Date: 2023-09-05T10:17:49+00:00

Actual source code: arnoldi.c
slepc-3.19.2 2023-09-05
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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 eigensolver: "arnoldi"

     13:    Method: Explicitly Restarted Arnoldi

     15:    Algorithm:

     17:        Arnoldi method with explicit restart and deflation.

     19:    References:

     21:        [1] "Arnoldi Methods in SLEPc", SLEPc Technical Report STR-4,
     22:            available at https://slepc.upv.es.
     23: */

     25: #include <slepc/private/epsimpl.h>

     27: typedef struct {
     28:   PetscBool delayed;
     29: } EPS_ARNOLDI;

     31: PetscErrorCode EPSSetUp_Arnoldi(EPS eps)
     32: {
     33:   PetscFunctionBegin;
     34:   EPSCheckDefinite(eps);
     35:   PetscCall(EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd));
     36:   PetscCheck(eps->ncv<=eps->nev+eps->mpd,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd");
     37:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     38:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
     39:   PetscCheck(eps->which!=EPS_ALL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
     40:   EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_TWOSIDED);

     42:   PetscCall(EPSAllocateSolution(eps,1));
     43:   PetscCall(EPS_SetInnerProduct(eps));
     44:   PetscCall(DSSetType(eps->ds,DSNHEP));
     45:   if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) PetscCall(DSSetRefined(eps->ds,PETSC_TRUE));
     46:   PetscCall(DSSetExtraRow(eps->ds,PETSC_TRUE));
     47:   PetscCall(DSAllocate(eps->ds,eps->ncv+1));
     48:   PetscFunctionReturn(PETSC_SUCCESS);
     49: }

     51: PetscErrorCode EPSSolve_Arnoldi(EPS eps)
     52: {
     53:   PetscInt           k,nv,ld;
     54:   Mat                U,Op,H;
     55:   PetscScalar        *Harray;
     56:   PetscReal          beta,gamma=1.0;
     57:   PetscBool          breakdown,harmonic,refined;
     58:   BVOrthogRefineType orthog_ref;
     59:   EPS_ARNOLDI        *arnoldi = (EPS_ARNOLDI*)eps->data;

     61:   PetscFunctionBegin;
     62:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
     63:   PetscCall(DSGetRefined(eps->ds,&refined));
     64:   harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
     65:   PetscCall(BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL,NULL));

     67:   /* Get the starting Arnoldi vector */
     68:   PetscCall(EPSGetStartVector(eps,0,NULL));

     70:   /* Restart loop */
     71:   while (eps->reason == EPS_CONVERGED_ITERATING) {
     72:     eps->its++;

     74:     /* Compute an nv-step Arnoldi factorization */
     75:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
     76:     PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0));
     77:     if (!arnoldi->delayed) {
     78:       PetscCall(STGetOperator(eps->st,&Op));
     79:       PetscCall(DSGetMat(eps->ds,DS_MAT_A,&H));
     80:       PetscCall(BVMatArnoldi(eps->V,Op,H,eps->nconv,&nv,&beta,&breakdown));
     81:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&H));
     82:       PetscCall(STRestoreOperator(eps->st,&Op));
     83:     } else if (orthog_ref == BV_ORTHOG_REFINE_NEVER) {
     84:       PetscCall(DSGetArray(eps->ds,DS_MAT_A,&Harray));
     85:       PetscCall(EPSDelayedArnoldi1(eps,Harray,ld,eps->nconv,&nv,&beta,&breakdown));
     86:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&Harray));
     87:     } else {
     88:       PetscCall(DSGetArray(eps->ds,DS_MAT_A,&Harray));
     89:       PetscCall(EPSDelayedArnoldi(eps,Harray,ld,eps->nconv,&nv,&beta,&breakdown));
     90:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&Harray));
     91:     }
     92:     PetscCall(DSSetState(eps->ds,DS_STATE_INTERMEDIATE));
     93:     PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));

     95:     /* Compute translation of Krylov decomposition if harmonic extraction used */
     96:     if (harmonic) PetscCall(DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,NULL,&gamma));

     98:     /* Solve projected problem */
     99:     PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
    100:     PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
    101:     PetscCall(DSUpdateExtraRow(eps->ds));
    102:     PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));

    104:     /* Check convergence */
    105:     PetscCall(EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,0.0,gamma,&k));
    106:     if (refined) {
    107:       PetscCall(DSGetMat(eps->ds,DS_MAT_X,&U));
    108:       PetscCall(BVMultInPlace(eps->V,U,eps->nconv,k+1));
    109:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&U));
    110:       PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_FALSE,NULL,NULL));
    111:     } else {
    112:       PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&U));
    113:       PetscCall(BVMultInPlace(eps->V,U,eps->nconv,PetscMin(k+1,nv)));
    114:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&U));
    115:     }
    116:     PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx));
    117:     if (eps->reason == EPS_CONVERGED_ITERATING && breakdown) {
    118:       PetscCall(PetscInfo(eps,"Breakdown in Arnoldi method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta));
    119:       PetscCall(EPSGetStartVector(eps,k,&breakdown));
    120:       if (breakdown) {
    121:         eps->reason = EPS_DIVERGED_BREAKDOWN;
    122:         PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
    123:       }
    124:     }
    125:     eps->nconv = k;
    126:     PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv));
    127:   }
    128:   PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE));
    129:   PetscFunctionReturn(PETSC_SUCCESS);
    130: }

    132: PetscErrorCode EPSSetFromOptions_Arnoldi(EPS eps,PetscOptionItems *PetscOptionsObject)
    133: {
    134:   PetscBool      set,val;
    135:   EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI*)eps->data;

    137:   PetscFunctionBegin;
    138:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS Arnoldi Options");

    140:     PetscCall(PetscOptionsBool("-eps_arnoldi_delayed","Use delayed reorthogonalization","EPSArnoldiSetDelayed",arnoldi->delayed,&val,&set));
    141:     if (set) PetscCall(EPSArnoldiSetDelayed(eps,val));

    143:   PetscOptionsHeadEnd();
    144:   PetscFunctionReturn(PETSC_SUCCESS);
    145: }

    147: static PetscErrorCode EPSArnoldiSetDelayed_Arnoldi(EPS eps,PetscBool delayed)
    148: {
    149:   EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data;

    151:   PetscFunctionBegin;
    152:   arnoldi->delayed = delayed;
    153:   PetscFunctionReturn(PETSC_SUCCESS);
    154: }

    156: /*@
    157:    EPSArnoldiSetDelayed - Activates or deactivates delayed reorthogonalization
    158:    in the Arnoldi iteration.

    160:    Logically Collective

    162:    Input Parameters:
    163: +  eps - the eigenproblem solver context
    164: -  delayed - boolean flag

    166:    Options Database Key:
    167: .  -eps_arnoldi_delayed - Activates delayed reorthogonalization in Arnoldi

    169:    Note:
    170:    Delayed reorthogonalization is an aggressive optimization for the Arnoldi
    171:    eigensolver than may provide better scalability, but sometimes makes the
    172:    solver converge less than the default algorithm.

    174:    Level: advanced

    176: .seealso: EPSArnoldiGetDelayed()
    177: @*/
    178: PetscErrorCode EPSArnoldiSetDelayed(EPS eps,PetscBool delayed)
    179: {
    180:   PetscFunctionBegin;
    183:   PetscTryMethod(eps,"EPSArnoldiSetDelayed_C",(EPS,PetscBool),(eps,delayed));
    184:   PetscFunctionReturn(PETSC_SUCCESS);
    185: }

    187: static PetscErrorCode EPSArnoldiGetDelayed_Arnoldi(EPS eps,PetscBool *delayed)
    188: {
    189:   EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data;

    191:   PetscFunctionBegin;
    192:   *delayed = arnoldi->delayed;
    193:   PetscFunctionReturn(PETSC_SUCCESS);
    194: }

    196: /*@
    197:    EPSArnoldiGetDelayed - Gets the type of reorthogonalization used during the Arnoldi
    198:    iteration.

    200:    Not Collective

    202:    Input Parameter:
    203: .  eps - the eigenproblem solver context

    205:    Output Parameter:
    206: .  delayed - boolean flag indicating if delayed reorthogonalization has been enabled

    208:    Level: advanced

    210: .seealso: EPSArnoldiSetDelayed()
    211: @*/
    212: PetscErrorCode EPSArnoldiGetDelayed(EPS eps,PetscBool *delayed)
    213: {
    214:   PetscFunctionBegin;
    217:   PetscUseMethod(eps,"EPSArnoldiGetDelayed_C",(EPS,PetscBool*),(eps,delayed));
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: PetscErrorCode EPSDestroy_Arnoldi(EPS eps)
    222: {
    223:   PetscFunctionBegin;
    224:   PetscCall(PetscFree(eps->data));
    225:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",NULL));
    226:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",NULL));
    227:   PetscFunctionReturn(PETSC_SUCCESS);
    228: }

    230: PetscErrorCode EPSView_Arnoldi(EPS eps,PetscViewer viewer)
    231: {
    232:   PetscBool      isascii;
    233:   EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI*)eps->data;

    235:   PetscFunctionBegin;
    236:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    237:   if (isascii && arnoldi->delayed) PetscCall(PetscViewerASCIIPrintf(viewer,"  using delayed reorthogonalization\n"));
    238:   PetscFunctionReturn(PETSC_SUCCESS);
    239: }

    241: SLEPC_EXTERN PetscErrorCode EPSCreate_Arnoldi(EPS eps)
    242: {
    243:   EPS_ARNOLDI    *ctx;

    245:   PetscFunctionBegin;
    246:   PetscCall(PetscNew(&ctx));
    247:   eps->data = (void*)ctx;

    249:   eps->useds = PETSC_TRUE;

    251:   eps->ops->solve          = EPSSolve_Arnoldi;
    252:   eps->ops->setup          = EPSSetUp_Arnoldi;
    253:   eps->ops->setupsort      = EPSSetUpSort_Default;
    254:   eps->ops->setfromoptions = EPSSetFromOptions_Arnoldi;
    255:   eps->ops->destroy        = EPSDestroy_Arnoldi;
    256:   eps->ops->view           = EPSView_Arnoldi;
    257:   eps->ops->backtransform  = EPSBackTransform_Default;
    258:   eps->ops->computevectors = EPSComputeVectors_Schur;

    260:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",EPSArnoldiSetDelayed_Arnoldi));
    261:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",EPSArnoldiGetDelayed_Arnoldi));
    262:   PetscFunctionReturn(PETSC_SUCCESS);
    263: }