Actual source code: qslice.c
slepc-3.15.2 2021-09-20
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: SLEPc 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: {
48: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
49: PEP_SR sr=ctx->sr;
50: PEP_shift s;
51: PetscInt i;
54: if (sr) {
55: /* Reviewing list of shifts to free memory */
56: s = sr->s0;
57: if (s) {
58: while (s->neighb[1]) {
59: s = s->neighb[1];
60: PetscFree(s->neighb[0]);
61: }
62: PetscFree(s);
63: }
64: PetscFree(sr->S);
65: for (i=0;i<pep->nconv;i++) {PetscFree(sr->qinfo[i].q);}
66: PetscFree(sr->qinfo);
67: for (i=0;i<3;i++) {VecDestroy(&sr->v[i]);}
68: EPSDestroy(&sr->eps);
69: PetscFree(sr);
70: }
71: ctx->sr = NULL;
72: return(0);
73: }
75: PetscErrorCode PEPReset_STOAR_QSlice(PEP pep)
76: {
78: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
81: PEPQSliceResetSR(pep);
82: PetscFree(ctx->inertias);
83: PetscFree(ctx->shifts);
84: return(0);
85: }
87: /*
88: PEPQSliceAllocateSolution - Allocate memory storage for common variables such
89: as eigenvalues and eigenvectors.
90: */
91: static PetscErrorCode PEPQSliceAllocateSolution(PEP pep)
92: {
94: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
95: PetscInt k;
96: PetscLogDouble cnt;
97: BVType type;
98: Vec t;
99: PEP_SR sr = ctx->sr;
102: /* allocate space for eigenvalues and friends */
103: k = PetscMax(1,sr->numEigs);
104: PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
105: PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
106: PetscFree(sr->qinfo);
107: PetscCalloc1(k,&sr->qinfo);
108: cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
109: PetscLogObjectMemory((PetscObject)pep,cnt);
111: /* allocate sr->V and transfer options from pep->V */
112: BVDestroy(&sr->V);
113: BVCreate(PetscObjectComm((PetscObject)pep),&sr->V);
114: PetscLogObjectParent((PetscObject)pep,(PetscObject)sr->V);
115: if (!pep->V) { PEPGetBV(pep,&pep->V); }
116: if (!((PetscObject)(pep->V))->type_name) {
117: BVSetType(sr->V,BVSVEC);
118: } else {
119: BVGetType(pep->V,&type);
120: BVSetType(sr->V,type);
121: }
122: STMatCreateVecsEmpty(pep->st,&t,NULL);
123: BVSetSizesFromVec(sr->V,t,k+1);
124: VecDestroy(&t);
125: sr->ld = k;
126: PetscFree(sr->S);
127: PetscMalloc1((k+1)*sr->ld*(pep->nmat-1),&sr->S);
128: return(0);
129: }
131: /* Convergence test to compute positive Ritz values */
132: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
133: {
135: *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
136: return(0);
137: }
139: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
140: {
141: KSP ksp,kspr;
142: PC pc;
143: Mat F;
144: PetscBool flg;
148: if (!pep->solvematcoeffs) {
149: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
150: }
151: if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
152: pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
153: } else {
154: PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL);
155: }
156: STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs);
157: STGetKSP(pep->st,&ksp);
158: KSPGetPC(ksp,&pc);
159: PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg);
160: if (flg) {
161: PCRedundantGetKSP(pc,&kspr);
162: KSPGetPC(kspr,&pc);
163: }
164: PCFactorGetMatrix(pc,&F);
165: MatGetInertia(F,inertia,zeros,NULL);
166: return(0);
167: }
169: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
170: {
172: KSP ksp;
173: Mat P;
174: PetscReal nzshift=0.0;
175: PetscScalar dot;
176: PetscRandom rand;
177: PetscInt nconv;
178: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
179: PEP_SR sr=ctx->sr;
182: if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
183: *inertia = 0;
184: } else if (shift <= PETSC_MIN_REAL) {
185: *inertia = 0;
186: if (zeros) *zeros = 0;
187: } else {
188: /* If the shift is zero, perturb it to a very small positive value.
189: The goal is that the nonzero pattern is the same in all cases and reuse
190: the symbolic factorizations */
191: nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
192: PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros);
193: STSetShift(pep->st,nzshift);
194: }
195: if (!correction) {
196: if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
197: else if (shift>PETSC_MIN_REAL) {
198: STGetKSP(pep->st,&ksp);
199: KSPGetOperators(ksp,&P,NULL);
200: if (*inertia!=pep->n && !sr->v[0]) {
201: MatCreateVecs(P,&sr->v[0],NULL);
202: VecDuplicate(sr->v[0],&sr->v[1]);
203: VecDuplicate(sr->v[0],&sr->v[2]);
204: BVGetRandomContext(pep->V,&rand);
205: VecSetRandom(sr->v[0],rand);
206: }
207: if (*inertia<pep->n && *inertia>0) {
208: if (!sr->eps) {
209: EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps);
210: EPSSetProblemType(sr->eps,EPS_HEP);
211: EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL);
212: }
213: EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL);
214: EPSSetOperators(sr->eps,P,NULL);
215: EPSSolve(sr->eps);
216: EPSGetConverged(sr->eps,&nconv);
217: if (!nconv) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",nzshift);
218: EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]);
219: }
220: if (*inertia!=pep->n) {
221: MatMult(pep->A[1],sr->v[0],sr->v[1]);
222: MatMult(pep->A[2],sr->v[0],sr->v[2]);
223: VecAXPY(sr->v[1],2*nzshift,sr->v[2]);
224: VecDot(sr->v[1],sr->v[0],&dot);
225: if (PetscRealPart(dot)>0.0) *inertia = 2*pep->n-*inertia;
226: }
227: }
228: } else if (correction<0) *inertia = 2*pep->n-*inertia;
229: return(0);
230: }
232: /*
233: Check eigenvalue type - used only in non-hyperbolic problems.
234: All computed eigenvalues must have the same definite type (positive or negative).
235: If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
236: closest to shift and determine its type.
237: */
238: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
239: {
241: PEP pep2;
242: ST st;
243: PetscInt nconv;
244: PetscScalar lambda,dot;
245: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
246: PEP_SR sr=ctx->sr;
249: if (!ini) {
250: if (-(omega/(shift*ctx->alpha+ctx->beta))*sr->type<0) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)shift);
251: } else {
252: PEPCreate(PetscObjectComm((PetscObject)pep),&pep2);
253: PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix);
254: PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_");
255: PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4);
256: PEPSetType(pep2,PEPTOAR);
257: PEPSetOperators(pep2,pep->nmat,pep->A);
258: PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE);
259: PEPGetRG(pep2,&pep2->rg);
260: RGSetType(pep2->rg,RGINTERVAL);
261: #if defined(PETSC_USE_COMPLEX)
262: RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON);
263: #else
264: RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0);
265: #endif
266: pep2->target = shift;
267: st = pep2->st;
268: pep2->st = pep->st;
269: PEPSolve(pep2);
270: PEPGetConverged(pep2,&nconv);
271: if (nconv) {
272: PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL);
273: MatMult(pep->A[1],pep2->work[0],pep2->work[1]);
274: MatMult(pep->A[2],pep2->work[0],pep2->work[2]);
275: VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]);
276: VecDot(pep2->work[1],pep2->work[0],&dot);
277: PetscInfo2(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(PetscRealPart(dot)>0.0)?"positive":"negative");
278: if (!sr->type) sr->type = (PetscRealPart(dot)>0.0)?1:-1;
279: else {
280: if (sr->type*PetscRealPart(dot)<0.0) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)PetscRealPart(lambda));
281: }
282: }
283: pep2->st = st;
284: PEPDestroy(&pep2);
285: }
286: return(0);
287: }
289: PETSC_STATIC_INLINE PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
290: {
291: PetscReal ap,bp,cp,dis;
292: PetscScalar ts;
296: MatMult(pep->A[0],u,w);
297: VecDot(w,u,&ts);
298: cp = PetscRealPart(ts);
299: MatMult(pep->A[1],u,w);
300: VecDot(w,u,&ts);
301: bp = PetscRealPart(ts);
302: MatMult(pep->A[2],u,w);
303: VecDot(w,u,&ts);
304: ap = PetscRealPart(ts);
305: dis = bp*bp-4*ap*cp;
306: if (dis>=0.0 && smas) {
307: if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
308: else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
309: else {
310: if (bp >0) *smas = -cp/bp;
311: else *smas = PETSC_MAX_REAL;
312: }
313: }
314: if (dis>=0.0 && smenos) {
315: if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
316: else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
317: else {
318: if (bp<0) *smenos = -cp/bp;
319: else *smenos = PETSC_MAX_REAL;
320: }
321: }
322: if (d) *d = dis;
323: return(0);
324: }
326: PETSC_STATIC_INLINE PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
327: {
331: MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN);
332: MatAXPY(M,x,pep->A[1],str);
333: MatAXPY(M,x*x,pep->A[2],str);
334: return(0);
335: }
337: /*@
338: PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
339: is definite or not.
341: Logically Collective on pep
343: Input Parameter:
344: . pep - eigensolver context
346: Output Parameters:
347: + xi - first computed parameter
348: . mu - second computed parameter
349: . definite - flag indicating that the problem is definite
350: - hyperbolic - flag indicating that the problem is hyperbolic
352: Notes:
353: This function is intended for quadratic eigenvalue problems, Q(lambda)=A*lambda^2+B*lambda+C,
354: with symmetric (or Hermitian) coefficient matrices A,B,C.
356: On output, the flag 'definite' may have the values -1 (meaning that the QEP is not
357: definite), 1 (if the problem is definite), or 0 if the algorithm was not able to
358: determine whether the problem is definite or not.
360: If definite=1, the output flag 'hyperbolic' informs in a similar way about whether the
361: problem is hyperbolic or not.
363: If definite=1, the computed values xi and mu satisfy Q(xi)<0 and Q(mu)>0, as
364: obtained via the method proposed in [Niendorf and Voss, LAA 2010]. Furthermore, if
365: hyperbolic=1 then only xi is computed.
367: Level: advanced
368: @*/
369: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
370: {
372: PetscRandom rand;
373: Vec u,w;
374: PetscReal d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
375: PetscInt k,its=10,hyp=0,check=0,nconv,inertia,n;
376: Mat M=NULL;
377: MatStructure str;
378: EPS eps;
379: PetscBool transform,ptypehyp;
382: if (pep->problem_type!=PEP_HERMITIAN && pep->problem_type!=PEP_HYPERBOLIC) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only available for Hermitian (or hyperbolic) problems");
383: ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
384: if (!pep->st) { PEPGetST(pep,&pep->st); }
385: PEPSetDefaultST(pep);
386: STSetMatrices(pep->st,pep->nmat,pep->A);
387: MatGetSize(pep->A[0],&n,NULL);
388: STGetTransform(pep->st,&transform);
389: STSetTransform(pep->st,PETSC_FALSE);
390: STSetUp(pep->st);
391: MatCreateVecs(pep->A[0],&u,&w);
392: PEPGetBV(pep,&pep->V);
393: BVGetRandomContext(pep->V,&rand);
394: VecSetRandom(u,rand);
395: VecNormalize(u,NULL);
396: PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL);
397: if (d<0.0) check = -1;
398: if (!check) {
399: EPSCreate(PetscObjectComm((PetscObject)pep),&eps);
400: EPSSetProblemType(eps,EPS_HEP);
401: EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
402: EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE);
403: MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M);
404: STGetMatStructure(pep->st,&str);
405: }
406: for (k=0;k<its&&!check;k++) {
407: PEPQSliceEvaluateQEP(pep,s,M,str);
408: EPSSetOperators(eps,M,NULL);
409: EPSSolve(eps);
410: EPSGetConverged(eps,&nconv);
411: if (!nconv) break;
412: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
413: sp = s;
414: PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
415: if (d<0.0) {check = -1; break;}
416: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
417: if (s>sp) {hyp = -1;}
418: mut = 2*s-sp;
419: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
420: if (inertia == n) {check = 1; break;}
421: }
422: for (;k<its&&!check;k++) {
423: mut = (s-omg)/2;
424: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
425: if (inertia == n) {check = 1; break;}
426: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
427: PEPQSliceEvaluateQEP(pep,omg,M,str);
428: EPSSetOperators(eps,M,NULL);
429: EPSSolve(eps);
430: EPSGetConverged(eps,&nconv);
431: if (!nconv) break;
432: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
433: omgp = omg;
434: PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
435: if (d<0.0) {check = -1; break;}
436: if (omg<omgp) hyp = -1;
437: }
438: if (check==1) *xi = mut;
439: if (hyp==-1 && ptypehyp) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Problem does not satisfy hyperbolic test; consider removing the hyperbolicity flag");
440: if (check==1 && hyp==0) {
441: PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL);
442: if (inertia == 0) hyp = 1;
443: else hyp = -1;
444: }
445: if (check==1 && hyp!=1) {
446: check = 0;
447: EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
448: for (;k<its&&!check;k++) {
449: PEPQSliceEvaluateQEP(pep,s,M,str);
450: EPSSetOperators(eps,M,NULL);
451: EPSSolve(eps);
452: EPSGetConverged(eps,&nconv);
453: if (!nconv) break;
454: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
455: sp = s;
456: PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg);
457: if (d<0.0) {check = -1; break;}
458: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
459: mut = 2*s-sp;
460: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
461: if (inertia == 0) {check = 1; break;}
462: }
463: for (;k<its&&!check;k++) {
464: mut = (s-omg)/2;
465: PEPQSliceMatGetInertia(pep,mut,&inertia,NULL);
466: if (inertia == 0) {check = 1; break;}
467: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
468: PEPQSliceEvaluateQEP(pep,omg,M,str);
469: EPSSetOperators(eps,M,NULL);
470: EPSSolve(eps);
471: EPSGetConverged(eps,&nconv);
472: if (!nconv) break;
473: EPSGetEigenpair(eps,0,NULL,NULL,u,w);
474: PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg);
475: if (d<0.0) {check = -1; break;}
476: }
477: }
478: if (check==1) *mu = mut;
479: *definite = check;
480: *hyperbolic = hyp;
481: if (M) { MatDestroy(&M); }
482: VecDestroy(&u);
483: VecDestroy(&w);
484: EPSDestroy(&eps);
485: STSetTransform(pep->st,transform);
486: return(0);
487: }
489: /*
490: Dummy backtransform operation
491: */
492: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
493: {
495: return(0);
496: }
498: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
499: {
501: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
502: PEP_SR sr;
503: PetscInt ld,i,zeros=0;
504: SlepcSC sc;
505: PetscReal r;
508: PEPCheckSinvertCayley(pep);
509: if (pep->inta==pep->intb) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues unless you provide a computational interval with PEPSetInterval()");
510: if (pep->intb >= PETSC_MAX_REAL && pep->inta <= PETSC_MIN_REAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
511: PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
512: if (pep->tol==PETSC_DEFAULT) {
513: #if defined(PETSC_USE_REAL_SINGLE)
514: pep->tol = SLEPC_DEFAULT_TOL;
515: #else
516: /* use tighter tolerance */
517: pep->tol = SLEPC_DEFAULT_TOL*1e-2;
518: #endif
519: }
520: if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n); /* nev not set, use default value */
521: if (pep->n>10 && ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
522: pep->ops->backtransform = PEPBackTransform_Skip;
523: if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;
525: /* create spectrum slicing context and initialize it */
526: PEPQSliceResetSR(pep);
527: PetscNewLog(pep,&sr);
528: ctx->sr = sr;
529: sr->itsKs = 0;
530: sr->nleap = 0;
531: sr->sPres = NULL;
533: if (pep->solvematcoeffs) { PetscFree(pep->solvematcoeffs); }
534: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
535: if (!pep->st) { PEPGetST(pep,&pep->st); }
536: STSetTransform(pep->st,PETSC_FALSE);
537: STSetUp(pep->st);
539: ctx->hyperbolic = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
541: /* check presence of ends and finding direction */
542: if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
543: sr->int0 = pep->inta;
544: sr->int1 = pep->intb;
545: sr->dir = 1;
546: if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
547: sr->hasEnd = PETSC_FALSE;
548: } else sr->hasEnd = PETSC_TRUE;
549: } else {
550: sr->int0 = pep->intb;
551: sr->int1 = pep->inta;
552: sr->dir = -1;
553: sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
554: }
556: /* compute inertia0 */
557: PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
558: if (zeros && (sr->int0==pep->inta || sr->int0==pep->intb)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
559: if (!ctx->hyperbolic && ctx->checket) {
560: PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE);
561: }
563: /* compute inertia1 */
564: PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1);
565: if (zeros) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
566: if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
567: PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE);
568: if (!sr->type && (sr->inertia1-sr->inertia0)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"No information of eigenvalue type in Interval");
569: if (sr->type && !(sr->inertia1-sr->inertia0)) SETERRQ(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected");
570: if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
571: sr->intcorr = -1;
572: sr->inertia0 = 2*pep->n-sr->inertia0;
573: sr->inertia1 = 2*pep->n-sr->inertia1;
574: } else sr->intcorr = 1;
575: } else {
576: if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
577: else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
578: }
580: if (sr->hasEnd) {
581: sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
582: i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
583: }
585: /* number of eigenvalues in interval */
586: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
587: PetscInfo3(pep,"QSlice setup: allocating for %D eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb);
588: if (sr->numEigs) {
589: PEPQSliceAllocateSolution(pep);
590: PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd);
591: pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
592: ld = ctx->ncv+2;
593: DSSetType(pep->ds,DSGHIEP);
594: DSSetCompact(pep->ds,PETSC_TRUE);
595: DSSetExtraRow(pep->ds,PETSC_TRUE);
596: DSAllocate(pep->ds,ld);
597: DSGetSlepcSC(pep->ds,&sc);
598: sc->rg = NULL;
599: sc->comparison = SlepcCompareLargestMagnitude;
600: sc->comparisonctx = NULL;
601: sc->map = NULL;
602: sc->mapobj = NULL;
603: } else {pep->ncv = 0; pep->nev = 0; pep->mpd = 0;}
604: return(0);
605: }
607: /*
608: Fills the fields of a shift structure
609: */
610: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
611: {
613: PEP_shift s,*pending2;
614: PetscInt i;
615: PEP_SR sr;
616: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
619: sr = ctx->sr;
620: PetscNewLog(pep,&s);
621: s->value = val;
622: s->neighb[0] = neighb0;
623: if (neighb0) neighb0->neighb[1] = s;
624: s->neighb[1] = neighb1;
625: if (neighb1) neighb1->neighb[0] = s;
626: s->comp[0] = PETSC_FALSE;
627: s->comp[1] = PETSC_FALSE;
628: s->index = -1;
629: s->neigs = 0;
630: s->nconv[0] = s->nconv[1] = 0;
631: s->nsch[0] = s->nsch[1]=0;
632: /* Inserts in the stack of pending shifts */
633: /* If needed, the array is resized */
634: if (sr->nPend >= sr->maxPend) {
635: sr->maxPend *= 2;
636: PetscMalloc1(sr->maxPend,&pending2);
637: PetscLogObjectMemory((PetscObject)pep,sr->maxPend*sizeof(PEP_shift*));
638: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
639: PetscFree(sr->pending);
640: sr->pending = pending2;
641: }
642: sr->pending[sr->nPend++]=s;
643: return(0);
644: }
646: /* Provides next shift to be computed */
647: static PetscErrorCode PEPExtractShift(PEP pep)
648: {
650: PetscInt iner,zeros=0;
651: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
652: PEP_SR sr;
653: PetscReal newShift,aux;
654: PEP_shift sPres;
657: sr = ctx->sr;
658: if (sr->nPend > 0) {
659: if (sr->dirch) {
660: aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
661: iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
662: sr->dir *= -1;
663: PetscFree(sr->s0->neighb[1]);
664: PetscFree(sr->s0);
665: sr->nPend--;
666: PEPCreateShift(pep,sr->int0,NULL,NULL);
667: sr->sPrev = NULL;
668: sr->sPres = sr->pending[--sr->nPend];
669: pep->target = sr->sPres->value;
670: sr->s0 = sr->sPres;
671: pep->reason = PEP_CONVERGED_ITERATING;
672: } else {
673: sr->sPrev = sr->sPres;
674: sr->sPres = sr->pending[--sr->nPend];
675: }
676: sPres = sr->sPres;
677: PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
678: if (zeros) {
679: newShift = sPres->value*(1.0+SLICE_PTOL);
680: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
681: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
682: PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
683: if (zeros) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
684: sPres->value = newShift;
685: }
686: sr->sPres->inertia = iner;
687: pep->target = sr->sPres->value;
688: pep->reason = PEP_CONVERGED_ITERATING;
689: pep->its = 0;
690: } else sr->sPres = NULL;
691: return(0);
692: }
694: /*
695: Obtains value of subsequent shift
696: */
697: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
698: {
699: PetscReal lambda,d_prev;
700: PetscInt i,idxP;
701: PEP_SR sr;
702: PEP_shift sPres,s;
703: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
706: sr = ctx->sr;
707: sPres = sr->sPres;
708: if (sPres->neighb[side]) {
709: /* Completing a previous interval */
710: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
711: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
712: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
713: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
714: } else { /* (Only for side=1). Creating a new interval. */
715: if (sPres->neigs==0) {/* No value has been accepted*/
716: if (sPres->neighb[0]) {
717: /* Multiplying by 10 the previous distance */
718: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
719: sr->nleap++;
720: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
721: if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unable to compute the wanted eigenvalues with open interval");
722: } else { /* First shift */
723: if (pep->nconv != 0) {
724: /* Unaccepted values give information for next shift */
725: idxP=0;/* Number of values left from shift */
726: for (i=0;i<pep->nconv;i++) {
727: lambda = PetscRealPart(pep->eigr[i]);
728: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
729: else break;
730: }
731: /* Avoiding subtraction of eigenvalues (might be the same).*/
732: if (idxP>0) {
733: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
734: } else {
735: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
736: }
737: *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
738: sr->dirch = PETSC_FALSE;
739: } else { /* No values found, no information for next shift */
740: if (!sr->dirch) {
741: sr->dirch = PETSC_TRUE;
742: *newS = sr->int1;
743: } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"First shift renders no information");
744: }
745: }
746: } else { /* Accepted values found */
747: sr->dirch = PETSC_FALSE;
748: sr->nleap = 0;
749: /* Average distance of values in previous subinterval */
750: s = sPres->neighb[0];
751: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
752: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
753: }
754: if (s) {
755: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
756: } else { /* First shift. Average distance obtained with values in this shift */
757: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
758: 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)) {
759: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
760: } else {
761: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
762: }
763: }
764: /* Average distance is used for next shift by adding it to value on the right or to shift */
765: if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
766: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
767: } else { /* Last accepted value is on the left of shift. Adding to shift */
768: *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
769: }
770: }
771: /* End of interval can not be surpassed */
772: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
773: }/* of neighb[side]==null */
774: return(0);
775: }
777: /*
778: Function for sorting an array of real values
779: */
780: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
781: {
782: PetscReal re;
783: PetscInt i,j,tmp;
786: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
787: /* Insertion sort */
788: for (i=1;i<nr;i++) {
789: re = PetscRealPart(r[perm[i]]);
790: j = i-1;
791: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
792: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
793: }
794: }
795: return(0);
796: }
798: /* Stores the pairs obtained since the last shift in the global arrays */
799: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
800: {
802: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
803: PetscReal lambda,err,*errest;
804: PetscInt i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
805: PetscBool iscayley,divide=PETSC_FALSE;
806: PEP_SR sr = ctx->sr;
807: PEP_shift sPres;
808: Vec w,vomega;
809: Mat MS;
810: BV tV;
811: PetscScalar *S,*eigr,*tS,*omega;
814: sPres = sr->sPres;
815: sPres->index = sr->indexEig;
817: if (nconv>sr->ndef0+sr->ndef1) {
818: /* Back-transform */
819: STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
820: for (i=0;i<nconv;i++) {
821: #if defined(PETSC_USE_COMPLEX)
822: if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
823: #else
824: if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
825: #endif
826: }
827: PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
828: /* Sort eigenvalues */
829: sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
830: VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
831: BVGetSignature(ctx->V,vomega);
832: VecGetArray(vomega,&omega);
833: BVGetSizes(pep->V,NULL,NULL,&ld);
834: BVTensorGetFactors(ctx->V,NULL,&MS);
835: MatDenseGetArray(MS,&S);
836: /* Values stored in global array */
837: PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
838: ndef = sr->ndef0+sr->ndef1;
839: for (i=0;i<nconv;i++) {
840: lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
841: err = pep->errest[pep->perm[i]];
842: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
843: if (sr->indexEig+count-ndef>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unexpected error in Spectrum Slicing");
844: PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
845: eigr[count] = lambda;
846: errest[count] = err;
847: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
848: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
849: PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
850: PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
851: count++;
852: }
853: }
854: VecRestoreArray(vomega,&omega);
855: VecDestroy(&vomega);
856: for (i=0;i<count;i++) {
857: PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
858: PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
859: }
860: MatDenseRestoreArray(MS,&S);
861: BVTensorRestoreFactors(ctx->V,NULL,&MS);
862: BVSetActiveColumns(ctx->V,0,count);
863: BVTensorCompress(ctx->V,count);
864: if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
865: divide = PETSC_TRUE;
866: BVTensorGetFactors(ctx->V,NULL,&MS);
867: MatDenseGetArray(MS,&S);
868: PetscArrayzero(tS,nconv*nconv*d);
869: for (i=0;i<count;i++) {
870: PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
871: PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
872: }
873: MatDenseRestoreArray(MS,&S);
874: BVTensorRestoreFactors(ctx->V,NULL,&MS);
875: BVSetActiveColumns(pep->V,0,count);
876: BVDuplicateResize(pep->V,count,&tV);
877: BVCopy(pep->V,tV);
878: }
879: if (sr->sPres->nconv[0]) {
880: if (divide) {
881: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
882: BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
883: }
884: for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
885: for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
886: BVTensorGetFactors(ctx->V,NULL,&MS);
887: MatDenseGetArray(MS,&S);
888: for (i=0;i<sr->sPres->nconv[0];i++) {
889: sr->eigr[aux[i]] = eigr[i];
890: sr->errest[aux[i]] = errest[i];
891: BVGetColumn(pep->V,i,&w);
892: BVInsertVec(sr->V,aux[i],w);
893: BVRestoreColumn(pep->V,i,&w);
894: idx = sr->ld*d*aux[i];
895: PetscArrayzero(sr->S+idx,sr->ld*d);
896: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
897: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
898: PetscFree(sr->qinfo[aux[i]].q);
899: PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
900: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
901: sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
902: }
903: MatDenseRestoreArray(MS,&S);
904: BVTensorRestoreFactors(ctx->V,NULL,&MS);
905: }
907: if (sr->sPres->nconv[1]) {
908: if (divide) {
909: BVTensorGetFactors(ctx->V,NULL,&MS);
910: MatDenseGetArray(MS,&S);
911: for (i=0;i<sr->sPres->nconv[1];i++) {
912: PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
913: PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
914: }
915: MatDenseRestoreArray(MS,&S);
916: BVTensorRestoreFactors(ctx->V,NULL,&MS);
917: BVSetActiveColumns(pep->V,0,count);
918: BVCopy(tV,pep->V);
919: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
920: BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
921: }
922: for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
923: for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
924: BVTensorGetFactors(ctx->V,NULL,&MS);
925: MatDenseGetArray(MS,&S);
926: for (i=0;i<sr->sPres->nconv[1];i++) {
927: sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
928: sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
929: BVGetColumn(pep->V,i,&w);
930: BVInsertVec(sr->V,aux[i],w);
931: BVRestoreColumn(pep->V,i,&w);
932: idx = sr->ld*d*aux[i];
933: PetscArrayzero(sr->S+idx,sr->ld*d);
934: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
935: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
936: PetscFree(sr->qinfo[aux[i]].q);
937: PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
938: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
939: sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
940: }
941: MatDenseRestoreArray(MS,&S);
942: BVTensorRestoreFactors(ctx->V,NULL,&MS);
943: }
944: sPres->neigs = count-sr->ndef0-sr->ndef1;
945: sr->indexEig += sPres->neigs;
946: sPres->nconv[0]-= sr->ndef0;
947: sPres->nconv[1]-= sr->ndef1;
948: PetscFree4(eigr,errest,tS,aux);
949: } else {
950: sPres->neigs = 0;
951: sPres->nconv[0]= 0;
952: sPres->nconv[1]= 0;
953: }
954: /* Global ordering array updating */
955: sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
956: /* Check for completion */
957: sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
958: sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
959: if (sPres->nconv[0] > sPres->nsch[0] || sPres->nconv[1] > sPres->nsch[1]) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
960: if (divide) { BVDestroy(&tV); }
961: return(0);
962: }
964: static PetscErrorCode PEPLookForDeflation(PEP pep)
965: {
966: PetscReal val;
967: PetscInt i,count0=0,count1=0;
968: PEP_shift sPres;
969: PetscInt ini,fin;
970: PEP_SR sr;
971: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
974: sr = ctx->sr;
975: sPres = sr->sPres;
977: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
978: else ini = 0;
979: fin = sr->indexEig;
980: /* Selection of ends for searching new values */
981: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
982: else sPres->ext[0] = sPres->neighb[0]->value;
983: if (!sPres->neighb[1]) {
984: if (sr->hasEnd) sPres->ext[1] = sr->int1;
985: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
986: } else sPres->ext[1] = sPres->neighb[1]->value;
987: /* Selection of values between right and left ends */
988: for (i=ini;i<fin;i++) {
989: val=PetscRealPart(sr->eigr[sr->perm[i]]);
990: /* Values to the right of left shift */
991: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
992: if ((sr->dir)*(val - sPres->value) < 0) count0++;
993: else count1++;
994: } else break;
995: }
996: /* The number of values on each side are found */
997: if (sPres->neighb[0]) {
998: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
999: if (sPres->nsch[0]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
1000: } else sPres->nsch[0] = 0;
1002: if (sPres->neighb[1]) {
1003: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1004: if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
1005: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
1007: /* Completing vector of indexes for deflation */
1008: for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
1009: sr->ndef0 = count0;
1010: for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
1011: sr->ndef1 = count1;
1012: return(0);
1013: }
1015: /*
1016: Compute a run of Lanczos iterations
1017: */
1018: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
1019: {
1021: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1022: PetscInt i,j,m=*M,l,lock;
1023: PetscInt lds,d,ld,offq,nqt,ldds;
1024: Vec v=t_[0],t=t_[1],q=t_[2];
1025: PetscReal norm,sym=0.0,fro=0.0,*f;
1026: PetscScalar *y,*S,sigma;
1027: PetscBLASInt j_,one=1;
1028: PetscBool lindep;
1029: Mat MS;
1032: PetscMalloc1(*M,&y);
1033: BVGetSizes(pep->V,NULL,NULL,&ld);
1034: BVTensorGetDegree(ctx->V,&d);
1035: BVGetActiveColumns(pep->V,&lock,&nqt);
1036: lds = d*ld;
1037: offq = ld;
1038: DSGetLeadingDimension(pep->ds,&ldds);
1040: *breakdown = PETSC_FALSE; /* ----- */
1041: STGetShift(pep->st,&sigma);
1042: DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
1043: BVSetActiveColumns(ctx->V,0,m);
1044: BVSetActiveColumns(pep->V,0,nqt);
1045: for (j=k;j<m;j++) {
1046: /* apply operator */
1047: BVTensorGetFactors(ctx->V,NULL,&MS);
1048: MatDenseGetArray(MS,&S);
1049: BVGetColumn(pep->V,nqt,&t);
1050: BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1051: MatMult(pep->A[1],v,q);
1052: MatMult(pep->A[2],v,t);
1053: VecAXPY(q,sigma*pep->sfactor,t);
1054: VecScale(q,pep->sfactor);
1055: BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1056: MatMult(pep->A[2],v,t);
1057: VecAXPY(q,pep->sfactor*pep->sfactor,t);
1058: STMatSolve(pep->st,q,t);
1059: VecScale(t,-1.0);
1060: BVRestoreColumn(pep->V,nqt,&t);
1062: /* orthogonalize */
1063: BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1064: if (!lindep) {
1065: *(S+(j+1)*lds+nqt) = norm;
1066: BVScaleColumn(pep->V,nqt,1.0/norm);
1067: nqt++;
1068: }
1069: for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1070: BVSetActiveColumns(pep->V,0,nqt);
1071: MatDenseRestoreArray(MS,&S);
1072: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1074: /* level-2 orthogonalization */
1075: BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1076: a[j] = PetscRealPart(y[j]);
1077: omega[j+1] = (norm > 0)?1.0:-1.0;
1078: BVScaleColumn(ctx->V,j+1,1.0/norm);
1079: b[j] = PetscAbsReal(norm);
1081: /* check symmetry */
1082: DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1083: if (j==k) {
1084: for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1085: for (i=0;i<l;i++) y[i] = 0.0;
1086: }
1087: DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1088: if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1089: PetscBLASIntCast(j,&j_);
1090: sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1091: fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1092: if (j>0) fro = SlepcAbs(fro,b[j-1]);
1093: if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1094: *symmlost = PETSC_TRUE;
1095: *M=j;
1096: break;
1097: }
1098: }
1099: BVSetActiveColumns(pep->V,lock,nqt);
1100: BVSetActiveColumns(ctx->V,0,*M);
1101: PetscFree(y);
1102: return(0);
1103: }
1105: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1106: {
1108: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1109: PetscInt j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1110: PetscInt nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1111: PetscScalar *om,sigma,*back,*S,*pQ;
1112: PetscReal beta,norm=1.0,*omega,*a,*b,eta,lambda;
1113: PetscBool breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1114: Mat MS,MQ;
1115: Vec v,vomega;
1116: PEP_SR sr;
1117: BVOrthogType otype;
1118: BVOrthogBlockType obtype;
1121: /* Resize if needed for deflating vectors */
1122: sr = ctx->sr;
1123: sigma = sr->sPres->value;
1124: k = sr->ndef0+sr->ndef1;
1125: pep->ncv = ctx->ncv+k;
1126: pep->nev = ctx->nev+k;
1127: PEPAllocateSolution(pep,3);
1128: BVDestroy(&ctx->V);
1129: BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1130: BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1131: BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1132: DSAllocate(pep->ds,pep->ncv+2);
1133: PetscMalloc1(pep->ncv,&back);
1134: DSGetLeadingDimension(pep->ds,&ldds);
1135: BVSetMatrix(ctx->V,B,PETSC_TRUE);
1136: if (ctx->lock) {
1137: /* undocumented option to use a cheaper locking instead of the true locking */
1138: PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1139: } else SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
1140: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1141: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1142: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
1144: /* Get the starting Arnoldi vector */
1145: BVSetActiveColumns(pep->V,0,1);
1146: BVTensorBuildFirstColumn(ctx->V,pep->nini);
1147: BVSetActiveColumns(ctx->V,0,1);
1148: if (k) {
1149: /* Insert deflated vectors */
1150: BVSetActiveColumns(pep->V,0,0);
1151: idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1152: for (j=0;j<k;j++) {
1153: BVGetColumn(pep->V,j,&v);
1154: BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1155: BVRestoreColumn(pep->V,j,&v);
1156: }
1157: /* Update innerproduct matrix */
1158: BVSetActiveColumns(ctx->V,0,0);
1159: BVTensorGetFactors(ctx->V,NULL,&MS);
1160: BVSetActiveColumns(pep->V,0,k);
1161: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1163: BVGetSizes(pep->V,NULL,NULL,&ld);
1164: BVTensorGetFactors(ctx->V,NULL,&MS);
1165: MatDenseGetArray(MS,&S);
1166: for (j=0;j<sr->ndef0;j++) {
1167: PetscArrayzero(S+j*ld*deg,ld*deg);
1168: PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
1169: PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
1170: pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1171: pep->errest[j] = sr->errest[sr->idxDef0[j]];
1172: }
1173: for (j=0;j<sr->ndef1;j++) {
1174: PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
1175: PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
1176: PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
1177: pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1178: pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1179: }
1180: MatDenseRestoreArray(MS,&S);
1181: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1182: BVSetActiveColumns(ctx->V,0,k+1);
1183: VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1184: VecGetArray(vomega,&om);
1185: for (j=0;j<k;j++) {
1186: BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1187: BVScaleColumn(ctx->V,j,1/norm);
1188: om[j] = (norm>=0.0)?1.0:-1.0;
1189: }
1190: BVTensorGetFactors(ctx->V,NULL,&MS);
1191: MatDenseGetArray(MS,&S);
1192: for (j=0;j<deg;j++) {
1193: BVSetRandomColumn(pep->V,k+j);
1194: BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1195: BVScaleColumn(pep->V,k+j,1.0/norm);
1196: S[k*ld*deg+j*ld+k+j] = norm;
1197: }
1198: MatDenseRestoreArray(MS,&S);
1199: BVSetActiveColumns(pep->V,0,k+deg);
1200: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1201: BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1202: BVScaleColumn(ctx->V,k,1.0/norm);
1203: om[k] = (norm>=0.0)?1.0:-1.0;
1204: VecRestoreArray(vomega,&om);
1205: BVSetSignature(ctx->V,vomega);
1206: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1207: VecGetArray(vomega,&om);
1208: for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1209: VecRestoreArray(vomega,&om);
1210: VecDestroy(&vomega);
1211: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1212: DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1213: PetscArrayzero(pQ,ldds*k);
1214: for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1215: DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1216: }
1217: BVSetActiveColumns(ctx->V,0,k+1);
1218: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1219: VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1220: BVGetSignature(ctx->V,vomega);
1221: VecGetArray(vomega,&om);
1222: for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
1223: VecRestoreArray(vomega,&om);
1224: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1225: VecDestroy(&vomega);
1227: PetscInfo7(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%D right=%D, searching: left=%D right=%D\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]);
1229: /* Restart loop */
1230: l = 0;
1231: pep->nconv = k;
1232: while (pep->reason == PEP_CONVERGED_ITERATING) {
1233: pep->its++;
1234: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1235: b = a+ldds;
1236: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1238: /* Compute an nv-step Lanczos factorization */
1239: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1240: PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1241: beta = b[nv-1];
1242: if (symmlost && nv==pep->nconv+l) {
1243: pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1244: pep->nconv = nconv;
1245: PetscInfo2(pep,"Symmetry lost in STOAR sigma=%g nconv=%D\n",(double)sr->sPres->value,nconv);
1246: if (falselock || !ctx->lock) {
1247: BVSetActiveColumns(ctx->V,0,pep->nconv);
1248: BVTensorCompress(ctx->V,0);
1249: }
1250: break;
1251: }
1252: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1253: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1254: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
1255: if (l==0) {
1256: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1257: } else {
1258: DSSetState(pep->ds,DS_STATE_RAW);
1259: }
1261: /* Solve projected problem */
1262: DSSolve(pep->ds,pep->eigr,pep->eigi);
1263: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1264: DSUpdateExtraRow(pep->ds);
1265: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
1267: /* Check convergence */
1268: /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1269: norm = 1.0;
1270: DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
1271: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1272: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1273: for (j=0;j<k;j++) back[j] = pep->eigr[j];
1274: STBackTransform(pep->st,k,back,pep->eigi);
1275: count0=count1=0;
1276: for (j=0;j<k;j++) {
1277: lambda = PetscRealPart(back[j]);
1278: if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1279: if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1280: }
1281: if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1282: /* Update l */
1283: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1284: else {
1285: l = PetscMax(1,(PetscInt)((nv-k)/2));
1286: l = PetscMin(l,t);
1287: DSGetTruncateSize(pep->ds,k,t,&l);
1288: if (!breakdown) {
1289: /* Prepare the Rayleigh quotient for restart */
1290: DSTruncate(pep->ds,k+l,PETSC_FALSE);
1291: }
1292: }
1293: nconv = k;
1294: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1295: if (l) { PetscInfo1(pep,"Preparing to restart keeping l=%D vectors\n",l); }
1297: /* Update S */
1298: DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1299: BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1300: MatDestroy(&MQ);
1302: /* Copy last column of S */
1303: BVCopyColumn(ctx->V,nv,k+l);
1304: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1305: VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
1306: VecGetArray(vomega,&om);
1307: for (j=0;j<k+l;j++) om[j] = omega[j];
1308: VecRestoreArray(vomega,&om);
1309: BVSetActiveColumns(ctx->V,0,k+l);
1310: BVSetSignature(ctx->V,vomega);
1311: VecDestroy(&vomega);
1312: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1314: if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1315: /* stop if breakdown */
1316: PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
1317: pep->reason = PEP_DIVERGED_BREAKDOWN;
1318: }
1319: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1320: BVGetActiveColumns(pep->V,NULL,&nq);
1321: if (k+l+deg<=nq) {
1322: BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1323: if (!falselock && ctx->lock) {
1324: BVTensorCompress(ctx->V,k-pep->nconv);
1325: } else {
1326: BVTensorCompress(ctx->V,0);
1327: }
1328: }
1329: pep->nconv = k;
1330: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1331: }
1332: sr->itsKs += pep->its;
1333: if (pep->nconv>0) {
1334: BVSetActiveColumns(ctx->V,0,pep->nconv);
1335: BVGetActiveColumns(pep->V,NULL,&nq);
1336: BVSetActiveColumns(pep->V,0,nq);
1337: if (nq>pep->nconv) {
1338: BVTensorCompress(ctx->V,pep->nconv);
1339: BVSetActiveColumns(pep->V,0,pep->nconv);
1340: }
1341: for (j=0;j<pep->nconv;j++) {
1342: pep->eigr[j] *= pep->sfactor;
1343: pep->eigi[j] *= pep->sfactor;
1344: }
1345: }
1346: PetscInfo4(pep,"Finished STOAR: nconv=%D (deflated=%D, left=%D, right=%D)\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1);
1347: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1348: RGPopScale(pep->rg);
1350: if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv<sr->ndef0+sr->ndef1) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1351: if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1352: if (++sr->symmlost>10) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1353: } else sr->symmlost = 0;
1355: DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
1356: PetscFree(back);
1357: return(0);
1358: }
1360: #define SWAP(a,b,t) {t=a;a=b;b=t;}
1362: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1363: {
1364: PetscErrorCode ierr;
1365: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1366: PEP_SR sr=ctx->sr;
1367: PetscInt i=0,j,tmpi;
1368: PetscReal v,tmpr;
1369: PEP_shift s;
1372: if (!pep->state) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
1373: if (!sr) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
1374: if (!sr->s0) { /* PEPSolve not called yet */
1375: *n = 2;
1376: } else {
1377: *n = 1;
1378: s = sr->s0;
1379: while (s) {
1380: (*n)++;
1381: s = s->neighb[1];
1382: }
1383: }
1384: PetscMalloc1(*n,shifts);
1385: PetscMalloc1(*n,inertias);
1386: if (!sr->s0) { /* PEPSolve not called yet */
1387: (*shifts)[0] = sr->int0;
1388: (*shifts)[1] = sr->int1;
1389: (*inertias)[0] = sr->inertia0;
1390: (*inertias)[1] = sr->inertia1;
1391: } else {
1392: s = sr->s0;
1393: while (s) {
1394: (*shifts)[i] = s->value;
1395: (*inertias)[i++] = s->inertia;
1396: s = s->neighb[1];
1397: }
1398: (*shifts)[i] = sr->int1;
1399: (*inertias)[i] = sr->inertia1;
1400: }
1401: /* remove possible duplicate in last position */
1402: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1403: /* sort result */
1404: for (i=0;i<*n;i++) {
1405: v = (*shifts)[i];
1406: for (j=i+1;j<*n;j++) {
1407: if (v > (*shifts)[j]) {
1408: SWAP((*shifts)[i],(*shifts)[j],tmpr);
1409: SWAP((*inertias)[i],(*inertias)[j],tmpi);
1410: v = (*shifts)[i];
1411: }
1412: }
1413: }
1414: return(0);
1415: }
1417: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1418: {
1420: PetscInt i,j,ti,deg=pep->nmat-1;
1421: PetscReal newS;
1422: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1423: PEP_SR sr=ctx->sr;
1424: Mat S,B;
1425: PetscScalar *pS;
1428: PetscCitationsRegister(citation,&cited);
1430: /* Only with eigenvalues present in the interval ...*/
1431: if (sr->numEigs==0) {
1432: pep->reason = PEP_CONVERGED_TOL;
1433: return(0);
1434: }
1436: /* Inner product matrix */
1437: PEPSTOARSetUpInnerMatrix(pep,&B);
1439: /* Array of pending shifts */
1440: sr->maxPend = 100; /* Initial size */
1441: sr->nPend = 0;
1442: PetscMalloc1(sr->maxPend,&sr->pending);
1443: PetscLogObjectMemory((PetscObject)pep,sr->maxPend*sizeof(PEP_shift*));
1444: PEPCreateShift(pep,sr->int0,NULL,NULL);
1445: /* extract first shift */
1446: sr->sPrev = NULL;
1447: sr->sPres = sr->pending[--sr->nPend];
1448: sr->sPres->inertia = sr->inertia0;
1449: pep->target = sr->sPres->value;
1450: sr->s0 = sr->sPres;
1451: sr->indexEig = 0;
1453: for (i=0;i<sr->numEigs;i++) {
1454: sr->eigr[i] = 0.0;
1455: sr->eigi[i] = 0.0;
1456: sr->errest[i] = 0.0;
1457: sr->perm[i] = i;
1458: }
1459: /* Vectors for deflation */
1460: PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1461: PetscLogObjectMemory((PetscObject)pep,2*sr->numEigs*sizeof(PetscInt));
1462: sr->indexEig = 0;
1463: while (sr->sPres) {
1464: /* Search for deflation */
1465: PEPLookForDeflation(pep);
1466: /* KrylovSchur */
1467: PEPSTOAR_QSlice(pep,B);
1469: PEPStoreEigenpairs(pep);
1470: /* Select new shift */
1471: if (!sr->sPres->comp[1]) {
1472: PEPGetNewShiftValue(pep,1,&newS);
1473: PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1474: }
1475: if (!sr->sPres->comp[0]) {
1476: /* Completing earlier interval */
1477: PEPGetNewShiftValue(pep,0,&newS);
1478: PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1479: }
1480: /* Preparing for a new search of values */
1481: PEPExtractShift(pep);
1482: }
1484: /* Updating pep values prior to exit */
1485: PetscFree2(sr->idxDef0,sr->idxDef1);
1486: PetscFree(sr->pending);
1487: pep->nconv = sr->indexEig;
1488: pep->reason = PEP_CONVERGED_TOL;
1489: pep->its = sr->itsKs;
1490: pep->nev = sr->indexEig;
1491: MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1492: MatDenseGetArray(S,&pS);
1493: for (i=0;i<pep->nconv;i++) {
1494: 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);
1495: }
1496: MatDenseRestoreArray(S,&pS);
1497: BVSetActiveColumns(sr->V,0,pep->nconv);
1498: BVMultInPlace(sr->V,S,0,pep->nconv);
1499: MatDestroy(&S);
1500: BVDestroy(&pep->V);
1501: pep->V = sr->V;
1502: PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1503: pep->eigr = sr->eigr;
1504: pep->eigi = sr->eigi;
1505: pep->perm = sr->perm;
1506: pep->errest = sr->errest;
1507: if (sr->dir<0) {
1508: for (i=0;i<pep->nconv/2;i++) {
1509: ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1510: }
1511: }
1512: PetscFree(ctx->inertias);
1513: PetscFree(ctx->shifts);
1514: MatDestroy(&B);
1515: PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1516: return(0);
1517: }