1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2018, 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: NEP routines related to the solution process
12: */
14: #include <slepc/private/nepimpl.h> /*I "slepcnep.h" I*/
15: #include <petscdraw.h>
17: PetscErrorCode NEPComputeVectors(NEP nep) 18: {
22: NEPCheckSolved(nep,1);
23: if (nep->state==NEP_STATE_SOLVED && nep->ops->computevectors) {
24: (*nep->ops->computevectors)(nep);
25: }
26: nep->state = NEP_STATE_EIGENVECTORS;
27: return(0);
28: }
30: /*@
31: NEPSolve - Solves the nonlinear eigensystem.
33: Collective on NEP 35: Input Parameter:
36: . nep - eigensolver context obtained from NEPCreate()
38: Options Database Keys:
39: + -nep_view - print information about the solver used
40: . -nep_view_vectors binary - save the computed eigenvectors to the default binary viewer
41: . -nep_view_values - print computed eigenvalues
42: . -nep_converged_reason - print reason for convergence, and number of iterations
43: . -nep_error_absolute - print absolute errors of each eigenpair
44: - -nep_error_relative - print relative errors of each eigenpair
46: Level: beginner
48: .seealso: NEPCreate(), NEPSetUp(), NEPDestroy(), NEPSetTolerances()
49: @*/
50: PetscErrorCode NEPSolve(NEP nep) 51: {
53: PetscInt i;
57: if (nep->state>=NEP_STATE_SOLVED) return(0);
58: PetscLogEventBegin(NEP_Solve,nep,0,0,0);
60: /* call setup */
61: NEPSetUp(nep);
62: nep->nconv = 0;
63: nep->its = 0;
64: for (i=0;i<nep->ncv;i++) {
65: nep->eigr[i] = 0.0;
66: nep->eigi[i] = 0.0;
67: nep->errest[i] = 0.0;
68: nep->perm[i] = i;
69: }
70: NEPViewFromOptions(nep,NULL,"-nep_view_pre");
71: RGViewFromOptions(nep->rg,NULL,"-rg_view");
73: (*nep->ops->solve)(nep);
74: nep->state = NEP_STATE_SOLVED;
76: if (!nep->reason) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
78: if (nep->refine==NEP_REFINE_SIMPLE && nep->rits>0 && nep->nconv>0) {
79: NEPComputeVectors(nep);
80: NEPNewtonRefinementSimple(nep,&nep->rits,nep->rtol,nep->nconv);
81: nep->state = NEP_STATE_EIGENVECTORS;
82: }
84: /* sort eigenvalues according to nep->which parameter */
85: SlepcSortEigenvalues(nep->sc,nep->nconv,nep->eigr,nep->eigi,nep->perm);
86: PetscLogEventEnd(NEP_Solve,nep,0,0,0);
88: /* various viewers */
89: NEPViewFromOptions(nep,NULL,"-nep_view");
90: NEPReasonViewFromOptions(nep);
91: NEPErrorViewFromOptions(nep);
92: NEPValuesViewFromOptions(nep);
93: NEPVectorsViewFromOptions(nep);
95: /* Remove the initial subspace */
96: nep->nini = 0;
97: return(0);
98: }
100: /*@
101: NEPProjectOperator - Computes the projection of the nonlinear operator.
103: Collective on NEP105: Input Parameters:
106: + nep - the nonlinear eigensolver context
107: . j0 - initial index
108: - j1 - final index
110: Notes:
111: This is available for split operator only.
113: The nonlinear operator T(lambda) is projected onto span(V), where V is
114: an orthonormal basis built internally by the solver. The projected
115: operator is equal to sum_i V'*A_i*V*f_i(lambda), so this function
116: computes all matrices Ei = V'*A_i*V, and stores them in the extra
117: matrices inside DS. Only rows/columns in the range [j0,j1-1] are computed,
118: the previous ones are assumed to be available already.
120: Level: developer
122: .seealso: NEPSetSplitOperator()
123: @*/
124: PetscErrorCode NEPProjectOperator(NEP nep,PetscInt j0,PetscInt j1)125: {
127: PetscInt k;
128: Mat G;
134: NEPCheckProblem(nep,1);
135: NEPCheckSplit(nep,1);
136: BVSetActiveColumns(nep->V,j0,j1);
137: for (k=0;k<nep->nt;k++) {
138: DSGetMat(nep->ds,DSMatExtra[k],&G);
139: BVMatProject(nep->V,nep->A[k],nep->V,G);
140: DSRestoreMat(nep->ds,DSMatExtra[k],&G);
141: }
142: return(0);
143: }
145: /*@
146: NEPApplyFunction - Applies the nonlinear function T(lambda) to a given vector.
148: Collective on NEP150: Input Parameters:
151: + nep - the nonlinear eigensolver context
152: . lambda - scalar argument
153: . x - vector to be multiplied against
154: - v - workspace vector (used only in the case of split form)
156: Output Parameters:
157: + y - result vector
158: . A - Function matrix
159: - B - optional preconditioning matrix
161: Note:
162: If the nonlinear operator is represented in split form, the result
163: y = T(lambda)*x is computed without building T(lambda) explicitly. In
164: that case, parameters A and B are not used. Otherwise, the matrix
165: T(lambda) is built and the effect is the same as a call to
166: NEPComputeFunction() followed by a MatMult().
168: Level: developer
170: .seealso: NEPSetSplitOperator(), NEPComputeFunction()
171: @*/
172: PetscErrorCode NEPApplyFunction(NEP nep,PetscScalar lambda,Vec x,Vec v,Vec y,Mat A,Mat B)173: {
175: PetscInt i;
176: PetscScalar alpha;
187: if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
188: VecSet(y,0.0);
189: for (i=0;i<nep->nt;i++) {
190: FNEvaluateFunction(nep->f[i],lambda,&alpha);
191: MatMult(nep->A[i],x,v);
192: VecAXPY(y,alpha,v);
193: }
194: } else {
195: NEPComputeFunction(nep,lambda,A,B);
196: MatMult(A,x,y);
197: }
198: return(0);
199: }
201: /*@
202: NEPApplyJacobian - Applies the nonlinear Jacobian T'(lambda) to a given vector.
204: Collective on NEP206: Input Parameters:
207: + nep - the nonlinear eigensolver context
208: . lambda - scalar argument
209: . x - vector to be multiplied against
210: - v - workspace vector (used only in the case of split form)
212: Output Parameters:
213: + y - result vector
214: - A - Jacobian matrix
216: Note:
217: If the nonlinear operator is represented in split form, the result
218: y = T'(lambda)*x is computed without building T'(lambda) explicitly. In
219: that case, parameter A is not used. Otherwise, the matrix
220: T'(lambda) is built and the effect is the same as a call to
221: NEPComputeJacobian() followed by a MatMult().
223: Level: developer
225: .seealso: NEPSetSplitOperator(), NEPComputeJacobian()
226: @*/
227: PetscErrorCode NEPApplyJacobian(NEP nep,PetscScalar lambda,Vec x,Vec v,Vec y,Mat A)228: {
230: PetscInt i;
231: PetscScalar alpha;
241: if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
242: VecSet(y,0.0);
243: for (i=0;i<nep->nt;i++) {
244: FNEvaluateDerivative(nep->f[i],lambda,&alpha);
245: MatMult(nep->A[i],x,v);
246: VecAXPY(y,alpha,v);
247: }
248: } else {
249: NEPComputeJacobian(nep,lambda,A);
250: MatMult(A,x,y);
251: }
252: return(0);
253: }
255: /*@
256: NEPGetIterationNumber - Gets the current iteration number. If the
257: call to NEPSolve() is complete, then it returns the number of iterations
258: carried out by the solution method.
260: Not Collective
262: Input Parameter:
263: . nep - the nonlinear eigensolver context
265: Output Parameter:
266: . its - number of iterations
268: Note:
269: During the i-th iteration this call returns i-1. If NEPSolve() is
270: complete, then parameter "its" contains either the iteration number at
271: which convergence was successfully reached, or failure was detected.
272: Call NEPGetConvergedReason() to determine if the solver converged or
273: failed and why.
275: Level: intermediate
277: .seealso: NEPGetConvergedReason(), NEPSetTolerances()
278: @*/
279: PetscErrorCode NEPGetIterationNumber(NEP nep,PetscInt *its)280: {
284: *its = nep->its;
285: return(0);
286: }
288: /*@
289: NEPGetConverged - Gets the number of converged eigenpairs.
291: Not Collective
293: Input Parameter:
294: . nep - the nonlinear eigensolver context
296: Output Parameter:
297: . nconv - number of converged eigenpairs
299: Note:
300: This function should be called after NEPSolve() has finished.
302: Level: beginner
304: .seealso: NEPSetDimensions(), NEPSolve()
305: @*/
306: PetscErrorCode NEPGetConverged(NEP nep,PetscInt *nconv)307: {
311: NEPCheckSolved(nep,1);
312: *nconv = nep->nconv;
313: return(0);
314: }
316: /*@
317: NEPGetConvergedReason - Gets the reason why the NEPSolve() iteration was
318: stopped.
320: Not Collective
322: Input Parameter:
323: . nep - the nonlinear eigensolver context
325: Output Parameter:
326: . reason - negative value indicates diverged, positive value converged
328: Notes:
330: Possible values for reason are
331: + NEP_CONVERGED_TOL - converged up to tolerance
332: . NEP_CONVERGED_USER - converged due to a user-defined condition
333: . NEP_DIVERGED_ITS - required more than max_it iterations to reach convergence
334: . NEP_DIVERGED_BREAKDOWN - generic breakdown in method
335: - NEP_DIVERGED_LINEAR_SOLVE - inner linear solve failed
337: Can only be called after the call to NEPSolve() is complete.
339: Level: intermediate
341: .seealso: NEPSetTolerances(), NEPSolve(), NEPConvergedReason342: @*/
343: PetscErrorCode NEPGetConvergedReason(NEP nep,NEPConvergedReason *reason)344: {
348: NEPCheckSolved(nep,1);
349: *reason = nep->reason;
350: return(0);
351: }
353: /*@C
354: NEPGetEigenpair - Gets the i-th solution of the eigenproblem as computed by
355: NEPSolve(). The solution consists in both the eigenvalue and the eigenvector.
357: Logically Collective on NEP359: Input Parameters:
360: + nep - nonlinear eigensolver context
361: - i - index of the solution
363: Output Parameters:
364: + eigr - real part of eigenvalue
365: . eigi - imaginary part of eigenvalue
366: . Vr - real part of eigenvector
367: - Vi - imaginary part of eigenvector
369: Notes:
370: It is allowed to pass NULL for Vr and Vi, if the eigenvector is not
371: required. Otherwise, the caller must provide valid Vec objects, i.e.,
372: they must be created by the calling program with e.g. MatCreateVecs().
374: If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is
375: configured with complex scalars the eigenvalue is stored
376: directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is
377: set to zero). In both cases, the user can pass NULL in eigi and Vi.
379: The index i should be a value between 0 and nconv-1 (see NEPGetConverged()).
380: Eigenpairs are indexed according to the ordering criterion established
381: with NEPSetWhichEigenpairs().
383: Level: beginner
385: .seealso: NEPSolve(), NEPGetConverged(), NEPSetWhichEigenpairs()
386: @*/
387: PetscErrorCode NEPGetEigenpair(NEP nep,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi)388: {
389: PetscInt k;
397: NEPCheckSolved(nep,1);
398: if (i<0 || i>=nep->nconv) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
400: NEPComputeVectors(nep);
401: k = nep->perm[i];
403: /* eigenvalue */
404: #if defined(PETSC_USE_COMPLEX)
405: if (eigr) *eigr = nep->eigr[k];
406: if (eigi) *eigi = 0;
407: #else
408: if (eigr) *eigr = nep->eigr[k];
409: if (eigi) *eigi = nep->eigi[k];
410: #endif
412: /* eigenvector */
413: #if defined(PETSC_USE_COMPLEX)
414: if (Vr) { BVCopyVec(nep->V,k,Vr); }
415: if (Vi) { VecSet(Vi,0.0); }
416: #else
417: if (nep->eigi[k]>0) { /* first value of conjugate pair */
418: if (Vr) { BVCopyVec(nep->V,k,Vr); }
419: if (Vi) { BVCopyVec(nep->V,k+1,Vi); }
420: } else if (nep->eigi[k]<0) { /* second value of conjugate pair */
421: if (Vr) { BVCopyVec(nep->V,k-1,Vr); }
422: if (Vi) {
423: BVCopyVec(nep->V,k,Vi);
424: VecScale(Vi,-1.0);
425: }
426: } else { /* real eigenvalue */
427: if (Vr) { BVCopyVec(nep->V,k,Vr); }
428: if (Vi) { VecSet(Vi,0.0); }
429: }
430: #endif
431: return(0);
432: }
434: /*@
435: NEPGetErrorEstimate - Returns the error estimate associated to the i-th
436: computed eigenpair.
438: Not Collective
440: Input Parameter:
441: + nep - nonlinear eigensolver context
442: - i - index of eigenpair
444: Output Parameter:
445: . errest - the error estimate
447: Notes:
448: This is the error estimate used internally by the eigensolver. The actual
449: error bound can be computed with NEPComputeRelativeError().
451: Level: advanced
453: .seealso: NEPComputeRelativeError()
454: @*/
455: PetscErrorCode NEPGetErrorEstimate(NEP nep,PetscInt i,PetscReal *errest)456: {
460: NEPCheckSolved(nep,1);
461: if (i<0 || i>=nep->nconv) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
462: *errest = nep->errest[nep->perm[i]];
463: return(0);
464: }
466: /*
467: NEPComputeResidualNorm_Private - Computes the norm of the residual vector
468: associated with an eigenpair.
470: Input Parameters:
471: lambda - eigenvalue
472: x - eigenvector
473: w - array of work vectors (two vectors in split form, one vector otherwise)
474: */
475: PetscErrorCode NEPComputeResidualNorm_Private(NEP nep,PetscScalar lambda,Vec x,Vec *w,PetscReal *norm)476: {
478: Vec y,z=NULL;
481: y = w[0];
482: if (nep->fui==NEP_USER_INTERFACE_SPLIT) z = w[1];
483: NEPApplyFunction(nep,lambda,x,z,y,nep->function,nep->function_pre);
484: VecNorm(y,NORM_2,norm);
485: return(0);
486: }
488: /*@
489: NEPComputeError - Computes the error (based on the residual norm) associated
490: with the i-th computed eigenpair.
492: Collective on NEP494: Input Parameter:
495: + nep - the nonlinear eigensolver context
496: . i - the solution index
497: - type - the type of error to compute
499: Output Parameter:
500: . error - the error
502: Notes:
503: The error can be computed in various ways, all of them based on the residual
504: norm computed as ||T(lambda)x||_2 where lambda is the eigenvalue and x is the
505: eigenvector.
507: Level: beginner
509: .seealso: NEPErrorType, NEPSolve(), NEPGetErrorEstimate()
510: @*/
511: PetscErrorCode NEPComputeError(NEP nep,PetscInt i,NEPErrorType type,PetscReal *error)512: {
514: Vec xr,xi=NULL;
515: PetscInt j,nwork,issplit=0;
516: PetscScalar kr,ki,s;
517: PetscReal er,z=0.0;
518: PetscBool flg;
525: NEPCheckSolved(nep,1);
527: /* allocate work vectors */
528: #if defined(PETSC_USE_COMPLEX)
529: nwork = 2;
530: #else
531: nwork = 3;
532: #endif
533: if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
534: issplit = 1;
535: nwork++; /* need an extra work vector for NEPComputeResidualNorm_Private */
536: }
537: NEPSetWorkVecs(nep,nwork);
538: xr = nep->work[issplit+1];
539: #if !defined(PETSC_USE_COMPLEX)
540: xi = nep->work[issplit+2];
541: #endif
543: /* compute residual norms */
544: NEPGetEigenpair(nep,i,&kr,&ki,xr,xi);
545: #if !defined(PETSC_USE_COMPLEX)
546: if (ki) SETERRQ(PetscObjectComm((PetscObject)nep),1,"Not implemented for complex eigenvalues with real scalars");
547: #endif
548: NEPComputeResidualNorm_Private(nep,kr,xr,nep->work,error);
549: VecNorm(xr,NORM_2,&er);
551: /* compute error */
552: switch (type) {
553: case NEP_ERROR_ABSOLUTE:
554: break;
555: case NEP_ERROR_RELATIVE:
556: *error /= PetscAbsScalar(kr)*er;
557: break;
558: case NEP_ERROR_BACKWARD:
559: if (nep->fui!=NEP_USER_INTERFACE_SPLIT) {
560: *error = 0.0;
561: PetscInfo(nep,"Backward error only available in split form\n");
562: break;
563: }
564: /* initialization of matrix norms */
565: if (!nep->nrma[0]) {
566: for (j=0;j<nep->nt;j++) {
567: MatHasOperation(nep->A[j],MATOP_NORM,&flg);
568: if (!flg) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation");
569: MatNorm(nep->A[j],NORM_INFINITY,&nep->nrma[j]);
570: }
571: }
572: for (j=0;j<nep->nt;j++) {
573: FNEvaluateFunction(nep->f[j],kr,&s);
574: z = z + nep->nrma[j]*PetscAbsScalar(s);
575: }
576: *error /= z;
577: break;
578: default:579: SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
580: }
581: return(0);
582: }
584: /*@
585: NEPComputeFunction - Computes the function matrix T(lambda) that has been
586: set with NEPSetFunction().
588: Collective on NEP and Mat
590: Input Parameters:
591: + nep - the NEP context
592: - lambda - the scalar argument
594: Output Parameters:
595: + A - Function matrix
596: - B - optional preconditioning matrix
598: Notes:
599: NEPComputeFunction() is typically used within nonlinear eigensolvers
600: implementations, so most users would not generally call this routine
601: themselves.
603: Level: developer
605: .seealso: NEPSetFunction(), NEPGetFunction()
606: @*/
607: PetscErrorCode NEPComputeFunction(NEP nep,PetscScalar lambda,Mat A,Mat B)608: {
610: PetscInt i;
611: PetscScalar alpha;
615: NEPCheckProblem(nep,1);
616: switch (nep->fui) {
617: case NEP_USER_INTERFACE_CALLBACK:
618: if (!nep->computefunction) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_USER,"Must call NEPSetFunction() first");
619: PetscLogEventBegin(NEP_FunctionEval,nep,A,B,0);
620: PetscStackPush("NEP user Function function");
621: (*nep->computefunction)(nep,lambda,A,B,nep->functionctx);
622: PetscStackPop;
623: PetscLogEventEnd(NEP_FunctionEval,nep,A,B,0);
624: break;
625: case NEP_USER_INTERFACE_SPLIT:
626: MatZeroEntries(A);
627: for (i=0;i<nep->nt;i++) {
628: FNEvaluateFunction(nep->f[i],lambda,&alpha);
629: MatAXPY(A,alpha,nep->A[i],nep->mstr);
630: }
631: if (A != B) SETERRQ(PetscObjectComm((PetscObject)nep),1,"Not implemented");
632: break;
633: case NEP_USER_INTERFACE_DERIVATIVES:
634: PetscLogEventBegin(NEP_DerivativesEval,nep,A,B,0);
635: PetscStackPush("NEP user Derivatives function");
636: (*nep->computederivatives)(nep,lambda,0,A,nep->derivativesctx);
637: PetscStackPop;
638: PetscLogEventEnd(NEP_DerivativesEval,nep,A,B,0);
639: break;
640: }
641: return(0);
642: }
644: /*@
645: NEPComputeJacobian - Computes the Jacobian matrix T'(lambda) that has been
646: set with NEPSetJacobian().
648: Collective on NEP and Mat
650: Input Parameters:
651: + nep - the NEP context
652: - lambda - the scalar argument
654: Output Parameters:
655: . A - Jacobian matrix
657: Notes:
658: Most users should not need to explicitly call this routine, as it
659: is used internally within the nonlinear eigensolvers.
661: Level: developer
663: .seealso: NEPSetJacobian(), NEPGetJacobian()
664: @*/
665: PetscErrorCode NEPComputeJacobian(NEP nep,PetscScalar lambda,Mat A)666: {
668: PetscInt i;
669: PetscScalar alpha;
673: NEPCheckProblem(nep,1);
674: switch (nep->fui) {
675: case NEP_USER_INTERFACE_CALLBACK:
676: if (!nep->computejacobian) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_USER,"Must call NEPSetJacobian() first");
677: PetscLogEventBegin(NEP_JacobianEval,nep,A,0,0);
678: PetscStackPush("NEP user Jacobian function");
679: (*nep->computejacobian)(nep,lambda,A,nep->jacobianctx);
680: PetscStackPop;
681: PetscLogEventEnd(NEP_JacobianEval,nep,A,0,0);
682: break;
683: case NEP_USER_INTERFACE_SPLIT:
684: MatZeroEntries(A);
685: for (i=0;i<nep->nt;i++) {
686: FNEvaluateDerivative(nep->f[i],lambda,&alpha);
687: MatAXPY(A,alpha,nep->A[i],nep->mstr);
688: }
689: break;
690: case NEP_USER_INTERFACE_DERIVATIVES:
691: PetscLogEventBegin(NEP_DerivativesEval,nep,A,0,0);
692: PetscStackPush("NEP user Derivatives function");
693: (*nep->computederivatives)(nep,lambda,1,A,nep->derivativesctx);
694: PetscStackPop;
695: PetscLogEventEnd(NEP_DerivativesEval,nep,A,0,0);
696: break;
697: }
698: return(0);
699: }