Date: 2022-03-31T15:29:32+00:00

Actual source code: narnoldi.c
slepc-3.17.0 2022-03-31
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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:   PetscFunctionReturn(0);
     44: }

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

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

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

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

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

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

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

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

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

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

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

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

    129:     /* convergence test */
    130:     VecNorm(r,NORM_2,&resnorm);
    131:     if (nep->its>1) perr=nep->errest[nep->nconv];
    132:     (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
    133:     if (nep->errest[nep->nconv]<=nep->tol) {
    134:       nep->nconv = nep->nconv + 1;
    135:       NEPDeflationLocking(extop,u,lambda);
    136:       skip = PETSC_TRUE;
    137:     }
    138:     (*nep->stopping)(nep,nep->its,nep->max_it,nep->nconv,nep->nev,&nep->reason,nep->stoppingctx);
    139:     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);

    141:     if (nep->reason == NEP_CONVERGED_ITERATING) {
    142:       if (!skip) {
    143:         if (n>=nep->ncv) {
    144:           nep->reason = NEP_DIVERGED_SUBSPACE_EXHAUSTED;
    145:           break;
    146:         }
    147:         if (ctx->lag && !(nep->its%ctx->lag) && nep->its>=2*ctx->lag && perr && nep->errest[nep->nconv]>.5*perr) NEPDeflationSolveSetUp(extop,lambda2);

    149:         /* continuation vector: f = T(sigma)\r */
    150:         BVGetColumn(Vext,n,&f);
    151:         NEPDeflationFunctionSolve(extop,r,f);
    152:         BVRestoreColumn(Vext,n,&f);
    153:         KSPGetConvergedReason(ctx->ksp,&kspreason);
    154:         if (kspreason<0) {
    155:           PetscInfo(nep,"iter=%" PetscInt_FMT ", linear solve failed, stopping solve\n",nep->its);
    156:           nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
    157:           break;
    158:         }

    160:         /* orthonormalize */
    161:         BVOrthonormalizeColumn(Vext,n,PETSC_FALSE,&beta,&breakdown);
    162:         if (breakdown || beta==0.0) {
    163:           PetscInfo(nep,"iter=%" PetscInt_FMT ", orthogonalization failed, stopping solve\n",nep->its);
    164:           nep->reason = NEP_DIVERGED_BREAKDOWN;
    165:           break;
    166:         }

    168:         /* update projected matrices */
    169:         DSSetDimensions(ds,n+1,0,0);
    170:         NEPDeflationProjectOperator(extop,Vext,ds,n,n+1);
    171:         n++;
    172:       } else {
    173:         nep->its--;  /* do not count this as a full iteration */
    174:         BVGetColumn(Vext,0,&f);
    175:         NEPDeflationSetRandomVec(extop,f);
    176:         NEPDeflationSolveSetUp(extop,sigma);
    177:         VecCopy(f,r);
    178:         NEPDeflationFunctionSolve(extop,r,f);
    179:         VecNorm(f,NORM_2,&nrm);
    180:         VecScale(f,1.0/nrm);
    181:         BVRestoreColumn(Vext,0,&f);
    182:         n = 1;
    183:         DSSetDimensions(ds,n,0,0);
    184:         NEPDeflationProjectOperator(extop,Vext,ds,n-1,n);
    185:         skip = PETSC_FALSE;
    186:       }
    187:     }
    188:   }

    190:   NEPDeflationGetInvariantPair(extop,NULL,&H);
    191:   MatGetSize(H,NULL,&ldh);
    192:   DSSetType(nep->ds,DSNHEP);
    193:   DSAllocate(nep->ds,PetscMax(nep->nconv,1));
    194:   DSGetLeadingDimension(nep->ds,&ldds);
    195:   MatDenseGetArrayRead(H,&Hp);
    196:   DSGetArray(nep->ds,DS_MAT_A,&Ap);
    197:   for (j=0;j<nep->nconv;j++)
    198:     for (i=0;i<nep->nconv;i++) Ap[j*ldds+i] = Hp[j*ldh+i];
    199:   DSRestoreArray(nep->ds,DS_MAT_A,&Ap);
    200:   MatDenseRestoreArrayRead(H,&Hp);
    201:   MatDestroy(&H);
    202:   DSSetDimensions(nep->ds,nep->nconv,0,nep->nconv);
    203:   DSSolve(nep->ds,nep->eigr,nep->eigi);
    204:   NEPDeflationReset(extop);
    205:   VecDestroy(&u);
    206:   VecDestroy(&r);
    207:   BVDestroy(&Vext);
    208:   DSDestroy(&ds);
    209:   PetscFree(eigr);
    210:   PetscFunctionReturn(0);
    211: }

    213: static PetscErrorCode NEPNArnoldiSetLagPreconditioner_NArnoldi(NEP nep,PetscInt lag)
    214: {
    215:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    218:   ctx->lag = lag;
    219:   PetscFunctionReturn(0);
    220: }

    222: /*@
    223:    NEPNArnoldiSetLagPreconditioner - Determines when the preconditioner is rebuilt in the
    224:    nonlinear solve.

    226:    Logically Collective on nep

    228:    Input Parameters:
    229: +  nep - nonlinear eigenvalue solver
    230: -  lag - 0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is
    231:           computed within the nonlinear iteration, 2 means every second time
    232:           the Jacobian is built, etc.

    234:    Options Database Keys:
    235: .  -nep_narnoldi_lag_preconditioner <lag> - the lag value

    237:    Notes:
    238:    The default is 1.
    239:    The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

    241:    Level: intermediate

    243: .seealso: NEPNArnoldiGetLagPreconditioner()
    244: @*/
    245: PetscErrorCode NEPNArnoldiSetLagPreconditioner(NEP nep,PetscInt lag)
    246: {
    249:   PetscTryMethod(nep,"NEPNArnoldiSetLagPreconditioner_C",(NEP,PetscInt),(nep,lag));
    250:   PetscFunctionReturn(0);
    251: }

    253: static PetscErrorCode NEPNArnoldiGetLagPreconditioner_NArnoldi(NEP nep,PetscInt *lag)
    254: {
    255:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

    257:   *lag = ctx->lag;
    258:   PetscFunctionReturn(0);
    259: }

    261: /*@
    262:    NEPNArnoldiGetLagPreconditioner - Indicates how often the preconditioner is rebuilt.

    264:    Not Collective

    266:    Input Parameter:
    267: .  nep - nonlinear eigenvalue solver

    269:    Output Parameter:
    270: .  lag - the lag parameter

    272:    Level: intermediate

    274: .seealso: NEPNArnoldiSetLagPreconditioner()
    275: @*/
    276: PetscErrorCode NEPNArnoldiGetLagPreconditioner(NEP nep,PetscInt *lag)
    277: {
    280:   PetscUseMethod(nep,"NEPNArnoldiGetLagPreconditioner_C",(NEP,PetscInt*),(nep,lag));
    281:   PetscFunctionReturn(0);
    282: }

    284: PetscErrorCode NEPSetFromOptions_NArnoldi(PetscOptionItems *PetscOptionsObject,NEP nep)
    285: {
    286:   PetscInt       i;
    287:   PetscBool      flg;
    288:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    290:   PetscOptionsHead(PetscOptionsObject,"NEP N-Arnoldi Options");
    291:     i = 0;
    292:     PetscOptionsInt("-nep_narnoldi_lag_preconditioner","Interval to rebuild preconditioner","NEPNArnoldiSetLagPreconditioner",ctx->lag,&i,&flg);
    293:     if (flg) NEPNArnoldiSetLagPreconditioner(nep,i);

    295:   PetscOptionsTail();

    297:   if (!ctx->ksp) NEPNArnoldiGetKSP(nep,&ctx->ksp);
    298:   KSPSetFromOptions(ctx->ksp);
    299:   PetscFunctionReturn(0);
    300: }

    302: static PetscErrorCode NEPNArnoldiSetKSP_NArnoldi(NEP nep,KSP ksp)
    303: {
    304:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    306:   PetscObjectReference((PetscObject)ksp);
    307:   KSPDestroy(&ctx->ksp);
    308:   ctx->ksp = ksp;
    309:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
    310:   nep->state = NEP_STATE_INITIAL;
    311:   PetscFunctionReturn(0);
    312: }

    314: /*@
    315:    NEPNArnoldiSetKSP - Associate a linear solver object (KSP) to the nonlinear
    316:    eigenvalue solver.

    318:    Collective on nep

    320:    Input Parameters:
    321: +  nep - eigenvalue solver
    322: -  ksp - the linear solver object

    324:    Level: advanced

    326: .seealso: NEPNArnoldiGetKSP()
    327: @*/
    328: PetscErrorCode NEPNArnoldiSetKSP(NEP nep,KSP ksp)
    329: {
    333:   PetscTryMethod(nep,"NEPNArnoldiSetKSP_C",(NEP,KSP),(nep,ksp));
    334:   PetscFunctionReturn(0);
    335: }

    337: static PetscErrorCode NEPNArnoldiGetKSP_NArnoldi(NEP nep,KSP *ksp)
    338: {
    339:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    341:   if (!ctx->ksp) {
    342:     KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp);
    343:     PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)nep,1);
    344:     KSPSetOptionsPrefix(ctx->ksp,((PetscObject)nep)->prefix);
    345:     KSPAppendOptionsPrefix(ctx->ksp,"nep_narnoldi_");
    346:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
    347:     PetscObjectSetOptions((PetscObject)ctx->ksp,((PetscObject)nep)->options);
    348:     KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE);
    349:     KSPSetTolerances(ctx->ksp,SlepcDefaultTol(nep->tol),PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    350:   }
    351:   *ksp = ctx->ksp;
    352:   PetscFunctionReturn(0);
    353: }

    355: /*@
    356:    NEPNArnoldiGetKSP - Retrieve the linear solver object (KSP) associated with
    357:    the nonlinear eigenvalue solver.

    359:    Not Collective

    361:    Input Parameter:
    362: .  nep - nonlinear eigenvalue solver

    364:    Output Parameter:
    365: .  ksp - the linear solver object

    367:    Level: advanced

    369: .seealso: NEPNArnoldiSetKSP()
    370: @*/
    371: PetscErrorCode NEPNArnoldiGetKSP(NEP nep,KSP *ksp)
    372: {
    375:   PetscUseMethod(nep,"NEPNArnoldiGetKSP_C",(NEP,KSP*),(nep,ksp));
    376:   PetscFunctionReturn(0);
    377: }

    379: PetscErrorCode NEPView_NArnoldi(NEP nep,PetscViewer viewer)
    380: {
    381:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;
    382:   PetscBool      isascii;

    384:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    385:   if (isascii) {
    386:     if (ctx->lag) PetscViewerASCIIPrintf(viewer,"  updating the preconditioner every %" PetscInt_FMT " iterations\n",ctx->lag);
    387:     if (!ctx->ksp) NEPNArnoldiGetKSP(nep,&ctx->ksp);
    388:     PetscViewerASCIIPushTab(viewer);
    389:     KSPView(ctx->ksp,viewer);
    390:     PetscViewerASCIIPopTab(viewer);
    391:   }
    392:   PetscFunctionReturn(0);
    393: }

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

    399:   KSPReset(ctx->ksp);
    400:   PetscFunctionReturn(0);
    401: }

    403: PetscErrorCode NEPDestroy_NArnoldi(NEP nep)
    404: {
    405:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

    407:   KSPDestroy(&ctx->ksp);
    408:   PetscFree(nep->data);
    409:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NULL);
    410:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NULL);
    411:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NULL);
    412:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NULL);
    413:   PetscFunctionReturn(0);
    414: }

    416: SLEPC_EXTERN PetscErrorCode NEPCreate_NArnoldi(NEP nep)
    417: {
    418:   NEP_NARNOLDI   *ctx;

    420:   PetscNewLog(nep,&ctx);
    421:   nep->data = (void*)ctx;
    422:   ctx->lag  = 1;

    424:   nep->useds = PETSC_TRUE;

    426:   nep->ops->solve          = NEPSolve_NArnoldi;
    427:   nep->ops->setup          = NEPSetUp_NArnoldi;
    428:   nep->ops->setfromoptions = NEPSetFromOptions_NArnoldi;
    429:   nep->ops->reset          = NEPReset_NArnoldi;
    430:   nep->ops->destroy        = NEPDestroy_NArnoldi;
    431:   nep->ops->view           = NEPView_NArnoldi;
    432:   nep->ops->computevectors = NEPComputeVectors_Schur;

    434:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NEPNArnoldiSetLagPreconditioner_NArnoldi);
    435:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NEPNArnoldiGetLagPreconditioner_NArnoldi);
    436:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NEPNArnoldiSetKSP_NArnoldi);
    437:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NEPNArnoldiGetKSP_NArnoldi);
    438:   PetscFunctionReturn(0);
    439: }