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

Actual source code: narnoldi.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: "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>
     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: {
     35:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
     37:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = nep->nev*nep->ncv;
     38:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
     40:   NEPCheckUnsupported(nep,NEP_FEATURE_CALLBACK | NEP_FEATURE_REGION | NEP_FEATURE_TWOSIDED);
     41:   NEPAllocateSolution(nep,0);
     42:   NEPSetWorkVecs(nep,3);
     43:   return 0;
     44: }

     46: PetscErrorCode NEPSolve_NArnoldi(NEP nep)
     47: {
     48:   NEP_NARNOLDI       *ctx = (NEP_NARNOLDI*)nep->data;
     49:   Mat                T,H,A;
     50:   Vec                f,r,u,uu;
     51:   PetscScalar        *X,lambda=0.0,lambda2=0.0,*eigr,sigma;
     52:   PetscReal          beta,resnorm=0.0,nrm,perr=0.0;
     53:   PetscInt           n;
     54:   PetscBool          breakdown,skip=PETSC_FALSE;
     55:   BV                 Vext;
     56:   DS                 ds;
     57:   NEP_EXT_OP         extop=NULL;
     58:   SlepcSC            sc;
     59:   KSPConvergedReason kspreason;

     61:   /* get initial space and shift */
     62:   NEPGetDefaultShift(nep,&sigma);
     63:   if (!nep->nini) {
     64:     BVSetRandomColumn(nep->V,0);
     65:     BVNormColumn(nep->V,0,NORM_2,&nrm);
     66:     BVScaleColumn(nep->V,0,1.0/nrm);
     67:     n = 1;
     68:   } else n = nep->nini;

     70:   if (!ctx->ksp) NEPNArnoldiGetKSP(nep,&ctx->ksp);
     71:   NEPDeflationInitialize(nep,nep->V,ctx->ksp,PETSC_FALSE,nep->nev,&extop);
     72:   NEPDeflationCreateBV(extop,nep->ncv,&Vext);

     74:   /* prepare linear solver */
     75:   NEPDeflationSolveSetUp(extop,sigma);

     77:   BVGetColumn(Vext,0,&f);
     78:   VecDuplicate(f,&r);
     79:   VecDuplicate(f,&u);
     80:   BVGetColumn(nep->V,0,&uu);
     81:   NEPDeflationCopyToExtendedVec(extop,uu,NULL,f,PETSC_FALSE);
     82:   BVRestoreColumn(nep->V,0,&uu);
     83:   VecCopy(f,r);
     84:   NEPDeflationFunctionSolve(extop,r,f);
     85:   VecNorm(f,NORM_2,&nrm);
     86:   VecScale(f,1.0/nrm);
     87:   BVRestoreColumn(Vext,0,&f);

     89:   DSCreate(PetscObjectComm((PetscObject)nep),&ds);
     90:   DSSetType(ds,DSNEP);
     91:   DSNEPSetFN(ds,nep->nt,nep->f);
     92:   DSAllocate(ds,nep->ncv);
     93:   DSGetSlepcSC(ds,&sc);
     94:   sc->comparison    = nep->sc->comparison;
     95:   sc->comparisonctx = nep->sc->comparisonctx;
     96:   DSSetFromOptions(ds);

     98:   /* build projected matrices for initial space */
     99:   DSSetDimensions(ds,n,0,0);
    100:   NEPDeflationProjectOperator(extop,Vext,ds,0,n);

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

    104:   /* Restart loop */
    105:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    106:     nep->its++;

    108:     /* solve projected problem */
    109:     DSSetDimensions(ds,n,0,0);
    110:     DSSetState(ds,DS_STATE_RAW);
    111:     DSSolve(ds,eigr,NULL);
    112:     DSSynchronize(ds,eigr,NULL);
    113:     if (nep->its>1) lambda2 = lambda;
    114:     lambda = eigr[0];
    115:     nep->eigr[nep->nconv] = lambda;

    117:     /* compute Ritz vector, x = V*s */
    118:     DSGetArray(ds,DS_MAT_X,&X);
    119:     BVSetActiveColumns(Vext,0,n);
    120:     BVMultVec(Vext,1.0,0.0,u,X);
    121:     DSRestoreArray(ds,DS_MAT_X,&X);

    123:     /* compute the residual, r = T(lambda)*x */
    124:     NEPDeflationComputeFunction(extop,lambda,&T);
    125:     MatMult(T,u,r);

    127:     /* convergence test */
    128:     VecNorm(r,NORM_2,&resnorm);
    129:     if (nep->its>1) perr=nep->errest[nep->nconv];
    130:     (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
    131:     if (nep->errest[nep->nconv]<=nep->tol) {
    132:       nep->nconv = nep->nconv + 1;
    133:       NEPDeflationLocking(extop,u,lambda);
    134:       skip = PETSC_TRUE;
    135:     }
    136:     (*nep->stopping)(nep,nep->its,nep->max_it,nep->nconv,nep->nev,&nep->reason,nep->stoppingctx);
    137:     if (!skip || nep->reason>0) NEPMonitor(nep,nep->its,nep->nconv,nep->eigr,nep->eigi,nep->errest,(nep->reason>0)?nep->nconv:nep->nconv+1);

    139:     if (nep->reason == NEP_CONVERGED_ITERATING) {
    140:       if (!skip) {
    141:         if (n>=nep->ncv) {
    142:           nep->reason = NEP_DIVERGED_SUBSPACE_EXHAUSTED;
    143:           break;
    144:         }
    145:         if (ctx->lag && !(nep->its%ctx->lag) && nep->its>=2*ctx->lag && perr && nep->errest[nep->nconv]>.5*perr) NEPDeflationSolveSetUp(extop,lambda2);

    147:         /* continuation vector: f = T(sigma)\r */
    148:         BVGetColumn(Vext,n,&f);
    149:         NEPDeflationFunctionSolve(extop,r,f);
    150:         BVRestoreColumn(Vext,n,&f);
    151:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    152:         if (kspreason<0) {
    153:           PetscInfo(nep,"iter=%" PetscInt_FMT ", linear solve failed, stopping solve\n",nep->its);
    154:           nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
    155:           break;
    156:         }

    158:         /* orthonormalize */
    159:         BVOrthonormalizeColumn(Vext,n,PETSC_FALSE,&beta,&breakdown);
    160:         if (breakdown || beta==0.0) {
    161:           PetscInfo(nep,"iter=%" PetscInt_FMT ", orthogonalization failed, stopping solve\n",nep->its);
    162:           nep->reason = NEP_DIVERGED_BREAKDOWN;
    163:           break;
    164:         }

    166:         /* update projected matrices */
    167:         DSSetDimensions(ds,n+1,0,0);
    168:         NEPDeflationProjectOperator(extop,Vext,ds,n,n+1);
    169:         n++;
    170:       } else {
    171:         nep->its--;  /* do not count this as a full iteration */
    172:         BVGetColumn(Vext,0,&f);
    173:         NEPDeflationSetRandomVec(extop,f);
    174:         NEPDeflationSolveSetUp(extop,sigma);
    175:         VecCopy(f,r);
    176:         NEPDeflationFunctionSolve(extop,r,f);
    177:         VecNorm(f,NORM_2,&nrm);
    178:         VecScale(f,1.0/nrm);
    179:         BVRestoreColumn(Vext,0,&f);
    180:         n = 1;
    181:         DSSetDimensions(ds,n,0,0);
    182:         NEPDeflationProjectOperator(extop,Vext,ds,n-1,n);
    183:         skip = PETSC_FALSE;
    184:       }
    185:     }
    186:   }

    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:   BVDestroy(&Vext);
    201:   DSDestroy(&ds);
    202:   PetscFree(eigr);
    203:   return 0;
    204: }

    206: static PetscErrorCode NEPNArnoldiSetLagPreconditioner_NArnoldi(NEP nep,PetscInt lag)
    207: {
    208:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    211:   ctx->lag = lag;
    212:   return 0;
    213: }

    215: /*@
    216:    NEPNArnoldiSetLagPreconditioner - Determines when the preconditioner is rebuilt in the
    217:    nonlinear solve.

    219:    Logically Collective on nep

    221:    Input Parameters:
    222: +  nep - nonlinear eigenvalue solver
    223: -  lag - 0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is
    224:           computed within the nonlinear iteration, 2 means every second time
    225:           the Jacobian is built, etc.

    227:    Options Database Keys:
    228: .  -nep_narnoldi_lag_preconditioner <lag> - the lag value

    230:    Notes:
    231:    The default is 1.
    232:    The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

    234:    Level: intermediate

    236: .seealso: NEPNArnoldiGetLagPreconditioner()
    237: @*/
    238: PetscErrorCode NEPNArnoldiSetLagPreconditioner(NEP nep,PetscInt lag)
    239: {
    242:   PetscTryMethod(nep,"NEPNArnoldiSetLagPreconditioner_C",(NEP,PetscInt),(nep,lag));
    243:   return 0;
    244: }

    246: static PetscErrorCode NEPNArnoldiGetLagPreconditioner_NArnoldi(NEP nep,PetscInt *lag)
    247: {
    248:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    250:   *lag = ctx->lag;
    251:   return 0;
    252: }

    254: /*@
    255:    NEPNArnoldiGetLagPreconditioner - Indicates how often the preconditioner is rebuilt.

    257:    Not Collective

    259:    Input Parameter:
    260: .  nep - nonlinear eigenvalue solver

    262:    Output Parameter:
    263: .  lag - the lag parameter

    265:    Level: intermediate

    267: .seealso: NEPNArnoldiSetLagPreconditioner()
    268: @*/
    269: PetscErrorCode NEPNArnoldiGetLagPreconditioner(NEP nep,PetscInt *lag)
    270: {
    273:   PetscUseMethod(nep,"NEPNArnoldiGetLagPreconditioner_C",(NEP,PetscInt*),(nep,lag));
    274:   return 0;
    275: }

    277: PetscErrorCode NEPSetFromOptions_NArnoldi(NEP nep,PetscOptionItems *PetscOptionsObject)
    278: {
    279:   PetscInt       i;
    280:   PetscBool      flg;
    281:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    283:   PetscOptionsHeadBegin(PetscOptionsObject,"NEP N-Arnoldi Options");
    284:     i = 0;
    285:     PetscOptionsInt("-nep_narnoldi_lag_preconditioner","Interval to rebuild preconditioner","NEPNArnoldiSetLagPreconditioner",ctx->lag,&i,&flg);
    286:     if (flg) NEPNArnoldiSetLagPreconditioner(nep,i);

    288:   PetscOptionsHeadEnd();

    290:   if (!ctx->ksp) NEPNArnoldiGetKSP(nep,&ctx->ksp);
    291:   KSPSetFromOptions(ctx->ksp);
    292:   return 0;
    293: }

    295: static PetscErrorCode NEPNArnoldiSetKSP_NArnoldi(NEP nep,KSP ksp)
    296: {
    297:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    299:   PetscObjectReference((PetscObject)ksp);
    300:   KSPDestroy(&ctx->ksp);
    301:   ctx->ksp = ksp;
    302:   nep->state = NEP_STATE_INITIAL;
    303:   return 0;
    304: }

    306: /*@
    307:    NEPNArnoldiSetKSP - Associate a linear solver object (KSP) to the nonlinear
    308:    eigenvalue solver.

    310:    Collective on nep

    312:    Input Parameters:
    313: +  nep - eigenvalue solver
    314: -  ksp - the linear solver object

    316:    Level: advanced

    318: .seealso: NEPNArnoldiGetKSP()
    319: @*/
    320: PetscErrorCode NEPNArnoldiSetKSP(NEP nep,KSP ksp)
    321: {
    325:   PetscTryMethod(nep,"NEPNArnoldiSetKSP_C",(NEP,KSP),(nep,ksp));
    326:   return 0;
    327: }

    329: static PetscErrorCode NEPNArnoldiGetKSP_NArnoldi(NEP nep,KSP *ksp)
    330: {
    331:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    333:   if (!ctx->ksp) {
    334:     KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp);
    335:     PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)nep,1);
    336:     KSPSetOptionsPrefix(ctx->ksp,((PetscObject)nep)->prefix);
    337:     KSPAppendOptionsPrefix(ctx->ksp,"nep_narnoldi_");
    338:     PetscObjectSetOptions((PetscObject)ctx->ksp,((PetscObject)nep)->options);
    339:     KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE);
    340:     KSPSetTolerances(ctx->ksp,SlepcDefaultTol(nep->tol),PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    341:   }
    342:   *ksp = ctx->ksp;
    343:   return 0;
    344: }

    346: /*@
    347:    NEPNArnoldiGetKSP - Retrieve the linear solver object (KSP) associated with
    348:    the nonlinear eigenvalue solver.

    350:    Not Collective

    352:    Input Parameter:
    353: .  nep - nonlinear eigenvalue solver

    355:    Output Parameter:
    356: .  ksp - the linear solver object

    358:    Level: advanced

    360: .seealso: NEPNArnoldiSetKSP()
    361: @*/
    362: PetscErrorCode NEPNArnoldiGetKSP(NEP nep,KSP *ksp)
    363: {
    366:   PetscUseMethod(nep,"NEPNArnoldiGetKSP_C",(NEP,KSP*),(nep,ksp));
    367:   return 0;
    368: }

    370: PetscErrorCode NEPView_NArnoldi(NEP nep,PetscViewer viewer)
    371: {
    372:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;
    373:   PetscBool      isascii;

    375:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    376:   if (isascii) {
    377:     if (ctx->lag) PetscViewerASCIIPrintf(viewer,"  updating the preconditioner every %" PetscInt_FMT " iterations\n",ctx->lag);
    378:     if (!ctx->ksp) NEPNArnoldiGetKSP(nep,&ctx->ksp);
    379:     PetscViewerASCIIPushTab(viewer);
    380:     KSPView(ctx->ksp,viewer);
    381:     PetscViewerASCIIPopTab(viewer);
    382:   }
    383:   return 0;
    384: }

    386: PetscErrorCode NEPReset_NArnoldi(NEP nep)
    387: {
    388:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    390:   KSPReset(ctx->ksp);
    391:   return 0;
    392: }

    394: PetscErrorCode NEPDestroy_NArnoldi(NEP nep)
    395: {
    396:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    398:   KSPDestroy(&ctx->ksp);
    399:   PetscFree(nep->data);
    400:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NULL);
    401:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NULL);
    402:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NULL);
    403:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NULL);
    404:   return 0;
    405: }

    407: SLEPC_EXTERN PetscErrorCode NEPCreate_NArnoldi(NEP nep)
    408: {
    409:   NEP_NARNOLDI   *ctx;

    411:   PetscNew(&ctx);
    412:   nep->data = (void*)ctx;
    413:   ctx->lag  = 1;

    415:   nep->useds = PETSC_TRUE;

    417:   nep->ops->solve          = NEPSolve_NArnoldi;
    418:   nep->ops->setup          = NEPSetUp_NArnoldi;
    419:   nep->ops->setfromoptions = NEPSetFromOptions_NArnoldi;
    420:   nep->ops->reset          = NEPReset_NArnoldi;
    421:   nep->ops->destroy        = NEPDestroy_NArnoldi;
    422:   nep->ops->view           = NEPView_NArnoldi;
    423:   nep->ops->computevectors = NEPComputeVectors_Schur;

    425:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NEPNArnoldiSetLagPreconditioner_NArnoldi);
    426:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NEPNArnoldiGetLagPreconditioner_NArnoldi);
    427:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NEPNArnoldiSetKSP_NArnoldi);
    428:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NEPNArnoldiGetKSP_NArnoldi);
    429:   return 0;
    430: }