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: EPS routines related to the solution process
12: */
14: #include <slepc/private/epsimpl.h> 15: #include <slepc/private/bvimpl.h> 16: #include <petscdraw.h>
18: PetscErrorCode EPSComputeVectors(EPS eps) 19: {
23: EPSCheckSolved(eps,1);
24: if (eps->state==EPS_STATE_SOLVED && eps->ops->computevectors) {
25: (*eps->ops->computevectors)(eps);
26: }
27: eps->state = EPS_STATE_EIGENVECTORS;
28: return(0);
29: }
31: #define SWAP(a,b,t) {t=a;a=b;b=t;} 33: static PetscErrorCode EPSComputeValues(EPS eps) 34: {
36: PetscBool injective,iscomp,isfilter;
37: PetscInt i,n,aux,nconv0;
38: Mat A,B=NULL,G,Z;
41: switch (eps->categ) {
42: case EPS_CATEGORY_KRYLOV:
43: case EPS_CATEGORY_OTHER:
44: STIsInjective(eps->st,&injective);
45: if (injective) {
46: /* one-to-one mapping: backtransform eigenvalues */
47: if (eps->ops->backtransform) {
48: (*eps->ops->backtransform)(eps);
49: } else SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, spectral transform should have a backtransform operation");
50: } else {
51: /* compute eigenvalues from Rayleigh quotient */
52: DSGetDimensions(eps->ds,&n,NULL,NULL,NULL,NULL);
53: if (!n) break;
54: EPSGetOperators(eps,&A,&B);
55: BVSetActiveColumns(eps->V,0,n);
56: DSGetCompact(eps->ds,&iscomp);
57: DSSetCompact(eps->ds,PETSC_FALSE);
58: DSGetMat(eps->ds,DS_MAT_A,&G);
59: BVMatProject(eps->V,A,eps->V,G);
60: DSRestoreMat(eps->ds,DS_MAT_A,&G);
61: if (B) {
62: DSGetMat(eps->ds,DS_MAT_B,&G);
63: BVMatProject(eps->V,B,eps->V,G);
64: DSRestoreMat(eps->ds,DS_MAT_A,&G);
65: }
66: DSSolve(eps->ds,eps->eigr,eps->eigi);
67: DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
68: DSSynchronize(eps->ds,eps->eigr,eps->eigi);
69: DSSetCompact(eps->ds,iscomp);
70: if (eps->ishermitian && (!eps->isgeneralized || eps->ispositive)) { /* V = V * Z */
71: DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
72: DSGetMat(eps->ds,DS_MAT_X,&Z);
73: BVMultInPlace(eps->V,Z,0,n);
74: MatDestroy(&Z);
75: }
76: /* in case of STFILTER discard computed eigenvalues that lie outside the wanted interval */
77: PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilter);
78: if (isfilter) {
79: nconv0 = eps->nconv;
80: for (i=0;i<eps->nconv;i++) {
81: if (PetscRealPart(eps->eigr[eps->perm[i]])<eps->inta || PetscRealPart(eps->eigr[eps->perm[i]])>eps->intb) {
82: eps->nconv--;
83: if (i<eps->nconv) { SWAP(eps->perm[i],eps->perm[eps->nconv],aux); i--; }
84: }
85: }
86: if (nconv0>eps->nconv) {
87: PetscInfo1(eps,"Discarded %D computed eigenvalues lying outside the interval\n",nconv0-eps->nconv);
88: }
89: }
90: }
91: break;
92: case EPS_CATEGORY_PRECOND:
93: case EPS_CATEGORY_CONTOUR:
94: /* eigenvalues already available as an output of the solver */
95: break;
96: }
97: return(0);
98: }
100: /*@
101: EPSSolve - Solves the eigensystem.
103: Collective on eps
105: Input Parameter:
106: . eps - eigensolver context obtained from EPSCreate()
108: Options Database Keys:
109: + -eps_view - print information about the solver used
110: . -eps_view_mat0 binary - save the first matrix (A) to the default binary viewer
111: . -eps_view_mat1 binary - save the second matrix (B) to the default binary viewer
112: . -eps_view_vectors binary - save the computed eigenvectors to the default binary viewer
113: . -eps_view_values - print computed eigenvalues
114: . -eps_converged_reason - print reason for convergence, and number of iterations
115: . -eps_error_absolute - print absolute errors of each eigenpair
116: . -eps_error_relative - print relative errors of each eigenpair
117: - -eps_error_backward - print backward errors of each eigenpair
119: Level: beginner
121: .seealso: EPSCreate(), EPSSetUp(), EPSDestroy(), EPSSetTolerances()
122: @*/
123: PetscErrorCode EPSSolve(EPS eps)124: {
126: PetscInt i;
127: STMatMode matmode;
128: Mat A,B;
132: if (eps->state>=EPS_STATE_SOLVED) return(0);
133: PetscLogEventBegin(EPS_Solve,eps,0,0,0);
135: /* Call setup */
136: EPSSetUp(eps);
137: eps->nconv = 0;
138: eps->its = 0;
139: for (i=0;i<eps->ncv;i++) {
140: eps->eigr[i] = 0.0;
141: eps->eigi[i] = 0.0;
142: eps->errest[i] = 0.0;
143: eps->perm[i] = i;
144: }
145: EPSViewFromOptions(eps,NULL,"-eps_view_pre");
146: RGViewFromOptions(eps->rg,NULL,"-rg_view");
148: /* Call solver */
149: (*eps->ops->solve)(eps);
150: if (!eps->reason) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
151: eps->state = EPS_STATE_SOLVED;
153: /* Only the first nconv columns contain useful information (except in CISS) */
154: BVSetActiveColumns(eps->V,0,eps->nconv);
155: if (eps->twosided) { BVSetActiveColumns(eps->W,0,eps->nconv); }
157: /* If inplace, purify eigenvectors before reverting operator */
158: STGetMatMode(eps->st,&matmode);
159: if (matmode == ST_MATMODE_INPLACE && eps->ispositive) {
160: EPSComputeVectors(eps);
161: }
162: STPostSolve(eps->st);
164: /* Map eigenvalues back to the original problem if appropriate */
165: EPSComputeValues(eps);
167: #if !defined(PETSC_USE_COMPLEX)
168: /* Reorder conjugate eigenvalues (positive imaginary first) */
169: for (i=0;i<eps->nconv-1;i++) {
170: if (eps->eigi[i] != 0) {
171: if (eps->eigi[i] < 0) {
172: eps->eigi[i] = -eps->eigi[i];
173: eps->eigi[i+1] = -eps->eigi[i+1];
174: /* the next correction only works with eigenvectors */
175: EPSComputeVectors(eps);
176: BVScaleColumn(eps->V,i+1,-1.0);
177: }
178: i++;
179: }
180: }
181: #endif
183: /* Sort eigenvalues according to eps->which parameter */
184: SlepcSortEigenvalues(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm);
185: PetscLogEventEnd(EPS_Solve,eps,0,0,0);
187: /* Various viewers */
188: EPSViewFromOptions(eps,NULL,"-eps_view");
189: EPSConvergedReasonViewFromOptions(eps);
190: EPSErrorViewFromOptions(eps);
191: EPSValuesViewFromOptions(eps);
192: EPSVectorsViewFromOptions(eps);
193: EPSGetOperators(eps,&A,&B);
194: MatViewFromOptions(A,(PetscObject)eps,"-eps_view_mat0");
195: if (eps->isgeneralized) {
196: MatViewFromOptions(B,(PetscObject)eps,"-eps_view_mat1");
197: }
199: /* Remove deflation and initial subspaces */
200: if (eps->nds) {
201: BVSetNumConstraints(eps->V,0);
202: eps->nds = 0;
203: }
204: eps->nini = 0;
205: return(0);
206: }
208: /*@
209: EPSGetIterationNumber - Gets the current iteration number. If the
210: call to EPSSolve() is complete, then it returns the number of iterations
211: carried out by the solution method.
213: Not Collective
215: Input Parameter:
216: . eps - the eigensolver context
218: Output Parameter:
219: . its - number of iterations
221: Note:
222: During the i-th iteration this call returns i-1. If EPSSolve() is
223: complete, then parameter "its" contains either the iteration number at
224: which convergence was successfully reached, or failure was detected.
225: Call EPSGetConvergedReason() to determine if the solver converged or
226: failed and why.
228: Level: intermediate
230: .seealso: EPSGetConvergedReason(), EPSSetTolerances()
231: @*/
232: PetscErrorCode EPSGetIterationNumber(EPS eps,PetscInt *its)233: {
237: *its = eps->its;
238: return(0);
239: }
241: /*@
242: EPSGetConverged - Gets the number of converged eigenpairs.
244: Not Collective
246: Input Parameter:
247: . eps - the eigensolver context
249: Output Parameter:
250: . nconv - number of converged eigenpairs
252: Note:
253: This function should be called after EPSSolve() has finished.
255: Level: beginner
257: .seealso: EPSSetDimensions(), EPSSolve()
258: @*/
259: PetscErrorCode EPSGetConverged(EPS eps,PetscInt *nconv)260: {
264: EPSCheckSolved(eps,1);
265: *nconv = eps->nconv;
266: return(0);
267: }
269: /*@
270: EPSGetConvergedReason - Gets the reason why the EPSSolve() iteration was
271: stopped.
273: Not Collective
275: Input Parameter:
276: . eps - the eigensolver context
278: Output Parameter:
279: . reason - negative value indicates diverged, positive value converged
281: Notes:
282: Possible values for reason are
283: + EPS_CONVERGED_TOL - converged up to tolerance
284: . EPS_CONVERGED_USER - converged due to a user-defined condition
285: . EPS_DIVERGED_ITS - required more than max_it iterations to reach convergence
286: . EPS_DIVERGED_BREAKDOWN - generic breakdown in method
287: - EPS_DIVERGED_SYMMETRY_LOST - pseudo-Lanczos was not able to keep symmetry
289: Can only be called after the call to EPSSolve() is complete.
291: Level: intermediate
293: .seealso: EPSSetTolerances(), EPSSolve(), EPSConvergedReason294: @*/
295: PetscErrorCode EPSGetConvergedReason(EPS eps,EPSConvergedReason *reason)296: {
300: EPSCheckSolved(eps,1);
301: *reason = eps->reason;
302: return(0);
303: }
305: /*@
306: EPSGetInvariantSubspace - Gets an orthonormal basis of the computed invariant
307: subspace.
309: Not Collective, but vectors are shared by all processors that share the EPS311: Input Parameter:
312: . eps - the eigensolver context
314: Output Parameter:
315: . v - an array of vectors
317: Notes:
318: This function should be called after EPSSolve() has finished.
320: The user should provide in v an array of nconv vectors, where nconv is
321: the value returned by EPSGetConverged().
323: The first k vectors returned in v span an invariant subspace associated
324: with the first k computed eigenvalues (note that this is not true if the
325: k-th eigenvalue is complex and matrix A is real; in this case the first
326: k+1 vectors should be used). An invariant subspace X of A satisfies Ax
327: in X for all x in X (a similar definition applies for generalized
328: eigenproblems).
330: Level: intermediate
332: .seealso: EPSGetEigenpair(), EPSGetConverged(), EPSSolve()
333: @*/
334: PetscErrorCode EPSGetInvariantSubspace(EPS eps,Vec v[])335: {
337: PetscInt i;
338: BV V=eps->V;
339: Vec w;
345: EPSCheckSolved(eps,1);
346: if (!eps->ishermitian && eps->state==EPS_STATE_EIGENVECTORS) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"EPSGetInvariantSubspace must be called before EPSGetEigenpair,EPSGetEigenvector or EPSComputeError");
347: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
348: BVDuplicateResize(eps->V,eps->nconv,&V);
349: BVSetActiveColumns(eps->V,0,eps->nconv);
350: BVCopy(eps->V,V);
351: for (i=0;i<eps->nconv;i++) {
352: BVGetColumn(V,i,&w);
353: VecPointwiseDivide(w,w,eps->D);
354: BVRestoreColumn(V,i,&w);
355: }
356: BVOrthogonalize(V,NULL);
357: }
358: for (i=0;i<eps->nconv;i++) {
359: BVCopyVec(V,i,v[i]);
360: }
361: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
362: BVDestroy(&V);
363: }
364: return(0);
365: }
367: /*@C
368: EPSGetEigenpair - Gets the i-th solution of the eigenproblem as computed by
369: EPSSolve(). The solution consists in both the eigenvalue and the eigenvector.
371: Logically Collective on eps
373: Input Parameters:
374: + eps - eigensolver context
375: - i - index of the solution
377: Output Parameters:
378: + eigr - real part of eigenvalue
379: . eigi - imaginary part of eigenvalue
380: . Vr - real part of eigenvector
381: - Vi - imaginary part of eigenvector
383: Notes:
384: It is allowed to pass NULL for Vr and Vi, if the eigenvector is not
385: required. Otherwise, the caller must provide valid Vec objects, i.e.,
386: they must be created by the calling program with e.g. MatCreateVecs().
388: If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is
389: configured with complex scalars the eigenvalue is stored
390: directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is
391: set to zero). In both cases, the user can pass NULL in eigi and Vi.
393: The index i should be a value between 0 and nconv-1 (see EPSGetConverged()).
394: Eigenpairs are indexed according to the ordering criterion established
395: with EPSSetWhichEigenpairs().
397: The 2-norm of the eigenvector is one unless the problem is generalized
398: Hermitian. In this case the eigenvector is normalized with respect to the
399: norm defined by the B matrix.
401: Level: beginner
403: .seealso: EPSGetEigenvalue(), EPSGetEigenvector(), EPSGetLeftEigenvector(), EPSSolve(),
404: EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetInvariantSubspace()
405: @*/
406: PetscErrorCode EPSGetEigenpair(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi)407: {
413: EPSCheckSolved(eps,1);
414: if (i<0 || i>=eps->nconv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
415: EPSGetEigenvalue(eps,i,eigr,eigi);
416: if (Vr || Vi) { EPSGetEigenvector(eps,i,Vr,Vi); }
417: return(0);
418: }
420: /*@C
421: EPSGetEigenvalue - Gets the i-th eigenvalue as computed by EPSSolve().
423: Not Collective
425: Input Parameters:
426: + eps - eigensolver context
427: - i - index of the solution
429: Output Parameters:
430: + eigr - real part of eigenvalue
431: - eigi - imaginary part of eigenvalue
433: Notes:
434: If the eigenvalue is real, then eigi is set to zero. If PETSc is
435: configured with complex scalars the eigenvalue is stored
436: directly in eigr (eigi is set to zero).
438: The index i should be a value between 0 and nconv-1 (see EPSGetConverged()).
439: Eigenpairs are indexed according to the ordering criterion established
440: with EPSSetWhichEigenpairs().
442: Level: beginner
444: .seealso: EPSSolve(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetEigenpair()
445: @*/
446: PetscErrorCode EPSGetEigenvalue(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi)447: {
448: PetscInt k;
452: EPSCheckSolved(eps,1);
453: if (i<0 || i>=eps->nconv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
454: k = eps->perm[i];
455: #if defined(PETSC_USE_COMPLEX)
456: if (eigr) *eigr = eps->eigr[k];
457: if (eigi) *eigi = 0;
458: #else
459: if (eigr) *eigr = eps->eigr[k];
460: if (eigi) *eigi = eps->eigi[k];
461: #endif
462: return(0);
463: }
465: /*@
466: EPSGetEigenvector - Gets the i-th right eigenvector as computed by EPSSolve().
468: Logically Collective on eps
470: Input Parameters:
471: + eps - eigensolver context
472: - i - index of the solution
474: Output Parameters:
475: + Vr - real part of eigenvector
476: - Vi - imaginary part of eigenvector
478: Notes:
479: The caller must provide valid Vec objects, i.e., they must be created
480: by the calling program with e.g. MatCreateVecs().
482: If the corresponding eigenvalue is real, then Vi is set to zero. If PETSc is
483: configured with complex scalars the eigenvector is stored
484: directly in Vr (Vi is set to zero). In any case, the user can pass NULL in Vr
485: or Vi if one of them is not required.
487: The index i should be a value between 0 and nconv-1 (see EPSGetConverged()).
488: Eigenpairs are indexed according to the ordering criterion established
489: with EPSSetWhichEigenpairs().
491: The 2-norm of the eigenvector is one unless the problem is generalized
492: Hermitian. In this case the eigenvector is normalized with respect to the
493: norm defined by the B matrix.
495: Level: beginner
497: .seealso: EPSSolve(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetEigenpair(), EPSGetLeftEigenvector()
498: @*/
499: PetscErrorCode EPSGetEigenvector(EPS eps,PetscInt i,Vec Vr,Vec Vi)500: {
502: PetscInt k;
509: EPSCheckSolved(eps,1);
510: if (i<0 || i>=eps->nconv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
511: EPSComputeVectors(eps);
512: k = eps->perm[i];
513: BV_GetEigenvector(eps->V,k,eps->eigi[k],Vr,Vi);
514: return(0);
515: }
517: /*@
518: EPSGetLeftEigenvector - Gets the i-th left eigenvector as computed by EPSSolve().
520: Logically Collective on eps
522: Input Parameters:
523: + eps - eigensolver context
524: - i - index of the solution
526: Output Parameters:
527: + Wr - real part of left eigenvector
528: - Wi - imaginary part of left eigenvector
530: Notes:
531: The caller must provide valid Vec objects, i.e., they must be created
532: by the calling program with e.g. MatCreateVecs().
534: If the corresponding eigenvalue is real, then Wi is set to zero. If PETSc is
535: configured with complex scalars the eigenvector is stored directly in Wr
536: (Wi is set to zero). In any case, the user can pass NULL in Wr or Wi if
537: one of them is not required.
539: The index i should be a value between 0 and nconv-1 (see EPSGetConverged()).
540: Eigensolutions are indexed according to the ordering criterion established
541: with EPSSetWhichEigenpairs().
543: Left eigenvectors are available only if the twosided flag was set, see
544: EPSSetTwoSided().
546: Level: intermediate
548: .seealso: EPSGetEigenvector(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSSetTwoSided()
549: @*/
550: PetscErrorCode EPSGetLeftEigenvector(EPS eps,PetscInt i,Vec Wr,Vec Wi)551: {
553: PetscInt k;
560: EPSCheckSolved(eps,1);
561: if (!eps->twosided) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must request left vectors with EPSSetTwoSided");
562: if (i<0 || i>=eps->nconv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
563: EPSComputeVectors(eps);
564: k = eps->perm[i];
565: BV_GetEigenvector(eps->W,k,eps->eigi[k],Wr,Wi);
566: return(0);
567: }
569: /*@
570: EPSGetErrorEstimate - Returns the error estimate associated to the i-th
571: computed eigenpair.
573: Not Collective
575: Input Parameter:
576: + eps - eigensolver context
577: - i - index of eigenpair
579: Output Parameter:
580: . errest - the error estimate
582: Notes:
583: This is the error estimate used internally by the eigensolver. The actual
584: error bound can be computed with EPSComputeError(). See also the users
585: manual for details.
587: Level: advanced
589: .seealso: EPSComputeError()
590: @*/
591: PetscErrorCode EPSGetErrorEstimate(EPS eps,PetscInt i,PetscReal *errest)592: {
596: EPSCheckSolved(eps,1);
597: if (i<0 || i>=eps->nconv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
598: *errest = eps->errest[eps->perm[i]];
599: return(0);
600: }
602: /*
603: EPSComputeResidualNorm_Private - Computes the norm of the residual vector
604: associated with an eigenpair.
606: Input Parameters:
607: trans - whether A' must be used instead of A
608: kr,ki - eigenvalue
609: xr,xi - eigenvector
610: z - three work vectors (the second one not referenced in complex scalars)
611: */
612: PetscErrorCode EPSComputeResidualNorm_Private(EPS eps,PetscBool trans,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)613: {
615: PetscInt nmat;
616: Mat A,B;
617: Vec u,w;
618: PetscScalar alpha;
619: #if !defined(PETSC_USE_COMPLEX)
620: Vec v;
621: PetscReal ni,nr;
622: #endif
623: PetscErrorCode (*matmult)(Mat,Vec,Vec) = trans? MatMultHermitianTranspose: MatMult;
626: u = z[0]; w = z[2];
627: STGetNumMatrices(eps->st,&nmat);
628: STGetMatrix(eps->st,0,&A);
629: if (nmat>1) { STGetMatrix(eps->st,1,&B); }
631: #if !defined(PETSC_USE_COMPLEX)
632: v = z[1];
633: if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) {
634: #endif
635: (*matmult)(A,xr,u); /* u=A*x */
636: if (PetscAbsScalar(kr) > PETSC_MACHINE_EPSILON) {
637: if (nmat>1) { (*matmult)(B,xr,w); }
638: else { VecCopy(xr,w); } /* w=B*x */
639: alpha = trans? -PetscConj(kr): -kr;
640: VecAXPY(u,alpha,w); /* u=A*x-k*B*x */
641: }
642: VecNorm(u,NORM_2,norm);
643: #if !defined(PETSC_USE_COMPLEX)
644: } else {
645: (*matmult)(A,xr,u); /* u=A*xr */
646: if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
647: if (nmat>1) { (*matmult)(B,xr,v); }
648: else { VecCopy(xr,v); } /* v=B*xr */
649: VecAXPY(u,-kr,v); /* u=A*xr-kr*B*xr */
650: if (nmat>1) { (*matmult)(B,xi,w); }
651: else { VecCopy(xi,w); } /* w=B*xi */
652: VecAXPY(u,trans?-ki:ki,w); /* u=A*xr-kr*B*xr+ki*B*xi */
653: }
654: VecNorm(u,NORM_2,&nr);
655: (*matmult)(A,xi,u); /* u=A*xi */
656: if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
657: VecAXPY(u,-kr,w); /* u=A*xi-kr*B*xi */
658: VecAXPY(u,trans?ki:-ki,v); /* u=A*xi-kr*B*xi-ki*B*xr */
659: }
660: VecNorm(u,NORM_2,&ni);
661: *norm = SlepcAbsEigenvalue(nr,ni);
662: }
663: #endif
664: return(0);
665: }
667: /*@
668: EPSComputeError - Computes the error (based on the residual norm) associated
669: with the i-th computed eigenpair.
671: Collective on eps
673: Input Parameter:
674: + eps - the eigensolver context
675: . i - the solution index
676: - type - the type of error to compute
678: Output Parameter:
679: . error - the error
681: Notes:
682: The error can be computed in various ways, all of them based on the residual
683: norm ||Ax-kBx||_2 where k is the eigenvalue and x is the eigenvector.
685: Level: beginner
687: .seealso: EPSErrorType, EPSSolve(), EPSGetErrorEstimate()
688: @*/
689: PetscErrorCode EPSComputeError(EPS eps,PetscInt i,EPSErrorType type,PetscReal *error)690: {
692: Mat A,B;
693: Vec xr,xi,w[3];
694: PetscReal t,vecnorm=1.0,errorl;
695: PetscScalar kr,ki;
696: PetscBool flg;
703: EPSCheckSolved(eps,1);
705: /* allocate work vectors */
706: #if defined(PETSC_USE_COMPLEX)
707: EPSSetWorkVecs(eps,3);
708: xi = NULL;
709: w[1] = NULL;
710: #else
711: EPSSetWorkVecs(eps,5);
712: xi = eps->work[3];
713: w[1] = eps->work[4];
714: #endif
715: xr = eps->work[0];
716: w[0] = eps->work[1];
717: w[2] = eps->work[2];
719: /* compute residual norm */
720: EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);
721: EPSComputeResidualNorm_Private(eps,PETSC_FALSE,kr,ki,xr,xi,w,error);
723: /* compute 2-norm of eigenvector */
724: if (eps->problem_type==EPS_GHEP) {
725: VecNorm(xr,NORM_2,&vecnorm);
726: }
728: /* if two-sided, compute left residual norm and take the maximum */
729: if (eps->twosided) {
730: EPSGetLeftEigenvector(eps,i,xr,xi);
731: EPSComputeResidualNorm_Private(eps,PETSC_TRUE,kr,ki,xr,xi,w,&errorl);
732: *error = PetscMax(*error,errorl);
733: }
735: /* compute error */
736: switch (type) {
737: case EPS_ERROR_ABSOLUTE:
738: break;
739: case EPS_ERROR_RELATIVE:
740: *error /= SlepcAbsEigenvalue(kr,ki)*vecnorm;
741: break;
742: case EPS_ERROR_BACKWARD:
743: /* initialization of matrix norms */
744: if (!eps->nrma) {
745: STGetMatrix(eps->st,0,&A);
746: MatHasOperation(A,MATOP_NORM,&flg);
747: if (!flg) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation");
748: MatNorm(A,NORM_INFINITY,&eps->nrma);
749: }
750: if (eps->isgeneralized) {
751: if (!eps->nrmb) {
752: STGetMatrix(eps->st,1,&B);
753: MatHasOperation(B,MATOP_NORM,&flg);
754: if (!flg) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation");
755: MatNorm(B,NORM_INFINITY,&eps->nrmb);
756: }
757: } else eps->nrmb = 1.0;
758: t = SlepcAbsEigenvalue(kr,ki);
759: *error /= (eps->nrma+t*eps->nrmb)*vecnorm;
760: break;
761: default:762: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
763: }
764: return(0);
765: }
767: /*
768: EPSGetStartVector - Generate a suitable vector to be used as the starting vector
769: for the recurrence that builds the right subspace.
771: Collective on eps
773: Input Parameters:
774: + eps - the eigensolver context
775: - i - iteration number
777: Output Parameters:
778: . breakdown - flag indicating that a breakdown has occurred
780: Notes:
781: The start vector is computed from another vector: for the first step (i=0),
782: the first initial vector is used (see EPSSetInitialSpace()); otherwise a random
783: vector is created. Then this vector is forced to be in the range of OP (only
784: for generalized definite problems) and orthonormalized with respect to all
785: V-vectors up to i-1. The resulting vector is placed in V[i].
787: The flag breakdown is set to true if either i=0 and the vector belongs to the
788: deflation space, or i>0 and the vector is linearly dependent with respect
789: to the V-vectors.
790: */
791: PetscErrorCode EPSGetStartVector(EPS eps,PetscInt i,PetscBool *breakdown)792: {
794: PetscReal norm;
795: PetscBool lindep;
796: Vec w,z;
802: /* For the first step, use the first initial vector, otherwise a random one */
803: if (i>0 || eps->nini==0) {
804: BVSetRandomColumn(eps->V,i);
805: }
807: /* Force the vector to be in the range of OP for definite generalized problems */
808: if (eps->ispositive || (eps->isgeneralized && eps->ishermitian)) {
809: BVCreateVec(eps->V,&w);
810: BVCopyVec(eps->V,i,w);
811: BVGetColumn(eps->V,i,&z);
812: STApply(eps->st,w,z);
813: BVRestoreColumn(eps->V,i,&z);
814: VecDestroy(&w);
815: }
817: /* Orthonormalize the vector with respect to previous vectors */
818: BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&lindep);
819: if (breakdown) *breakdown = lindep;
820: else if (lindep || norm == 0.0) {
821: if (i==0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Initial vector is zero or belongs to the deflation space");
822: else SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to generate more start vectors");
823: }
824: BVScaleColumn(eps->V,i,1.0/norm);
825: return(0);
826: }
828: /*
829: EPSGetLeftStartVector - Generate a suitable vector to be used as the left starting
830: vector for the recurrence that builds the left subspace. See EPSGetStartVector().
831: */
832: PetscErrorCode EPSGetLeftStartVector(EPS eps,PetscInt i,PetscBool *breakdown)833: {
835: PetscReal norm;
836: PetscBool lindep;
842: /* For the first step, use the first initial vector, otherwise a random one */
843: if (i>0 || eps->ninil==0) {
844: BVSetRandomColumn(eps->W,i);
845: }
847: /* Orthonormalize the vector with respect to previous vectors */
848: BVOrthogonalizeColumn(eps->W,i,NULL,&norm,&lindep);
849: if (breakdown) *breakdown = lindep;
850: else if (lindep || norm == 0.0) {
851: if (i==0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Left initial vector is zero");
852: else SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to generate more left start vectors");
853: }
854: BVScaleColumn(eps->W,i,1.0/norm);
855: return(0);
856: }