Date: 2018-10-23T10:32:39+00:00

Actual source code: narnoldi.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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: "narnoldi"

     13:    Method: Nonlinear Arnoldi

     15:    Algorithm:

     17:        Arnoldi for nonlinear eigenproblems.

     19:    References:

     21:        [1] H. Voss, "An Arnoldi method for nonlinear eigenvalue problems",
     22:            BIT 44:387-401, 2004.
     23: */

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

     28: typedef struct {
     29:   PetscInt  lag;            /* interval to rebuild preconditioner */
     30:   KSP      ksp;             /* linear solver object */
     31: } NEP_NARNOLDI;

     33: PetscErrorCode NEPSetUp_NArnoldi(NEP nep)
     34: {
     36:   PetscBool      istrivial;

     39:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
     40:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
     41:   if (!nep->max_it) nep->max_it = nep->nev*nep->ncv;
     42:   if (nep->which && nep->which!=NEP_TARGET_MAGNITUDE) SETERRQ(PetscObjectComm((PetscObject)nep),1,"Wrong value of which");
     43:   if (nep->fui!=NEP_USER_INTERFACE_SPLIT) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NARNOLDI only available for split operator");

     45:   RGIsTrivial(nep->rg,&istrivial);
     46:   if (!istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver does not support region filtering");

     48:   NEPAllocateSolution(nep,0);
     49:   NEPSetWorkVecs(nep,3);
     50:   return(0);
     51: }

     53: PetscErrorCode NEPSolve_NArnoldi(NEP nep)
     54: {
     55:   PetscErrorCode     ierr;
     56:   NEP_NARNOLDI       *ctx = (NEP_NARNOLDI*)nep->data;
     57:   Mat                T,H;
     58:   Vec                f,r,u,uu;
     59:   PetscScalar        *X,lambda=0.0,lambda2=0.0,*eigr,*Hp,*Ap,sigma;
     60:   PetscReal          beta,resnorm=0.0,nrm,perr=0.0;
     61:   PetscInt           n,i,j,ldds,ldh;
     62:   PetscBool          breakdown,skip=PETSC_FALSE;
     63:   BV                 Vext;
     64:   DS                 ds;
     65:   NEP_EXT_OP         extop=NULL;
     66:   SlepcSC            sc;
     67:   KSPConvergedReason kspreason;

     70:   /* get initial space and shift */
     71:   NEPGetDefaultShift(nep,&sigma);
     72:   if (!nep->nini) {
     73:     BVSetRandomColumn(nep->V,0);
     74:     BVNormColumn(nep->V,0,NORM_2,&nrm);
     75:     BVScaleColumn(nep->V,0,1.0/nrm);
     76:     n = 1;
     77:   } else n = nep->nini;

     79:   if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
     80:   NEPDeflationInitialize(nep,nep->V,ctx->ksp,PETSC_FALSE,nep->nev,&extop);
     81:   NEPDeflationCreateBV(extop,nep->ncv,&Vext);

     83:   /* prepare linear solver */
     84:   NEPDeflationSolveSetUp(extop,sigma);

     86:   BVGetColumn(Vext,0,&f);
     87:   VecDuplicate(f,&r);
     88:   VecDuplicate(f,&u);
     89:   BVGetColumn(nep->V,0,&uu);
     90:   NEPDeflationCopyToExtendedVec(extop,uu,NULL,f,PETSC_FALSE);
     91:   BVRestoreColumn(nep->V,0,&uu);
     92:   VecCopy(f,r);
     93:   NEPDeflationFunctionSolve(extop,r,f);
     94:   VecNorm(f,NORM_2,&nrm);
     95:   VecScale(f,1.0/nrm);
     96:   BVRestoreColumn(Vext,0,&f);

     98:   DSCreate(PetscObjectComm((PetscObject)nep),&ds);
     99:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ds);
    100:   DSSetType(ds,DSNEP);
    101:   DSNEPSetFN(ds,nep->nt,nep->f);
    102:   DSAllocate(ds,nep->ncv);
    103:   DSGetSlepcSC(ds,&sc);
    104:   sc->comparison    = nep->sc->comparison;
    105:   sc->comparisonctx = nep->sc->comparisonctx;
    106:   DSSetFromOptions(ds);

    108:   /* build projected matrices for initial space */
    109:   DSSetDimensions(ds,n,0,0,0);
    110:   NEPDeflationProjectOperator(extop,Vext,ds,0,n);

    112:   PetscMalloc1(nep->ncv,&eigr);

    114:   /* Restart loop */
    115:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    116:     nep->its++;

    118:     /* solve projected problem */
    119:     DSSetDimensions(ds,n,0,0,0);
    120:     DSSetState(ds,DS_STATE_RAW);
    121:     DSSolve(ds,eigr,NULL);
    122:     DSSynchronize(ds,eigr,NULL);
    123:     if (nep->its>1) lambda2 = lambda;
    124:     lambda = eigr[0];
    125:     nep->eigr[nep->nconv] = lambda;

    127:     /* compute Ritz vector, x = V*s */
    128:     DSGetArray(ds,DS_MAT_X,&X);
    129:     BVSetActiveColumns(Vext,0,n);
    130:     BVMultVec(Vext,1.0,0.0,u,X);
    131:     DSRestoreArray(ds,DS_MAT_X,&X);

    133:     /* compute the residual, r = T(lambda)*x */
    134:     NEPDeflationComputeFunction(extop,lambda,&T);
    135:     MatMult(T,u,r);

    137:     /* convergence test */
    138:     VecNorm(r,NORM_2,&resnorm);
    139:     if (nep->its>1) perr=nep->errest[nep->nconv];
    140:     (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
    141:     if (nep->errest[nep->nconv]<=nep->tol) {
    142:       nep->nconv = nep->nconv + 1;
    143:       NEPDeflationLocking(extop,u,lambda);
    144:       skip = PETSC_TRUE;
    145:     }
    146:     (*nep->stopping)(nep,nep->its,nep->max_it,nep->nconv,nep->nev,&nep->reason,nep->stoppingctx);
    147:     if (!skip || nep->reason>0) {
    148:       NEPMonitor(nep,nep->its,nep->nconv,nep->eigr,nep->eigi,nep->errest,(nep->reason>0)?nep->nconv:nep->nconv+1);
    149:     }

    151:     if (nep->reason == NEP_CONVERGED_ITERATING) {
    152:       if (!skip) {
    153:         if (n>=nep->ncv) {
    154:           nep->reason = NEP_DIVERGED_SUBSPACE_EXHAUSTED;
    155:           break;
    156:         }
    157:         if (ctx->lag && !(nep->its%ctx->lag) && nep->its>=2*ctx->lag && perr && nep->errest[nep->nconv]>.5*perr) {
    158:           NEPDeflationSolveSetUp(extop,lambda2);
    159:         }

    161:         /* continuation vector: f = T(sigma)\r */
    162:         BVGetColumn(Vext,n,&f);
    163:         NEPDeflationFunctionSolve(extop,r,f);
    164:         BVRestoreColumn(Vext,n,&f);
    165:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    166:         if (kspreason<0) {
    167:           PetscInfo1(nep,"iter=%D, linear solve failed, stopping solve\n",nep->its);
    168:           nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
    169:           break;
    170:         }

    172:         /* orthonormalize */
    173:         BVOrthonormalizeColumn(Vext,n,PETSC_FALSE,&beta,&breakdown);
    174:         if (breakdown || beta==0.0) {
    175:           PetscInfo1(nep,"iter=%D, orthogonalization failed, stopping solve\n",nep->its);
    176:           nep->reason = NEP_DIVERGED_BREAKDOWN;
    177:           break;
    178:         }

    180:         /* update projected matrices */
    181:         DSSetDimensions(ds,n+1,0,0,0);
    182:         NEPDeflationProjectOperator(extop,Vext,ds,n,n+1);
    183:         n++;
    184:       } else {
    185:         nep->its--;  /* do not count this as a full iteration */
    186:         BVGetColumn(Vext,0,&f);
    187:         NEPDeflationSetRandomVec(extop,f);
    188:         NEPDeflationSolveSetUp(extop,sigma);
    189:         VecCopy(f,r);
    190:         NEPDeflationFunctionSolve(extop,r,f);
    191:         VecNorm(f,NORM_2,&nrm);
    192:         VecScale(f,1.0/nrm);
    193:         BVRestoreColumn(Vext,0,&f);
    194:         n = 1;
    195:         DSSetDimensions(ds,n,0,0,0);
    196:         NEPDeflationProjectOperator(extop,Vext,ds,n-1,n);
    197:         skip = PETSC_FALSE;
    198:       }
    199:     }
    200:   }

    202:   NEPDeflationGetInvariantPair(extop,NULL,&H);
    203:   MatGetSize(H,NULL,&ldh);
    204:   DSSetType(nep->ds,DSNHEP);
    205:   DSAllocate(nep->ds,PetscMax(nep->nconv,1));
    206:   DSGetLeadingDimension(nep->ds,&ldds);
    207:   MatDenseGetArray(H,&Hp);
    208:   DSGetArray(nep->ds,DS_MAT_A,&Ap);
    209:   for (j=0;j<nep->nconv;j++)
    210:     for (i=0;i<nep->nconv;i++) Ap[j*ldds+i] = Hp[j*ldh+i];
    211:   DSRestoreArray(nep->ds,DS_MAT_A,&Ap);
    212:   MatDenseRestoreArray(H,&Hp);
    213:   MatDestroy(&H);
    214:   DSSetDimensions(nep->ds,nep->nconv,0,0,nep->nconv);
    215:   DSSolve(nep->ds,nep->eigr,nep->eigi);
    216:   NEPDeflationReset(extop);
    217:   VecDestroy(&u);
    218:   VecDestroy(&r);
    219:   BVDestroy(&Vext);
    220:   DSDestroy(&ds);
    221:   PetscFree(eigr);
    222:   return(0);
    223: }

    225: static PetscErrorCode NEPNArnoldiSetLagPreconditioner_NArnoldi(NEP nep,PetscInt lag)
    226: {
    227:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    230:   if (lag<0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Lag must be non-negative");
    231:   ctx->lag = lag;
    232:   return(0);
    233: }

    235: /*@
    236:    NEPNArnoldiSetLagPreconditioner - Determines when the preconditioner is rebuilt in the
    237:    nonlinear solve.

    239:    Logically Collective on NEP

    241:    Input Parameters:
    242: +  nep - nonlinear eigenvalue solver
    243: -  lag - 0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is
    244:           computed within the nonlinear iteration, 2 means every second time
    245:           the Jacobian is built, etc.

    247:    Options Database Keys:
    248: .  -nep_narnoldi_lag_preconditioner <lag>

    250:    Notes:
    251:    The default is 1.
    252:    The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

    254:    Level: intermediate

    256: .seealso: NEPNArnoldiGetLagPreconditioner()
    257: @*/
    258: PetscErrorCode NEPNArnoldiSetLagPreconditioner(NEP nep,PetscInt lag)
    259: {

    265:   PetscTryMethod(nep,"NEPNArnoldiSetLagPreconditioner_C",(NEP,PetscInt),(nep,lag));
    266:   return(0);
    267: }

    269: static PetscErrorCode NEPNArnoldiGetLagPreconditioner_NArnoldi(NEP nep,PetscInt *lag)
    270: {
    271:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    274:   *lag = ctx->lag;
    275:   return(0);
    276: }

    278: /*@
    279:    NEPNArnoldiGetLagPreconditioner - Indicates how often the preconditioner is rebuilt.

    281:    Not Collective

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

    286:    Output Parameter:
    287: .  lag - the lag parameter

    289:    Level: intermediate

    291: .seealso: NEPNArnoldiSetLagPreconditioner()
    292: @*/
    293: PetscErrorCode NEPNArnoldiGetLagPreconditioner(NEP nep,PetscInt *lag)
    294: {

    300:   PetscUseMethod(nep,"NEPNArnoldiGetLagPreconditioner_C",(NEP,PetscInt*),(nep,lag));
    301:   return(0);
    302: }

    304: PetscErrorCode NEPSetFromOptions_NArnoldi(PetscOptionItems *PetscOptionsObject,NEP nep)
    305: {
    307:   PetscInt       i;
    308:   PetscBool      flg;
    309:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    312:   PetscOptionsHead(PetscOptionsObject,"NEP N-Arnoldi Options");
    313:     i = 0;
    314:     PetscOptionsInt("-nep_narnoldi_lag_preconditioner","Interval to rebuild preconditioner","NEPNArnoldiSetLagPreconditioner",ctx->lag,&i,&flg);
    315:     if (flg) { NEPNArnoldiSetLagPreconditioner(nep,i); }

    317:   PetscOptionsTail();

    319:   if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
    320:   KSPSetFromOptions(ctx->ksp);
    321:   return(0);
    322: }

    324: static PetscErrorCode NEPNArnoldiSetKSP_NArnoldi(NEP nep,KSP ksp)
    325: {
    327:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    330:   PetscObjectReference((PetscObject)ksp);
    331:   KSPDestroy(&ctx->ksp);
    332:   ctx->ksp = ksp;
    333:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
    334:   nep->state = NEP_STATE_INITIAL;
    335:   return(0);
    336: }

    338: /*@
    339:    NEPNArnoldiSetKSP - Associate a linear solver object (KSP) to the nonlinear
    340:    eigenvalue solver.

    342:    Collective on NEP

    344:    Input Parameters:
    345: +  nep - eigenvalue solver
    346: -  ksp - the linear solver object

    348:    Level: advanced

    350: .seealso: NEPNArnoldiGetKSP()
    351: @*/
    352: PetscErrorCode NEPNArnoldiSetKSP(NEP nep,KSP ksp)
    353: {

    360:   PetscTryMethod(nep,"NEPNArnoldiSetKSP_C",(NEP,KSP),(nep,ksp));
    361:   return(0);
    362: }

    364: static PetscErrorCode NEPNArnoldiGetKSP_NArnoldi(NEP nep,KSP *ksp)
    365: {
    367:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    370:   if (!ctx->ksp) {
    371:     KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp);
    372:     PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)nep,1);
    373:     KSPSetOptionsPrefix(ctx->ksp,((PetscObject)nep)->prefix);
    374:     KSPAppendOptionsPrefix(ctx->ksp,"nep_narnoldi_");
    375:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
    376:     KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE);
    377:     KSPSetTolerances(ctx->ksp,SLEPC_DEFAULT_TOL,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    378:   }
    379:   *ksp = ctx->ksp;
    380:   return(0);
    381: }

    383: /*@
    384:    NEPNArnoldiGetKSP - Retrieve the linear solver object (KSP) associated with
    385:    the nonlinear eigenvalue solver.

    387:    Not Collective

    389:    Input Parameter:
    390: .  nep - nonlinear eigenvalue solver

    392:    Output Parameter:
    393: .  ksp - the linear solver object

    395:    Level: advanced

    397: .seealso: NEPNArnoldiSetKSP()
    398: @*/
    399: PetscErrorCode NEPNArnoldiGetKSP(NEP nep,KSP *ksp)
    400: {

    406:   PetscUseMethod(nep,"NEPNArnoldiGetKSP_C",(NEP,KSP*),(nep,ksp));
    407:   return(0);
    408: }

    410: PetscErrorCode NEPView_NArnoldi(NEP nep,PetscViewer viewer)
    411: {
    413:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;
    414:   PetscBool      isascii;

    417:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    418:   if (isascii) {
    419:     if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
    420:     KSPView(ctx->ksp,viewer);
    421:   }
    422:   return(0);
    423: }

    425: PetscErrorCode NEPReset_NArnoldi(NEP nep)
    426: {
    428:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    431:   KSPReset(ctx->ksp);
    432:   return(0);
    433: }

    435: PetscErrorCode NEPDestroy_NArnoldi(NEP nep)
    436: {
    438:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    441:   KSPDestroy(&ctx->ksp);
    442:   PetscFree(nep->data);
    443:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NULL);
    444:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NULL);
    445:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NULL);
    446:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NULL);
    447:   return(0);
    448: }

    450: PETSC_EXTERN PetscErrorCode NEPCreate_NArnoldi(NEP nep)
    451: {
    453:   NEP_NARNOLDI   *ctx;

    456:   PetscNewLog(nep,&ctx);
    457:   nep->data = (void*)ctx;

    459:   nep->ops->solve          = NEPSolve_NArnoldi;
    460:   nep->ops->setup          = NEPSetUp_NArnoldi;
    461:   nep->ops->setfromoptions = NEPSetFromOptions_NArnoldi;
    462:   nep->ops->reset          = NEPReset_NArnoldi;
    463:   nep->ops->destroy        = NEPDestroy_NArnoldi;
    464:   nep->ops->view           = NEPView_NArnoldi;
    465:   nep->ops->computevectors = NEPComputeVectors_Schur;

    467:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NEPNArnoldiSetLagPreconditioner_NArnoldi);
    468:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NEPNArnoldiGetLagPreconditioner_NArnoldi);
    469:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NEPNArnoldiSetKSP_NArnoldi);
    470:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NEPNArnoldiGetKSP_NArnoldi);
    471:   return(0);
    472: }