Date: 2022-11-02T11:47:33+00:00

Actual source code: rii.c
slepc-3.18.1 2022-11-02
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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:    SLEPc nonlinear eigensolver: "rii"

     13:    Method: Residual inverse iteration

     15:    Algorithm:

     17:        Simple residual inverse iteration with varying shift.

     19:    References:

     21:        [1] A. Neumaier, "Residual inverse iteration for the nonlinear
     22:            eigenvalue problem", SIAM J. Numer. Anal. 22(5):914-923, 1985.
     23: */

     25: #include <slepc/private/nepimpl.h>
     26: #include <../src/nep/impls/nepdefl.h>

     28: typedef struct {
     29:   PetscInt  max_inner_it;     /* maximum number of Newton iterations */
     30:   PetscInt  lag;              /* interval to rebuild preconditioner */
     31:   PetscBool cctol;            /* constant correction tolerance */
     32:   PetscBool herm;             /* whether the Hermitian version of the scalar equation must be used */
     33:   PetscReal deftol;           /* tolerance for the deflation (threshold) */
     34:   KSP       ksp;              /* linear solver object */
     35: } NEP_RII;

     37: PetscErrorCode NEPSetUp_RII(NEP nep)
     38: {
     39:   if (nep->ncv!=PETSC_DEFAULT) PetscInfo(nep,"Setting ncv = nev, ignoring user-provided value\n");
     40:   nep->ncv = nep->nev;
     41:   if (nep->mpd!=PETSC_DEFAULT) PetscInfo(nep,"Setting mpd = nev, ignoring user-provided value\n");
     42:   nep->mpd = nep->nev;
     43:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
     44:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
     46:   NEPCheckUnsupported(nep,NEP_FEATURE_REGION | NEP_FEATURE_TWOSIDED);
     47:   NEPAllocateSolution(nep,0);
     48:   NEPSetWorkVecs(nep,2);
     49:   return 0;
     50: }

     52: PetscErrorCode NEPSolve_RII(NEP nep)
     53: {
     54:   NEP_RII            *ctx = (NEP_RII*)nep->data;
     55:   Mat                T,Tp,H,A;
     56:   Vec                uu,u,r,delta,t;
     57:   PetscScalar        lambda,lambda2,sigma,a1,a2,corr;
     58:   PetscReal          nrm,resnorm=1.0,ktol=0.1,perr,rtol;
     59:   PetscBool          skip=PETSC_FALSE,lock=PETSC_FALSE;
     60:   PetscInt           inner_its,its=0;
     61:   NEP_EXT_OP         extop=NULL;
     62:   KSPConvergedReason kspreason;

     64:   /* get initial approximation of eigenvalue and eigenvector */
     65:   NEPGetDefaultShift(nep,&sigma);
     66:   lambda = sigma;
     67:   if (!nep->nini) {
     68:     BVSetRandomColumn(nep->V,0);
     69:     BVNormColumn(nep->V,0,NORM_2,&nrm);
     70:     BVScaleColumn(nep->V,0,1.0/nrm);
     71:   }
     72:   if (!ctx->ksp) NEPRIIGetKSP(nep,&ctx->ksp);
     73:   NEPDeflationInitialize(nep,nep->V,ctx->ksp,PETSC_FALSE,nep->nev,&extop);
     74:   NEPDeflationCreateVec(extop,&u);
     75:   VecDuplicate(u,&r);
     76:   VecDuplicate(u,&delta);
     77:   BVGetColumn(nep->V,0,&uu);
     78:   NEPDeflationCopyToExtendedVec(extop,uu,NULL,u,PETSC_FALSE);
     79:   BVRestoreColumn(nep->V,0,&uu);

     81:   /* prepare linear solver */
     82:   NEPDeflationSolveSetUp(extop,sigma);
     83:   KSPGetTolerances(ctx->ksp,&rtol,NULL,NULL,NULL);

     85:   VecCopy(u,r);
     86:   NEPDeflationFunctionSolve(extop,r,u);
     87:   VecNorm(u,NORM_2,&nrm);
     88:   VecScale(u,1.0/nrm);

     90:   /* Restart loop */
     91:   while (nep->reason == NEP_CONVERGED_ITERATING) {
     92:     its++;

     94:     /* Use Newton's method to compute nonlinear Rayleigh functional. Current eigenvalue
     95:        estimate as starting value. */
     96:     inner_its=0;
     97:     lambda2 = lambda;
     98:     do {
     99:       NEPDeflationComputeFunction(extop,lambda,&T);
    100:       MatMult(T,u,r);
    101:       if (!ctx->herm) {
    102:         NEPDeflationFunctionSolve(extop,r,delta);
    103:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    104:         if (kspreason<0) PetscInfo(nep,"iter=%" PetscInt_FMT ", linear solve failed\n",nep->its);
    105:         t = delta;
    106:       } else t = r;
    107:       VecDot(t,u,&a1);
    108:       NEPDeflationComputeJacobian(extop,lambda,&Tp);
    109:       MatMult(Tp,u,r);
    110:       if (!ctx->herm) {
    111:         NEPDeflationFunctionSolve(extop,r,delta);
    112:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    113:         if (kspreason<0) PetscInfo(nep,"iter=%" PetscInt_FMT ", linear solve failed\n",nep->its);
    114:         t = delta;
    115:       } else t = r;
    116:       VecDot(t,u,&a2);
    117:       corr = a1/a2;
    118:       lambda = lambda - corr;
    119:       inner_its++;
    120:     } while (PetscAbsScalar(corr)/PetscAbsScalar(lambda)>PETSC_SQRT_MACHINE_EPSILON && inner_its<ctx->max_inner_it);

    122:     /* form residual,  r = T(lambda)*u */
    123:     NEPDeflationComputeFunction(extop,lambda,&T);
    124:     MatMult(T,u,r);

    126:     /* convergence test */
    127:     perr = nep->errest[nep->nconv];
    128:     VecNorm(r,NORM_2,&resnorm);
    129:     (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
    130:     nep->eigr[nep->nconv] = lambda;
    131:     if (its>1 && (nep->errest[nep->nconv]<=nep->tol || nep->errest[nep->nconv]<=ctx->deftol)) {
    132:       if (nep->errest[nep->nconv]<=ctx->deftol && !extop->ref && nep->nconv) {
    133:         NEPDeflationExtractEigenpair(extop,nep->nconv,u,lambda,nep->ds);
    134:         NEPDeflationSetRefine(extop,PETSC_TRUE);
    135:         MatMult(T,u,r);
    136:         VecNorm(r,NORM_2,&resnorm);
    137:         (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
    138:         if (nep->errest[nep->nconv]<=nep->tol) lock = PETSC_TRUE;
    139:       } else if (nep->errest[nep->nconv]<=nep->tol) lock = PETSC_TRUE;
    140:     }
    141:     if (lock) {
    142:       NEPDeflationSetRefine(extop,PETSC_FALSE);
    143:       nep->nconv = nep->nconv + 1;
    144:       NEPDeflationLocking(extop,u,lambda);
    145:       nep->its += its;
    146:       skip = PETSC_TRUE;
    147:       lock = PETSC_FALSE;
    148:     }
    149:     (*nep->stopping)(nep,nep->its+its,nep->max_it,nep->nconv,nep->nev,&nep->reason,nep->stoppingctx);
    150:     if (!skip || nep->reason>0) NEPMonitor(nep,nep->its+its,nep->nconv,nep->eigr,nep->eigi,nep->errest,(nep->reason>0)?nep->nconv:nep->nconv+1);

    152:     if (nep->reason == NEP_CONVERGED_ITERATING) {
    153:       if (!skip) {
    154:         /* update preconditioner and set adaptive tolerance */
    155:         if (ctx->lag && !(its%ctx->lag) && its>=2*ctx->lag && perr && nep->errest[nep->nconv]>.5*perr) NEPDeflationSolveSetUp(extop,lambda2);
    156:         if (!ctx->cctol) {
    157:           ktol = PetscMax(ktol/2.0,rtol);
    158:           KSPSetTolerances(ctx->ksp,ktol,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    159:         }

    161:         /* eigenvector correction: delta = T(sigma)\r */
    162:         NEPDeflationFunctionSolve(extop,r,delta);
    163:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    164:         if (kspreason<0) {
    165:           PetscInfo(nep,"iter=%" PetscInt_FMT ", linear solve failed, stopping solve\n",nep->its);
    166:           nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
    167:           break;
    168:         }

    170:         /* update eigenvector: u = u - delta */
    171:         VecAXPY(u,-1.0,delta);

    173:         /* normalize eigenvector */
    174:         VecNormalize(u,NULL);
    175:       } else {
    176:         its = -1;
    177:         NEPDeflationSetRandomVec(extop,u);
    178:         NEPDeflationSolveSetUp(extop,sigma);
    179:         VecCopy(u,r);
    180:         NEPDeflationFunctionSolve(extop,r,u);
    181:         VecNorm(u,NORM_2,&nrm);
    182:         VecScale(u,1.0/nrm);
    183:         lambda = sigma;
    184:         skip = PETSC_FALSE;
    185:       }
    186:     }
    187:   }
    188:   NEPDeflationGetInvariantPair(extop,NULL,&H);
    189:   DSSetType(nep->ds,DSNHEP);
    190:   DSAllocate(nep->ds,PetscMax(nep->nconv,1));
    191:   DSSetDimensions(nep->ds,nep->nconv,0,nep->nconv);
    192:   DSGetMat(nep->ds,DS_MAT_A,&A);
    193:   MatCopy(H,A,SAME_NONZERO_PATTERN);
    194:   DSRestoreMat(nep->ds,DS_MAT_A,&A);
    195:   MatDestroy(&H);
    196:   DSSolve(nep->ds,nep->eigr,nep->eigi);
    197:   NEPDeflationReset(extop);
    198:   VecDestroy(&u);
    199:   VecDestroy(&r);
    200:   VecDestroy(&delta);
    201:   return 0;
    202: }

    204: PetscErrorCode NEPSetFromOptions_RII(NEP nep,PetscOptionItems *PetscOptionsObject)
    205: {
    206:   NEP_RII        *ctx = (NEP_RII*)nep->data;
    207:   PetscBool      flg;
    208:   PetscInt       i;
    209:   PetscReal      r;

    211:   PetscOptionsHeadBegin(PetscOptionsObject,"NEP RII Options");

    213:     i = 0;
    214:     PetscOptionsInt("-nep_rii_max_it","Maximum number of Newton iterations for updating Rayleigh functional","NEPRIISetMaximumIterations",ctx->max_inner_it,&i,&flg);
    215:     if (flg) NEPRIISetMaximumIterations(nep,i);

    217:     PetscOptionsBool("-nep_rii_const_correction_tol","Constant correction tolerance for the linear solver","NEPRIISetConstCorrectionTol",ctx->cctol,&ctx->cctol,NULL);

    219:     PetscOptionsBool("-nep_rii_hermitian","Use Hermitian version of the scalar nonlinear equation","NEPRIISetHermitian",ctx->herm,&ctx->herm,NULL);

    221:     i = 0;
    222:     PetscOptionsInt("-nep_rii_lag_preconditioner","Interval to rebuild preconditioner","NEPRIISetLagPreconditioner",ctx->lag,&i,&flg);
    223:     if (flg) NEPRIISetLagPreconditioner(nep,i);

    225:     r = 0.0;
    226:     PetscOptionsReal("-nep_rii_deflation_threshold","Tolerance used as a threshold for including deflated eigenpairs","NEPRIISetDeflationThreshold",ctx->deftol,&r,&flg);
    227:     if (flg) NEPRIISetDeflationThreshold(nep,r);

    229:   PetscOptionsHeadEnd();

    231:   if (!ctx->ksp) NEPRIIGetKSP(nep,&ctx->ksp);
    232:   KSPSetFromOptions(ctx->ksp);
    233:   return 0;
    234: }

    236: static PetscErrorCode NEPRIISetMaximumIterations_RII(NEP nep,PetscInt its)
    237: {
    238:   NEP_RII *ctx = (NEP_RII*)nep->data;

    240:   if (its==PETSC_DEFAULT) ctx->max_inner_it = 10;
    241:   else {
    243:     ctx->max_inner_it = its;
    244:   }
    245:   return 0;
    246: }

    248: /*@
    249:    NEPRIISetMaximumIterations - Sets the maximum number of inner iterations to be
    250:    used in the RII solver. These are the Newton iterations related to the computation
    251:    of the nonlinear Rayleigh functional.

    253:    Logically Collective on nep

    255:    Input Parameters:
    256: +  nep - nonlinear eigenvalue solver
    257: -  its - maximum inner iterations

    259:    Level: advanced

    261: .seealso: NEPRIIGetMaximumIterations()
    262: @*/
    263: PetscErrorCode NEPRIISetMaximumIterations(NEP nep,PetscInt its)
    264: {
    267:   PetscTryMethod(nep,"NEPRIISetMaximumIterations_C",(NEP,PetscInt),(nep,its));
    268:   return 0;
    269: }

    271: static PetscErrorCode NEPRIIGetMaximumIterations_RII(NEP nep,PetscInt *its)
    272: {
    273:   NEP_RII *ctx = (NEP_RII*)nep->data;

    275:   *its = ctx->max_inner_it;
    276:   return 0;
    277: }

    279: /*@
    280:    NEPRIIGetMaximumIterations - Gets the maximum number of inner iterations of RII.

    282:    Not Collective

    284:    Input Parameter:
    285: .  nep - nonlinear eigenvalue solver

    287:    Output Parameter:
    288: .  its - maximum inner iterations

    290:    Level: advanced

    292: .seealso: NEPRIISetMaximumIterations()
    293: @*/
    294: PetscErrorCode NEPRIIGetMaximumIterations(NEP nep,PetscInt *its)
    295: {
    298:   PetscUseMethod(nep,"NEPRIIGetMaximumIterations_C",(NEP,PetscInt*),(nep,its));
    299:   return 0;
    300: }

    302: static PetscErrorCode NEPRIISetLagPreconditioner_RII(NEP nep,PetscInt lag)
    303: {
    304:   NEP_RII *ctx = (NEP_RII*)nep->data;

    307:   ctx->lag = lag;
    308:   return 0;
    309: }

    311: /*@
    312:    NEPRIISetLagPreconditioner - Determines when the preconditioner is rebuilt in the
    313:    nonlinear solve.

    315:    Logically Collective on nep

    317:    Input Parameters:
    318: +  nep - nonlinear eigenvalue solver
    319: -  lag - 0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is
    320:           computed within the nonlinear iteration, 2 means every second time
    321:           the Jacobian is built, etc.

    323:    Options Database Keys:
    324: .  -nep_rii_lag_preconditioner <lag> - the lag value

    326:    Notes:
    327:    The default is 1.
    328:    The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

    330:    Level: intermediate

    332: .seealso: NEPRIIGetLagPreconditioner()
    333: @*/
    334: PetscErrorCode NEPRIISetLagPreconditioner(NEP nep,PetscInt lag)
    335: {
    338:   PetscTryMethod(nep,"NEPRIISetLagPreconditioner_C",(NEP,PetscInt),(nep,lag));
    339:   return 0;
    340: }

    342: static PetscErrorCode NEPRIIGetLagPreconditioner_RII(NEP nep,PetscInt *lag)
    343: {
    344:   NEP_RII *ctx = (NEP_RII*)nep->data;

    346:   *lag = ctx->lag;
    347:   return 0;
    348: }

    350: /*@
    351:    NEPRIIGetLagPreconditioner - Indicates how often the preconditioner is rebuilt.

    353:    Not Collective

    355:    Input Parameter:
    356: .  nep - nonlinear eigenvalue solver

    358:    Output Parameter:
    359: .  lag - the lag parameter

    361:    Level: intermediate

    363: .seealso: NEPRIISetLagPreconditioner()
    364: @*/
    365: PetscErrorCode NEPRIIGetLagPreconditioner(NEP nep,PetscInt *lag)
    366: {
    369:   PetscUseMethod(nep,"NEPRIIGetLagPreconditioner_C",(NEP,PetscInt*),(nep,lag));
    370:   return 0;
    371: }

    373: static PetscErrorCode NEPRIISetConstCorrectionTol_RII(NEP nep,PetscBool cct)
    374: {
    375:   NEP_RII *ctx = (NEP_RII*)nep->data;

    377:   ctx->cctol = cct;
    378:   return 0;
    379: }

    381: /*@
    382:    NEPRIISetConstCorrectionTol - Sets a flag to keep the tolerance used
    383:    in the linear solver constant.

    385:    Logically Collective on nep

    387:    Input Parameters:
    388: +  nep - nonlinear eigenvalue solver
    389: -  cct - a boolean value

    391:    Options Database Keys:
    392: .  -nep_rii_const_correction_tol <bool> - set the boolean flag

    394:    Notes:
    395:    By default, an exponentially decreasing tolerance is set in the KSP used
    396:    within the nonlinear iteration, so that each Newton iteration requests
    397:    better accuracy than the previous one. The constant correction tolerance
    398:    flag stops this behaviour.

    400:    Level: intermediate

    402: .seealso: NEPRIIGetConstCorrectionTol()
    403: @*/
    404: PetscErrorCode NEPRIISetConstCorrectionTol(NEP nep,PetscBool cct)
    405: {
    408:   PetscTryMethod(nep,"NEPRIISetConstCorrectionTol_C",(NEP,PetscBool),(nep,cct));
    409:   return 0;
    410: }

    412: static PetscErrorCode NEPRIIGetConstCorrectionTol_RII(NEP nep,PetscBool *cct)
    413: {
    414:   NEP_RII *ctx = (NEP_RII*)nep->data;

    416:   *cct = ctx->cctol;
    417:   return 0;
    418: }

    420: /*@
    421:    NEPRIIGetConstCorrectionTol - Returns the constant tolerance flag.

    423:    Not Collective

    425:    Input Parameter:
    426: .  nep - nonlinear eigenvalue solver

    428:    Output Parameter:
    429: .  cct - the value of the constant tolerance flag

    431:    Level: intermediate

    433: .seealso: NEPRIISetConstCorrectionTol()
    434: @*/
    435: PetscErrorCode NEPRIIGetConstCorrectionTol(NEP nep,PetscBool *cct)
    436: {
    439:   PetscUseMethod(nep,"NEPRIIGetConstCorrectionTol_C",(NEP,PetscBool*),(nep,cct));
    440:   return 0;
    441: }

    443: static PetscErrorCode NEPRIISetHermitian_RII(NEP nep,PetscBool herm)
    444: {
    445:   NEP_RII *ctx = (NEP_RII*)nep->data;

    447:   ctx->herm = herm;
    448:   return 0;
    449: }

    451: /*@
    452:    NEPRIISetHermitian - Sets a flag to indicate if the Hermitian version of the
    453:    scalar nonlinear equation must be used by the solver.

    455:    Logically Collective on nep

    457:    Input Parameters:
    458: +  nep  - nonlinear eigenvalue solver
    459: -  herm - a boolean value

    461:    Options Database Keys:
    462: .  -nep_rii_hermitian <bool> - set the boolean flag

    464:    Notes:
    465:    By default, the scalar nonlinear equation x'*inv(T(sigma))*T(z)*x=0 is solved
    466:    at each step of the nonlinear iteration. When this flag is set the simpler
    467:    form x'*T(z)*x=0 is used, which is supposed to be valid only for Hermitian
    468:    problems.

    470:    Level: intermediate

    472: .seealso: NEPRIIGetHermitian()
    473: @*/
    474: PetscErrorCode NEPRIISetHermitian(NEP nep,PetscBool herm)
    475: {
    478:   PetscTryMethod(nep,"NEPRIISetHermitian_C",(NEP,PetscBool),(nep,herm));
    479:   return 0;
    480: }

    482: static PetscErrorCode NEPRIIGetHermitian_RII(NEP nep,PetscBool *herm)
    483: {
    484:   NEP_RII *ctx = (NEP_RII*)nep->data;

    486:   *herm = ctx->herm;
    487:   return 0;
    488: }

    490: /*@
    491:    NEPRIIGetHermitian - Returns the flag about using the Hermitian version of
    492:    the scalar nonlinear equation.

    494:    Not Collective

    496:    Input Parameter:
    497: .  nep - nonlinear eigenvalue solver

    499:    Output Parameter:
    500: .  herm - the value of the hermitian flag

    502:    Level: intermediate

    504: .seealso: NEPRIISetHermitian()
    505: @*/
    506: PetscErrorCode NEPRIIGetHermitian(NEP nep,PetscBool *herm)
    507: {
    510:   PetscUseMethod(nep,"NEPRIIGetHermitian_C",(NEP,PetscBool*),(nep,herm));
    511:   return 0;
    512: }

    514: static PetscErrorCode NEPRIISetDeflationThreshold_RII(NEP nep,PetscReal deftol)
    515: {
    516:   NEP_RII *ctx = (NEP_RII*)nep->data;

    518:   ctx->deftol = deftol;
    519:   return 0;
    520: }

    522: /*@
    523:    NEPRIISetDeflationThreshold - Sets the threshold value used to switch between
    524:    deflated and non-deflated iteration.

    526:    Logically Collective on nep

    528:    Input Parameters:
    529: +  nep    - nonlinear eigenvalue solver
    530: -  deftol - the threshold value

    532:    Options Database Keys:
    533: .  -nep_rii_deflation_threshold <deftol> - set the threshold

    535:    Notes:
    536:    Normally, the solver iterates on the extended problem in order to deflate
    537:    previously converged eigenpairs. If this threshold is set to a nonzero value,
    538:    then once the residual error is below this threshold the solver will
    539:    continue the iteration without deflation. The intention is to be able to
    540:    improve the current eigenpair further, despite having previous eigenpairs
    541:    with somewhat bad precision.

    543:    Level: advanced

    545: .seealso: NEPRIIGetDeflationThreshold()
    546: @*/
    547: PetscErrorCode NEPRIISetDeflationThreshold(NEP nep,PetscReal deftol)
    548: {
    551:   PetscTryMethod(nep,"NEPRIISetDeflationThreshold_C",(NEP,PetscReal),(nep,deftol));
    552:   return 0;
    553: }

    555: static PetscErrorCode NEPRIIGetDeflationThreshold_RII(NEP nep,PetscReal *deftol)
    556: {
    557:   NEP_RII *ctx = (NEP_RII*)nep->data;

    559:   *deftol = ctx->deftol;
    560:   return 0;
    561: }

    563: /*@
    564:    NEPRIIGetDeflationThreshold - Returns the threshold value that controls deflation.

    566:    Not Collective

    568:    Input Parameter:
    569: .  nep - nonlinear eigenvalue solver

    571:    Output Parameter:
    572: .  deftol - the threshold

    574:    Level: advanced

    576: .seealso: NEPRIISetDeflationThreshold()
    577: @*/
    578: PetscErrorCode NEPRIIGetDeflationThreshold(NEP nep,PetscReal *deftol)
    579: {
    582:   PetscUseMethod(nep,"NEPRIIGetDeflationThreshold_C",(NEP,PetscReal*),(nep,deftol));
    583:   return 0;
    584: }

    586: static PetscErrorCode NEPRIISetKSP_RII(NEP nep,KSP ksp)
    587: {
    588:   NEP_RII        *ctx = (NEP_RII*)nep->data;

    590:   PetscObjectReference((PetscObject)ksp);
    591:   KSPDestroy(&ctx->ksp);
    592:   ctx->ksp = ksp;
    593:   nep->state = NEP_STATE_INITIAL;
    594:   return 0;
    595: }

    597: /*@
    598:    NEPRIISetKSP - Associate a linear solver object (KSP) to the nonlinear
    599:    eigenvalue solver.

    601:    Collective on nep

    603:    Input Parameters:
    604: +  nep - eigenvalue solver
    605: -  ksp - the linear solver object

    607:    Level: advanced

    609: .seealso: NEPRIIGetKSP()
    610: @*/
    611: PetscErrorCode NEPRIISetKSP(NEP nep,KSP ksp)
    612: {
    616:   PetscTryMethod(nep,"NEPRIISetKSP_C",(NEP,KSP),(nep,ksp));
    617:   return 0;
    618: }

    620: static PetscErrorCode NEPRIIGetKSP_RII(NEP nep,KSP *ksp)
    621: {
    622:   NEP_RII        *ctx = (NEP_RII*)nep->data;

    624:   if (!ctx->ksp) {
    625:     KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp);
    626:     PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)nep,1);
    627:     KSPSetOptionsPrefix(ctx->ksp,((PetscObject)nep)->prefix);
    628:     KSPAppendOptionsPrefix(ctx->ksp,"nep_rii_");
    629:     PetscObjectSetOptions((PetscObject)ctx->ksp,((PetscObject)nep)->options);
    630:     KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE);
    631:     KSPSetTolerances(ctx->ksp,SlepcDefaultTol(nep->tol),PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    632:   }
    633:   *ksp = ctx->ksp;
    634:   return 0;
    635: }

    637: /*@
    638:    NEPRIIGetKSP - Retrieve the linear solver object (KSP) associated with
    639:    the nonlinear eigenvalue solver.

    641:    Not Collective

    643:    Input Parameter:
    644: .  nep - nonlinear eigenvalue solver

    646:    Output Parameter:
    647: .  ksp - the linear solver object

    649:    Level: advanced

    651: .seealso: NEPRIISetKSP()
    652: @*/
    653: PetscErrorCode NEPRIIGetKSP(NEP nep,KSP *ksp)
    654: {
    657:   PetscUseMethod(nep,"NEPRIIGetKSP_C",(NEP,KSP*),(nep,ksp));
    658:   return 0;
    659: }

    661: PetscErrorCode NEPView_RII(NEP nep,PetscViewer viewer)
    662: {
    663:   NEP_RII        *ctx = (NEP_RII*)nep->data;
    664:   PetscBool      isascii;

    666:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    667:   if (isascii) {
    668:     PetscViewerASCIIPrintf(viewer,"  maximum number of inner iterations: %" PetscInt_FMT "\n",ctx->max_inner_it);
    669:     if (ctx->cctol) PetscViewerASCIIPrintf(viewer,"  using a constant tolerance for the linear solver\n");
    670:     if (ctx->herm) PetscViewerASCIIPrintf(viewer,"  using the Hermitian version of the scalar nonlinear equation\n");
    671:     if (ctx->lag) PetscViewerASCIIPrintf(viewer,"  updating the preconditioner every %" PetscInt_FMT " iterations\n",ctx->lag);
    672:     if (ctx->deftol) PetscViewerASCIIPrintf(viewer,"  deflation threshold: %g\n",(double)ctx->deftol);
    673:     if (!ctx->ksp) NEPRIIGetKSP(nep,&ctx->ksp);
    674:     PetscViewerASCIIPushTab(viewer);
    675:     KSPView(ctx->ksp,viewer);
    676:     PetscViewerASCIIPopTab(viewer);
    677:   }
    678:   return 0;
    679: }

    681: PetscErrorCode NEPReset_RII(NEP nep)
    682: {
    683:   NEP_RII        *ctx = (NEP_RII*)nep->data;

    685:   KSPReset(ctx->ksp);
    686:   return 0;
    687: }

    689: PetscErrorCode NEPDestroy_RII(NEP nep)
    690: {
    691:   NEP_RII        *ctx = (NEP_RII*)nep->data;

    693:   KSPDestroy(&ctx->ksp);
    694:   PetscFree(nep->data);
    695:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetMaximumIterations_C",NULL);
    696:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetMaximumIterations_C",NULL);
    697:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetLagPreconditioner_C",NULL);
    698:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetLagPreconditioner_C",NULL);
    699:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetConstCorrectionTol_C",NULL);
    700:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetConstCorrectionTol_C",NULL);
    701:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetHermitian_C",NULL);
    702:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetHermitian_C",NULL);
    703:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetDeflationThreshold_C",NULL);
    704:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetDeflationThreshold_C",NULL);
    705:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetKSP_C",NULL);
    706:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetKSP_C",NULL);
    707:   return 0;
    708: }

    710: SLEPC_EXTERN PetscErrorCode NEPCreate_RII(NEP nep)
    711: {
    712:   NEP_RII        *ctx;

    714:   PetscNew(&ctx);
    715:   nep->data = (void*)ctx;
    716:   ctx->max_inner_it = 10;
    717:   ctx->lag          = 1;
    718:   ctx->cctol        = PETSC_FALSE;
    719:   ctx->herm         = PETSC_FALSE;
    720:   ctx->deftol       = 0.0;

    722:   nep->useds = PETSC_TRUE;

    724:   nep->ops->solve          = NEPSolve_RII;
    725:   nep->ops->setup          = NEPSetUp_RII;
    726:   nep->ops->setfromoptions = NEPSetFromOptions_RII;
    727:   nep->ops->reset          = NEPReset_RII;
    728:   nep->ops->destroy        = NEPDestroy_RII;
    729:   nep->ops->view           = NEPView_RII;
    730:   nep->ops->computevectors = NEPComputeVectors_Schur;

    732:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetMaximumIterations_C",NEPRIISetMaximumIterations_RII);
    733:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetMaximumIterations_C",NEPRIIGetMaximumIterations_RII);
    734:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetLagPreconditioner_C",NEPRIISetLagPreconditioner_RII);
    735:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetLagPreconditioner_C",NEPRIIGetLagPreconditioner_RII);
    736:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetConstCorrectionTol_C",NEPRIISetConstCorrectionTol_RII);
    737:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetConstCorrectionTol_C",NEPRIIGetConstCorrectionTol_RII);
    738:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetHermitian_C",NEPRIISetHermitian_RII);
    739:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetHermitian_C",NEPRIIGetHermitian_RII);
    740:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetDeflationThreshold_C",NEPRIISetDeflationThreshold_RII);
    741:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetDeflationThreshold_C",NEPRIIGetDeflationThreshold_RII);
    742:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIISetKSP_C",NEPRIISetKSP_RII);
    743:   PetscObjectComposeFunction((PetscObject)nep,"NEPRIIGetKSP_C",NEPRIIGetKSP_RII);
    744:   return 0;
    745: }