = EPS_CONVERGED_TOL;
776: return(0);
777: }
778: /* Array of pending shifts */
779: sr->maxPend = 100; /* Initial size */
780: sr->nPend = 0;
781: PetscMalloc1(sr->maxPend,&sr->pending);
782: PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
783: EPSCreateShift(eps,sr->int0,NULL,NULL);
784: /* extract first shift */
785: sr->sPrev = NULL;
786: sr->sPres = sr->pending[--sr->nPend];
787: sr->sPres->inertia = sr->inertia0;
788: eps->target = sr->sPres->value;
789: sr->s0 = sr->sPres;
790: sr->indexEig = 0;
791: /* Memory reservation for auxiliary variables */
792: lds = PetscMin(ctx->mpd,ctx->ncv);
793: PetscCalloc1(lds*lds,&sr->S);
794: PetscMalloc1(ctx->ncv,&sr->back);
795: PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*ctx->ncv)*sizeof(PetscScalar));
796: for (i=0;i<ctx->ncv;i++) {
797: sr->eigr[i] = 0.0;
798: sr->eigi[i] = 0.0;
799: sr->errest[i] = 0.0;
800: }
801: for (i=0;i<sr->numEigs;i++) eps->perm[i] = i;
802: /* Vectors for deflation */
803: PetscMalloc1(sr->numEigs,&sr->idxDef);
804: PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
805: sr->indexEig = 0;
806: /* Main loop */
807: while (sr->sPres) {
808: /* Search for deflation */
809: EPSLookForDeflation(eps);
810: /* KrylovSchur */
811: EPSKrylovSchur_Slice(eps);
813: EPSStoreEigenpairs(eps);
814: /* Select new shift */
815: if (!sr->sPres->comp[1]) {
816: EPSGetNewShiftValue(eps,1,&newS);
817: EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
818: }
819: if (!sr->sPres->comp[0]) {
820: /* Completing earlier interval */
821: EPSGetNewShiftValue(eps,0,&newS);
822: EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
823: }
824: /* Preparing for a new search of values */
825: EPSExtractShift(eps);
826: }
828: /* Updating eps values prior to exit */
829: BVDestroy(&sr->V);
830: PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
831: PetscFree(sr->S);
832: PetscFree(sr->idxDef);
833: PetscFree(sr->pending);
834: PetscFree(sr->back);
835: eps->nconv = sr->indexEig;
836: eps->reason = EPS_CONVERGED_TOL;
837: eps->its = sr->itsKs;
838: eps->nds = 0;
839: return(0);
840: }