Date: 2020-01-13T12:01:15+00:00

Actual source code: pepsolve.c
slepc-3.12.2 2020-01-13
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      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(), PEPConvergedReason
    254: @*/
    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 pep

    271:    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 pep

    453:    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: }