1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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: PEP routines related to the solution process
12: */
14: #include <slepc/private/pepimpl.h> /*I "slepcpep.h" I*/
15: #include <slepc/private/bvimpl.h> /*I "slepcbv.h" I*/
16: #include <petscdraw.h>
18: static PetscBool cited = PETSC_FALSE;
19: static const char citation[] =
20: "@Article{slepc-pep-refine,\n"
21: " author = \"C. Campos and J. E. Roman\",\n"
22: " title = \"Parallel iterative refinement in polynomial eigenvalue problems\",\n"
23: " journal = \"Numer. Linear Algebra Appl.\",\n"
24: " volume = \"23\",\n"
25: " number = \"4\",\n"
26: " pages = \"730--745\",\n"
27: " year = \"2016,\"\n"
28: " doi = \"https://doi.org/10.1002/nla.2052\"\n"
29: "}\n";
31: PetscErrorCode PEPComputeVectors(PEP pep) 32: {
36: PEPCheckSolved(pep,1);
37: if (pep->state==PEP_STATE_SOLVED && pep->ops->computevectors) {
38: (*pep->ops->computevectors)(pep);
39: }
40: pep->state = PEP_STATE_EIGENVECTORS;
41: return(0);
42: }
44: PetscErrorCode PEPExtractVectors(PEP pep) 45: {
49: PEPCheckSolved(pep,1);
50: if (pep->state==PEP_STATE_SOLVED && pep->ops->extractvectors) {
51: (*pep->ops->extractvectors)(pep);
52: }
53: return(0);
54: }
56: /*@
57: PEPSolve - Solves the polynomial eigensystem.
59: Collective on PEP 61: Input Parameter:
62: . pep - eigensolver context obtained from PEPCreate()
64: Options Database Keys:
65: + -pep_view - print information about the solver used
66: . -pep_view_matk binary - save any of the coefficient matrices (Ak) to the
67: default binary viewer (replace k by an integer from 0 to nmat-1)
68: . -pep_view_vectors binary - save the computed eigenvectors to the default binary viewer
69: . -pep_view_values - print computed eigenvalues
70: . -pep_converged_reason - print reason for convergence, and number of iterations
71: . -pep_error_absolute - print absolute errors of each eigenpair
72: . -pep_error_relative - print relative errors of each eigenpair
73: - -pep_error_backward - print backward errors of each eigenpair
75: Level: beginner
77: .seealso: PEPCreate(), PEPSetUp(), PEPDestroy(), PEPSetTolerances()
78: @*/
79: PetscErrorCode PEPSolve(PEP pep) 80: {
82: PetscInt i,k;
83: PetscBool flg,islinear;
84: #define OPTLEN 16 85: char str[OPTLEN];
89: if (pep->state>=PEP_STATE_SOLVED) return(0);
90: PetscLogEventBegin(PEP_Solve,pep,0,0,0);
92: /* call setup */
93: PEPSetUp(pep);
94: pep->nconv = 0;
95: pep->its = 0;
96: k = pep->lineariz? pep->ncv: pep->ncv*(pep->nmat-1);
97: for (i=0;i<k;i++) {
98: pep->eigr[i] = 0.0;
99: pep->eigi[i] = 0.0;
100: pep->errest[i] = 0.0;
101: pep->perm[i] = i;
102: }
103: PEPViewFromOptions(pep,NULL,"-pep_view_pre");
104: RGViewFromOptions(pep->rg,NULL,"-rg_view");
106: (*pep->ops->solve)(pep);
108: if (!pep->reason) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
110: PetscObjectTypeCompare((PetscObject)pep,PEPLINEAR,&islinear);
111: if (!islinear) {
112: STPostSolve(pep->st);
113: /* Map eigenvalues back to the original problem */
114: STGetTransform(pep->st,&flg);
115: if (flg && pep->ops->backtransform) {
116: (*pep->ops->backtransform)(pep);
117: }
118: }
120: pep->state = PEP_STATE_SOLVED;
122: #if !defined(PETSC_USE_COMPLEX)
123: /* reorder conjugate eigenvalues (positive imaginary first) */
124: for (i=0;i<pep->nconv-1;i++) {
125: if (pep->eigi[i] != 0) {
126: if (pep->eigi[i] < 0) {
127: pep->eigi[i] = -pep->eigi[i];
128: pep->eigi[i+1] = -pep->eigi[i+1];
129: /* the next correction only works with eigenvectors */
130: PEPComputeVectors(pep);
131: BVScaleColumn(pep->V,i+1,-1.0);
132: }
133: i++;
134: }
135: }
136: #endif
138: if (pep->refine!=PEP_REFINE_NONE) {
139: PetscCitationsRegister(citation,&cited);
140: }
142: if (pep->refine==PEP_REFINE_SIMPLE && pep->rits>0 && pep->nconv>0) {
143: PEPComputeVectors(pep);
144: PEPNewtonRefinementSimple(pep,&pep->rits,pep->rtol,pep->nconv);
145: }
147: /* sort eigenvalues according to pep->which parameter */
148: SlepcSortEigenvalues(pep->sc,pep->nconv,pep->eigr,pep->eigi,pep->perm);
149: PetscLogEventEnd(PEP_Solve,pep,0,0,0);
151: /* various viewers */
152: PEPViewFromOptions(pep,NULL,"-pep_view");
153: PEPReasonViewFromOptions(pep);
154: PEPErrorViewFromOptions(pep);
155: PEPValuesViewFromOptions(pep);
156: PEPVectorsViewFromOptions(pep);
157: for (i=0;i<pep->nmat;i++) {
158: PetscSNPrintf(str,OPTLEN,"-pep_view_mat%d",(int)i);
159: MatViewFromOptions(pep->A[i],(PetscObject)pep,str);
160: }
162: /* Remove the initial subspace */
163: pep->nini = 0;
164: return(0);
165: }
167: /*@
168: PEPGetIterationNumber - Gets the current iteration number. If the
169: call to PEPSolve() is complete, then it returns the number of iterations
170: carried out by the solution method.
172: Not Collective
174: Input Parameter:
175: . pep - the polynomial eigensolver context
177: Output Parameter:
178: . its - number of iterations
180: Note:
181: During the i-th iteration this call returns i-1. If PEPSolve() is
182: complete, then parameter "its" contains either the iteration number at
183: which convergence was successfully reached, or failure was detected.
184: Call PEPGetConvergedReason() to determine if the solver converged or
185: failed and why.
187: Level: intermediate
189: .seealso: PEPGetConvergedReason(), PEPSetTolerances()
190: @*/
191: PetscErrorCode PEPGetIterationNumber(PEP pep,PetscInt *its)192: {
196: *its = pep->its;
197: return(0);
198: }
200: /*@
201: PEPGetConverged - Gets the number of converged eigenpairs.
203: Not Collective
205: Input Parameter:
206: . pep - the polynomial eigensolver context
208: Output Parameter:
209: . nconv - number of converged eigenpairs
211: Note:
212: This function should be called after PEPSolve() has finished.
214: Level: beginner
216: .seealso: PEPSetDimensions(), PEPSolve()
217: @*/
218: PetscErrorCode PEPGetConverged(PEP pep,PetscInt *nconv)219: {
223: PEPCheckSolved(pep,1);
224: *nconv = pep->nconv;
225: return(0);
226: }
228: /*@
229: PEPGetConvergedReason - Gets the reason why the PEPSolve() iteration was
230: stopped.
232: Not Collective
234: Input Parameter:
235: . pep - the polynomial eigensolver context
237: Output Parameter:
238: . reason - negative value indicates diverged, positive value converged
240: Notes:
242: Possible values for reason are
243: + PEP_CONVERGED_TOL - converged up to tolerance
244: . PEP_CONVERGED_USER - converged due to a user-defined condition
245: . PEP_DIVERGED_ITS - required more than max_it iterations to reach convergence
246: . PEP_DIVERGED_BREAKDOWN - generic breakdown in method
247: - PEP_DIVERGED_SYMMETRY_LOST - pseudo-Lanczos was not able to keep symmetry
249: Can only be called after the call to PEPSolve() is complete.
251: Level: intermediate
253: .seealso: PEPSetTolerances(), PEPSolve(), PEPConvergedReason254: @*/
255: PetscErrorCode PEPGetConvergedReason(PEP pep,PEPConvergedReason *reason)256: {
260: PEPCheckSolved(pep,1);
261: *reason = pep->reason;
262: return(0);
263: }
265: /*@C
266: PEPGetEigenpair - Gets the i-th solution of the eigenproblem as computed by
267: PEPSolve(). The solution consists in both the eigenvalue and the eigenvector.
269: Logically Collective on EPS271: Input Parameters:
272: + pep - polynomial eigensolver context
273: - i - index of the solution
275: Output Parameters:
276: + eigr - real part of eigenvalue
277: . eigi - imaginary part of eigenvalue
278: . Vr - real part of eigenvector
279: - Vi - imaginary part of eigenvector
281: Notes:
282: It is allowed to pass NULL for Vr and Vi, if the eigenvector is not
283: required. Otherwise, the caller must provide valid Vec objects, i.e.,
284: they must be created by the calling program with e.g. MatCreateVecs().
286: If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is
287: configured with complex scalars the eigenvalue is stored
288: directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is
289: set to zero). In any case, the user can pass NULL in Vr or Vi if one of
290: them is not required.
292: The index i should be a value between 0 and nconv-1 (see PEPGetConverged()).
293: Eigenpairs are indexed according to the ordering criterion established
294: with PEPSetWhichEigenpairs().
296: Level: beginner
298: .seealso: PEPSolve(), PEPGetConverged(), PEPSetWhichEigenpairs()
299: @*/
300: PetscErrorCode PEPGetEigenpair(PEP pep,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi)301: {
302: PetscInt k;
310: PEPCheckSolved(pep,1);
311: if (i<0 || i>=pep->nconv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
313: PEPComputeVectors(pep);
314: k = pep->perm[i];
316: /* eigenvalue */
317: #if defined(PETSC_USE_COMPLEX)
318: if (eigr) *eigr = pep->eigr[k];
319: if (eigi) *eigi = 0;
320: #else
321: if (eigr) *eigr = pep->eigr[k];
322: if (eigi) *eigi = pep->eigi[k];
323: #endif
325: /* eigenvector */
326: BV_GetEigenvector(pep->V,k,pep->eigi[k],Vr,Vi);
327: return(0);
328: }
330: /*@
331: PEPGetErrorEstimate - Returns the error estimate associated to the i-th
332: computed eigenpair.
334: Not Collective
336: Input Parameter:
337: + pep - polynomial eigensolver context
338: - i - index of eigenpair
340: Output Parameter:
341: . errest - the error estimate
343: Notes:
344: This is the error estimate used internally by the eigensolver. The actual
345: error bound can be computed with PEPComputeError(). See also the users
346: manual for details.
348: Level: advanced
350: .seealso: PEPComputeError()
351: @*/
352: PetscErrorCode PEPGetErrorEstimate(PEP pep,PetscInt i,PetscReal *errest)353: {
357: PEPCheckSolved(pep,1);
358: if (i<0 || i>=pep->nconv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Argument 2 out of range");
359: *errest = pep->errest[pep->perm[i]];
360: return(0);
361: }
363: /*
364: PEPComputeResidualNorm_Private - Computes the norm of the residual vector
365: associated with an eigenpair.
367: Input Parameters:
368: kr,ki - eigenvalue
369: xr,xi - eigenvector
370: z - array of 4 work vectors (z[2],z[3] not referenced in complex scalars)
371: */
372: PetscErrorCode PEPComputeResidualNorm_Private(PEP pep,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)373: {
375: Mat *A=pep->A;
376: PetscInt i,nmat=pep->nmat;
377: PetscScalar t[20],*vals=t,*ivals=NULL;
378: Vec u,w;
379: #if !defined(PETSC_USE_COMPLEX)
380: Vec ui,wi;
381: PetscReal ni;
382: PetscBool imag;
383: PetscScalar it[20];
384: #endif
387: u = z[0]; w = z[1];
388: VecSet(u,0.0);
389: #if !defined(PETSC_USE_COMPLEX)
390: ui = z[2]; wi = z[3];
391: ivals = it;
392: #endif
393: if (nmat>20) {
394: PetscMalloc1(nmat,&vals);
395: #if !defined(PETSC_USE_COMPLEX)
396: PetscMalloc1(nmat,&ivals);
397: #endif
398: }
399: PEPEvaluateBasis(pep,kr,ki,vals,ivals);
400: #if !defined(PETSC_USE_COMPLEX)
401: if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON))
402: imag = PETSC_FALSE;
403: else {
404: imag = PETSC_TRUE;
405: VecSet(ui,0.0);
406: }
407: #endif
408: for (i=0;i<nmat;i++) {
409: if (vals[i]!=0.0) {
410: MatMult(A[i],xr,w);
411: VecAXPY(u,vals[i],w);
412: }
413: #if !defined(PETSC_USE_COMPLEX)
414: if (imag) {
415: if (ivals[i]!=0 || vals[i]!=0) {
416: MatMult(A[i],xi,wi);
417: if (vals[i]==0) {
418: MatMult(A[i],xr,w);
419: }
420: }
421: if (ivals[i]!=0){
422: VecAXPY(u,-ivals[i],wi);
423: VecAXPY(ui,ivals[i],w);
424: }
425: if (vals[i]!=0) {
426: VecAXPY(ui,vals[i],wi);
427: }
428: }
429: #endif
430: }
431: VecNorm(u,NORM_2,norm);
432: #if !defined(PETSC_USE_COMPLEX)
433: if (imag) {
434: VecNorm(ui,NORM_2,&ni);
435: *norm = SlepcAbsEigenvalue(*norm,ni);
436: }
437: #endif
438: if (nmat>20) {
439: PetscFree(vals);
440: #if !defined(PETSC_USE_COMPLEX)
441: PetscFree(ivals);
442: #endif
443: }
444: return(0);
445: }
447: /*@
448: PEPComputeError - Computes the error (based on the residual norm) associated
449: with the i-th computed eigenpair.
451: Collective on PEP453: Input Parameter:
454: + pep - the polynomial eigensolver context
455: . i - the solution index
456: - type - the type of error to compute
458: Output Parameter:
459: . error - the error
461: Notes:
462: The error can be computed in various ways, all of them based on the residual
463: norm ||P(l)x||_2 where l is the eigenvalue and x is the eigenvector.
464: See the users guide for additional details.
466: Level: beginner
468: .seealso: PEPErrorType, PEPSolve(), PEPGetErrorEstimate()
469: @*/
470: PetscErrorCode PEPComputeError(PEP pep,PetscInt i,PEPErrorType type,PetscReal *error)471: {
473: Vec xr,xi,w[4];
474: PetscScalar kr,ki;
475: PetscReal t,z=0.0;
476: PetscInt j;
477: PetscBool flg;
484: PEPCheckSolved(pep,1);
486: /* allocate work vectors */
487: #if defined(PETSC_USE_COMPLEX)
488: PEPSetWorkVecs(pep,3);
489: xi = NULL;
490: w[2] = NULL;
491: w[3] = NULL;
492: #else
493: PEPSetWorkVecs(pep,6);
494: xi = pep->work[3];
495: w[2] = pep->work[4];
496: w[3] = pep->work[5];
497: #endif
498: xr = pep->work[0];
499: w[0] = pep->work[1];
500: w[1] = pep->work[2];
502: /* compute residual norms */
503: PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);
504: PEPComputeResidualNorm_Private(pep,kr,ki,xr,xi,w,error);
506: /* compute error */
507: switch (type) {
508: case PEP_ERROR_ABSOLUTE:
509: break;
510: case PEP_ERROR_RELATIVE:
511: *error /= SlepcAbsEigenvalue(kr,ki);
512: break;
513: case PEP_ERROR_BACKWARD:
514: /* initialization of matrix norms */
515: if (!pep->nrma[pep->nmat-1]) {
516: for (j=0;j<pep->nmat;j++) {
517: MatHasOperation(pep->A[j],MATOP_NORM,&flg);
518: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation");
519: MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]);
520: }
521: }
522: t = SlepcAbsEigenvalue(kr,ki);
523: for (j=pep->nmat-1;j>=0;j--) {
524: z = z*t+pep->nrma[j];
525: }
526: *error /= z;
527: break;
528: default:529: SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
530: }
531: return(0);
532: }