Date: 2013-09-02T10:08:02+00:00

Actual source code: rii.c

      1: /*

      3:    SLEPc nonlinear eigensolver: "rii"

      5:    Method: Residual inverse iteration

      7:    Algorithm:

      9:        Simple residual inverse iteration with varying shift.

     11:    References:

     13:        [1] A. Neumaier, "Residual inverse iteration for the nonlinear
     14:            eigenvalue problem", SIAM J. Numer. Anal. 22(5):914-923, 1985.

     16:    Last update: Feb 2013

     18:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     19:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     20:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

     22:    This file is part of SLEPc.

     24:    SLEPc is free software: you can redistribute it and/or modify it under  the
     25:    terms of version 3 of the GNU Lesser General Public License as published by
     26:    the Free Software Foundation.

     28:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     29:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     30:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     31:    more details.

     33:    You  should have received a copy of the GNU Lesser General  Public  License
     34:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     35:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     36: */

     38: #include <slepc-private/nepimpl.h>         /*I "slepcnep.h" I*/

     42: PetscErrorCode NEPSetUp_RII(NEP nep)
     43: {

     47:   if (nep->ncv) { /* ncv set */
     48:     if (nep->ncv<nep->nev) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must be at least nev");
     49:   } else if (nep->mpd) { /* mpd set */
     50:     nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
     51:   } else { /* neither set: defaults depend on nev being small or large */
     52:     if (nep->nev<500) nep->ncv = PetscMin(nep->n,PetscMax(2*nep->nev,nep->nev+15));
     53:     else {
     54:       nep->mpd = 500;
     55:       nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
     56:     }
     57:   }
     58:   if (!nep->mpd) nep->mpd = nep->ncv;
     59:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
     60:   if (nep->nev>1) { PetscInfo(nep,"Warning: requested more than one eigenpair but RII can only compute one\n"); }
     61:   if (!nep->max_it) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     62:   if (!nep->max_funcs) nep->max_funcs = nep->max_it;

     64:   NEPAllocateSolution(nep);
     65:   NEPSetWorkVecs(nep,2);
     66:   return(0);
     67: }

     71: PetscErrorCode NEPSolve_RII(NEP nep)
     72: {
     73:   PetscErrorCode     ierr;
     74:   Mat                T=nep->function,Tp=nep->jacobian,Tsigma;
     75:   Vec                u=nep->V[0],r=nep->work[0],delta=nep->work[1];
     76:   PetscScalar        lambda,a1,a2;
     77:   PetscReal          relerr;
     78:   PetscBool          hascopy;
     79:   MatStructure       mats;
     80:   KSPConvergedReason kspreason;

     83:   /* get initial approximation of eigenvalue and eigenvector */
     84:   NEPGetDefaultShift(nep,&lambda);
     85:   if (!nep->nini) {
     86:     SlepcVecSetRandom(u,nep->rand);
     87:   }

     89:   /* correct eigenvalue approximation: lambda = lambda - (u'*T*u)/(u'*Tp*u) */
     90:   NEPComputeFunction(nep,lambda,&T,&T,&mats);
     91:   MatMult(T,u,r);
     92:   VecDot(u,r,&a1);
     93:   NEPApplyJacobian(nep,lambda,u,delta,r,&Tp,&mats);
     94:   VecDot(u,r,&a2);
     95:   lambda = lambda - a1/a2;

     97:   /* prepare linear solver */
     98:   MatDuplicate(T,MAT_COPY_VALUES,&Tsigma);
     99:   KSPSetOperators(nep->ksp,Tsigma,Tsigma,DIFFERENT_NONZERO_PATTERN);

    101:   /* Restart loop */
    102:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    103:     nep->its++;

    105:     /* update preconditioner and set adaptive tolerance */
    106:     if (nep->lag && !(nep->its%nep->lag) && nep->its>2*nep->lag && relerr<1e-2) {
    107:       MatHasOperation(T,MATOP_COPY,&hascopy);
    108:       if (hascopy) {
    109:         MatCopy(T,Tsigma,mats);
    110:       } else {
    111:         MatDestroy(&Tsigma);
    112:         MatDuplicate(T,MAT_COPY_VALUES,&Tsigma);
    113:       }
    114:       KSPSetOperators(nep->ksp,Tsigma,Tsigma,mats);
    115:     }
    116:     if (!nep->cctol) {
    117:       nep->ktol = PetscMax(nep->ktol/2.0,PETSC_MACHINE_EPSILON*10.0);
    118:       KSPSetTolerances(nep->ksp,nep->ktol,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    119:     }

    121:     /* form residual,  r = T(lambda)*u */
    122:     NEPApplyFunction(nep,lambda,u,delta,r,&T,&T,&mats);

    124:     /* convergence test */
    125:     VecNorm(r,NORM_2,&relerr);
    126:     nep->errest[nep->nconv] = relerr;
    127:     nep->eig[nep->nconv] = lambda;
    128:     if (relerr<=nep->rtol) {
    129:       nep->nconv = nep->nconv + 1;
    130:       nep->reason = NEP_CONVERGED_FNORM_RELATIVE;
    131:     }
    132:     NEPMonitor(nep,nep->its,nep->nconv,nep->eig,nep->errest,1);

    134:     if (!nep->nconv) {
    135:       /* eigenvector correction: delta = T(sigma)\r */
    136:       NEP_KSPSolve(nep,r,delta);
    137:       KSPGetConvergedReason(nep->ksp,&kspreason);
    138:       if (kspreason<0) {
    139:         PetscInfo1(nep,"iter=%D, linear solve failed, stopping solve\n",nep->its);
    140:         nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
    141:         break;
    142:       }

    144:       /* update eigenvector: u = u - delta */
    145:       VecAXPY(u,-1.0,delta);

    147:       /* normalize eigenvector */
    148:       VecNormalize(u,NULL);

    150:       /* correct eigenvalue: lambda = lambda - (u'*T*u)/(u'*Tp*u) */
    151:       NEPApplyFunction(nep,lambda,u,delta,r,&T,&T,&mats);
    152:       VecDot(u,r,&a1);
    153:       NEPApplyJacobian(nep,lambda,u,delta,r,&Tp,&mats);
    154:       VecDot(u,r,&a2);
    155:       lambda = lambda - a1/a2;
    156:     }
    157:     if (nep->its >= nep->max_it) nep->reason = NEP_DIVERGED_MAX_IT;
    158:   }
    159:   MatDestroy(&Tsigma);
    160:   return(0);
    161: }

    165: PETSC_EXTERN PetscErrorCode NEPCreate_RII(NEP nep)
    166: {
    168:   nep->ops->solve        = NEPSolve_RII;
    169:   nep->ops->setup        = NEPSetUp_RII;
    170:   nep->ops->reset        = NEPReset_Default;
    171:   return(0);
    172: }