Actual source code: qslice.c
slepc-3.21.1 2024-04-26
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: SLEPc polynomial eigensolver: "stoar"
13: Method: S-TOAR with spectrum slicing for symmetric quadratic eigenproblems
15: Algorithm:
17: Symmetric Two-Level Orthogonal Arnoldi.
19: References:
21: [1] C. Campos and J.E. Roman, "Inertia-based spectrum slicing
22: for symmetric quadratic eigenvalue problems", Numer. Linear
23: Algebra Appl. 27(4):e2293, 2020.
24: */
26: #include <slepc/private/pepimpl.h>
27: #include "../src/pep/impls/krylov/pepkrylov.h"
28: #include <slepcblaslapack.h>
30: static PetscBool cited = PETSC_FALSE;
31: static const char citation[] =
32: "@Article{slepc-slice-qep,\n"
33: " author = \"C. Campos and J. E. Roman\",\n"
34: " title = \"Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems\",\n"
35: " journal = \"Numer. Linear Algebra Appl.\",\n"
36: " volume = \"27\",\n"
37: " number = \"4\",\n"
38: " pages = \"e2293\",\n"
39: " year = \"2020,\"\n"
40: " doi = \"https://doi.org/10.1002/nla.2293\"\n"
41: "}\n";
43: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON
45: static PetscErrorCode PEPQSliceResetSR(PEP pep)
46: {
47: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
48: PEP_SR sr=ctx->sr;
49: PEP_shift s;
50: PetscInt i;
52: PetscFunctionBegin;
53: if (sr) {
54: /* Reviewing list of shifts to free memory */
55: s = sr->s0;
56: if (s) {
57: while (s->neighb[1]) {
58: s = s->neighb[1];
59: PetscCall(PetscFree(s->neighb[0]));
60: }
61: PetscCall(PetscFree(s));
62: }
63: PetscCall(PetscFree(sr->S));
64: for (i=0;i<pep->nconv;i++) PetscCall(PetscFree(sr->qinfo[i].q));
65: PetscCall(PetscFree(sr->qinfo));
66: for (i=0;i<3;i++) PetscCall(VecDestroy(&sr->v[i]));
67: PetscCall(EPSDestroy(&sr->eps));
68: PetscCall(PetscFree(sr));
69: }
70: ctx->sr = NULL;
71: PetscFunctionReturn(PETSC_SUCCESS);
72: }
74: PetscErrorCode PEPReset_STOAR_QSlice(PEP pep)
75: {
76: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
78: PetscFunctionBegin;
79: PetscCall(PEPQSliceResetSR(pep));
80: PetscCall(PetscFree(ctx->inertias));
81: PetscCall(PetscFree(ctx->shifts));
82: PetscFunctionReturn(PETSC_SUCCESS);
83: }
85: /*
86: PEPQSliceAllocateSolution - Allocate memory storage for common variables such
87: as eigenvalues and eigenvectors.
88: */
89: static PetscErrorCode PEPQSliceAllocateSolution(PEP pep)
90: {
91: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
92: PetscInt k;
93: BVType type;
94: Vec t;
95: PEP_SR sr = ctx->sr;
97: PetscFunctionBegin;
98: /* allocate space for eigenvalues and friends */
99: k = PetscMax(1,sr->numEigs);
100: PetscCall(PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm));
101: PetscCall(PetscCalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm));
102: PetscCall(PetscFree(sr->qinfo));
103: PetscCall(PetscCalloc1(k,&sr->qinfo));
105: /* allocate sr->V and transfer options from pep->V */
106: PetscCall(BVDestroy(&sr->V));
107: PetscCall(BVCreate(PetscObjectComm((PetscObject)pep),&sr->V));
108: if (!pep->V) PetscCall(PEPGetBV(pep,&pep->V));
109: if (!((PetscObject)pep->V)->type_name) PetscCall(BVSetType(sr->V,BVMAT));
110: else {
111: PetscCall(BVGetType(pep->V,&type));
112: PetscCall(BVSetType(sr->V,type));
113: }
114: PetscCall(STMatCreateVecsEmpty(pep->st,&t,NULL));
115: PetscCall(BVSetSizesFromVec(sr->V,t,k+1));
116: PetscCall(VecDestroy(&t));
117: sr->ld = k;
118: PetscCall(PetscFree(sr->S));
119: PetscCall(PetscMalloc1((k+1)*sr->ld*(pep->nmat-1),&sr->S));
120: PetscFunctionReturn(PETSC_SUCCESS);
121: }
123: /* Convergence test to compute positive Ritz values */
124: static PetscErrorCode ConvergedPositive(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
125: {
126: PetscFunctionBegin;
127: *errest = (PetscRealPart(eigr)>0.0)?0.0:res;
128: PetscFunctionReturn(PETSC_SUCCESS);
129: }
131: static PetscErrorCode PEPQSliceMatGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
132: {
133: KSP ksp,kspr;
134: PC pc;
135: Mat F;
136: PetscBool flg;
138: PetscFunctionBegin;
139: if (!pep->solvematcoeffs) PetscCall(PetscMalloc1(pep->nmat,&pep->solvematcoeffs));
140: if (shift==PETSC_MAX_REAL) { /* Inertia of matrix A[2] */
141: pep->solvematcoeffs[0] = 0.0; pep->solvematcoeffs[1] = 0.0; pep->solvematcoeffs[2] = 1.0;
142: } else PetscCall(PEPEvaluateBasis(pep,shift,0,pep->solvematcoeffs,NULL));
143: PetscCall(STMatSetUp(pep->st,pep->sfactor,pep->solvematcoeffs));
144: PetscCall(STGetKSP(pep->st,&ksp));
145: PetscCall(KSPGetPC(ksp,&pc));
146: PetscCall(PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg));
147: if (flg) {
148: PetscCall(PCRedundantGetKSP(pc,&kspr));
149: PetscCall(KSPGetPC(kspr,&pc));
150: }
151: PetscCall(PCFactorGetMatrix(pc,&F));
152: PetscCall(MatGetInertia(F,inertia,zeros,NULL));
153: PetscFunctionReturn(PETSC_SUCCESS);
154: }
156: static PetscErrorCode PEPQSliceGetInertia(PEP pep,PetscReal shift,PetscInt *inertia,PetscInt *zeros,PetscInt correction)
157: {
158: KSP ksp;
159: Mat P;
160: PetscReal nzshift=0.0,dot;
161: PetscRandom rand;
162: PetscInt nconv;
163: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
164: PEP_SR sr=ctx->sr;
166: PetscFunctionBegin;
167: if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
168: *inertia = 0;
169: } else if (shift <= PETSC_MIN_REAL) {
170: *inertia = 0;
171: if (zeros) *zeros = 0;
172: } else {
173: /* If the shift is zero, perturb it to a very small positive value.
174: The goal is that the nonzero pattern is the same in all cases and reuse
175: the symbolic factorizations */
176: nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
177: PetscCall(PEPQSliceMatGetInertia(pep,nzshift,inertia,zeros));
178: PetscCall(STSetShift(pep->st,nzshift));
179: }
180: if (!correction) {
181: if (shift >= PETSC_MAX_REAL) *inertia = 2*pep->n;
182: else if (shift>PETSC_MIN_REAL) {
183: PetscCall(STGetKSP(pep->st,&ksp));
184: PetscCall(KSPGetOperators(ksp,&P,NULL));
185: if (*inertia!=pep->n && !sr->v[0]) {
186: PetscCall(MatCreateVecs(P,&sr->v[0],NULL));
187: PetscCall(VecDuplicate(sr->v[0],&sr->v[1]));
188: PetscCall(VecDuplicate(sr->v[0],&sr->v[2]));
189: PetscCall(BVGetRandomContext(pep->V,&rand));
190: PetscCall(VecSetRandom(sr->v[0],rand));
191: }
192: if (*inertia<pep->n && *inertia>0) {
193: if (!sr->eps) {
194: PetscCall(EPSCreate(PetscObjectComm((PetscObject)pep),&sr->eps));
195: PetscCall(EPSSetProblemType(sr->eps,EPS_HEP));
196: PetscCall(EPSSetWhichEigenpairs(sr->eps,EPS_LARGEST_REAL));
197: }
198: PetscCall(EPSSetConvergenceTestFunction(sr->eps,ConvergedPositive,NULL,NULL));
199: PetscCall(EPSSetOperators(sr->eps,P,NULL));
200: PetscCall(EPSSolve(sr->eps));
201: PetscCall(EPSGetConverged(sr->eps,&nconv));
202: PetscCheck(nconv,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",(double)nzshift);
203: PetscCall(EPSGetEigenpair(sr->eps,0,NULL,NULL,sr->v[0],sr->v[1]));
204: }
205: if (*inertia!=pep->n) {
206: PetscCall(MatMult(pep->A[1],sr->v[0],sr->v[1]));
207: PetscCall(MatMult(pep->A[2],sr->v[0],sr->v[2]));
208: PetscCall(VecAXPY(sr->v[1],2*nzshift,sr->v[2]));
209: PetscCall(VecDotRealPart(sr->v[1],sr->v[0],&dot));
210: if (dot>0.0) *inertia = 2*pep->n-*inertia;
211: }
212: }
213: } else if (correction<0) *inertia = 2*pep->n-*inertia;
214: PetscFunctionReturn(PETSC_SUCCESS);
215: }
217: /*
218: Check eigenvalue type - used only in non-hyperbolic problems.
219: All computed eigenvalues must have the same definite type (positive or negative).
220: If ini=TRUE the type is available in omega, otherwise we compute an eigenvalue
221: closest to shift and determine its type.
222: */
223: static PetscErrorCode PEPQSliceCheckEigenvalueType(PEP pep,PetscReal shift,PetscReal omega,PetscBool ini)
224: {
225: PEP pep2;
226: ST st;
227: PetscInt nconv;
228: PetscScalar lambda;
229: PetscReal dot;
230: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
231: PEP_SR sr=ctx->sr;
233: PetscFunctionBegin;
234: if (!ini) {
235: PetscCheck(-(omega/(shift*ctx->alpha+ctx->beta))*sr->type>=0,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)shift);
236: } else {
237: PetscCall(PEPCreate(PetscObjectComm((PetscObject)pep),&pep2));
238: PetscCall(PEPSetOptionsPrefix(pep2,((PetscObject)pep)->prefix));
239: PetscCall(PEPAppendOptionsPrefix(pep2,"pep_eigenvalue_type_"));
240: PetscCall(PEPSetTolerances(pep2,PETSC_DEFAULT,pep->max_it/4));
241: PetscCall(PEPSetType(pep2,PEPTOAR));
242: PetscCall(PEPSetOperators(pep2,pep->nmat,pep->A));
243: PetscCall(PEPSetWhichEigenpairs(pep2,PEP_TARGET_MAGNITUDE));
244: PetscCall(PEPGetRG(pep2,&pep2->rg));
245: PetscCall(RGSetType(pep2->rg,RGINTERVAL));
246: #if defined(PETSC_USE_COMPLEX)
247: PetscCall(RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,-PETSC_SQRT_MACHINE_EPSILON,PETSC_SQRT_MACHINE_EPSILON));
248: #else
249: PetscCall(RGIntervalSetEndpoints(pep2->rg,pep->inta,pep->intb,0.0,0.0));
250: #endif
251: pep2->target = shift;
252: st = pep2->st;
253: pep2->st = pep->st;
254: PetscCall(PEPSolve(pep2));
255: PetscCall(PEPGetConverged(pep2,&nconv));
256: if (nconv) {
257: PetscCall(PEPGetEigenpair(pep2,0,&lambda,NULL,pep2->work[0],NULL));
258: PetscCall(MatMult(pep->A[1],pep2->work[0],pep2->work[1]));
259: PetscCall(MatMult(pep->A[2],pep2->work[0],pep2->work[2]));
260: PetscCall(VecAXPY(pep2->work[1],2.0*lambda*pep->sfactor,pep2->work[2]));
261: PetscCall(VecDotRealPart(pep2->work[1],pep2->work[0],&dot));
262: PetscCall(PetscInfo(pep,"lambda=%g, %s type\n",(double)PetscRealPart(lambda),(dot>0.0)?"positive":"negative"));
263: if (!sr->type) sr->type = (dot>0.0)?1:-1;
264: else PetscCheck(sr->type*dot>=0.0,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected in eigenvalue %g",(double)PetscRealPart(lambda));
265: }
266: pep2->st = st;
267: PetscCall(PEPDestroy(&pep2));
268: }
269: PetscFunctionReturn(PETSC_SUCCESS);
270: }
272: static inline PetscErrorCode PEPQSliceDiscriminant(PEP pep,Vec u,Vec w,PetscReal *d,PetscReal *smas,PetscReal *smenos)
273: {
274: PetscReal ap,bp,cp,dis;
276: PetscFunctionBegin;
277: PetscCall(MatMult(pep->A[0],u,w));
278: PetscCall(VecDotRealPart(w,u,&cp));
279: PetscCall(MatMult(pep->A[1],u,w));
280: PetscCall(VecDotRealPart(w,u,&bp));
281: PetscCall(MatMult(pep->A[2],u,w));
282: PetscCall(VecDotRealPart(w,u,&ap));
283: dis = bp*bp-4*ap*cp;
284: if (dis>=0.0 && smas) {
285: if (ap>0) *smas = (-bp+PetscSqrtReal(dis))/(2*ap);
286: else if (ap<0) *smas = (-bp-PetscSqrtReal(dis))/(2*ap);
287: else {
288: if (bp >0) *smas = -cp/bp;
289: else *smas = PETSC_MAX_REAL;
290: }
291: }
292: if (dis>=0.0 && smenos) {
293: if (ap>0) *smenos = (-bp-PetscSqrtReal(dis))/(2*ap);
294: else if (ap<0) *smenos = (-bp+PetscSqrtReal(dis))/(2*ap);
295: else {
296: if (bp<0) *smenos = -cp/bp;
297: else *smenos = PETSC_MAX_REAL;
298: }
299: }
300: if (d) *d = dis;
301: PetscFunctionReturn(PETSC_SUCCESS);
302: }
304: static inline PetscErrorCode PEPQSliceEvaluateQEP(PEP pep,PetscScalar x,Mat M,MatStructure str)
305: {
306: PetscFunctionBegin;
307: PetscCall(MatCopy(pep->A[0],M,SAME_NONZERO_PATTERN));
308: PetscCall(MatAXPY(M,x,pep->A[1],str));
309: PetscCall(MatAXPY(M,x*x,pep->A[2],str));
310: PetscFunctionReturn(PETSC_SUCCESS);
311: }
313: /*@
314: PEPCheckDefiniteQEP - Determines if a symmetric/Hermitian quadratic eigenvalue problem
315: is definite or not.
317: Collective
319: Input Parameter:
320: . pep - eigensolver context
322: Output Parameters:
323: + xi - first computed parameter
324: . mu - second computed parameter
325: . definite - flag indicating that the problem is definite
326: - hyperbolic - flag indicating that the problem is hyperbolic
328: Notes:
329: This function is intended for quadratic eigenvalue problems, Q(lambda)=A*lambda^2+B*lambda+C,
330: with symmetric (or Hermitian) coefficient matrices A,B,C.
332: On output, the flag 'definite' may have the values -1 (meaning that the QEP is not
333: definite), 1 (if the problem is definite), or 0 if the algorithm was not able to
334: determine whether the problem is definite or not.
336: If definite=1, the output flag 'hyperbolic' informs in a similar way about whether the
337: problem is hyperbolic or not.
339: If definite=1, the computed values xi and mu satisfy Q(xi)<0 and Q(mu)>0, as
340: obtained via the method proposed in [Niendorf and Voss, LAA 2010]. Furthermore, if
341: hyperbolic=1 then only xi is computed.
343: Level: advanced
345: .seealso: PEPSetProblemType()
346: @*/
347: PetscErrorCode PEPCheckDefiniteQEP(PEP pep,PetscReal *xi,PetscReal *mu,PetscInt *definite,PetscInt *hyperbolic)
348: {
349: PetscRandom rand;
350: Vec u,w;
351: PetscReal d=0.0,s=0.0,sp,mut=0.0,omg=0.0,omgp;
352: PetscInt k,its=10,hyp=0,check=0,nconv,inertia,n;
353: Mat M=NULL;
354: MatStructure str;
355: EPS eps;
356: PetscBool transform,ptypehyp;
358: PetscFunctionBegin;
359: PetscCheck(pep->problem_type==PEP_HERMITIAN || pep->problem_type==PEP_HYPERBOLIC,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only available for Hermitian (or hyperbolic) problems");
360: ptypehyp = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
361: if (!pep->st) PetscCall(PEPGetST(pep,&pep->st));
362: PetscCall(PEPSetDefaultST(pep));
363: PetscCall(STSetMatrices(pep->st,pep->nmat,pep->A));
364: PetscCall(MatGetSize(pep->A[0],&n,NULL));
365: PetscCall(STGetTransform(pep->st,&transform));
366: PetscCall(STSetTransform(pep->st,PETSC_FALSE));
367: PetscCall(STSetUp(pep->st));
368: PetscCall(MatCreateVecs(pep->A[0],&u,&w));
369: PetscCall(PEPGetBV(pep,&pep->V));
370: PetscCall(BVGetRandomContext(pep->V,&rand));
371: PetscCall(VecSetRandom(u,rand));
372: PetscCall(VecNormalize(u,NULL));
373: PetscCall(PEPQSliceDiscriminant(pep,u,w,&d,&s,NULL));
374: if (d<0.0) check = -1;
375: if (!check) {
376: PetscCall(EPSCreate(PetscObjectComm((PetscObject)pep),&eps));
377: PetscCall(EPSSetProblemType(eps,EPS_HEP));
378: PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
379: PetscCall(EPSSetTolerances(eps,PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON),PETSC_DECIDE));
380: PetscCall(MatDuplicate(pep->A[0],MAT_DO_NOT_COPY_VALUES,&M));
381: PetscCall(STGetMatStructure(pep->st,&str));
382: }
383: for (k=0;k<its&&!check;k++) {
384: PetscCall(PEPQSliceEvaluateQEP(pep,s,M,str));
385: PetscCall(EPSSetOperators(eps,M,NULL));
386: PetscCall(EPSSolve(eps));
387: PetscCall(EPSGetConverged(eps,&nconv));
388: if (!nconv) break;
389: PetscCall(EPSGetEigenpair(eps,0,NULL,NULL,u,w));
390: sp = s;
391: PetscCall(PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg));
392: if (d<0.0) {check = -1; break;}
393: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
394: if (s>sp) {hyp = -1;}
395: mut = 2*s-sp;
396: PetscCall(PEPQSliceMatGetInertia(pep,mut,&inertia,NULL));
397: if (inertia == n) {check = 1; break;}
398: }
399: for (;k<its&&!check;k++) {
400: mut = (s-omg)/2;
401: PetscCall(PEPQSliceMatGetInertia(pep,mut,&inertia,NULL));
402: if (inertia == n) {check = 1; break;}
403: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
404: PetscCall(PEPQSliceEvaluateQEP(pep,omg,M,str));
405: PetscCall(EPSSetOperators(eps,M,NULL));
406: PetscCall(EPSSolve(eps));
407: PetscCall(EPSGetConverged(eps,&nconv));
408: if (!nconv) break;
409: PetscCall(EPSGetEigenpair(eps,0,NULL,NULL,u,w));
410: omgp = omg;
411: PetscCall(PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg));
412: if (d<0.0) {check = -1; break;}
413: if (omg<omgp) hyp = -1;
414: }
415: if (check==1) *xi = mut;
416: PetscCheck(hyp!=-1 || !ptypehyp,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Problem does not satisfy hyperbolic test; consider removing the hyperbolicity flag");
417: if (check==1 && hyp==0) {
418: PetscCall(PEPQSliceMatGetInertia(pep,PETSC_MAX_REAL,&inertia,NULL));
419: if (inertia == 0) hyp = 1;
420: else hyp = -1;
421: }
422: if (check==1 && hyp!=1) {
423: check = 0;
424: PetscCall(EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL));
425: for (;k<its&&!check;k++) {
426: PetscCall(PEPQSliceEvaluateQEP(pep,s,M,str));
427: PetscCall(EPSSetOperators(eps,M,NULL));
428: PetscCall(EPSSolve(eps));
429: PetscCall(EPSGetConverged(eps,&nconv));
430: if (!nconv) break;
431: PetscCall(EPSGetEigenpair(eps,0,NULL,NULL,u,w));
432: sp = s;
433: PetscCall(PEPQSliceDiscriminant(pep,u,w,&d,&s,&omg));
434: if (d<0.0) {check = -1; break;}
435: if (PetscAbsReal((s-sp)/s)<100*PETSC_MACHINE_EPSILON) break;
436: mut = 2*s-sp;
437: PetscCall(PEPQSliceMatGetInertia(pep,mut,&inertia,NULL));
438: if (inertia == 0) {check = 1; break;}
439: }
440: for (;k<its&&!check;k++) {
441: mut = (s-omg)/2;
442: PetscCall(PEPQSliceMatGetInertia(pep,mut,&inertia,NULL));
443: if (inertia == 0) {check = 1; break;}
444: if (PetscAbsReal((s-omg)/omg)<100*PETSC_MACHINE_EPSILON) break;
445: PetscCall(PEPQSliceEvaluateQEP(pep,omg,M,str));
446: PetscCall(EPSSetOperators(eps,M,NULL));
447: PetscCall(EPSSolve(eps));
448: PetscCall(EPSGetConverged(eps,&nconv));
449: if (!nconv) break;
450: PetscCall(EPSGetEigenpair(eps,0,NULL,NULL,u,w));
451: PetscCall(PEPQSliceDiscriminant(pep,u,w,&d,NULL,&omg));
452: if (d<0.0) {check = -1; break;}
453: }
454: }
455: if (check==1) *mu = mut;
456: *definite = check;
457: *hyperbolic = hyp;
458: if (M) PetscCall(MatDestroy(&M));
459: PetscCall(VecDestroy(&u));
460: PetscCall(VecDestroy(&w));
461: PetscCall(EPSDestroy(&eps));
462: PetscCall(STSetTransform(pep->st,transform));
463: PetscFunctionReturn(PETSC_SUCCESS);
464: }
466: /*
467: Dummy backtransform operation
468: */
469: static PetscErrorCode PEPBackTransform_Skip(PEP pep)
470: {
471: PetscFunctionBegin;
472: PetscFunctionReturn(PETSC_SUCCESS);
473: }
475: PetscErrorCode PEPSetUp_STOAR_QSlice(PEP pep)
476: {
477: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
478: PEP_SR sr;
479: PetscInt ld,i,zeros=0;
480: SlepcSC sc;
481: PetscReal r;
483: PetscFunctionBegin;
484: PEPCheckSinvertCayley(pep);
485: PetscCheck(pep->inta<pep->intb,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues unless you provide a computational interval with PEPSetInterval()");
486: PetscCheck(pep->intb<PETSC_MAX_REAL || pep->inta>PETSC_MIN_REAL,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
487: PEPCheckUnsupportedCondition(pep,PEP_FEATURE_STOPPING,PETSC_TRUE," (with spectrum slicing)");
488: if (pep->tol==(PetscReal)PETSC_DEFAULT) {
489: #if defined(PETSC_USE_REAL_SINGLE)
490: pep->tol = SLEPC_DEFAULT_TOL;
491: #else
492: /* use tighter tolerance */
493: pep->tol = SLEPC_DEFAULT_TOL*1e-2;
494: #endif
495: }
496: if (ctx->nev==1) ctx->nev = PetscMin(20,pep->n); /* nev not set, use default value */
497: PetscCheck(pep->n<=10 || ctx->nev>=10,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
498: pep->ops->backtransform = PEPBackTransform_Skip;
499: if (pep->max_it==PETSC_DEFAULT) pep->max_it = 100;
501: /* create spectrum slicing context and initialize it */
502: PetscCall(PEPQSliceResetSR(pep));
503: PetscCall(PetscNew(&sr));
504: ctx->sr = sr;
505: sr->itsKs = 0;
506: sr->nleap = 0;
507: sr->sPres = NULL;
509: if (pep->solvematcoeffs) PetscCall(PetscFree(pep->solvematcoeffs));
510: PetscCall(PetscMalloc1(pep->nmat,&pep->solvematcoeffs));
511: if (!pep->st) PetscCall(PEPGetST(pep,&pep->st));
512: PetscCall(STSetTransform(pep->st,PETSC_FALSE));
513: PetscCall(STSetUp(pep->st));
515: ctx->hyperbolic = (pep->problem_type==PEP_HYPERBOLIC)? PETSC_TRUE: PETSC_FALSE;
517: /* check presence of ends and finding direction */
518: if (pep->inta > PETSC_MIN_REAL || pep->intb >= PETSC_MAX_REAL) {
519: sr->int0 = pep->inta;
520: sr->int1 = pep->intb;
521: sr->dir = 1;
522: if (pep->intb >= PETSC_MAX_REAL) { /* Right-open interval */
523: sr->hasEnd = PETSC_FALSE;
524: } else sr->hasEnd = PETSC_TRUE;
525: } else {
526: sr->int0 = pep->intb;
527: sr->int1 = pep->inta;
528: sr->dir = -1;
529: sr->hasEnd = PetscNot(pep->inta <= PETSC_MIN_REAL);
530: }
532: /* compute inertia0 */
533: PetscCall(PEPQSliceGetInertia(pep,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1));
534: PetscCheck(!zeros || (sr->int0!=pep->inta && sr->int0!=pep->intb),((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
535: if (!ctx->hyperbolic && ctx->checket) PetscCall(PEPQSliceCheckEigenvalueType(pep,sr->int0,0.0,PETSC_TRUE));
537: /* compute inertia1 */
538: PetscCall(PEPQSliceGetInertia(pep,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL,ctx->hyperbolic?0:1));
539: PetscCheck(!zeros,((PetscObject)pep)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
540: if (!ctx->hyperbolic && ctx->checket && sr->hasEnd) {
541: PetscCall(PEPQSliceCheckEigenvalueType(pep,sr->int1,0.0,PETSC_TRUE));
542: PetscCheck(sr->type || sr->inertia1==sr->inertia0,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"No information of eigenvalue type in interval");
543: PetscCheck(!sr->type || sr->inertia1!=sr->inertia0,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Different positive/negative type detected");
544: if (sr->dir*(sr->inertia1-sr->inertia0)<0) {
545: sr->intcorr = -1;
546: sr->inertia0 = 2*pep->n-sr->inertia0;
547: sr->inertia1 = 2*pep->n-sr->inertia1;
548: } else sr->intcorr = 1;
549: } else {
550: if (sr->inertia0<=pep->n && sr->inertia1<=pep->n) sr->intcorr = 1;
551: else if (sr->inertia0>=pep->n && sr->inertia1>=pep->n) sr->intcorr = -1;
552: }
554: if (sr->hasEnd) {
555: sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
556: i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
557: }
559: /* number of eigenvalues in interval */
560: sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
561: PetscCall(PetscInfo(pep,"QSlice setup: allocating for %" PetscInt_FMT " eigenvalues in [%g,%g]\n",sr->numEigs,(double)pep->inta,(double)pep->intb));
562: if (sr->numEigs) {
563: PetscCall(PEPQSliceAllocateSolution(pep));
564: PetscCall(PEPSetDimensions_Default(pep,ctx->nev,&ctx->ncv,&ctx->mpd));
565: pep->nev = ctx->nev; pep->ncv = ctx->ncv; pep->mpd = ctx->mpd;
566: ld = ctx->ncv+2;
567: PetscCall(DSSetType(pep->ds,DSGHIEP));
568: PetscCall(DSSetCompact(pep->ds,PETSC_TRUE));
569: PetscCall(DSSetExtraRow(pep->ds,PETSC_TRUE));
570: PetscCall(DSAllocate(pep->ds,ld));
571: PetscCall(DSGetSlepcSC(pep->ds,&sc));
572: sc->rg = NULL;
573: sc->comparison = SlepcCompareLargestMagnitude;
574: sc->comparisonctx = NULL;
575: sc->map = NULL;
576: sc->mapobj = NULL;
577: } else {pep->ncv = 0; pep->nev = 0; pep->mpd = 0;}
578: PetscFunctionReturn(PETSC_SUCCESS);
579: }
581: /*
582: Fills the fields of a shift structure
583: */
584: static PetscErrorCode PEPCreateShift(PEP pep,PetscReal val,PEP_shift neighb0,PEP_shift neighb1)
585: {
586: PEP_shift s,*pending2;
587: PetscInt i;
588: PEP_SR sr;
589: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
591: PetscFunctionBegin;
592: sr = ctx->sr;
593: PetscCall(PetscNew(&s));
594: s->value = val;
595: s->neighb[0] = neighb0;
596: if (neighb0) neighb0->neighb[1] = s;
597: s->neighb[1] = neighb1;
598: if (neighb1) neighb1->neighb[0] = s;
599: s->comp[0] = PETSC_FALSE;
600: s->comp[1] = PETSC_FALSE;
601: s->index = -1;
602: s->neigs = 0;
603: s->nconv[0] = s->nconv[1] = 0;
604: s->nsch[0] = s->nsch[1]=0;
605: /* Inserts in the stack of pending shifts */
606: /* If needed, the array is resized */
607: if (sr->nPend >= sr->maxPend) {
608: sr->maxPend *= 2;
609: PetscCall(PetscMalloc1(sr->maxPend,&pending2));
610: for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
611: PetscCall(PetscFree(sr->pending));
612: sr->pending = pending2;
613: }
614: sr->pending[sr->nPend++]=s;
615: PetscFunctionReturn(PETSC_SUCCESS);
616: }
618: /* Provides next shift to be computed */
619: static PetscErrorCode PEPExtractShift(PEP pep)
620: {
621: PetscInt iner,zeros=0;
622: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
623: PEP_SR sr;
624: PetscReal newShift,aux;
625: PEP_shift sPres;
627: PetscFunctionBegin;
628: sr = ctx->sr;
629: if (sr->nPend > 0) {
630: if (sr->dirch) {
631: aux = sr->int1; sr->int1 = sr->int0; sr->int0 = aux;
632: iner = sr->inertia1; sr->inertia1 = sr->inertia0; sr->inertia0 = iner;
633: sr->dir *= -1;
634: PetscCall(PetscFree(sr->s0->neighb[1]));
635: PetscCall(PetscFree(sr->s0));
636: sr->nPend--;
637: PetscCall(PEPCreateShift(pep,sr->int0,NULL,NULL));
638: sr->sPrev = NULL;
639: sr->sPres = sr->pending[--sr->nPend];
640: pep->target = sr->sPres->value;
641: sr->s0 = sr->sPres;
642: pep->reason = PEP_CONVERGED_ITERATING;
643: } else {
644: sr->sPrev = sr->sPres;
645: sr->sPres = sr->pending[--sr->nPend];
646: }
647: sPres = sr->sPres;
648: PetscCall(PEPQSliceGetInertia(pep,sPres->value,&iner,ctx->detect?&zeros:NULL,sr->intcorr));
649: if (zeros) {
650: newShift = sPres->value*(1.0+SLICE_PTOL);
651: if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
652: else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
653: PetscCall(PEPQSliceGetInertia(pep,newShift,&iner,&zeros,sr->intcorr));
654: PetscCheck(!zeros,((PetscObject)pep)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",(double)newShift);
655: sPres->value = newShift;
656: }
657: sr->sPres->inertia = iner;
658: pep->target = sr->sPres->value;
659: pep->reason = PEP_CONVERGED_ITERATING;
660: pep->its = 0;
661: } else sr->sPres = NULL;
662: PetscFunctionReturn(PETSC_SUCCESS);
663: }
665: /*
666: Obtains value of subsequent shift
667: */
668: static PetscErrorCode PEPGetNewShiftValue(PEP pep,PetscInt side,PetscReal *newS)
669: {
670: PetscReal lambda,d_prev;
671: PetscInt i,idxP;
672: PEP_SR sr;
673: PEP_shift sPres,s;
674: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
676: PetscFunctionBegin;
677: sr = ctx->sr;
678: sPres = sr->sPres;
679: if (sPres->neighb[side]) {
680: /* Completing a previous interval */
681: if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
682: if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
683: else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
684: } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
685: } else { /* (Only for side=1). Creating a new interval. */
686: if (sPres->neigs==0) {/* No value has been accepted*/
687: if (sPres->neighb[0]) {
688: /* Multiplying by 10 the previous distance */
689: *newS = sPres->value + 10*sr->dir*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
690: sr->nleap++;
691: /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
692: PetscCheck(sr->hasEnd || sr->nleap<=5,PetscObjectComm((PetscObject)pep),PETSC_ERR_CONV_FAILED,"Unable to compute the wanted eigenvalues with open interval");
693: } else { /* First shift */
694: if (pep->nconv != 0) {
695: /* Unaccepted values give information for next shift */
696: idxP=0;/* Number of values left from shift */
697: for (i=0;i<pep->nconv;i++) {
698: lambda = PetscRealPart(pep->eigr[i]);
699: if (sr->dir*(lambda - sPres->value) <0) idxP++;
700: else break;
701: }
702: /* Avoiding subtraction of eigenvalues (might be the same).*/
703: if (idxP>0) {
704: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[0]))/(idxP+0.3);
705: } else {
706: d_prev = PetscAbsReal(sPres->value - PetscRealPart(pep->eigr[pep->nconv-1]))/(pep->nconv+0.3);
707: }
708: *newS = sPres->value + (sr->dir*d_prev*pep->nev)/2;
709: sr->dirch = PETSC_FALSE;
710: } else { /* No values found, no information for next shift */
711: PetscCheck(!sr->dirch,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"First shift renders no information");
712: sr->dirch = PETSC_TRUE;
713: *newS = sr->int1;
714: }
715: }
716: } else { /* Accepted values found */
717: sr->dirch = PETSC_FALSE;
718: sr->nleap = 0;
719: /* Average distance of values in previous subinterval */
720: s = sPres->neighb[0];
721: while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
722: s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
723: }
724: if (s) {
725: d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
726: } else { /* First shift. Average distance obtained with values in this shift */
727: /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
728: 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)) {
729: d_prev = PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
730: } else {
731: d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
732: }
733: }
734: /* Average distance is used for next shift by adding it to value on the right or to shift */
735: if (sr->dir*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
736: *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ (sr->dir*d_prev*pep->nev)/2;
737: } else { /* Last accepted value is on the left of shift. Adding to shift */
738: *newS = sPres->value + (sr->dir*d_prev*pep->nev)/2;
739: }
740: }
741: /* End of interval can not be surpassed */
742: if (sr->dir*(sr->int1 - *newS) < 0) *newS = sr->int1;
743: }/* of neighb[side]==null */
744: PetscFunctionReturn(PETSC_SUCCESS);
745: }
747: /*
748: Function for sorting an array of real values
749: */
750: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
751: {
752: PetscReal re;
753: PetscInt i,j,tmp;
755: PetscFunctionBegin;
756: if (!prev) for (i=0;i<nr;i++) perm[i] = i;
757: /* Insertion sort */
758: for (i=1;i<nr;i++) {
759: re = PetscRealPart(r[perm[i]]);
760: j = i-1;
761: while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
762: tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
763: }
764: }
765: PetscFunctionReturn(PETSC_SUCCESS);
766: }
768: /* Stores the pairs obtained since the last shift in the global arrays */
769: static PetscErrorCode PEPStoreEigenpairs(PEP pep)
770: {
771: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
772: PetscReal lambda,err,*errest;
773: PetscInt i,*aux,count=0,ndef,ld,nconv=pep->nconv,d=pep->nmat-1,idx;
774: PetscBool iscayley,divide=PETSC_FALSE;
775: PEP_SR sr = ctx->sr;
776: PEP_shift sPres;
777: Vec w,vomega;
778: Mat MS;
779: BV tV;
780: PetscScalar *S,*eigr,*tS,*omega;
782: PetscFunctionBegin;
783: sPres = sr->sPres;
784: sPres->index = sr->indexEig;
786: if (nconv>sr->ndef0+sr->ndef1) {
787: /* Back-transform */
788: PetscCall(STBackTransform(pep->st,nconv,pep->eigr,pep->eigi));
789: for (i=0;i<nconv;i++) {
790: #if defined(PETSC_USE_COMPLEX)
791: if (PetscImaginaryPart(pep->eigr[i])) pep->eigr[i] = sr->int0-sr->dir;
792: #else
793: if (pep->eigi[i]) pep->eigr[i] = sr->int0-sr->dir;
794: #endif
795: }
796: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STCAYLEY,&iscayley));
797: /* Sort eigenvalues */
798: PetscCall(sortRealEigenvalues(pep->eigr,pep->perm,nconv,PETSC_FALSE,sr->dir));
799: PetscCall(VecCreateSeq(PETSC_COMM_SELF,nconv,&vomega));
800: PetscCall(BVGetSignature(ctx->V,vomega));
801: PetscCall(VecGetArray(vomega,&omega));
802: PetscCall(BVGetSizes(pep->V,NULL,NULL,&ld));
803: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
804: PetscCall(MatDenseGetArray(MS,&S));
805: /* Values stored in global array */
806: PetscCall(PetscCalloc4(nconv,&eigr,nconv,&errest,nconv*nconv*d,&tS,nconv,&aux));
807: ndef = sr->ndef0+sr->ndef1;
808: for (i=0;i<nconv;i++) {
809: lambda = PetscRealPart(pep->eigr[pep->perm[i]]);
810: err = pep->errest[pep->perm[i]];
811: if (sr->dir*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
812: PetscCheck(sr->indexEig+count-ndef<sr->numEigs,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Unexpected error in Spectrum Slicing");
813: PetscCall(PEPQSliceCheckEigenvalueType(pep,lambda,PetscRealPart(omega[pep->perm[i]]),PETSC_FALSE));
814: eigr[count] = lambda;
815: errest[count] = err;
816: if ((sr->dir*(sPres->value - lambda) > 0) && (sr->dir*(lambda - sPres->ext[0]) > 0)) sPres->nconv[0]++;
817: if ((sr->dir*(lambda - sPres->value) > 0) && (sr->dir*(sPres->ext[1] - lambda) > 0)) sPres->nconv[1]++;
818: PetscCall(PetscArraycpy(tS+count*(d*nconv),S+pep->perm[i]*(d*ld),nconv));
819: PetscCall(PetscArraycpy(tS+count*(d*nconv)+nconv,S+pep->perm[i]*(d*ld)+ld,nconv));
820: count++;
821: }
822: }
823: PetscCall(VecRestoreArray(vomega,&omega));
824: PetscCall(VecDestroy(&vomega));
825: for (i=0;i<count;i++) {
826: PetscCall(PetscArraycpy(S+i*(d*ld),tS+i*nconv*d,nconv));
827: PetscCall(PetscArraycpy(S+i*(d*ld)+ld,tS+i*nconv*d+nconv,nconv));
828: }
829: PetscCall(MatDenseRestoreArray(MS,&S));
830: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
831: PetscCall(BVSetActiveColumns(ctx->V,0,count));
832: PetscCall(BVTensorCompress(ctx->V,count));
833: if (sr->sPres->nconv[0] && sr->sPres->nconv[1]) {
834: divide = PETSC_TRUE;
835: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
836: PetscCall(MatDenseGetArray(MS,&S));
837: PetscCall(PetscArrayzero(tS,nconv*nconv*d));
838: for (i=0;i<count;i++) {
839: PetscCall(PetscArraycpy(tS+i*nconv*d,S+i*(d*ld),count));
840: PetscCall(PetscArraycpy(tS+i*nconv*d+nconv,S+i*(d*ld)+ld,count));
841: }
842: PetscCall(MatDenseRestoreArray(MS,&S));
843: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
844: PetscCall(BVSetActiveColumns(pep->V,0,count));
845: PetscCall(BVDuplicateResize(pep->V,count,&tV));
846: PetscCall(BVCopy(pep->V,tV));
847: }
848: if (sr->sPres->nconv[0]) {
849: if (divide) {
850: PetscCall(BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[0]));
851: PetscCall(BVTensorCompress(ctx->V,sr->sPres->nconv[0]));
852: }
853: for (i=0;i<sr->ndef0;i++) aux[i] = sr->idxDef0[i];
854: for (i=sr->ndef0;i<sr->sPres->nconv[0];i++) aux[i] = sr->indexEig+i-sr->ndef0;
855: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
856: PetscCall(MatDenseGetArray(MS,&S));
857: for (i=0;i<sr->sPres->nconv[0];i++) {
858: sr->eigr[aux[i]] = eigr[i];
859: sr->errest[aux[i]] = errest[i];
860: PetscCall(BVGetColumn(pep->V,i,&w));
861: PetscCall(BVInsertVec(sr->V,aux[i],w));
862: PetscCall(BVRestoreColumn(pep->V,i,&w));
863: idx = sr->ld*d*aux[i];
864: PetscCall(PetscArrayzero(sr->S+idx,sr->ld*d));
865: PetscCall(PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[0]));
866: PetscCall(PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[0]));
867: PetscCall(PetscFree(sr->qinfo[aux[i]].q));
868: PetscCall(PetscMalloc1(sr->sPres->nconv[0],&sr->qinfo[aux[i]].q));
869: PetscCall(PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[0]));
870: sr->qinfo[aux[i]].nq = sr->sPres->nconv[0];
871: }
872: PetscCall(MatDenseRestoreArray(MS,&S));
873: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
874: }
876: if (sr->sPres->nconv[1]) {
877: if (divide) {
878: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
879: PetscCall(MatDenseGetArray(MS,&S));
880: for (i=0;i<sr->sPres->nconv[1];i++) {
881: PetscCall(PetscArraycpy(S+i*(d*ld),tS+(sr->sPres->nconv[0]+i)*nconv*d,count));
882: PetscCall(PetscArraycpy(S+i*(d*ld)+ld,tS+(sr->sPres->nconv[0]+i)*nconv*d+nconv,count));
883: }
884: PetscCall(MatDenseRestoreArray(MS,&S));
885: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
886: PetscCall(BVSetActiveColumns(pep->V,0,count));
887: PetscCall(BVCopy(tV,pep->V));
888: PetscCall(BVSetActiveColumns(ctx->V,0,sr->sPres->nconv[1]));
889: PetscCall(BVTensorCompress(ctx->V,sr->sPres->nconv[1]));
890: }
891: for (i=0;i<sr->ndef1;i++) aux[i] = sr->idxDef1[i];
892: for (i=sr->ndef1;i<sr->sPres->nconv[1];i++) aux[i] = sr->indexEig+sr->sPres->nconv[0]-sr->ndef0+i-sr->ndef1;
893: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
894: PetscCall(MatDenseGetArray(MS,&S));
895: for (i=0;i<sr->sPres->nconv[1];i++) {
896: sr->eigr[aux[i]] = eigr[sr->sPres->nconv[0]+i];
897: sr->errest[aux[i]] = errest[sr->sPres->nconv[0]+i];
898: PetscCall(BVGetColumn(pep->V,i,&w));
899: PetscCall(BVInsertVec(sr->V,aux[i],w));
900: PetscCall(BVRestoreColumn(pep->V,i,&w));
901: idx = sr->ld*d*aux[i];
902: PetscCall(PetscArrayzero(sr->S+idx,sr->ld*d));
903: PetscCall(PetscArraycpy(sr->S+idx,S+i*(ld*d),sr->sPres->nconv[1]));
904: PetscCall(PetscArraycpy(sr->S+idx+sr->ld,S+i*(ld*d)+ld,sr->sPres->nconv[1]));
905: PetscCall(PetscFree(sr->qinfo[aux[i]].q));
906: PetscCall(PetscMalloc1(sr->sPres->nconv[1],&sr->qinfo[aux[i]].q));
907: PetscCall(PetscArraycpy(sr->qinfo[aux[i]].q,aux,sr->sPres->nconv[1]));
908: sr->qinfo[aux[i]].nq = sr->sPres->nconv[1];
909: }
910: PetscCall(MatDenseRestoreArray(MS,&S));
911: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
912: }
913: sPres->neigs = count-sr->ndef0-sr->ndef1;
914: sr->indexEig += sPres->neigs;
915: sPres->nconv[0]-= sr->ndef0;
916: sPres->nconv[1]-= sr->ndef1;
917: PetscCall(PetscFree4(eigr,errest,tS,aux));
918: } else {
919: sPres->neigs = 0;
920: sPres->nconv[0]= 0;
921: sPres->nconv[1]= 0;
922: }
923: /* Global ordering array updating */
924: PetscCall(sortRealEigenvalues(sr->eigr,sr->perm,sr->indexEig,PETSC_FALSE,sr->dir));
925: /* Check for completion */
926: sPres->comp[0] = PetscNot(sPres->nconv[0] < sPres->nsch[0]);
927: sPres->comp[1] = PetscNot(sPres->nconv[1] < sPres->nsch[1]);
928: PetscCheck(sPres->nconv[0]<=sPres->nsch[0] && sPres->nconv[1]<=sPres->nsch[1],PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia");
929: if (divide) PetscCall(BVDestroy(&tV));
930: PetscFunctionReturn(PETSC_SUCCESS);
931: }
933: static PetscErrorCode PEPLookForDeflation(PEP pep)
934: {
935: PetscReal val;
936: PetscInt i,count0=0,count1=0;
937: PEP_shift sPres;
938: PetscInt ini,fin;
939: PEP_SR sr;
940: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
942: PetscFunctionBegin;
943: sr = ctx->sr;
944: sPres = sr->sPres;
946: if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
947: else ini = 0;
948: fin = sr->indexEig;
949: /* Selection of ends for searching new values */
950: if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
951: else sPres->ext[0] = sPres->neighb[0]->value;
952: if (!sPres->neighb[1]) {
953: if (sr->hasEnd) sPres->ext[1] = sr->int1;
954: else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
955: } else sPres->ext[1] = sPres->neighb[1]->value;
956: /* Selection of values between right and left ends */
957: for (i=ini;i<fin;i++) {
958: val=PetscRealPart(sr->eigr[sr->perm[i]]);
959: /* Values to the right of left shift */
960: if (sr->dir*(val - sPres->ext[1]) < 0) {
961: if (sr->dir*(val - sPres->value) < 0) count0++;
962: else count1++;
963: } else break;
964: }
965: /* The number of values on each side are found */
966: if (sPres->neighb[0]) {
967: sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
968: PetscCheck(sPres->nsch[0]>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia");
969: } else sPres->nsch[0] = 0;
971: if (sPres->neighb[1]) {
972: sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
973: PetscCheck(sPres->nsch[1]>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia");
974: } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);
976: /* Completing vector of indexes for deflation */
977: for (i=0;i<count0;i++) sr->idxDef0[i] = sr->perm[ini+i];
978: sr->ndef0 = count0;
979: for (i=0;i<count1;i++) sr->idxDef1[i] = sr->perm[ini+count0+i];
980: sr->ndef1 = count1;
981: PetscFunctionReturn(PETSC_SUCCESS);
982: }
984: /*
985: Compute a run of Lanczos iterations
986: */
987: static PetscErrorCode PEPSTOARrun_QSlice(PEP pep,PetscReal *a,PetscReal *b,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,Vec *t_)
988: {
989: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
990: PetscInt i,j,m=*M,l,lock;
991: PetscInt lds,d,ld,offq,nqt,ldds;
992: Vec v=t_[0],t=t_[1],q=t_[2];
993: PetscReal norm,sym=0.0,fro=0.0,*f;
994: PetscScalar *y,*S,sigma;
995: PetscBLASInt j_,one=1;
996: PetscBool lindep;
997: Mat MS;
999: PetscFunctionBegin;
1000: PetscCall(PetscMalloc1(*M,&y));
1001: PetscCall(BVGetSizes(pep->V,NULL,NULL,&ld));
1002: PetscCall(BVTensorGetDegree(ctx->V,&d));
1003: PetscCall(BVGetActiveColumns(pep->V,&lock,&nqt));
1004: lds = d*ld;
1005: offq = ld;
1006: PetscCall(DSGetLeadingDimension(pep->ds,&ldds));
1008: *breakdown = PETSC_FALSE; /* ----- */
1009: PetscCall(STGetShift(pep->st,&sigma));
1010: PetscCall(DSGetDimensions(pep->ds,NULL,&l,NULL,NULL));
1011: PetscCall(BVSetActiveColumns(ctx->V,0,m));
1012: PetscCall(BVSetActiveColumns(pep->V,0,nqt));
1013: for (j=k;j<m;j++) {
1014: /* apply operator */
1015: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
1016: PetscCall(MatDenseGetArray(MS,&S));
1017: PetscCall(BVGetColumn(pep->V,nqt,&t));
1018: PetscCall(BVMultVec(pep->V,1.0,0.0,v,S+j*lds));
1019: PetscCall(MatMult(pep->A[1],v,q));
1020: PetscCall(MatMult(pep->A[2],v,t));
1021: PetscCall(VecAXPY(q,sigma*pep->sfactor,t));
1022: PetscCall(VecScale(q,pep->sfactor));
1023: PetscCall(BVMultVec(pep->V,1.0,0.0,v,S+offq+j*lds));
1024: PetscCall(MatMult(pep->A[2],v,t));
1025: PetscCall(VecAXPY(q,pep->sfactor*pep->sfactor,t));
1026: PetscCall(STMatSolve(pep->st,q,t));
1027: PetscCall(VecScale(t,-1.0));
1028: PetscCall(BVRestoreColumn(pep->V,nqt,&t));
1030: /* orthogonalize */
1031: PetscCall(BVOrthogonalizeColumn(pep->V,nqt,S+(j+1)*lds,&norm,&lindep));
1032: if (!lindep) {
1033: *(S+(j+1)*lds+nqt) = norm;
1034: PetscCall(BVScaleColumn(pep->V,nqt,1.0/norm));
1035: nqt++;
1036: }
1037: for (i=0;i<nqt;i++) *(S+(j+1)*lds+offq+i) = *(S+j*lds+i)+sigma*(*(S+(j+1)*lds+i));
1038: PetscCall(BVSetActiveColumns(pep->V,0,nqt));
1039: PetscCall(MatDenseRestoreArray(MS,&S));
1040: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
1042: /* level-2 orthogonalization */
1043: PetscCall(BVOrthogonalizeColumn(ctx->V,j+1,y,&norm,&lindep));
1044: a[j] = PetscRealPart(y[j]);
1045: omega[j+1] = (norm > 0)?1.0:-1.0;
1046: PetscCall(BVScaleColumn(ctx->V,j+1,1.0/norm));
1047: b[j] = PetscAbsReal(norm);
1049: /* check symmetry */
1050: PetscCall(DSGetArrayReal(pep->ds,DS_MAT_T,&f));
1051: if (j==k) {
1052: for (i=l;i<j-1;i++) y[i] = PetscAbsScalar(y[i])-PetscAbsReal(f[2*ldds+i]);
1053: for (i=0;i<l;i++) y[i] = 0.0;
1054: }
1055: PetscCall(DSRestoreArrayReal(pep->ds,DS_MAT_T,&f));
1056: if (j>0) y[j-1] = PetscAbsScalar(y[j-1])-PetscAbsReal(b[j-1]);
1057: PetscCall(PetscBLASIntCast(j,&j_));
1058: sym = SlepcAbs(BLASnrm2_(&j_,y,&one),sym);
1059: fro = SlepcAbs(fro,SlepcAbs(a[j],b[j]));
1060: if (j>0) fro = SlepcAbs(fro,b[j-1]);
1061: if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*pep->tol)) {
1062: *symmlost = PETSC_TRUE;
1063: *M=j;
1064: break;
1065: }
1066: }
1067: PetscCall(BVSetActiveColumns(pep->V,lock,nqt));
1068: PetscCall(BVSetActiveColumns(ctx->V,0,*M));
1069: PetscCall(PetscFree(y));
1070: PetscFunctionReturn(PETSC_SUCCESS);
1071: }
1073: static PetscErrorCode PEPSTOAR_QSlice(PEP pep,Mat B)
1074: {
1075: PEP_STOAR *ctx = (PEP_STOAR*)pep->data;
1076: PetscInt j,k,l,nv=0,ld,ldds,t,nq=0,idx;
1077: PetscInt nconv=0,deg=pep->nmat-1,count0=0,count1=0;
1078: PetscScalar *om,sigma,*back,*S,*pQ;
1079: PetscReal beta,norm=1.0,*omega,*a,*b,eta,lambda;
1080: PetscBool breakdown,symmlost=PETSC_FALSE,sinv,falselock=PETSC_TRUE;
1081: Mat MS,MQ,D;
1082: Vec v,vomega;
1083: PEP_SR sr;
1084: BVOrthogType otype;
1085: BVOrthogBlockType obtype;
1087: PetscFunctionBegin;
1088: /* Resize if needed for deflating vectors */
1089: sr = ctx->sr;
1090: sigma = sr->sPres->value;
1091: k = sr->ndef0+sr->ndef1;
1092: pep->ncv = ctx->ncv+k;
1093: pep->nev = ctx->nev+k;
1094: PetscCall(PEPAllocateSolution(pep,3));
1095: PetscCall(BVDestroy(&ctx->V));
1096: PetscCall(BVCreateTensor(pep->V,pep->nmat-1,&ctx->V));
1097: PetscCall(BVGetOrthogonalization(pep->V,&otype,NULL,&eta,&obtype));
1098: PetscCall(BVSetOrthogonalization(ctx->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype));
1099: PetscCall(DSAllocate(pep->ds,pep->ncv+2));
1100: PetscCall(PetscMalloc1(pep->ncv,&back));
1101: PetscCall(DSGetLeadingDimension(pep->ds,&ldds));
1102: PetscCall(BVSetMatrix(ctx->V,B,PETSC_TRUE));
1103: PetscCheck(ctx->lock,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A locking variant is needed for spectrum slicing");
1104: /* undocumented option to use a cheaper locking instead of the true locking */
1105: PetscCall(PetscOptionsGetBool(NULL,NULL,"-pep_stoar_falselocking",&falselock,NULL));
1106: PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv));
1107: PetscCall(RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor));
1108: PetscCall(STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor));
1110: /* Get the starting Arnoldi vector */
1111: PetscCall(BVSetActiveColumns(pep->V,0,1));
1112: PetscCall(BVTensorBuildFirstColumn(ctx->V,pep->nini));
1113: PetscCall(BVSetActiveColumns(ctx->V,0,1));
1114: if (k) {
1115: /* Insert deflated vectors */
1116: PetscCall(BVSetActiveColumns(pep->V,0,0));
1117: idx = sr->ndef0?sr->idxDef0[0]:sr->idxDef1[0];
1118: for (j=0;j<k;j++) {
1119: PetscCall(BVGetColumn(pep->V,j,&v));
1120: PetscCall(BVCopyVec(sr->V,sr->qinfo[idx].q[j],v));
1121: PetscCall(BVRestoreColumn(pep->V,j,&v));
1122: }
1123: /* Update innerproduct matrix */
1124: PetscCall(BVSetActiveColumns(ctx->V,0,0));
1125: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
1126: PetscCall(BVSetActiveColumns(pep->V,0,k));
1127: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
1129: PetscCall(BVGetSizes(pep->V,NULL,NULL,&ld));
1130: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
1131: PetscCall(MatDenseGetArray(MS,&S));
1132: for (j=0;j<sr->ndef0;j++) {
1133: PetscCall(PetscArrayzero(S+j*ld*deg,ld*deg));
1134: PetscCall(PetscArraycpy(S+j*ld*deg,sr->S+sr->idxDef0[j]*sr->ld*deg,k));
1135: PetscCall(PetscArraycpy(S+j*ld*deg+ld,sr->S+sr->idxDef0[j]*sr->ld*deg+sr->ld,k));
1136: pep->eigr[j] = sr->eigr[sr->idxDef0[j]];
1137: pep->errest[j] = sr->errest[sr->idxDef0[j]];
1138: }
1139: for (j=0;j<sr->ndef1;j++) {
1140: PetscCall(PetscArrayzero(S+(j+sr->ndef0)*ld*deg,ld*deg));
1141: PetscCall(PetscArraycpy(S+(j+sr->ndef0)*ld*deg,sr->S+sr->idxDef1[j]*sr->ld*deg,k));
1142: PetscCall(PetscArraycpy(S+(j+sr->ndef0)*ld*deg+ld,sr->S+sr->idxDef1[j]*sr->ld*deg+sr->ld,k));
1143: pep->eigr[j+sr->ndef0] = sr->eigr[sr->idxDef1[j]];
1144: pep->errest[j+sr->ndef0] = sr->errest[sr->idxDef1[j]];
1145: }
1146: PetscCall(MatDenseRestoreArray(MS,&S));
1147: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
1148: PetscCall(BVSetActiveColumns(ctx->V,0,k+1));
1149: PetscCall(VecCreateSeq(PETSC_COMM_SELF,k+1,&vomega));
1150: PetscCall(VecGetArray(vomega,&om));
1151: for (j=0;j<k;j++) {
1152: PetscCall(BVOrthogonalizeColumn(ctx->V,j,NULL,&norm,NULL));
1153: PetscCall(BVScaleColumn(ctx->V,j,1/norm));
1154: om[j] = (norm>=0.0)?1.0:-1.0;
1155: }
1156: PetscCall(BVTensorGetFactors(ctx->V,NULL,&MS));
1157: PetscCall(MatDenseGetArray(MS,&S));
1158: for (j=0;j<deg;j++) {
1159: PetscCall(BVSetRandomColumn(pep->V,k+j));
1160: PetscCall(BVOrthogonalizeColumn(pep->V,k+j,S+k*ld*deg+j*ld,&norm,NULL));
1161: PetscCall(BVScaleColumn(pep->V,k+j,1.0/norm));
1162: S[k*ld*deg+j*ld+k+j] = norm;
1163: }
1164: PetscCall(MatDenseRestoreArray(MS,&S));
1165: PetscCall(BVSetActiveColumns(pep->V,0,k+deg));
1166: PetscCall(BVTensorRestoreFactors(ctx->V,NULL,&MS));
1167: PetscCall(BVOrthogonalizeColumn(ctx->V,k,NULL,&norm,NULL));
1168: PetscCall(BVScaleColumn(ctx->V,k,1.0/norm));
1169: om[k] = (norm>=0.0)?1.0:-1.0;
1170: PetscCall(VecRestoreArray(vomega,&om));
1171: PetscCall(BVSetSignature(ctx->V,vomega));
1172: PetscCall(DSGetArrayReal(pep->ds,DS_MAT_T,&a));
1173: PetscCall(VecGetArray(vomega,&om));
1174: for (j=0;j<k;j++) a[j] = PetscRealPart(om[j]/(pep->eigr[j]-sigma));
1175: PetscCall(VecRestoreArray(vomega,&om));
1176: PetscCall(VecDestroy(&vomega));
1177: PetscCall(DSRestoreArrayReal(pep->ds,DS_MAT_T,&a));
1178: PetscCall(DSGetArray(pep->ds,DS_MAT_Q,&pQ));
1179: PetscCall(PetscArrayzero(pQ,ldds*k));
1180: for (j=0;j<k;j++) pQ[j+j*ldds] = 1.0;
1181: PetscCall(DSRestoreArray(pep->ds,DS_MAT_Q,&pQ));
1182: }
1183: PetscCall(BVSetActiveColumns(ctx->V,0,k+1));
1184: PetscCall(DSSetDimensions(pep->ds,k+1,PETSC_DEFAULT,PETSC_DEFAULT));
1185: PetscCall(DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega));
1186: PetscCall(BVGetSignature(ctx->V,vomega));
1187: PetscCall(DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega));
1189: PetscCall(PetscInfo(pep,"Start STOAR: sigma=%g in [%g,%g], for deflation: left=%" PetscInt_FMT " right=%" PetscInt_FMT ", searching: left=%" PetscInt_FMT " right=%" PetscInt_FMT "\n",(double)sr->sPres->value,(double)(sr->sPres->neighb[0]?sr->sPres->neighb[0]->value:sr->int0),(double)(sr->sPres->neighb[1]?sr->sPres->neighb[1]->value:sr->int1),sr->ndef0,sr->ndef1,sr->sPres->nsch[0],sr->sPres->nsch[1]));
1191: /* Restart loop */
1192: l = 0;
1193: pep->nconv = k;
1194: while (pep->reason == PEP_CONVERGED_ITERATING) {
1195: pep->its++;
1196: PetscCall(DSGetArrayReal(pep->ds,DS_MAT_T,&a));
1197: b = a+ldds;
1198: PetscCall(DSGetArrayReal(pep->ds,DS_MAT_D,&omega));
1200: /* Compute an nv-step Lanczos factorization */
1201: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
1202: PetscCall(PEPSTOARrun_QSlice(pep,a,b,omega,pep->nconv+l,&nv,&breakdown,&symmlost,pep->work));
1203: beta = b[nv-1];
1204: if (symmlost && nv==pep->nconv+l) {
1205: pep->reason = PEP_DIVERGED_SYMMETRY_LOST;
1206: pep->nconv = nconv;
1207: PetscCall(PetscInfo(pep,"Symmetry lost in STOAR sigma=%g nconv=%" PetscInt_FMT "\n",(double)sr->sPres->value,nconv));
1208: if (falselock || !ctx->lock) {
1209: PetscCall(BVSetActiveColumns(ctx->V,0,pep->nconv));
1210: PetscCall(BVTensorCompress(ctx->V,0));
1211: }
1212: break;
1213: }
1214: PetscCall(DSRestoreArrayReal(pep->ds,DS_MAT_T,&a));
1215: PetscCall(DSRestoreArrayReal(pep->ds,DS_MAT_D,&omega));
1216: PetscCall(DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l));
1217: if (l==0) PetscCall(DSSetState(pep->ds,DS_STATE_INTERMEDIATE));
1218: else PetscCall(DSSetState(pep->ds,DS_STATE_RAW));
1220: /* Solve projected problem */
1221: PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
1222: PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL));
1223: PetscCall(DSUpdateExtraRow(pep->ds));
1224: PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
1226: /* Check convergence */
1227: /* PetscCall(PEPSTOARpreKConvergence(pep,nv,&norm,pep->work));*/
1228: norm = 1.0;
1229: PetscCall(DSGetDimensions(pep->ds,NULL,NULL,NULL,&t));
1230: PetscCall(PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,t-pep->nconv,PetscAbsReal(beta)*norm,&k));
1231: PetscCall((*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx));
1232: for (j=0;j<k;j++) back[j] = pep->eigr[j];
1233: PetscCall(STBackTransform(pep->st,k,back,pep->eigi));
1234: count0=count1=0;
1235: for (j=0;j<k;j++) {
1236: lambda = PetscRealPart(back[j]);
1237: if ((sr->dir*(sr->sPres->value - lambda) > 0) && (sr->dir*(lambda - sr->sPres->ext[0]) > 0)) count0++;
1238: if ((sr->dir*(lambda - sr->sPres->value) > 0) && (sr->dir*(sr->sPres->ext[1] - lambda) > 0)) count1++;
1239: }
1240: if ((count0-sr->ndef0 >= sr->sPres->nsch[0]) && (count1-sr->ndef1 >= sr->sPres->nsch[1])) pep->reason = PEP_CONVERGED_TOL;
1241: /* Update l */
1242: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
1243: else {
1244: l = PetscMax(1,(PetscInt)((nv-k)/2));
1245: l = PetscMin(l,t);
1246: PetscCall(DSGetTruncateSize(pep->ds,k,t,&l));
1247: if (!breakdown) {
1248: /* Prepare the Rayleigh quotient for restart */
1249: PetscCall(DSTruncate(pep->ds,k+l,PETSC_FALSE));
1250: }
1251: }
1252: nconv = k;
1253: if (!ctx->lock && pep->reason == PEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
1254: if (l) PetscCall(PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
1256: /* Update S */
1257: PetscCall(DSGetMat(pep->ds,DS_MAT_Q,&MQ));
1258: PetscCall(BVMultInPlace(ctx->V,MQ,pep->nconv,k+l));
1259: PetscCall(DSRestoreMat(pep->ds,DS_MAT_Q,&MQ));
1261: /* Copy last column of S */
1262: PetscCall(BVCopyColumn(ctx->V,nv,k+l));
1263: PetscCall(BVSetActiveColumns(ctx->V,0,k+l));
1264: if (k+l) {
1265: PetscCall(DSSetDimensions(pep->ds,k+l,PETSC_DEFAULT,PETSC_DEFAULT));
1266: PetscCall(DSGetMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega));
1267: PetscCall(BVSetSignature(ctx->V,vomega));
1268: PetscCall(DSRestoreMatAndColumn(pep->ds,DS_MAT_D,0,&D,&vomega));
1269: }
1271: if (breakdown && pep->reason == PEP_CONVERGED_ITERATING) {
1272: /* stop if breakdown */
1273: PetscCall(PetscInfo(pep,"Breakdown TOAR method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta));
1274: pep->reason = PEP_DIVERGED_BREAKDOWN;
1275: }
1276: if (pep->reason != PEP_CONVERGED_ITERATING) l--;
1277: PetscCall(BVGetActiveColumns(pep->V,NULL,&nq));
1278: if (k+l+deg<=nq) {
1279: PetscCall(BVSetActiveColumns(ctx->V,pep->nconv,k+l+1));
1280: if (!falselock && ctx->lock) PetscCall(BVTensorCompress(ctx->V,k-pep->nconv));
1281: else PetscCall(BVTensorCompress(ctx->V,0));
1282: }
1283: pep->nconv = k;
1284: PetscCall(PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv));
1285: }
1286: sr->itsKs += pep->its;
1287: if (pep->nconv>0) {
1288: PetscCall(BVSetActiveColumns(ctx->V,0,pep->nconv));
1289: PetscCall(BVGetActiveColumns(pep->V,NULL,&nq));
1290: PetscCall(BVSetActiveColumns(pep->V,0,nq));
1291: if (nq>pep->nconv) {
1292: PetscCall(BVTensorCompress(ctx->V,pep->nconv));
1293: PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv));
1294: }
1295: for (j=0;j<pep->nconv;j++) {
1296: pep->eigr[j] *= pep->sfactor;
1297: pep->eigi[j] *= pep->sfactor;
1298: }
1299: }
1300: PetscCall(PetscInfo(pep,"Finished STOAR: nconv=%" PetscInt_FMT " (deflated=%" PetscInt_FMT ", left=%" PetscInt_FMT ", right=%" PetscInt_FMT ")\n",pep->nconv,sr->ndef0+sr->ndef1,count0-sr->ndef0,count1-sr->ndef1));
1301: PetscCall(STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor));
1302: PetscCall(RGPopScale(pep->rg));
1304: PetscCheck(pep->reason!=PEP_DIVERGED_SYMMETRY_LOST || nconv>=sr->ndef0+sr->ndef1,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1305: if (pep->reason == PEP_DIVERGED_SYMMETRY_LOST && nconv==sr->ndef0+sr->ndef1) {
1306: PetscCheck(++sr->symmlost<=10,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Symmetry lost at sigma=%g",(double)sr->sPres->value);
1307: } else sr->symmlost = 0;
1309: PetscCall(DSTruncate(pep->ds,pep->nconv,PETSC_TRUE));
1310: PetscCall(PetscFree(back));
1311: PetscFunctionReturn(PETSC_SUCCESS);
1312: }
1314: #define SWAP(a,b,t) do {t=a;a=b;b=t;} while (0)
1316: static PetscErrorCode PEPQSliceGetInertias(PEP pep,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
1317: {
1318: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1319: PEP_SR sr=ctx->sr;
1320: PetscInt i=0,j,tmpi;
1321: PetscReal v,tmpr;
1322: PEP_shift s;
1324: PetscFunctionBegin;
1325: PetscCheck(pep->state,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Must call PEPSetUp() first");
1326: PetscCheck(sr,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see PEPSetInterval()");
1327: if (!sr->s0) { /* PEPSolve not called yet */
1328: *n = 2;
1329: } else {
1330: *n = 1;
1331: s = sr->s0;
1332: while (s) {
1333: (*n)++;
1334: s = s->neighb[1];
1335: }
1336: }
1337: PetscCall(PetscMalloc1(*n,shifts));
1338: PetscCall(PetscMalloc1(*n,inertias));
1339: if (!sr->s0) { /* PEPSolve not called yet */
1340: (*shifts)[0] = sr->int0;
1341: (*shifts)[1] = sr->int1;
1342: (*inertias)[0] = sr->inertia0;
1343: (*inertias)[1] = sr->inertia1;
1344: } else {
1345: s = sr->s0;
1346: while (s) {
1347: (*shifts)[i] = s->value;
1348: (*inertias)[i++] = s->inertia;
1349: s = s->neighb[1];
1350: }
1351: (*shifts)[i] = sr->int1;
1352: (*inertias)[i] = sr->inertia1;
1353: }
1354: /* remove possible duplicate in last position */
1355: if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
1356: /* sort result */
1357: for (i=0;i<*n;i++) {
1358: v = (*shifts)[i];
1359: for (j=i+1;j<*n;j++) {
1360: if (v > (*shifts)[j]) {
1361: SWAP((*shifts)[i],(*shifts)[j],tmpr);
1362: SWAP((*inertias)[i],(*inertias)[j],tmpi);
1363: v = (*shifts)[i];
1364: }
1365: }
1366: }
1367: PetscFunctionReturn(PETSC_SUCCESS);
1368: }
1370: PetscErrorCode PEPSolve_STOAR_QSlice(PEP pep)
1371: {
1372: PetscInt i,j,ti,deg=pep->nmat-1;
1373: PetscReal newS;
1374: PEP_STOAR *ctx=(PEP_STOAR*)pep->data;
1375: PEP_SR sr=ctx->sr;
1376: Mat S,B;
1377: PetscScalar *pS;
1379: PetscFunctionBegin;
1380: PetscCall(PetscCitationsRegister(citation,&cited));
1382: /* Only with eigenvalues present in the interval ...*/
1383: if (sr->numEigs==0) {
1384: pep->reason = PEP_CONVERGED_TOL;
1385: PetscFunctionReturn(PETSC_SUCCESS);
1386: }
1388: /* Inner product matrix */
1389: PetscCall(PEPSTOARSetUpInnerMatrix(pep,&B));
1391: /* Array of pending shifts */
1392: sr->maxPend = 100; /* Initial size */
1393: sr->nPend = 0;
1394: PetscCall(PetscMalloc1(sr->maxPend,&sr->pending));
1395: PetscCall(PEPCreateShift(pep,sr->int0,NULL,NULL));
1396: /* extract first shift */
1397: sr->sPrev = NULL;
1398: sr->sPres = sr->pending[--sr->nPend];
1399: sr->sPres->inertia = sr->inertia0;
1400: pep->target = sr->sPres->value;
1401: sr->s0 = sr->sPres;
1402: sr->indexEig = 0;
1404: for (i=0;i<sr->numEigs;i++) {
1405: sr->eigr[i] = 0.0;
1406: sr->eigi[i] = 0.0;
1407: sr->errest[i] = 0.0;
1408: sr->perm[i] = i;
1409: }
1410: /* Vectors for deflation */
1411: PetscCall(PetscMalloc2(sr->numEigs,&sr->idxDef0,sr->numEigs,&sr->idxDef1));
1412: sr->indexEig = 0;
1413: while (sr->sPres) {
1414: /* Search for deflation */
1415: PetscCall(PEPLookForDeflation(pep));
1416: /* KrylovSchur */
1417: PetscCall(PEPSTOAR_QSlice(pep,B));
1419: PetscCall(PEPStoreEigenpairs(pep));
1420: /* Select new shift */
1421: if (!sr->sPres->comp[1]) {
1422: PetscCall(PEPGetNewShiftValue(pep,1,&newS));
1423: PetscCall(PEPCreateShift(pep,newS,sr->sPres,sr->sPres->neighb[1]));
1424: }
1425: if (!sr->sPres->comp[0]) {
1426: /* Completing earlier interval */
1427: PetscCall(PEPGetNewShiftValue(pep,0,&newS));
1428: PetscCall(PEPCreateShift(pep,newS,sr->sPres->neighb[0],sr->sPres));
1429: }
1430: /* Preparing for a new search of values */
1431: PetscCall(PEPExtractShift(pep));
1432: }
1434: /* Updating pep values prior to exit */
1435: PetscCall(PetscFree2(sr->idxDef0,sr->idxDef1));
1436: PetscCall(PetscFree(sr->pending));
1437: pep->nconv = sr->indexEig;
1438: pep->reason = PEP_CONVERGED_TOL;
1439: pep->its = sr->itsKs;
1440: pep->nev = sr->indexEig;
1441: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,pep->nconv,pep->nconv,NULL,&S));
1442: PetscCall(MatDenseGetArray(S,&pS));
1443: for (i=0;i<pep->nconv;i++) {
1444: 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);
1445: }
1446: PetscCall(MatDenseRestoreArray(S,&pS));
1447: PetscCall(BVSetActiveColumns(sr->V,0,pep->nconv));
1448: PetscCall(BVMultInPlace(sr->V,S,0,pep->nconv));
1449: PetscCall(MatDestroy(&S));
1450: PetscCall(BVDestroy(&pep->V));
1451: pep->V = sr->V;
1452: PetscCall(PetscFree4(pep->eigr,pep->eigi,pep->errest,pep->perm));
1453: pep->eigr = sr->eigr;
1454: pep->eigi = sr->eigi;
1455: pep->perm = sr->perm;
1456: pep->errest = sr->errest;
1457: if (sr->dir<0) {
1458: for (i=0;i<pep->nconv/2;i++) {
1459: ti = sr->perm[i]; sr->perm[i] = sr->perm[pep->nconv-1-i]; sr->perm[pep->nconv-1-i] = ti;
1460: }
1461: }
1462: PetscCall(PetscFree(ctx->inertias));
1463: PetscCall(PetscFree(ctx->shifts));
1464: PetscCall(MatDestroy(&B));
1465: PetscCall(PEPQSliceGetInertias(pep,&ctx->nshifts,&ctx->shifts,&ctx->inertias));
1466: PetscFunctionReturn(PETSC_SUCCESS);
1467: }