Actual source code: qslice.c
slepc-3.14.1 2020-12-08
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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: DSAllocate(pep->ds,ld);
596: DSGetSlepcSC(pep->ds,&sc);
597: sc->rg = NULL;
598: sc->comparison = SlepcCompareLargestMagnitude;
599: sc->comparisonctx = NULL;
600: sc->map = NULL;
601: sc->mapobj = NULL;
602: }
603: return(0);
604: }
606: /*
607: Fills the fields of a shift structure
608: */
609: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
610: {
612: PEP_shift s,*pending2;
613: PetscInt i;
614: PEP_SR sr;
615: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
618: sr = ctx->sr;
619: PetscNewLog(pep,&s);
620: s->value = val;
621: s->neighb[0] = neighb0;
622: if (neighb0) neighb0->neighb[1] = s;
623: s->neighb[1] = neighb1;
624: if (neighb1) neighb1->neighb[0] = s;
625: s->comp[0] = PETSC_FALSE;
626: s->comp[1] = PETSC_FALSE;
627: s->index = -1;
628: s->neigs = 0;
629: s->nconv[0] = s->nconv[1] = 0;
630: s->nsch[0] = s->nsch[1]=0;
631: /* Inserts in the stack of pending shifts */
632: /* If needed, the array is resized */
633: if (sr->nPend >= sr->maxPend) {
634: sr->maxPend *= 2;
635: PetscMalloc1(sr->maxPend,&pending2);
636: PetscLogObjectMemory((PetscObject)pep,sizeof(PEP_shift));
637: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
638: PetscFree(sr->pending);
639: sr->pending = pending2;
640: }
641: sr->pending[sr->nPend++]=s;
642: return(0);
643: }
645: /* Provides next shift to be computed */
646: static PetscErrorCode PEPExtractShift(PEP pep)
647: {
649: PetscInt iner,zeros=0;
650: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
651: PEP_SR sr;
652: PetscReal newShift,aux;
653: PEP_shift sPres;
656: sr = ctx->sr;
657: if (sr->nPend > 0) {
658: if (sr->dirch) {
659: aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
660: iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
661: sr->dir *= -1;
662: PetscFree(sr->s0->neighb[1]);
663: PetscFree(sr->s0);
664: sr->nPend--;
665: PEPCreateShift(pep,sr->int0,NULL,NULL);
666: sr->sPrev = NULL;
667: sr->sPres = sr->pending[--sr->nPend];
668: pep->target = sr->sPres->value;
669: sr->s0 = sr->sPres;
670: pep->reason = PEP_CONVERGED_ITERATING;
671: } else {
672: sr->sPrev = sr->sPres;
673: sr->sPres = sr->pending[--sr->nPend];
674: }
675: sPres = sr->sPres;
676: PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr);
677: if (zeros) {
678: newShift = sPres->value*(1.0+SLICE_PTOL);
679: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
680: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
681: PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr);
682: if (zeros) SETERRQ1(((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
683: sPres->value = newShift;
684: }
685: sr->sPres->inertia = iner;
686: pep->target = sr->sPres->value;
687: pep->reason = PEP_CONVERGED_ITERATING;
688: pep->its = 0;
689: } else sr->sPres = NULL;
690: return(0);
691: }
693: /*
694: Obtains value of subsequent shift
695: */
696: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
697: {
698: PetscReal lambda,d_prev;
699: PetscInt i,idxP;
700: PEP_SR sr;
701: PEP_shift sPres,s;
702: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
705: sr = ctx->sr;
706: sPres = sr->sPres;
707: if (sPres->neighb[side]) {
708: /* Completing a previous interval */
709: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
710: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
711: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
712: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
713: } else { /* (Only for side=1). Creating a new interval. */
714: if (sPres->neigs==0) {/* No value has been accepted*/
715: if (sPres->neighb[0]) {
716: /* Multiplying by 10 the previous distance */
717: *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
718: sr->nleap++;
719: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
720: if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unable to compute the wanted eigenvalues with open interval");
721: } else { /* First shift */
722: if (pep->nconv != 0) {
723: /* Unaccepted values give information for next shift */
724: idxP=0;/* Number of values left from shift */
725: for (i=0;i<pep->nconv;i++) {
726: lambda = PetscRealPart(pep->eigr[i]);
727: if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
728: else break;
729: }
730: /* Avoiding subtraction of eigenvalues (might be the same).*/
731: if (idxP>0) {
732: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
733: } else {
734: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
735: }
736: *newS = sPres->value + ((sr->dir)*d_prev*pep->nev)/2;
737: sr->dirch = PETSC_FALSE;
738: } else { /* No values found, no information for next shift */
739: if (!sr->dirch) {
740: sr->dirch = PETSC_TRUE;
741: *newS = sr->int1;
742: } else SETERRQ(PetscObjectComm((PetscObject)pep),1,"First shift renders no information");
743: }
744: }
745: } else { /* Accepted values found */
746: sr->dirch = PETSC_FALSE;
747: sr->nleap = 0;
748: /* Average distance of values in previous subinterval */
749: s = sPres->neighb[0];
750: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
751: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
752: }
753: if (s) {
754: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
755: } else { /* First shift. Average distance obtained with values in this shift */
756: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
757: 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)) {
758: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
759: } else {
760: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
761: }
762: }
763: /* Average distance is used for next shift by adding it to value on the right or to shift */
764: if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
765: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(pep->nev))/2;
766: } else { /* Last accepted value is on the left of shift. Adding to shift */
767: *newS = sPres->value + ((sr->dir)*d_prev*(pep->nev))/2;
768: }
769: }
770: /* End of interval can not be surpassed */
771: if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
772: }/* of neighb[side]==null */
773: return(0);
774: }
776: /*
777: Function for sorting an array of real values
778: */
779: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
780: {
781: PetscReal re;
782: PetscInt i,j,tmp;
785: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
786: /* Insertion sort */
787: for (i=1;i<nr;i++) {
788: re = PetscRealPart(r[perm[i]]);
789: j = i-1;
790: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
791: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
792: }
793: }
794: return(0);
795: }
797: /* Stores the pairs obtained since the last shift in the global arrays */
798: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
799: {
801: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
802: PetscReal lambda,err,*errest;
803: PetscInt i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
804: PetscBool iscayley,divide=PETSC_FALSE;
805: PEP_SR sr = ctx->sr;
806: PEP_shift sPres;
807: Vec w,vomega;
808: Mat MS;
809: BV tV;
810: PetscScalar *S,*eigr,*tS,*omega;
813: sPres = sr->sPres;
814: sPres->index = sr->indexEig;
816: if (nconv>sr->ndef0+sr->ndef1) {
817: /* Back-transform */
818: STBackTransform(pep->st,nconv,pep->eigr,pep->eigi);
819: for (i=0;i<nconv;i++) {
820: #if defined(PETSC_USE_COMPLEX)
821: if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
822: #else
823: if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
824: #endif
825: }
826: PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley);
827: /* Sort eigenvalues */
828: sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir);
829: VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega);
830: BVGetSignature(ctx->V,vomega);
831: VecGetArray(vomega,&omega);
832: BVGetSizes(pep->V,NULL,NULL,&ld);
833: BVTensorGetFactors(ctx->V,NULL,&MS);
834: MatDenseGetArray(MS,&S);
835: /* Values stored in global array */
836: PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux);
837: ndef = sr->ndef0+sr->ndef1;
838: for (i=0;i<nconv;i++) {
839: lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
840: err = pep->errest[pep->perm[i]];
841: if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
842: if (sr->indexEig+count-ndef>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Unexpected error in Spectrum Slicing");
843: PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE);
844: eigr[count] = lambda;
845: errest[count] = err;
846: if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
847: if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
848: PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv);
849: PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv);
850: count++;
851: }
852: }
853: VecRestoreArray(vomega,&omega);
854: VecDestroy(&vomega);
855: for (i=0;i<count;i++) {
856: PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv);
857: PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv);
858: }
859: MatDenseRestoreArray(MS,&S);
860: BVTensorRestoreFactors(ctx->V,NULL,&MS);
861: BVSetActiveColumns(ctx->V,0,count);
862: BVTensorCompress(ctx->V,count);
863: if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
864: divide = PETSC_TRUE;
865: BVTensorGetFactors(ctx->V,NULL,&MS);
866: MatDenseGetArray(MS,&S);
867: PetscArrayzero(tS,nconv*nconv*d);
868: for (i=0;i<count;i++) {
869: PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count);
870: PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count);
871: }
872: MatDenseRestoreArray(MS,&S);
873: BVTensorRestoreFactors(ctx->V,NULL,&MS);
874: BVSetActiveColumns(pep->V,0,count);
875: BVDuplicateResize(pep->V,count,&tV);
876: BVCopy(pep->V,tV);
877: }
878: if (sr->sPres->nconv[0]) {
879: if (divide) {
880: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]);
881: BVTensorCompress(ctx->V,sr->sPres->nconv[0]);
882: }
883: for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
884: for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
885: BVTensorGetFactors(ctx->V,NULL,&MS);
886: MatDenseGetArray(MS,&S);
887: for (i=0;i<sr->sPres->nconv[0];i++) {
888: sr->eigr[aux[i]] = eigr[i];
889: sr->errest[aux[i]] = errest[i];
890: BVGetColumn(pep->V,i,&w);
891: BVInsertVec(sr->V,aux[i],w);
892: BVRestoreColumn(pep->V,i,&w);
893: idx = sr->ld*d*aux[i];
894: PetscArrayzero(sr->S+idx,sr->ld*d);
895: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]);
896: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]);
897: PetscFree(sr->qinfo[aux[i]].q);
898: PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q);
899: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]);
900: sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
901: }
902: MatDenseRestoreArray(MS,&S);
903: BVTensorRestoreFactors(ctx->V,NULL,&MS);
904: }
906: if (sr->sPres->nconv[1]) {
907: if (divide) {
908: BVTensorGetFactors(ctx->V,NULL,&MS);
909: MatDenseGetArray(MS,&S);
910: for (i=0;i<sr->sPres->nconv[1];i++) {
911: PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count);
912: PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count);
913: }
914: MatDenseRestoreArray(MS,&S);
915: BVTensorRestoreFactors(ctx->V,NULL,&MS);
916: BVSetActiveColumns(pep->V,0,count);
917: BVCopy(tV,pep->V);
918: BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]);
919: BVTensorCompress(ctx->V,sr->sPres->nconv[1]);
920: }
921: for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
922: for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
923: BVTensorGetFactors(ctx->V,NULL,&MS);
924: MatDenseGetArray(MS,&S);
925: for (i=0;i<sr->sPres->nconv[1];i++) {
926: sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
927: sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
928: BVGetColumn(pep->V,i,&w);
929: BVInsertVec(sr->V,aux[i],w);
930: BVRestoreColumn(pep->V,i,&w);
931: idx = sr->ld*d*aux[i];
932: PetscArrayzero(sr->S+idx,sr->ld*d);
933: PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]);
934: PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]);
935: PetscFree(sr->qinfo[aux[i]].q);
936: PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q);
937: PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]);
938: sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
939: }
940: MatDenseRestoreArray(MS,&S);
941: BVTensorRestoreFactors(ctx->V,NULL,&MS);
942: }
943: sPres->neigs = count-sr->ndef0-sr->ndef1;
944: sr->indexEig += sPres->neigs;
945: sPres->nconv[0]-= sr->ndef0;
946: sPres->nconv[1]-= sr->ndef1;
947: PetscFree4(eigr,errest,tS,aux);
948: } else {
949: sPres->neigs = 0;
950: sPres->nconv[0]= 0;
951: sPres->nconv[1]= 0;
952: }
953: /* Global ordering array updating */
954: sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir);
955: /* Check for completion */
956: sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
957: sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
958: 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");
959: if (divide) { BVDestroy(&tV); }
960: return(0);
961: }
963: static PetscErrorCode PEPLookForDeflation(PEP pep)
964: {
965: PetscReal val;
966: PetscInt i,count0=0,count1=0;
967: PEP_shift sPres;
968: PetscInt ini,fin;
969: PEP_SR sr;
970: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
973: sr = ctx->sr;
974: sPres = sr->sPres;
976: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
977: else ini = 0;
978: fin = sr->indexEig;
979: /* Selection of ends for searching new values */
980: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
981: else sPres->ext[0] = sPres->neighb[0]->value;
982: if (!sPres->neighb[1]) {
983: if (sr->hasEnd) sPres->ext[1] = sr->int1;
984: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
985: } else sPres->ext[1] = sPres->neighb[1]->value;
986: /* Selection of values between right and left ends */
987: for (i=ini;i<fin;i++) {
988: val=PetscRealPart(sr->eigr[sr->perm[i]]);
989: /* Values to the right of left shift */
990: if ((sr->dir)*(val - sPres->ext[1]) < 0) {
991: if ((sr->dir)*(val - sPres->value) < 0) count0++;
992: else count1++;
993: } else break;
994: }
995: /* The number of values on each side are found */
996: if (sPres->neighb[0]) {
997: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
998: if (sPres->nsch[0]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
999: } else sPres->nsch[0] = 0;
1001: if (sPres->neighb[1]) {
1002: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
1003: if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Mismatch between number of values found and information from inertia");
1004: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
1006: /* Completing vector of indexes for deflation */
1007: for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
1008: sr->ndef0 = count0;
1009: for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
1010: sr->ndef1 = count1;
1011: return(0);
1012: }
1014: /*
1015: Compute a run of Lanczos iterations
1016: */
1017: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
1018: {
1020: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1021: PetscInt i,j,m=*M,l,lock;
1022: PetscInt lds,d,ld,offq,nqt,ldds;
1023: Vec v=t_[0],t=t_[1],q=t_[2];
1024: PetscReal norm,sym=0.0,fro=0.0,*f;
1025: PetscScalar *y,*S,sigma;
1026: PetscBLASInt j_,one=1;
1027: PetscBool lindep;
1028: Mat MS;
1031: PetscMalloc1(*M,&y);
1032: BVGetSizes(pep->V,NULL,NULL,&ld);
1033: BVTensorGetDegree(ctx->V,&d);
1034: BVGetActiveColumns(pep->V,&lock,&nqt);
1035: lds = d*ld;
1036: offq = ld;
1037: DSGetLeadingDimension(pep->ds,&ldds);
1039: *breakdown = PETSC_FALSE; /* ----- */
1040: STGetShift(pep->st,&sigma);
1041: DSGetDimensions(pep->ds,NULL,NULL,&l,NULL,NULL);
1042: BVSetActiveColumns(ctx->V,0,m);
1043: BVSetActiveColumns(pep->V,0,nqt);
1044: for (j=k;j<m;j++) {
1045: /* apply operator */
1046: BVTensorGetFactors(ctx->V,NULL,&MS);
1047: MatDenseGetArray(MS,&S);
1048: BVGetColumn(pep->V,nqt,&t);
1049: BVMultVec(pep->V,1.0,0.0,v,S+j*lds);
1050: MatMult(pep->A[1],v,q);
1051: MatMult(pep->A[2],v,t);
1052: VecAXPY(q,sigma*pep->sfactor,t);
1053: VecScale(q,pep->sfactor);
1054: BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds);
1055: MatMult(pep->A[2],v,t);
1056: VecAXPY(q,pep->sfactor*pep->sfactor,t);
1057: STMatSolve(pep->st,q,t);
1058: VecScale(t,-1.0);
1059: BVRestoreColumn(pep->V,nqt,&t);
1061: /* orthogonalize */
1062: BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep);
1063: if (!lindep) {
1064: *(S+(j+1)*lds+nqt) = norm;
1065: BVScaleColumn(pep->V,nqt,1.0/norm);
1066: nqt++;
1067: }
1068: for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1069: BVSetActiveColumns(pep->V,0,nqt);
1070: MatDenseRestoreArray(MS,&S);
1071: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1073: /* level-2 orthogonalization */
1074: BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep);
1075: a[j] = PetscRealPart(y[j]);
1076: omega[j+1] = (norm > 0)?1.0:-1.0;
1077: BVScaleColumn(ctx->V,j+1,1.0/norm);
1078: b[j] = PetscAbsReal(norm);
1080: /* check symmetry */
1081: DSGetArrayReal(pep->ds,DS_MAT_T,&f);
1082: if (j==k) {
1083: for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1084: for (i=0;i<l;i++) y[i] = 0.0;
1085: }
1086: DSRestoreArrayReal(pep->ds,DS_MAT_T,&f);
1087: if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1088: PetscBLASIntCast(j,&j_);
1089: sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1090: fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1091: if (j>0) fro = SlepcAbs(fro,b[j-1]);
1092: if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1093: *symmlost = PETSC_TRUE;
1094: *M=j;
1095: break;
1096: }
1097: }
1098: BVSetActiveColumns(pep->V,lock,nqt);
1099: BVSetActiveColumns(ctx->V,0,*M);
1100: PetscFree(y);
1101: return(0);
1102: }
1104: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1105: {
1107: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1108: PetscInt j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1109: PetscInt nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1110: PetscScalar *Q,*om,sigma,*back,*S,*pQ;
1111: PetscReal beta,norm=1.0,*omega,*a,*b,*r,eta,lambda;
1112: PetscBool breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1113: Mat MS,MQ;
1114: Vec v,vomega;
1115: PEP_SR sr;
1116: BVOrthogType otype;
1117: BVOrthogBlockType obtype;
1120: /* Resize if needed for deflating vectors */
1121: sr = ctx->sr;
1122: sigma = sr->sPres->value;
1123: k = sr->ndef0+sr->ndef1;
1124: pep->ncv = ctx->ncv+k;
1125: pep->nev = ctx->nev+k;
1126: PEPAllocateSolution(pep,3);
1127: BVDestroy(&ctx->V);
1128: BVCreateTensor(pep->V,pep->nmat-1,&ctx->V);
1129: BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype);
1130: BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
1131: DSAllocate(pep->ds,pep->ncv+2);
1132: PetscMalloc1(pep->ncv,&back);
1133: DSGetLeadingDimension(pep->ds,&ldds);
1134: BVSetMatrix(ctx->V,B,PETSC_TRUE);
1135: if (ctx->lock) {
1136: /* undocumented option to use a cheaper locking instead of the true locking */
1137: PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL);
1138: } else SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
1139: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
1140: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
1141: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
1143: /* Get the starting Arnoldi vector */
1144: BVSetActiveColumns(pep->V,0,1);
1145: BVTensorBuildFirstColumn(ctx->V,pep->nini);
1146: BVSetActiveColumns(ctx->V,0,1);
1147: if (k) {
1148: /* Insert deflated vectors */
1149: BVSetActiveColumns(pep->V,0,0);
1150: idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1151: for (j=0;j<k;j++) {
1152: BVGetColumn(pep->V,j,&v);
1153: BVCopyVec(sr->V,sr->qinfo[idx].q[j],v);
1154: BVRestoreColumn(pep->V,j,&v);
1155: }
1156: /* Update innerproduct matrix */
1157: BVSetActiveColumns(ctx->V,0,0);
1158: BVTensorGetFactors(ctx->V,NULL,&MS);
1159: BVSetActiveColumns(pep->V,0,k);
1160: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1162: BVGetSizes(pep->V,NULL,NULL,&ld);
1163: BVTensorGetFactors(ctx->V,NULL,&MS);
1164: MatDenseGetArray(MS,&S);
1165: for (j=0;j<sr->ndef0;j++) {
1166: PetscArrayzero(S+j*ld*deg,ld*deg);
1167: PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k);
1168: PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k);
1169: pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1170: pep->errest[j] = sr->errest[sr->idxDef0[j]];
1171: }
1172: for (j=0;j<sr->ndef1;j++) {
1173: PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg);
1174: PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k);
1175: PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k);
1176: pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1177: pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1178: }
1179: MatDenseRestoreArray(MS,&S);
1180: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1181: BVSetActiveColumns(ctx->V,0,k+1);
1182: VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1183: VecGetArray(vomega,&om);
1184: for (j=0;j<k;j++) {
1185: BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL);
1186: BVScaleColumn(ctx->V,j,1/norm);
1187: om[j] = (norm>=0.0)?1.0:-1.0;
1188: }
1189: BVTensorGetFactors(ctx->V,NULL,&MS);
1190: MatDenseGetArray(MS,&S);
1191: for (j=0;j<deg;j++) {
1192: BVSetRandomColumn(pep->V,k+j);
1193: BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL);
1194: BVScaleColumn(pep->V,k+j,1.0/norm);
1195: S[k*ld*deg+j*ld+k+j] = norm;
1196: }
1197: MatDenseRestoreArray(MS,&S);
1198: BVSetActiveColumns(pep->V,0,k+deg);
1199: BVTensorRestoreFactors(ctx->V,NULL,&MS);
1200: BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL);
1201: BVScaleColumn(ctx->V,k,1.0/norm);
1202: om[k] = (norm>=0.0)?1.0:-1.0;
1203: VecRestoreArray(vomega,&om);
1204: BVSetSignature(ctx->V,vomega);
1205: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1206: VecGetArray(vomega,&om);
1207: for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1208: VecRestoreArray(vomega,&om);
1209: VecDestroy(&vomega);
1210: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1211: DSGetArray(pep->ds,DS_MAT_Q,&pQ);
1212: PetscArrayzero(pQ,ldds*k);
1213: for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1214: DSRestoreArray(pep->ds,DS_MAT_Q,&pQ);
1215: }
1216: BVSetActiveColumns(ctx->V,0,k+1);
1217: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1218: VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega);
1219: BVGetSignature(ctx->V,vomega);
1220: VecGetArray(vomega,&om);
1221: for (j=0;j<k+1;j++) omega[j] = PetscRealPart(om[j]);
1222: VecRestoreArray(vomega,&om);
1223: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1224: VecDestroy(&vomega);
1226: 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]);
1228: /* Restart loop */
1229: l = 0;
1230: pep->nconv = k;
1231: while (pep->reason == PEP_CONVERGED_ITERATING) {
1232: pep->its++;
1233: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1234: b = a+ldds;
1235: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1237: /* Compute an nv-step Lanczos factorization */
1238: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1239: PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work);
1240: beta = b[nv-1];
1241: if (symmlost && nv==pep->nconv+l) {
1242: pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1243: pep->nconv = nconv;
1244: PetscInfo2(pep,"Symmetry lost in STOAR sigma=%g nconv=%D\n",(double)sr->sPres->value,nconv);
1245: if (falselock || !ctx->lock) {
1246: BVSetActiveColumns(ctx->V,0,pep->nconv);
1247: BVTensorCompress(ctx->V,0);
1248: }
1249: break;
1250: }
1251: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1252: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1253: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
1254: if (l==0) {
1255: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
1256: } else {
1257: DSSetState(pep->ds,DS_STATE_RAW);
1258: }
1260: /* Solve projected problem */
1261: DSSolve(pep->ds,pep->eigr,pep->eigi);
1262: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
1263: DSSynchronize(pep->ds,pep->eigr,pep->eigi);
1265: /* Check convergence */
1266: /* PEPSTOARpreKConvergence(pep,nv,&norm,pep->work);*/
1267: norm = 1.0;
1268: DSGetDimensions(pep->ds,NULL,NULL,NULL,NULL,&t);
1269: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k);
1270: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
1271: for (j=0;j<k;j++) back[j] = pep->eigr[j];
1272: STBackTransform(pep->st,k,back,pep->eigi);
1273: count0=count1=0;
1274: for (j=0;j<k;j++) {
1275: lambda = PetscRealPart(back[j]);
1276: if (((sr->dir)*(sr->sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1277: if (((sr->dir)*(lambda - sr->sPres->value) > 0) && ((sr->dir)*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1278: }
1279: if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1280: /* Update l */
1281: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1282: else {
1283: l = PetscMax(1,(PetscInt)((nv-k)/2));
1284: l = PetscMin(l,t);
1285: if (!breakdown) {
1286: DSGetArrayReal(pep->ds,DS_MAT_T,&a);
1287: if (*(a+ldds+k+l-1)!=0) {
1288: if (k+l<nv-1) l = l+1;
1289: else l = l-1;
1290: }
1291: /* Prepare the Rayleigh quotient for restart */
1292: DSGetArray(pep->ds,DS_MAT_Q,&Q);
1293: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1294: r = a + 2*ldds;
1295: for (j=k;j<k+l;j++) {
1296: r[j] = PetscRealPart(Q[nv-1+j*ldds]*beta);
1297: }
1298: b = a+ldds;
1299: b[k+l-1] = r[k+l-1];
1300: omega[k+l] = omega[nv];
1301: DSRestoreArray(pep->ds,DS_MAT_Q,&Q);
1302: DSRestoreArrayReal(pep->ds,DS_MAT_T,&a);
1303: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1304: }
1305: }
1306: nconv = k;
1307: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1309: /* Update S */
1310: DSGetMat(pep->ds,DS_MAT_Q,&MQ);
1311: BVMultInPlace(ctx->V,MQ,pep->nconv,k+l);
1312: MatDestroy(&MQ);
1314: /* Copy last column of S */
1315: BVCopyColumn(ctx->V,nv,k+l);
1316: DSGetArrayReal(pep->ds,DS_MAT_D,&omega);
1317: VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
1318: VecGetArray(vomega,&om);
1319: for (j=0;j<k+l;j++) om[j] = omega[j];
1320: VecRestoreArray(vomega,&om);
1321: BVSetActiveColumns(ctx->V,0,k+l);
1322: BVSetSignature(ctx->V,vomega);
1323: VecDestroy(&vomega);
1324: DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega);
1326: if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1327: /* stop if breakdown */
1328: PetscInfo2(pep,"Breakdown TOAR method (it=%D norm=%g)\n",pep->its,(double)beta);
1329: pep->reason = PEP_DIVERGED_BREAKDOWN;
1330: }
1331: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1332: BVGetActiveColumns(pep->V,NULL,&nq);
1333: if (k+l+deg<=nq) {
1334: BVSetActiveColumns(ctx->V,pep->nconv,k+l+1);
1335: if (!falselock && ctx->lock) {
1336: BVTensorCompress(ctx->V,k-pep->nconv);
1337: } else {
1338: BVTensorCompress(ctx->V,0);
1339: }
1340: }
1341: pep->nconv = k;
1342: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
1343: }
1344: sr->itsKs += pep->its;
1345: if (pep->nconv>0) {
1346: BVSetActiveColumns(ctx->V,0,pep->nconv);
1347: BVGetActiveColumns(pep->V,NULL,&nq);
1348: BVSetActiveColumns(pep->V,0,nq);
1349: if (nq>pep->nconv) {
1350: BVTensorCompress(ctx->V,pep->nconv);
1351: BVSetActiveColumns(pep->V,0,pep->nconv);
1352: }
1353: for (j=0;j<pep->nconv;j++) {
1354: pep->eigr[j] *= pep->sfactor;
1355: pep->eigi[j] *= pep->sfactor;
1356: }
1357: }
1358: 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);
1359: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
1360: RGPopScale(pep->rg);
1362: 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);
1363: if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1364: if (++sr->symmlost>10) SETERRQ1(PetscObjectComm((PetscObject)pep),1,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1365: } else sr->symmlost = 0;
1367: /* truncate Schur decomposition and change the state to raw so that
1368: DSVectors() computes eigenvectors from scratch */
1369: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
1370: DSSetState(pep->ds,DS_STATE_RAW);
1371: PetscFree(back);
1372: return(0);
1373: }
1375: #define SWAP(a,b,t) {t=a;a=b;b=t;}
1377: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1378: {
1379: PetscErrorCode ierr;
1380: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1381: PEP_SR sr=ctx->sr;
1382: PetscInt i=0,j,tmpi;
1383: PetscReal v,tmpr;
1384: PEP_shift s;
1387: if (!pep->state) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
1388: if (!sr) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
1389: if (!sr->s0) { /* PEPSolve not called yet */
1390: *n = 2;
1391: } else {
1392: *n = 1;
1393: s = sr->s0;
1394: while (s) {
1395: (*n)++;
1396: s = s->neighb[1];
1397: }
1398: }
1399: PetscMalloc1(*n,shifts);
1400: PetscMalloc1(*n,inertias);
1401: if (!sr->s0) { /* PEPSolve not called yet */
1402: (*shifts)[0] = sr->int0;
1403: (*shifts)[1] = sr->int1;
1404: (*inertias)[0] = sr->inertia0;
1405: (*inertias)[1] = sr->inertia1;
1406: } else {
1407: s = sr->s0;
1408: while (s) {
1409: (*shifts)[i] = s->value;
1410: (*inertias)[i++] = s->inertia;
1411: s = s->neighb[1];
1412: }
1413: (*shifts)[i] = sr->int1;
1414: (*inertias)[i] = sr->inertia1;
1415: }
1416: /* remove possible duplicate in last position */
1417: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1418: /* sort result */
1419: for (i=0;i<*n;i++) {
1420: v = (*shifts)[i];
1421: for (j=i+1;j<*n;j++) {
1422: if (v > (*shifts)[j]) {
1423: SWAP((*shifts)[i],(*shifts)[j],tmpr);
1424: SWAP((*inertias)[i],(*inertias)[j],tmpi);
1425: v = (*shifts)[i];
1426: }
1427: }
1428: }
1429: return(0);
1430: }
1432: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1433: {
1435: PetscInt i,j,ti,deg=pep->nmat-1;
1436: PetscReal newS;
1437: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1438: PEP_SR sr=ctx->sr;
1439: Mat S,B;
1440: PetscScalar *pS;
1443: PetscCitationsRegister(citation,&cited);
1445: /* Only with eigenvalues present in the interval ...*/
1446: if (sr->numEigs==0) {
1447: pep->reason = PEP_CONVERGED_TOL;
1448: return(0);
1449: }
1451: /* Inner product matrix */
1452: PEPSTOARSetUpInnerMatrix(pep,&B);
1454: /* Array of pending shifts */
1455: sr->maxPend = 100; /* Initial size */
1456: sr->nPend = 0;
1457: PetscMalloc1(sr->maxPend,&sr->pending);
1458: PetscLogObjectMemory((PetscObject)pep,(sr->maxPend)*sizeof(PEP_shift));
1459: PEPCreateShift(pep,sr->int0,NULL,NULL);
1460: /* extract first shift */
1461: sr->sPrev = NULL;
1462: sr->sPres = sr->pending[--sr->nPend];
1463: sr->sPres->inertia = sr->inertia0;
1464: pep->target = sr->sPres->value;
1465: sr->s0 = sr->sPres;
1466: sr->indexEig = 0;
1468: /* Memory reservation for auxiliary variables */
1469: PetscLogObjectMemory((PetscObject)pep,(sr->numEigs+2*pep->ncv)*sizeof(PetscScalar));
1470: for (i=0;i<sr->numEigs;i++) {
1471: sr->eigr[i] = 0.0;
1472: sr->eigi[i] = 0.0;
1473: sr->errest[i] = 0.0;
1474: sr->perm[i] = i;
1475: }
1476: /* Vectors for deflation */
1477: PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1);
1478: PetscLogObjectMemory((PetscObject)pep,sr->numEigs*sizeof(PetscInt));
1479: sr->indexEig = 0;
1480: while (sr->sPres) {
1481: /* Search for deflation */
1482: PEPLookForDeflation(pep);
1483: /* KrylovSchur */
1484: PEPSTOAR_QSlice(pep,B);
1486: PEPStoreEigenpairs(pep);
1487: /* Select new shift */
1488: if (!sr->sPres->comp[1]) {
1489: PEPGetNewShiftValue(pep,1,&newS);
1490: PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]);
1491: }
1492: if (!sr->sPres->comp[0]) {
1493: /* Completing earlier interval */
1494: PEPGetNewShiftValue(pep,0,&newS);
1495: PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres);
1496: }
1497: /* Preparing for a new search of values */
1498: PEPExtractShift(pep);
1499: }
1501: /* Updating pep values prior to exit */
1502: PetscFree2(sr->idxDef0,sr->idxDef1);
1503: PetscFree(sr->pending);
1504: pep->nconv = sr->indexEig;
1505: pep->reason = PEP_CONVERGED_TOL;
1506: pep->its = sr->itsKs;
1507: pep->nev = sr->indexEig;
1508: MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S);
1509: MatDenseGetArray(S,&pS);
1510: for (i=0;i<pep->nconv;i++) {
1511: 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);
1512: }
1513: MatDenseRestoreArray(S,&pS);
1514: BVSetActiveColumns(sr->V,0,pep->nconv);
1515: BVMultInPlace(sr->V,S,0,pep->nconv);
1516: MatDestroy(&S);
1517: BVDestroy(&pep->V);
1518: pep->V = sr->V;
1519: PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm);
1520: pep->eigr = sr->eigr;
1521: pep->eigi = sr->eigi;
1522: pep->perm = sr->perm;
1523: pep->errest = sr->errest;
1524: if (sr->dir<0) {
1525: for (i=0;i<pep->nconv/2;i++) {
1526: ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1527: }
1528: }
1529: PetscFree(ctx->inertias);
1530: PetscFree(ctx->shifts);
1531: MatDestroy(&B);
1532: PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
1533: return(0);
1534: }