Actual source code: qslice.c
slepc-3.18.3 2023-03-24
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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 polynomial eigensolver: "stoar"
13: Method: S-TOAR with spectrum slicing for symmetric quadratic eigenproblems
15: Algorithm:
17: Symmetric Two-Level Orthogonal Arnoldi.
19: References:
21: [1] C. Campos and J.E. Roman, "Inertia-based spectrum slicing
22: for symmetric quadratic eigenvalue problems", Numer. Linear
23: Algebra Appl. 27(4):e2293, 2020.
24: */
26: #include <slepc/private/pepimpl.h>
27: #include "../src/pep/impls/krylov/pepkrylov.h"
28: #include <slepcblaslapack.h>
30: static PetscBool cited = PETSC_FALSE;
31: static const char citation[] =
32: "@Article{slepc-slice-qep,\n"
33: " author = \"C. Campos and J. E. Roman\",\n"
34: " title = \"Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems\",\n"
35: " journal = \"Numer. Linear Algebra Appl.\",\n"
36: " volume = \"27\",\n"
37: " number = \"4\",\n"
38: " pages = \"e2293\",\n"
39: " year = \"2020,\"\n"
40: " doi = \"https://doi.org/10.1002/nla.2293\"\n"
41: "}\n";
43: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON
45: static PetscErrorCode PEPQSliceResetSR(PEP pep)
46: {
47: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
48: PEP_SR sr=ctx->sr;
49: PEP_shift s;
50: PetscInt i;
52: if (sr) {
53: /* Reviewing list of shifts to free memory */
54: s = sr->s0;
55: if (s) {
56: while (s->neighb[1]) {
57: s = s->neighb[1];
58: PetscFree(s->neighb[0]);
59: }
60: PetscFree(s);
61: }
62: PetscFree(sr->S);
63: for (i=0;i<pep->nconv;i++) PetscFree(sr->qinfo[i].q);
64: PetscFree(sr->qinfo);
65: for (i=0;i<3;i++) VecDestroy(&sr->v[i]);
66: EPSDestroy(&sr->eps);
67: PetscFree(sr);
68: }
69: ctx->sr = NULL;
70: return 0;
71: }
73: PetscErrorCode PEPReset_STOAR_QSlice(PEP pep)
74: {
75: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
77: PEPQSliceResetSR(pep);
78: PetscFree(ctx->inertias);
79: PetscFree(ctx->shifts);
80: return 0;
81: }
83: /*
84: PEPQSliceAllocateSolution - Allocate memory storage for common variables such
85: as eigenvalues and eigenvectors.
86: */
87: static PetscErrorCode PEPQSliceAllocateSolution(PEP pep)
88: {
89: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
90: PetscInt k;
91: BVType type;
92: Vec t;
93: PEP_SR sr = ctx->sr;
95: /* allocate space for eigenvalues and friends */
96: k = PetscMax(1,sr->numEigs);
97: PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
98: PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
99: PetscFree(sr->qinfo);
100: PetscCalloc1(k,&sr->qinfo);
102: /* allocate sr->V and transfer options from pep->V */
103: BVDestroy(&sr->V);
104: BVCreate(PetscObjectComm((PetscObject)pep),&sr->V);
105: if (!pep->V) PEPGetBV(pep,&pep->V);
106: if (!((PetscObject)(pep->V))->type_name) BVSetType(sr->V,BVSVEC);
107: else {
108: BVGetType(pep->V,&type);
109: BVSetType(sr->V,type);
110: }
111: STMatCreateVecsEmpty(pep->st,&t,NULL);
112: BVSetSizesFromVec(sr->V,t,k+1);
113: VecDestroy(&t);
114: sr->ld = k;
115: PetscFree(sr->S);
116: PetscMalloc1((k+1)*sr->ld*(pep->nmat-1),&sr->S);
117: return 0;
118: }
120: /* Convergence test to compute positive Ritz values */
121: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
122: {
123: *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
124: return 0;
125: }
127: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
128: {
129: KSP ksp,kspr;
130: PC pc;
131: Mat F;
132: PetscBool flg;
134: if (!pep->solvematcoeffs) PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
135: if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
136: pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
137: } else PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL);
138: STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
139: STGetKSP(pep->st,&ksp);
140: KSPGetPC(ksp,&pc);
141: PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
142: if (flg) {
143: PCRedundantGetKSP(pc,&kspr);
144: KSPGetPC(kspr,&pc);
145: }
146: PCFactorGetMatrix(pc,&F);
147: MatGetInertia(F,inertia,zeros,NULL);
148: return 0;
149: }
151: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
152: {
153: KSP ksp;
154: Mat P;
155: PetscReal nzshift=0.0,dot;
156: PetscRandom rand;
157: PetscInt nconv;
158: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
159: PEP_SR sr=ctx->sr;
161: if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
162: *inertia = 0;
163: } else if (shift <= PETSC_MIN_REAL) {
164: *inertia = 0;
165: if (zeros) *zeros = 0;
166: } else {
167: /* If the shift is zero, perturb it to a very small positive value.
168: The goal is that the nonzero pattern is the same in all cases and reuse
169: the symbolic factorizations */
170: nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
171: PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
172: STSetShift(pep->st,nzshift);
173: }
174: if (!correction) {
175: if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
176: else if (shift>PETSC_MIN_REAL) {
177: STGetKSP(pep->st,&ksp);
178: KSPGetOperators(ksp,&P,NULL);
179: if (*inertia!=pep->n && !sr->v[0]) {
180: MatCreateVecs(P,&sr->v[0],NULL);
181: VecDuplicate(sr->v[0],&sr->v[1]);
182: VecDuplicate(sr->v[0],&sr->v[2]);
183: BVGetRandomContext(pep->V,&rand);
184: VecSetRandom(sr->v[0],rand);
185: }
186: if (*inertia<pep->n && *inertia>0) {
187: if (!sr->eps) {
188: EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
189: EPSSetProblemType(sr->eps,EPS_HEP);
190: EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
191: }
192: EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
193: EPSSetOperators(sr->eps,P,NULL);
194: EPSSolve(sr->eps);
195: EPSGetConverged(sr->eps,&nconv);
197: EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
198: }
199: if (*inertia!=pep->n) {
200: MatMult(pep->A[1],sr->v[0],sr->v[1]);
201: MatMult(pep->A[2],sr->v[0],sr->v[2]);
202: VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
203: VecDotRealPart(sr->v[1],sr->v[0],&dot);
204: if (dot>0.0) *inertia = 2*pep->n-*inertia;
205: }
206: }
207: } else if (correction<0) *inertia = 2*pep->n-*inertia;
208: return 0;
209: }
211: /*
212: Check eigenvalue type - used only in non-hyperbolic problems.
213: All computed eigenvalues must have the same definite type (positive or negative).
214: If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
215: closest to shift and determine its type.
216: */
217: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
218: {
219: PEP pep2;
220: ST st;
221: PetscInt nconv;
222: PetscScalar lambda;
223: PetscReal dot;
224: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
225: PEP_SR sr=ctx->sr;
227: if (!ini) {
229: } else {
230: PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
231: PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
232: PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
233: PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
234: PEPSetType(pep2,PEPTOAR);
235: PEPSetOperators(pep2,pep->nmat,pep->A);
236: PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
237: PEPGetRG(pep2,&pep2->rg);
238: RGSetType(pep2->rg,RGINTERVAL);
239: #if defined(PETSC_USE_COMPLEX)
240: RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
241: #else
242: RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
243: #endif
244: pep2->target = shift;
245: st = pep2->st;
246: pep2->st = pep->st;
247: PEPSolve(pep2);
248: PEPGetConverged(pep2,&nconv);
249: if (nconv) {
250: PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
251: MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
252: MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
253: VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
254: VecDotRealPart(pep2->work[1],pep2->work[0],&dot);
255: PetscInfo(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(dot>0.0)?"positive":"negative");
256: if (!sr->type) sr->type = (dot>0.0)?1:-1;
258: }
259: pep2->st = st;
260: PEPDestroy(&pep2);
261: }
262: return 0;
263: }
265: static inline PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
266: {
267: PetscReal ap,bp,cp,dis;
269: MatMult(pep->A[0],u,w);
270: VecDotRealPart(w,u,&cp);
271: MatMult(pep->A[1],u,w);
272: VecDotRealPart(w,u,&bp);
273: MatMult(pep->A[2],u,w);
274: VecDotRealPart(w,u,&ap);
275: dis = bp*bp-4*ap*cp;
276: if (dis>=0.0 && smas) {
277: if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
278: else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
279: else {
280: if (bp >0) *smas = -cp/bp;
281: else *smas = PETSC_MAX_REAL;
282: }
283: }
284: if (dis>=0.0 && smenos) {
285: if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
286: else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
287: else {
288: if (bp<0) *smenos = -cp/bp;
289: else *smenos = PETSC_MAX_REAL;
290: }
291: }
292: if (d) *d = dis;
293: return 0;
294: }
296: static inline PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
297: {
298: MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
299: MatAXPY(M,x,pep->A[1],str);
300: MatAXPY(M,x*x,pep->A[2],str);
301: return 0;
302: }
304: /*@
305: PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
306: is definite or not.
308: Logically Collective on pep
310: Input Parameter:
311: . pep - eigensolver context
313: Output Parameters:
314: + xi - first computed parameter
315: . mu - second computed parameter
316: . definite - flag indicating that the problem is definite
317: - hyperbolic - flag indicating that the problem is hyperbolic
319: Notes:
320: This function is intended for quadratic eigenvalue problems, Q(lambda)=A*lambda^2+B*lambda+C,
321: with symmetric (or Hermitian) coefficient matrices A,B,C.
323: On output, the flag 'definite' may have the values -1 (meaning that the QEP is not
324: definite), 1 (if the problem is definite), or 0 if the algorithm was not able to
325: determine whether the problem is definite or not.
327: If definite=1, the output flag 'hyperbolic' informs in a similar way about whether the
328: problem is hyperbolic or not.
330: If definite=1, the computed values xi and mu satisfy Q(xi)<0 and Q(mu)>0, as
331: obtained via the method proposed in [Niendorf and Voss, LAA 2010]. Furthermore, if
332: hyperbolic=1 then only xi is computed.
334: Level: advanced
336: .seealso: PEPSetProblemType()
337: @*/
338: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
339: {
340: PetscRandom rand;
341: Vec u,w;
342: PetscReal d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
343: PetscInt k,its=10,hyp=0,check=0,nconv,inertia,n;
344: Mat M=NULL;
345: MatStructure str;
346: EPS eps;
347: PetscBool transform,ptypehyp;
350: ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
351: if (!pep->st) PEPGetST(pep,&pep->st);
352: PEPSetDefaultST(pep);
353: STSetMatrices(pep->st,pep->nmat,pep->A);
354: MatGetSize(pep->A[0],&n,NULL);
355: STGetTransform(pep->st,&transform);
356: STSetTransform(pep->st,PETSC_FALSE);
357: STSetUp(pep->st);
358: MatCreateVecs(pep->A[0],&u,&w);
359: PEPGetBV(pep,&pep->V);
360: BVGetRandomContext(pep->V,&rand);
361: VecSetRandom(u,rand);
362: VecNormalize(u,NULL);
363: PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
364: if (d<0.0) check = -1;
365: if (!check) {
366: EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
367: EPSSetProblemType(eps,EPS_HEP);
368: EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
369: EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
370: MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
371: STGetMatStructure(pep->st,&str);
372: }
373: for (k=0;k<its&&!check;k++) {
374: PEPQSliceEvaluateQEP(pep,s,M,str);
375: EPSSetOperators(eps,M,NULL);
376: EPSSolve(eps);
377: EPSGetConverged(eps,&nconv);
378: if (!nconv) break;
379: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
380: sp = s;
381: PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
382: if (d<0.0) {check = -1; break;}
383: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
384: if (s>sp) {hyp = -1;}
385: mut = 2*s-sp;
386: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
387: if (inertia == n) {check = 1; break;}
388: }
389: for (;k<its&&!check;k++) {
390: mut = (s-omg)/2;
391: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
392: if (inertia == n) {check = 1; break;}
393: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
394: PEPQSliceEvaluateQEP(pep,omg,M,str);
395: EPSSetOperators(eps,M,NULL);
396: EPSSolve(eps);
397: EPSGetConverged(eps,&nconv);
398: if (!nconv) break;
399: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
400: omgp = omg;
401: PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
402: if (d<0.0) {check = -1; break;}
403: if (omg<omgp) hyp = -1;
404: }
405: if (check==1) *xi = mut;
407: if (check==1 && hyp==0) {
408: PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
409: if (inertia == 0) hyp = 1;
410: else hyp = -1;
411: }
412: if (check==1 && hyp!=1) {
413: check = 0;
414: EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
415: for (;k<its&&!check;k++) {
416: PEPQSliceEvaluateQEP(pep,s,M,str);
417: EPSSetOperators(eps,M,NULL);
418: EPSSolve(eps);
419: EPSGetConverged(eps,&nconv);
420: if (!nconv) break;
421: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
422: sp = s;
423: PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
424: if (d<0.0) {check = -1; break;}
425: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
426: mut = 2*s-sp;
427: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
428: if (inertia == 0) {check = 1; break;}
429: }
430: for (;k<its&&!check;k++) {
431: mut = (s-omg)/2;
432: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
433: if (inertia == 0) {check = 1; break;}
434: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
435: PEPQSliceEvaluateQEP(pep,omg,M,str);
436: EPSSetOperators(eps,M,NULL);
437: EPSSolve(eps);
438: EPSGetConverged(eps,&nconv);
439: if (!nconv) break;
440: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
441: PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
442: if (d<0.0) {check = -1; break;}
443: }
444: }
445: if (check==1) *mu = mut;
446: *definite = check;
447: *hyperbolic = hyp;
448: if (M) MatDestroy(&M);
449: VecDestroy(&u);
450: VecDestroy(&w);
451: EPSDestroy(&eps);
452: STSetTransform(pep->st,transform);
453: return 0;
454: }
456: /*
457: Dummy backtransform operation
458: */
459: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
460: {
461: return 0;
462: }
464: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
465: {
466: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
467: PEP_SR sr;
468: PetscInt ld,i,zeros=0;
469: SlepcSC sc;
470: PetscReal r;
472: PEPCheckSinvertCayley(pep);
475: PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
476: if (pep->tol==PETSC_DEFAULT) {
477: #if defined(PETSC_USE_REAL_SINGLE)
478: pep->tol = SLEPC_DEFAULT_TOL;
479: #else
480: /* use tighter tolerance */
481: pep->tol = SLEPC_DEFAULT_TOL*1e-2;
482: #endif
483: }
484: if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n); /* nev not set, use default value */
486: pep->ops->backtransform = PEPBackTransform_Skip;
487: if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;
489: /* create spectrum slicing context and initialize it */
490: PEPQSliceResetSR(pep);
491: PetscNew(&sr);
492: ctx->sr = sr;
493: sr->itsKs = 0;
494: sr->nleap = 0;
495: sr->sPres = NULL;
497: if (pep->solvematcoeffs) PetscFree(pep->solvematcoeffs);
498: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
499: if (!pep->st) PEPGetST(pep,&pep->st);
500: STSetTransform(pep->st,PETSC_FALSE);
501: STSetUp(pep->st);
503: ctx->hyperbolic = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
505: /* check presence of ends and finding direction */
506: if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
507: sr->int0 = pep->inta;
508: sr->int1 = pep->intb;
509: sr->dir = 1;
510: if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
511: sr->hasEnd = PETSC_FALSE;
512: } else sr->hasEnd = PETSC_TRUE;
513: } else {
514: sr->int0 = pep->intb;
515: sr->int1 = pep->inta;
516: sr->dir = -1;
517: sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
518: }
520: /* compute inertia0 */
521: PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
523: if (!ctx->hyperbolic && ctx->checket) PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE);
525: /* compute inertia1 */
526: PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
528: if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
529: PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE);
532: if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
533: sr->intcorr = -1;
534: sr->inertia0 = 2*pep->n-sr->inertia0;
535: sr->inertia1 = 2*pep->n-sr->inertia1;
536: } else sr->intcorr = 1;
537: } else {
538: if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
539: else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
540: }
542: if (sr->hasEnd) {
543: sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
544: i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
545: }
547: /* number of eigenvalues in interval */
548: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
549: PetscInfo(pep,"QSlice setup: allocating for %" PetscInt_FMT " eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb);
550: if (sr->numEigs) {
551: PEPQSliceAllocateSolution(pep);
552: PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd);
553: pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
554: ld = ctx->ncv+2;
555: DSSetType(pep->ds,DSGHIEP);
556: DSSetCompact(pep->ds,PETSC_TRUE);
557: DSSetExtraRow(pep->ds,PETSC_TRUE);
558: DSAllocate(pep->ds,ld);
559: DSGetSlepcSC(pep->ds,&sc);
560: sc->rg = NULL;
561: sc->comparison = SlepcCompareLargestMagnitude;
562: sc->comparisonctx = NULL;
563: sc->map = NULL;
564: sc->mapobj = NULL;
565: } else {pep->ncv = 0; pep->nev = 0; pep->mpd = 0;}
566: return 0;
567: }
569: /*
570: Fills the fields of a shift structure
571: */
572: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
573: {
574: PEP_shift s,*pending2;
575: PetscInt i;
576: PEP_SR sr;
577: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
579: sr = ctx->sr;
580: PetscNew(&s);
581: s->value = val;
582: s->neighb[0] = neighb0;
583: if (neighb0) neighb0->neighb[1] = s;
584: s->neighb[1] = neighb1;
585: if (neighb1) neighb1->neighb[0] = s;
586: s->comp[0] = PETSC_FALSE;
587: s->comp[1] = PETSC_FALSE;
588: s->index = -1;
589: s->neigs = 0;
590: s->nconv[0] = s->nconv[1] = 0;
591: s->nsch[0] = s->nsch[1]=0;
592: /* Inserts in the stack of pending shifts */
593: /* If needed, the array is resized */
594: if (sr->nPend >= sr->maxPend) {
595: sr->maxPend *= 2;
596: PetscMalloc1(sr->maxPend,&pending2);
597: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
598: PetscFree(sr->pending);
599: sr->pending = pending2;
600: }
601: sr->pending[sr->nPend++]=s;
602: return 0;
603: }
605: /* Provides next shift to be computed */
606: static PetscErrorCode PEPExtractShift(PEP pep)
607: {
608: PetscInt iner,zeros=0;
609: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
610: PEP_SR sr;
611: PetscReal newShift,aux;
612: PEP_shift sPres;
614: sr = ctx->sr;
615: if (sr->nPend > 0) {
616: if (sr->dirch) {
617: aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
618: iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
619: sr->dir *= -1;
620: PetscFree(sr->s0->neighb[1]);
621: PetscFree(sr->s0);
622: sr->nPend--;
623: PEPCreateShift(pep,sr->int0,NULL,NULL);
624: sr->sPrev = NULL;
625: sr->sPres = sr->pending[--sr->nPend];
626: pep->target = sr->sPres->value;
627: sr->s0 = sr->sPres;
628: pep->reason = PEP_CONVERGED_ITERATING;
629: } else {
630: sr->sPrev = sr->sPres;
631: sr->sPres = sr->pending[--sr->nPend];
632: }
633: sPres = sr->sPres;
634: PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
635: if (zeros) {
636: newShift = sPres->value*(1.0+SLICE_PTOL);
637: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
638: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
639: PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
641: sPres->value = newShift;
642: }
643: sr->sPres->inertia = iner;
644: pep->target = sr->sPres->value;
645: pep->reason = PEP_CONVERGED_ITERATING;
646: pep->its = 0;
647: } else sr->sPres = NULL;
648: return 0;
649: }
651: /*
652: Obtains value of subsequent shift
653: */
654: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
655: {
656: PetscReal lambda,d_prev;
657: PetscInt i,idxP;
658: PEP_SR sr;
659: PEP_shift sPres,s;
660: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
662: sr = ctx->sr;
663: sPres = sr->sPres;
664: if (sPres->neighb[side]) {
665: /* Completing a previous interval */
666: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
667: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
668: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
669: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
670: } else { /* (Only for side=1). Creating a new interval. */
671: if (sPres->neigs==0) {/* No value has been accepted*/
672: if (sPres->neighb[0]) {
673: /* Multiplying by 10 the previous distance */
674: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
675: sr->nleap++;
676: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
678: } else { /* First shift */
679: if (pep->nconv != 0) {
680: /* Unaccepted values give information for next shift */
681: idxP=0;/* Number of values left from shift */
682: for (i=0;i<pep->nconv;i++) {
683: lambda = PetscRealPart(pep->eigr[i]);
684: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
685: else break;
686: }
687: /* Avoiding subtraction of eigenvalues (might be the same).*/
688: if (idxP>0) {
689: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
690: } else {
691: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
692: }
693: *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
694: sr->dirch = PETSC_FALSE;
695: } else { /* No values found, no information for next shift */
697: sr->dirch = PETSC_TRUE;
698: *newS = sr->int1;
699: }
700: }
701: } else { /* Accepted values found */
702: sr->dirch = PETSC_FALSE;
703: sr->nleap = 0;
704: /* Average distance of values in previous subinterval */
705: s = sPres->neighb[0];
706: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
707: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
708: }
709: if (s) {
710: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
711: } else { /* First shift. Average distance obtained with values in this shift */
712: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
713: 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(pep->tol)) {
714: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
715: } else {
716: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
717: }
718: }
719: /* Average distance is used for next shift by adding it to value on the right or to shift */
720: if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
721: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
722: } else { /* Last accepted value is on the left of shift. Adding to shift */
723: *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
724: }
725: }
726: /* End of interval can not be surpassed */
727: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
728: }/* of neighb[side]==null */
729: return 0;
730: }
732: /*
733: Function for sorting an array of real values
734: */
735: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
736: {
737: PetscReal re;
738: PetscInt i,j,tmp;
740: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
741: /* Insertion sort */
742: for (i=1;i<nr;i++) {
743: re = PetscRealPart(r[perm[i]]);
744: j = i-1;
745: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
746: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
747: }
748: }
749: return 0;
750: }
752: /* Stores the pairs obtained since the last shift in the global arrays */
753: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
754: {
755: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
756: PetscReal lambda,err,*errest;
757: PetscInt i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
758: PetscBool iscayley,divide=PETSC_FALSE;
759: PEP_SR sr = ctx->sr;
760: PEP_shift sPres;
761: Vec w,vomega;
762: Mat MS;
763: BV tV;
764: PetscScalar *S,*eigr,*tS,*omega;
766: sPres = sr->sPres;
767: sPres->index = sr->indexEig;
769: if (nconv>sr->ndef0+sr->ndef1) {
770: /* Back-transform */
771: STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
772: for (i=0;i<nconv;i++) {
773: #if defined(PETSC_USE_COMPLEX)
774: if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
775: #else
776: if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
777: #endif
778: }
779: PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
780: /* Sort eigenvalues */
781: sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
782: VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
783: BVGetSignature(ctx->V,vomega);
784: VecGetArray(vomega,&omega);
785: BVGetSizes(pep->V,NULL,NULL,&ld);
786: BVTensorGetFactors(ctx->V,NULL,&MS);
787: MatDenseGetArray(MS,&S);
788: /* Values stored in global array */
789: PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
790: ndef = sr->ndef0+sr->ndef1;
791: for (i=0;i<nconv;i++) {
792: lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
793: err = pep->errest[pep->perm[i]];
794: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
796: PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
797: eigr[count] = lambda;
798: errest[count] = err;
799: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
800: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
801: PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
802: PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
803: count++;
804: }
805: }
806: VecRestoreArray(vomega,&omega);
807: VecDestroy(&vomega);
808: for (i=0;i<count;i++) {
809: PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
810: PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
811: }
812: MatDenseRestoreArray(MS,&S);
813: BVTensorRestoreFactors(ctx->V,NULL,&MS);
814: BVSetActiveColumns(ctx->V,0,count);
815: BVTensorCompress(ctx->V,count);
816: if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
817: divide = PETSC_TRUE;
818: BVTensorGetFactors(ctx->V,NULL,&MS);
819: MatDenseGetArray(MS,&S);
820: PetscArrayzero(tS,nconv*nconv*d);
821: for (i=0;i<count;i++) {
822: PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
823: PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
824: }
825: MatDenseRestoreArray(MS,&S);
826: BVTensorRestoreFactors(ctx->V,NULL,&MS);
827: BVSetActiveColumns(pep->V,0,count);
828: BVDuplicateResize(pep->V,count,&tV);
829: BVCopy(pep->V,tV);
830: }
831: if (sr->sPres->nconv[0]) {
832: if (divide) {
833: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
834: BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
835: }
836: for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
837: for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
838: BVTensorGetFactors(ctx->V,NULL,&MS);
839: MatDenseGetArray(MS,&S);
840: for (i=0;i<sr->sPres->nconv[0];i++) {
841: sr->eigr[aux[i]] = eigr[i];
842: sr->errest[aux[i]] = errest[i];
843: BVGetColumn(pep->V,i,&w);
844: BVInsertVec(sr->V,aux[i],w);
845: BVRestoreColumn(pep->V,i,&w);
846: idx = sr->ld*d*aux[i];
847: PetscArrayzero(sr->S+idx,sr->ld*d);
848: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
849: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
850: PetscFree(sr->qinfo[aux[i]].q);
851: PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
852: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
853: sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
854: }
855: MatDenseRestoreArray(MS,&S);
856: BVTensorRestoreFactors(ctx->V,NULL,&MS);
857: }
859: if (sr->sPres->nconv[1]) {
860: if (divide) {
861: BVTensorGetFactors(ctx->V,NULL,&MS);
862: MatDenseGetArray(MS,&S);
863: for (i=0;i<sr->sPres->nconv[1];i++) {
864: PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
865: PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
866: }
867: MatDenseRestoreArray(MS,&S);
868: BVTensorRestoreFactors(ctx->V,NULL,&MS);
869: BVSetActiveColumns(pep->V,0,count);
870: BVCopy(tV,pep->V);
871: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
872: BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
873: }
874: for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
875: for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
876: BVTensorGetFactors(ctx->V,NULL,&MS);
877: MatDenseGetArray(MS,&S);
878: for (i=0;i<sr->sPres->nconv[1];i++) {
879: sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
880: sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
881: BVGetColumn(pep->V,i,&w);
882: BVInsertVec(sr->V,aux[i],w);
883: BVRestoreColumn(pep->V,i,&w);
884: idx = sr->ld*d*aux[i];
885: PetscArrayzero(sr->S+idx,sr->ld*d);
886: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
887: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
888: PetscFree(sr->qinfo[aux[i]].q);
889: PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
890: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
891: sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
892: }
893: MatDenseRestoreArray(MS,&S);
894: BVTensorRestoreFactors(ctx->V,NULL,&MS);
895: }
896: sPres->neigs = count-sr->ndef0-sr->ndef1;
897: sr->indexEig += sPres->neigs;
898: sPres->nconv[0]-= sr->ndef0;
899: sPres->nconv[1]-= sr->ndef1;
900: PetscFree4(eigr,errest,tS,aux);
901: } else {
902: sPres->neigs = 0;
903: sPres->nconv[0]= 0;
904: sPres->nconv[1]= 0;
905: }
906: /* Global ordering array updating */
907: sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
908: /* Check for completion */
909: sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
910: sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
912: if (divide) BVDestroy(&tV);
913: return 0;
914: }
916: static PetscErrorCode PEPLookForDeflation(PEP pep)
917: {
918: PetscReal val;
919: PetscInt i,count0=0,count1=0;
920: PEP_shift sPres;
921: PetscInt ini,fin;
922: PEP_SR sr;
923: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
925: sr = ctx->sr;
926: sPres = sr->sPres;
928: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
929: else ini = 0;
930: fin = sr->indexEig;
931: /* Selection of ends for searching new values */
932: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
933: else sPres->ext[0] = sPres->neighb[0]->value;
934: if (!sPres->neighb[1]) {
935: if (sr->hasEnd) sPres->ext[1] = sr->int1;
936: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
937: } else sPres->ext[1] = sPres->neighb[1]->value;
938: /* Selection of values between right and left ends */
939: for (i=ini;i<fin;i++) {
940: val=PetscRealPart(sr->eigr[sr->perm[i]]);
941: /* Values to the right of left shift */
942: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
943: if ((sr->dir)*(val - sPres->value) < 0) count0++;
944: else count1++;
945: } else break;
946: }
947: /* The number of values on each side are found */
948: if (sPres->neighb[0]) {
949: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
951: } else sPres->nsch[0] = 0;
953: if (sPres->neighb[1]) {
954: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
956: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
958: /* Completing vector of indexes for deflation */
959: for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
960: sr->ndef0 = count0;
961: for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
962: sr->ndef1 = count1;
963: return 0;
964: }
966: /*
967: Compute a run of Lanczos iterations
968: */
969: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
970: {
971: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
972: PetscInt i,j,m=*M,l,lock;
973: PetscInt lds,d,ld,offq,nqt,ldds;
974: Vec v=t_[0],t=t_[1],q=t_[2];
975: PetscReal norm,sym=0.0,fro=0.0,*f;
976: PetscScalar *y,*S,sigma;
977: PetscBLASInt j_,one=1;
978: PetscBool lindep;
979: Mat MS;
981: PetscMalloc1(*M,&y);
982: BVGetSizes(pep->V,NULL,NULL,&ld);
983: BVTensorGetDegree(ctx->V,&d);
984: BVGetActiveColumns(pep->V,&lock,&nqt);
985: lds = d*ld;
986: offq = ld;
987: DSGetLeadingDimension(pep->ds,&ldds);
989: *breakdown = PETSC_FALSE; /* ----- */
990: STGetShift(pep->st,&sigma);
991: DSGetDimensions(pep->ds,NULL,&l,NULL,NULL);
992: BVSetActiveColumns(ctx->V,0,m);
993: BVSetActiveColumns(pep->V,0,nqt);
994: for (j=k;j<m;j++) {
995: /* apply operator */
996: BVTensorGetFactors(ctx->V,NULL,&MS);
997: MatDenseGetArray(MS,&S);
998: BVGetColumn(pep->V,nqt,&t);
999: BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1000: MatMult(pep->A[1],v,q);
1001: MatMult(pep->A[2],v,t);
1002: VecAXPY(q,sigma*pep->sfactor,t);
1003: VecScale(q,pep->sfactor);
1004: BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1005: MatMult(pep->A[2],v,t);
1006: VecAXPY(q,pep->sfactor*pep->sfactor,t);
1007: STMatSolve(pep->st,q,t);
1008: VecScale(t,-1.0);
1009: BVRestoreColumn(pep->V,nqt,&t);
1011: /* orthogonalize */
1012: BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1013: if (!lindep) {
1014: *(S+(j+1)*lds+nqt) = norm;
1015: BVScaleColumn(pep->V,nqt,1.0/norm);
1016: nqt++;
1017: }
1018: for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1019: BVSetActiveColumns(pep->V,0,nqt);
1020: MatDenseRestoreArray(MS,&S);
1021: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1023: /* level-2 orthogonalization */
1024: BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1025: a[j] = PetscRealPart(y[j]);
1026: omega[j+1] = (norm > 0)?1.0:-1.0;
1027: BVScaleColumn(ctx->V,j+1,1.0/norm);
1028: b[j] = PetscAbsReal(norm);
1030: /* check symmetry */
1031: DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1032: if (j==k) {
1033: for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1034: for (i=0;i<l;i++) y[i] = 0.0;
1035: }
1036: DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1037: if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1038: PetscBLASIntCast(j,&j_);
1039: sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1040: fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1041: if (j>0) fro = SlepcAbs(fro,b[j-1]);
1042: if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1043: *symmlost = PETSC_TRUE;
1044: *M=j;
1045: break;
1046: }
1047: }
1048: BVSetActiveColumns(pep->V,lock,nqt);
1049: BVSetActiveColumns(ctx->V,0,*M);
1050: PetscFree(y);
1051: return 0;
1052: }
1054: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1055: {
1056: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1057: PetscInt j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1058: PetscInt nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1059: PetscScalar *om,sigma,*back,*S,*pQ;
1060: PetscReal beta,norm=1.0,*omega,*a,*b,eta,lambda;
1061: PetscBool breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1062: Mat MS,MQ,D;
1063: Vec v,vomega;
1064: PEP_SR sr;
1065: BVOrthogType otype;
1066: BVOrthogBlockType obtype;
1068: /* Resize if needed for deflating vectors */
1069: sr = ctx->sr;
1070: sigma = sr->sPres->value;
1071: k = sr->ndef0+sr->ndef1;
1072: pep->ncv = ctx->ncv+k;
1073: pep->nev = ctx->nev+k;
1074: PEPAllocateSolution(pep,3);
1075: BVDestroy(&ctx->V);
1076: BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1077: BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1078: BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1079: DSAllocate(pep->ds,pep->ncv+2);
1080: PetscMalloc1(pep->ncv,&back);
1081: DSGetLeadingDimension(pep->ds,&ldds);
1082: BVSetMatrix(ctx->V,B,PETSC_TRUE);
1084: /* undocumented option to use a cheaper locking instead of the true locking */
1085: PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1086: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1087: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1088: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
1090: /* Get the starting Arnoldi vector */
1091: BVSetActiveColumns(pep->V,0,1);
1092: BVTensorBuildFirstColumn(ctx->V,pep->nini);
1093: BVSetActiveColumns(ctx->V,0,1);
1094: if (k) {
1095: /* Insert deflated vectors */
1096: BVSetActiveColumns(pep->V,0,0);
1097: idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1098: for (j=0;j<k;j++) {
1099: BVGetColumn(pep->V,j,&v);
1100: BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1101: BVRestoreColumn(pep->V,j,&v);
1102: }
1103: /* Update innerproduct matrix */
1104: BVSetActiveColumns(ctx->V,0,0);
1105: BVTensorGetFactors(ctx->V,NULL,&MS);
1106: BVSetActiveColumns(pep->V,0,k);
1107: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1109: BVGetSizes(pep->V,NULL,NULL,&ld);
1110: BVTensorGetFactors(ctx->V,NULL,&MS);
1111: MatDenseGetArray(MS,&S);
1112: for (j=0;j<sr->ndef0;j++) {
1113: PetscArrayzero(S+j*ld*deg,ld*deg);
1114: PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
1115: PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
1116: pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1117: pep->errest[j] = sr->errest[sr->idxDef0[j]];
1118: }
1119: for (j=0;j<sr->ndef1;j++) {
1120: PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
1121: PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
1122: PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
1123: pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1124: pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1125: }
1126: MatDenseRestoreArray(MS,&S);
1127: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1128: BVSetActiveColumns(ctx->V,0,k+1);
1129: VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1130: VecGetArray(vomega,&om);
1131: for (j=0;j<k;j++) {
1132: BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1133: BVScaleColumn(ctx->V,j,1/norm);
1134: om[j] = (norm>=0.0)?1.0:-1.0;
1135: }
1136: BVTensorGetFactors(ctx->V,NULL,&MS);
1137: MatDenseGetArray(MS,&S);
1138: for (j=0;j<deg;j++) {
1139: BVSetRandomColumn(pep->V,k+j);
1140: BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1141: BVScaleColumn(pep->V,k+j,1.0/norm);
1142: S[k*ld*deg+j*ld+k+j] = norm;
1143: }
1144: MatDenseRestoreArray(MS,&S);
1145: BVSetActiveColumns(pep->V,0,k+deg);
1146: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1147: BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1148: BVScaleColumn(ctx->V,k,1.0/norm);
1149: om[k] = (norm>=0.0)?1.0:-1.0;
1150: VecRestoreArray(vomega,&om);
1151: BVSetSignature(ctx->V,vomega);
1152: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1153: VecGetArray(vomega,&om);
1154: for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1155: VecRestoreArray(vomega,&om);
1156: VecDestroy(&vomega);
1157: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1158: DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1159: PetscArrayzero(pQ,ldds*k);
1160: for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1161: DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1162: }
1163: BVSetActiveColumns(ctx->V,0,k+1);
1164: DSSetDimensions(pep->ds,k+1,PETSC_DEFAULT,PETSC_DEFAULT);
1165: DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
1166: BVGetSignature(ctx->V,vomega);
1167: DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
1169: PetscInfo(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%" PetscInt_FMT " right=%" PetscInt_FMT ", searching: left=%" PetscInt_FMT " right=%" PetscInt_FMT "\n",(double)sr->sPres->value,(double)(sr->sPres->neighb[0]?sr->sPres->neighb[0]->value:sr->int0),(double)(sr->sPres->neighb[1]?sr->sPres->neighb[1]->value:sr->int1),sr->ndef0,sr->ndef1,sr->sPres->nsch[0],sr->sPres->nsch[1]);
1171: /* Restart loop */
1172: l = 0;
1173: pep->nconv = k;
1174: while (pep->reason == PEP_CONVERGED_ITERATING) {
1175: pep->its++;
1176: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1177: b = a+ldds;
1178: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1180: /* Compute an nv-step Lanczos factorization */
1181: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1182: PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1183: beta = b[nv-1];
1184: if (symmlost && nv==pep->nconv+l) {
1185: pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1186: pep->nconv = nconv;
1187: PetscInfo(pep,"Symmetry lost in STOAR sigma=%g nconv=%" PetscInt_FMT "\n",(double)sr->sPres->value,nconv);
1188: if (falselock || !ctx->lock) {
1189: BVSetActiveColumns(ctx->V,0,pep->nconv);
1190: BVTensorCompress(ctx->V,0);
1191: }
1192: break;
1193: }
1194: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1195: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1196: DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l);
1197: if (l==0) DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1198: else DSSetState(pep->ds,DS_STATE_RAW);
1200: /* Solve projected problem */
1201: DSSolve(pep->ds,pep->eigr,pep->eigi);
1202: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1203: DSUpdateExtraRow(pep->ds);
1204: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
1206: /* Check convergence */
1207: /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1208: norm = 1.0;
1209: DSGetDimensions(pep->ds,NULL,NULL,NULL,&t);
1210: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1211: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1212: for (j=0;j<k;j++) back[j] = pep->eigr[j];
1213: STBackTransform(pep->st,k,back,pep->eigi);
1214: count0=count1=0;
1215: for (j=0;j<k;j++) {
1216: lambda = PetscRealPart(back[j]);
1217: if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1218: if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1219: }
1220: if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1221: /* Update l */
1222: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1223: else {
1224: l = PetscMax(1,(PetscInt)((nv-k)/2));
1225: l = PetscMin(l,t);
1226: DSGetTruncateSize(pep->ds,k,t,&l);
1227: if (!breakdown) {
1228: /* Prepare the Rayleigh quotient for restart */
1229: DSTruncate(pep->ds,k+l,PETSC_FALSE);
1230: }
1231: }
1232: nconv = k;
1233: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1234: if (l) PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);
1236: /* Update S */
1237: DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1238: BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1239: DSRestoreMat(pep->ds,DS_MAT_Q,&MQ);
1241: /* Copy last column of S */
1242: BVCopyColumn(ctx->V,nv,k+l);
1243: BVSetActiveColumns(ctx->V,0,k+l);
1244: if (k+l) {
1245: DSSetDimensions(pep->ds,k+l,PETSC_DEFAULT,PETSC_DEFAULT);
1246: DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
1247: BVSetSignature(ctx->V,vomega);
1248: DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega);
1249: }
1251: if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1252: /* stop if breakdown */
1253: PetscInfo(pep,"Breakdown TOAR method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta);
1254: pep->reason = PEP_DIVERGED_BREAKDOWN;
1255: }
1256: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1257: BVGetActiveColumns(pep->V,NULL,&nq);
1258: if (k+l+deg<=nq) {
1259: BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1260: if (!falselock && ctx->lock) BVTensorCompress(ctx->V,k-pep->nconv);
1261: else BVTensorCompress(ctx->V,0);
1262: }
1263: pep->nconv = k;
1264: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1265: }
1266: sr->itsKs += pep->its;
1267: if (pep->nconv>0) {
1268: BVSetActiveColumns(ctx->V,0,pep->nconv);
1269: BVGetActiveColumns(pep->V,NULL,&nq);
1270: BVSetActiveColumns(pep->V,0,nq);
1271: if (nq>pep->nconv) {
1272: BVTensorCompress(ctx->V,pep->nconv);
1273: BVSetActiveColumns(pep->V,0,pep->nconv);
1274: }
1275: for (j=0;j<pep->nconv;j++) {
1276: pep->eigr[j] *= pep->sfactor;
1277: pep->eigi[j] *= pep->sfactor;
1278: }
1279: }
1280: PetscInfo(pep,"Finished STOAR: nconv=%" PetscInt_FMT " (deflated=%" PetscInt_FMT ", left=%" PetscInt_FMT ", right=%" PetscInt_FMT ")\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1);
1281: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1282: RGPopScale(pep->rg);
1285: if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1287: } else sr->symmlost = 0;
1289: DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
1290: PetscFree(back);
1291: return 0;
1292: }
1294: #define SWAP(a,b,t) {t=a;a=b;b=t;}
1296: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1297: {
1298: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1299: PEP_SR sr=ctx->sr;
1300: PetscInt i=0,j,tmpi;
1301: PetscReal v,tmpr;
1302: PEP_shift s;
1306: if (!sr->s0) { /* PEPSolve not called yet */
1307: *n = 2;
1308: } else {
1309: *n = 1;
1310: s = sr->s0;
1311: while (s) {
1312: (*n)++;
1313: s = s->neighb[1];
1314: }
1315: }
1316: PetscMalloc1(*n,shifts);
1317: PetscMalloc1(*n,inertias);
1318: if (!sr->s0) { /* PEPSolve not called yet */
1319: (*shifts)[0] = sr->int0;
1320: (*shifts)[1] = sr->int1;
1321: (*inertias)[0] = sr->inertia0;
1322: (*inertias)[1] = sr->inertia1;
1323: } else {
1324: s = sr->s0;
1325: while (s) {
1326: (*shifts)[i] = s->value;
1327: (*inertias)[i++] = s->inertia;
1328: s = s->neighb[1];
1329: }
1330: (*shifts)[i] = sr->int1;
1331: (*inertias)[i] = sr->inertia1;
1332: }
1333: /* remove possible duplicate in last position */
1334: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1335: /* sort result */
1336: for (i=0;i<*n;i++) {
1337: v = (*shifts)[i];
1338: for (j=i+1;j<*n;j++) {
1339: if (v > (*shifts)[j]) {
1340: SWAP((*shifts)[i],(*shifts)[j],tmpr);
1341: SWAP((*inertias)[i],(*inertias)[j],tmpi);
1342: v = (*shifts)[i];
1343: }
1344: }
1345: }
1346: return 0;
1347: }
1349: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1350: {
1351: PetscInt i,j,ti,deg=pep->nmat-1;
1352: PetscReal newS;
1353: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1354: PEP_SR sr=ctx->sr;
1355: Mat S,B;
1356: PetscScalar *pS;
1358: PetscCitationsRegister(citation,&cited);
1360: /* Only with eigenvalues present in the interval ...*/
1361: if (sr->numEigs==0) {
1362: pep->reason = PEP_CONVERGED_TOL;
1363: return 0;
1364: }
1366: /* Inner product matrix */
1367: PEPSTOARSetUpInnerMatrix(pep,&B);
1369: /* Array of pending shifts */
1370: sr->maxPend = 100; /* Initial size */
1371: sr->nPend = 0;
1372: PetscMalloc1(sr->maxPend,&sr->pending);
1373: PEPCreateShift(pep,sr->int0,NULL,NULL);
1374: /* extract first shift */
1375: sr->sPrev = NULL;
1376: sr->sPres = sr->pending[--sr->nPend];
1377: sr->sPres->inertia = sr->inertia0;
1378: pep->target = sr->sPres->value;
1379: sr->s0 = sr->sPres;
1380: sr->indexEig = 0;
1382: for (i=0;i<sr->numEigs;i++) {
1383: sr->eigr[i] = 0.0;
1384: sr->eigi[i] = 0.0;
1385: sr->errest[i] = 0.0;
1386: sr->perm[i] = i;
1387: }
1388: /* Vectors for deflation */
1389: PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1390: sr->indexEig = 0;
1391: while (sr->sPres) {
1392: /* Search for deflation */
1393: PEPLookForDeflation(pep);
1394: /* KrylovSchur */
1395: PEPSTOAR_QSlice(pep,B);
1397: PEPStoreEigenpairs(pep);
1398: /* Select new shift */
1399: if (!sr->sPres->comp[1]) {
1400: PEPGetNewShiftValue(pep,1,&newS);
1401: PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1402: }
1403: if (!sr->sPres->comp[0]) {
1404: /* Completing earlier interval */
1405: PEPGetNewShiftValue(pep,0,&newS);
1406: PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1407: }
1408: /* Preparing for a new search of values */
1409: PEPExtractShift(pep);
1410: }
1412: /* Updating pep values prior to exit */
1413: PetscFree2(sr->idxDef0,sr->idxDef1);
1414: PetscFree(sr->pending);
1415: pep->nconv = sr->indexEig;
1416: pep->reason = PEP_CONVERGED_TOL;
1417: pep->its = sr->itsKs;
1418: pep->nev = sr->indexEig;
1419: MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1420: MatDenseGetArray(S,&pS);
1421: for (i=0;i<pep->nconv;i++) {
1422: for (j=0;j<sr->qinfo[i].nq;j++) pS[i*pep->nconv+sr->qinfo[i].q[j]] = *(sr->S+i*sr->ld*deg+j);
1423: }
1424: MatDenseRestoreArray(S,&pS);
1425: BVSetActiveColumns(sr->V,0,pep->nconv);
1426: BVMultInPlace(sr->V,S,0,pep->nconv);
1427: MatDestroy(&S);
1428: BVDestroy(&pep->V);
1429: pep->V = sr->V;
1430: PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1431: pep->eigr = sr->eigr;
1432: pep->eigi = sr->eigi;
1433: pep->perm = sr->perm;
1434: pep->errest = sr->errest;
1435: if (sr->dir<0) {
1436: for (i=0;i<pep->nconv/2;i++) {
1437: ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1438: }
1439: }
1440: PetscFree(ctx->inertias);
1441: PetscFree(ctx->shifts);
1442: MatDestroy(&B);
1443: PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1444: return 0;
1445: }