Actual source code: pepsolve.c

slepc-3.20.1 2023-11-27
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  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:    PEP routines related to the solution process

 13:    References:

 15:        [1] C. Campos and J.E. Roman, "Parallel iterative refinement in
 16:            polynomial eigenvalue problems", Numer. Linear Algebra Appl.
 17:            23(4):730-745, 2016.
 18: */

 20: #include <slepc/private/pepimpl.h>
 21: #include <slepc/private/bvimpl.h>
 22: #include <petscdraw.h>

 24: static PetscBool  cited = PETSC_FALSE;
 25: static const char citation[] =
 26:   "@Article{slepc-pep-refine,\n"
 27:   "   author = \"C. Campos and J. E. Roman\",\n"
 28:   "   title = \"Parallel iterative refinement in polynomial eigenvalue problems\",\n"
 29:   "   journal = \"Numer. Linear Algebra Appl.\",\n"
 30:   "   volume = \"23\",\n"
 31:   "   number = \"4\",\n"
 32:   "   pages = \"730--745\",\n"
 33:   "   year = \"2016,\"\n"
 34:   "   doi = \"https://doi.org/10.1002/nla.2052\"\n"
 35:   "}\n";

 37: PetscErrorCode PEPComputeVectors(PEP pep)
 38: {
 39:   PetscFunctionBegin;
 40:   PEPCheckSolved(pep,1);
 41:   if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,computevectors);
 42:   pep->state = PEP_STATE_EIGENVECTORS;
 43:   PetscFunctionReturn(PETSC_SUCCESS);
 44: }

 46: PetscErrorCode PEPExtractVectors(PEP pep)
 47: {
 48:   PetscFunctionBegin;
 49:   PEPCheckSolved(pep,1);
 50:   if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,extractvectors);
 51:   PetscFunctionReturn(PETSC_SUCCESS);
 52: }

 54: /*@
 55:    PEPSolve - Solves the polynomial eigensystem.

 57:    Collective

 59:    Input Parameter:
 60: .  pep - eigensolver context obtained from PEPCreate()

 62:    Options Database Keys:
 63: +  -pep_view - print information about the solver used
 64: .  -pep_view_matk - view the coefficient matrix Ak (replace k by an integer from 0 to nmat-1)
 65: .  -pep_view_vectors - view the computed eigenvectors
 66: .  -pep_view_values - view the computed eigenvalues
 67: .  -pep_converged_reason - print reason for convergence, and number of iterations
 68: .  -pep_error_absolute - print absolute errors of each eigenpair
 69: .  -pep_error_relative - print relative errors of each eigenpair
 70: -  -pep_error_backward - print backward errors of each eigenpair

 72:    Notes:
 73:    All the command-line options listed above admit an optional argument specifying
 74:    the viewer type and options. For instance, use '-pep_view_mat0 binary:amatrix.bin'
 75:    to save the A matrix to a binary file, '-pep_view_values draw' to draw the computed
 76:    eigenvalues graphically, or '-pep_error_relative :myerr.m:ascii_matlab' to save
 77:    the errors in a file that can be executed in Matlab.

 79:    Level: beginner

 81: .seealso: PEPCreate(), PEPSetUp(), PEPDestroy(), PEPSetTolerances()
 82: @*/
 83: PetscErrorCode PEPSolve(PEP pep)
 84: {
 85:   PetscInt       i,k;
 86:   PetscBool      flg,islinear;
 87:   char           str[16];

 89:   PetscFunctionBegin;
 91:   if (pep->state>=PEP_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS);
 92:   PetscCall(PetscLogEventBegin(PEP_Solve,pep,0,0,0));

 94:   /* call setup */
 95:   PetscCall(PEPSetUp(pep));
 96:   pep->nconv = 0;
 97:   pep->its   = 0;
 98:   k = pep->lineariz? pep->ncv: pep->ncv*(pep->nmat-1);
 99:   for (i=0;i<k;i++) {
100:     pep->eigr[i]   = 0.0;
101:     pep->eigi[i]   = 0.0;
102:     pep->errest[i] = 0.0;
103:     pep->perm[i]   = i;
104:   }
105:   PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view_pre"));
106:   PetscCall(RGViewFromOptions(pep->rg,NULL,"-rg_view"));

108:   /* Call solver */
109:   PetscUseTypeMethod(pep,solve);
110:   PetscCheck(pep->reason,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
111:   pep->state = PEP_STATE_SOLVED;

113:   /* Only the first nconv columns contain useful information */
114:   PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv));

116:   PetscCall(PetscObjectTypeCompare((PetscObject)pep,PEPLINEAR,&islinear));
117:   if (!islinear) {
118:     PetscCall(STPostSolve(pep->st));
119:     /* Map eigenvalues back to the original problem */
120:     PetscCall(STGetTransform(pep->st,&flg));
121:     if (flg) PetscTryTypeMethod(pep,backtransform);
122:   }

124: #if !defined(PETSC_USE_COMPLEX)
125:   /* reorder conjugate eigenvalues (positive imaginary first) */
126:   for (i=0;i<pep->nconv-1;i++) {
127:     if (pep->eigi[i] != 0) {
128:       if (pep->eigi[i] < 0) {
129:         pep->eigi[i] = -pep->eigi[i];
130:         pep->eigi[i+1] = -pep->eigi[i+1];
131:         /* the next correction only works with eigenvectors */
132:         PetscCall(PEPComputeVectors(pep));
133:         PetscCall(BVScaleColumn(pep->V,i+1,-1.0));
134:       }
135:       i++;
136:     }
137:   }
138: #endif

140:   if (pep->refine!=PEP_REFINE_NONE) PetscCall(PetscCitationsRegister(citation,&cited));

142:   if (pep->refine==PEP_REFINE_SIMPLE && pep->rits>0 && pep->nconv>0) {
143:     PetscCall(PEPComputeVectors(pep));
144:     PetscCall(PEPNewtonRefinementSimple(pep,&pep->rits,pep->rtol,pep->nconv));
145:   }

147:   /* sort eigenvalues according to pep->which parameter */
148:   PetscCall(SlepcSortEigenvalues(pep->sc,pep->nconv,pep->eigr,pep->eigi,pep->perm));
149:   PetscCall(PetscLogEventEnd(PEP_Solve,pep,0,0,0));

151:   /* various viewers */
152:   PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view"));
153:   PetscCall(PEPConvergedReasonViewFromOptions(pep));
154:   PetscCall(PEPErrorViewFromOptions(pep));
155:   PetscCall(PEPValuesViewFromOptions(pep));
156:   PetscCall(PEPVectorsViewFromOptions(pep));
157:   for (i=0;i<pep->nmat;i++) {
158:     PetscCall(PetscSNPrintf(str,sizeof(str),"-pep_view_mat%" PetscInt_FMT,i));
159:     PetscCall(MatViewFromOptions(pep->A[i],(PetscObject)pep,str));
160:   }

162:   /* Remove the initial subspace */
163:   pep->nini = 0;
164:   PetscFunctionReturn(PETSC_SUCCESS);
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: {
193:   PetscFunctionBegin;
195:   PetscAssertPointer(its,2);
196:   *its = pep->its;
197:   PetscFunctionReturn(PETSC_SUCCESS);
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(), PEPGetEigenpair()
217: @*/
218: PetscErrorCode PEPGetConverged(PEP pep,PetscInt *nconv)
219: {
220:   PetscFunctionBegin;
222:   PetscAssertPointer(nconv,2);
223:   PEPCheckSolved(pep,1);
224:   *nconv = pep->nconv;
225:   PetscFunctionReturn(PETSC_SUCCESS);
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:    Options Database Key:
241: .  -pep_converged_reason - print the reason to a viewer

243:    Notes:
244:    Possible values for reason are
245: +  PEP_CONVERGED_TOL - converged up to tolerance
246: .  PEP_CONVERGED_USER - converged due to a user-defined condition
247: .  PEP_DIVERGED_ITS - required more than max_it iterations to reach convergence
248: .  PEP_DIVERGED_BREAKDOWN - generic breakdown in method
249: -  PEP_DIVERGED_SYMMETRY_LOST - pseudo-Lanczos was not able to keep symmetry

251:    Can only be called after the call to PEPSolve() is complete.

253:    Level: intermediate

255: .seealso: PEPSetTolerances(), PEPSolve(), PEPConvergedReason
256: @*/
257: PetscErrorCode PEPGetConvergedReason(PEP pep,PEPConvergedReason *reason)
258: {
259:   PetscFunctionBegin;
261:   PetscAssertPointer(reason,2);
262:   PEPCheckSolved(pep,1);
263:   *reason = pep->reason;
264:   PetscFunctionReturn(PETSC_SUCCESS);
265: }

267: /*@C
268:    PEPGetEigenpair - Gets the i-th solution of the eigenproblem as computed by
269:    PEPSolve(). The solution consists in both the eigenvalue and the eigenvector.

271:    Collective

273:    Input Parameters:
274: +  pep - polynomial eigensolver context
275: -  i   - index of the solution

277:    Output Parameters:
278: +  eigr - real part of eigenvalue
279: .  eigi - imaginary part of eigenvalue
280: .  Vr   - real part of eigenvector
281: -  Vi   - imaginary part of eigenvector

283:    Notes:
284:    It is allowed to pass NULL for Vr and Vi, if the eigenvector is not
285:    required. Otherwise, the caller must provide valid Vec objects, i.e.,
286:    they must be created by the calling program with e.g. MatCreateVecs().

288:    If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is
289:    configured with complex scalars the eigenvalue is stored
290:    directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is
291:    set to zero). In any case, the user can pass NULL in Vr or Vi if one of
292:    them is not required.

294:    The index i should be a value between 0 and nconv-1 (see PEPGetConverged()).
295:    Eigenpairs are indexed according to the ordering criterion established
296:    with PEPSetWhichEigenpairs().

298:    Level: beginner

300: .seealso: PEPSolve(), PEPGetConverged(), PEPSetWhichEigenpairs()
301: @*/
302: PetscErrorCode PEPGetEigenpair(PEP pep,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi)
303: {
304:   PetscInt       k;

306:   PetscFunctionBegin;
311:   PEPCheckSolved(pep,1);
312:   PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative");
313:   PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()");

315:   PetscCall(PEPComputeVectors(pep));
316:   k = pep->perm[i];

318:   /* eigenvalue */
319: #if defined(PETSC_USE_COMPLEX)
320:   if (eigr) *eigr = pep->eigr[k];
321:   if (eigi) *eigi = 0;
322: #else
323:   if (eigr) *eigr = pep->eigr[k];
324:   if (eigi) *eigi = pep->eigi[k];
325: #endif

327:   /* eigenvector */
328:   PetscCall(BV_GetEigenvector(pep->V,k,pep->eigi[k],Vr,Vi));
329:   PetscFunctionReturn(PETSC_SUCCESS);
330: }

332: /*@
333:    PEPGetErrorEstimate - Returns the error estimate associated to the i-th
334:    computed eigenpair.

336:    Not Collective

338:    Input Parameters:
339: +  pep - polynomial eigensolver context
340: -  i   - index of eigenpair

342:    Output Parameter:
343: .  errest - the error estimate

345:    Notes:
346:    This is the error estimate used internally by the eigensolver. The actual
347:    error bound can be computed with PEPComputeError(). See also the users
348:    manual for details.

350:    Level: advanced

352: .seealso: PEPComputeError()
353: @*/
354: PetscErrorCode PEPGetErrorEstimate(PEP pep,PetscInt i,PetscReal *errest)
355: {
356:   PetscFunctionBegin;
358:   PetscAssertPointer(errest,3);
359:   PEPCheckSolved(pep,1);
360:   PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative");
361:   PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()");
362:   *errest = pep->errest[pep->perm[i]];
363:   PetscFunctionReturn(PETSC_SUCCESS);
364: }

366: /*
367:    PEPComputeResidualNorm_Private - Computes the norm of the residual vector
368:    associated with an eigenpair.

370:    Input Parameters:
371:      kr,ki - eigenvalue
372:      xr,xi - eigenvector
373:      z     - array of 4 work vectors (z[2],z[3] not referenced in complex scalars)
374: */
375: PetscErrorCode PEPComputeResidualNorm_Private(PEP pep,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm)
376: {
377:   Mat            *A=pep->A;
378:   PetscInt       i,nmat=pep->nmat;
379:   PetscScalar    t[20],*vals=t,*ivals=NULL;
380:   Vec            u,w;
381: #if !defined(PETSC_USE_COMPLEX)
382:   Vec            ui,wi;
383:   PetscReal      ni;
384:   PetscBool      imag;
385:   PetscScalar    it[20];
386: #endif

388:   PetscFunctionBegin;
389:   u = z[0]; w = z[1];
390:   PetscCall(VecSet(u,0.0));
391: #if !defined(PETSC_USE_COMPLEX)
392:   ui = z[2]; wi = z[3];
393:   ivals = it;
394: #endif
395:   if (nmat>20) {
396:     PetscCall(PetscMalloc1(nmat,&vals));
397: #if !defined(PETSC_USE_COMPLEX)
398:     PetscCall(PetscMalloc1(nmat,&ivals));
399: #endif
400:   }
401:   PetscCall(PEPEvaluateBasis(pep,kr,ki,vals,ivals));
402: #if !defined(PETSC_USE_COMPLEX)
403:   if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON))
404:     imag = PETSC_FALSE;
405:   else {
406:     imag = PETSC_TRUE;
407:     PetscCall(VecSet(ui,0.0));
408:   }
409: #endif
410:   for (i=0;i<nmat;i++) {
411:     if (vals[i]!=0.0) {
412:       PetscCall(MatMult(A[i],xr,w));
413:       PetscCall(VecAXPY(u,vals[i],w));
414:     }
415: #if !defined(PETSC_USE_COMPLEX)
416:     if (imag) {
417:       if (ivals[i]!=0 || vals[i]!=0) {
418:         PetscCall(MatMult(A[i],xi,wi));
419:         if (vals[i]==0) PetscCall(MatMult(A[i],xr,w));
420:       }
421:       if (ivals[i]!=0) {
422:         PetscCall(VecAXPY(u,-ivals[i],wi));
423:         PetscCall(VecAXPY(ui,ivals[i],w));
424:       }
425:       if (vals[i]!=0) PetscCall(VecAXPY(ui,vals[i],wi));
426:     }
427: #endif
428:   }
429:   PetscCall(VecNorm(u,NORM_2,norm));
430: #if !defined(PETSC_USE_COMPLEX)
431:   if (imag) {
432:     PetscCall(VecNorm(ui,NORM_2,&ni));
433:     *norm = SlepcAbsEigenvalue(*norm,ni);
434:   }
435: #endif
436:   if (nmat>20) {
437:     PetscCall(PetscFree(vals));
438: #if !defined(PETSC_USE_COMPLEX)
439:     PetscCall(PetscFree(ivals));
440: #endif
441:   }
442:   PetscFunctionReturn(PETSC_SUCCESS);
443: }

445: /*@
446:    PEPComputeError - Computes the error (based on the residual norm) associated
447:    with the i-th computed eigenpair.

449:    Collective

451:    Input Parameters:
452: +  pep  - the polynomial eigensolver context
453: .  i    - the solution index
454: -  type - the type of error to compute

456:    Output Parameter:
457: .  error - the error

459:    Notes:
460:    The error can be computed in various ways, all of them based on the residual
461:    norm ||P(l)x||_2 where l is the eigenvalue and x is the eigenvector.
462:    See the users guide for additional details.

464:    Level: beginner

466: .seealso: PEPErrorType, PEPSolve(), PEPGetErrorEstimate()
467: @*/
468: PetscErrorCode PEPComputeError(PEP pep,PetscInt i,PEPErrorType type,PetscReal *error)
469: {
470:   Vec            xr,xi,w[4];
471:   PetscScalar    kr,ki;
472:   PetscReal      t,z=0.0;
473:   PetscInt       j;
474:   PetscBool      flg;

476:   PetscFunctionBegin;
480:   PetscAssertPointer(error,4);
481:   PEPCheckSolved(pep,1);

483:   /* allocate work vectors */
484: #if defined(PETSC_USE_COMPLEX)
485:   PetscCall(PEPSetWorkVecs(pep,3));
486:   xi   = NULL;
487:   w[2] = NULL;
488:   w[3] = NULL;
489: #else
490:   PetscCall(PEPSetWorkVecs(pep,6));
491:   xi   = pep->work[3];
492:   w[2] = pep->work[4];
493:   w[3] = pep->work[5];
494: #endif
495:   xr   = pep->work[0];
496:   w[0] = pep->work[1];
497:   w[1] = pep->work[2];

499:   /* compute residual norms */
500:   PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi));
501:   PetscCall(PEPComputeResidualNorm_Private(pep,kr,ki,xr,xi,w,error));

503:   /* compute error */
504:   switch (type) {
505:     case PEP_ERROR_ABSOLUTE:
506:       break;
507:     case PEP_ERROR_RELATIVE:
508:       *error /= SlepcAbsEigenvalue(kr,ki);
509:       break;
510:     case PEP_ERROR_BACKWARD:
511:       /* initialization of matrix norms */
512:       if (!pep->nrma[pep->nmat-1]) {
513:         for (j=0;j<pep->nmat;j++) {
514:           PetscCall(MatHasOperation(pep->A[j],MATOP_NORM,&flg));
515:           PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation");
516:           PetscCall(MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]));
517:         }
518:       }
519:       t = SlepcAbsEigenvalue(kr,ki);
520:       for (j=pep->nmat-1;j>=0;j--) {
521:         z = z*t+pep->nrma[j];
522:       }
523:       *error /= z;
524:       break;
525:     default:
526:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
527:   }
528:   PetscFunctionReturn(PETSC_SUCCESS);
529: }