Date: 2020-01-13T12:00:11+00:00

Actual source code: arnoldi.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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 http://slepc.upv.es.
     23: */

     25: #include <slepc/private/epsimpl.h>                /*I "slepceps.h" I*/

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

     31: PetscErrorCode EPSSetUp_Arnoldi(EPS eps)
     32: {

     36:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
     37:   if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd");
     38:   if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     39:   if (!eps->which) { EPSSetWhichEigenpairs_Default(eps); }
     40:   if (eps->which==EPS_ALL || (eps->ishermitian && eps->ispositive && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which");

     42:   if (!eps->extraction) {
     43:     EPSSetExtraction(eps,EPS_RITZ);
     44:   }
     45:   if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");

     47:   EPSAllocateSolution(eps,1);
     48:   EPS_SetInnerProduct(eps);
     49:   DSSetType(eps->ds,DSNHEP);
     50:   if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) {
     51:     DSSetRefined(eps->ds,PETSC_TRUE);
     52:   }
     53:   DSSetExtraRow(eps->ds,PETSC_TRUE);
     54:   DSAllocate(eps->ds,eps->ncv+1);

     56:   if (eps->isgeneralized && eps->ishermitian && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method does not work for indefinite problems");
     57:   return(0);
     58: }

     60: PetscErrorCode EPSSolve_Arnoldi(EPS eps)
     61: {
     62:   PetscErrorCode     ierr;
     63:   PetscInt           k,nv,ld;
     64:   Mat                U;
     65:   PetscScalar        *H;
     66:   PetscReal          beta,gamma=1.0;
     67:   PetscBool          breakdown,harmonic,refined;
     68:   BVOrthogRefineType orthog_ref;
     69:   EPS_ARNOLDI        *arnoldi = (EPS_ARNOLDI*)eps->data;

     72:   DSGetLeadingDimension(eps->ds,&ld);
     73:   DSGetRefined(eps->ds,&refined);
     74:   harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
     75:   BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL,NULL);

     77:   /* Get the starting Arnoldi vector */
     78:   EPSGetStartVector(eps,0,NULL);

     80:   /* Restart loop */
     81:   while (eps->reason == EPS_CONVERGED_ITERATING) {
     82:     eps->its++;

     84:     /* Compute an nv-step Arnoldi factorization */
     85:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
     86:     DSSetDimensions(eps->ds,nv,0,eps->nconv,0);
     87:     DSGetArray(eps->ds,DS_MAT_A,&H);
     88:     if (!arnoldi->delayed) {
     89:       EPSBasicArnoldi(eps,PETSC_FALSE,H,ld,eps->nconv,&nv,&beta,&breakdown);
     90:     } else if (orthog_ref == BV_ORTHOG_REFINE_NEVER) {
     91:       EPSDelayedArnoldi1(eps,H,ld,eps->nconv,&nv,&beta,&breakdown);
     92:     } else {
     93:       EPSDelayedArnoldi(eps,H,ld,eps->nconv,&nv,&beta,&breakdown);
     94:     }
     95:     DSRestoreArray(eps->ds,DS_MAT_A,&H);
     96:     DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
     97:     BVSetActiveColumns(eps->V,eps->nconv,nv);

     99:     /* Compute translation of Krylov decomposition if harmonic extraction used */
    100:     if (harmonic) {
    101:       DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,NULL,&gamma);
    102:     }

    104:     /* Solve projected problem */
    105:     DSSolve(eps->ds,eps->eigr,eps->eigi);
    106:     DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
    107:     DSUpdateExtraRow(eps->ds);
    108:     DSSynchronize(eps->ds,eps->eigr,eps->eigi);

    110:     /* Check convergence */
    111:     EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,0.0,gamma,&k);
    112:     if (refined) {
    113:       DSGetMat(eps->ds,DS_MAT_X,&U);
    114:       BVMultInPlace(eps->V,U,eps->nconv,k+1);
    115:       MatDestroy(&U);
    116:       BVOrthonormalizeColumn(eps->V,k,PETSC_FALSE,NULL,NULL);
    117:     } else {
    118:       DSGetMat(eps->ds,DS_MAT_Q,&U);
    119:       BVMultInPlace(eps->V,U,eps->nconv,PetscMin(k+1,nv));
    120:       MatDestroy(&U);
    121:     }
    122:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
    123:     if (eps->reason == EPS_CONVERGED_ITERATING && breakdown) {
    124:       PetscInfo2(eps,"Breakdown in Arnoldi method (it=%D norm=%g)\n",eps->its,(double)beta);
    125:       EPSGetStartVector(eps,k,&breakdown);
    126:       if (breakdown) {
    127:         eps->reason = EPS_DIVERGED_BREAKDOWN;
    128:         PetscInfo(eps,"Unable to generate more start vectors\n");
    129:       }
    130:     }
    131:     eps->nconv = k;
    132:     EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
    133:   }

    135:   /* truncate Schur decomposition and change the state to raw so that
    136:      DSVectors() computes eigenvectors from scratch */
    137:   DSSetDimensions(eps->ds,eps->nconv,0,0,0);
    138:   DSSetState(eps->ds,DS_STATE_RAW);
    139:   return(0);
    140: }

    142: PetscErrorCode EPSSetFromOptions_Arnoldi(PetscOptionItems *PetscOptionsObject,EPS eps)
    143: {
    145:   PetscBool      set,val;
    146:   EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI*)eps->data;

    149:   PetscOptionsHead(PetscOptionsObject,"EPS Arnoldi Options");

    151:     PetscOptionsBool("-eps_arnoldi_delayed","Use delayed reorthogonalization","EPSArnoldiSetDelayed",arnoldi->delayed,&val,&set);
    152:     if (set) { EPSArnoldiSetDelayed(eps,val); }

    154:   PetscOptionsTail();
    155:   return(0);
    156: }

    158: static PetscErrorCode EPSArnoldiSetDelayed_Arnoldi(EPS eps,PetscBool delayed)
    159: {
    160:   EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data;

    163:   arnoldi->delayed = delayed;
    164:   return(0);
    165: }

    167: /*@
    168:    EPSArnoldiSetDelayed - Activates or deactivates delayed reorthogonalization
    169:    in the Arnoldi iteration.

    171:    Logically Collective on eps

    173:    Input Parameters:
    174: +  eps - the eigenproblem solver context
    175: -  delayed - boolean flag

    177:    Options Database Key:
    178: .  -eps_arnoldi_delayed - Activates delayed reorthogonalization in Arnoldi

    180:    Note:
    181:    Delayed reorthogonalization is an aggressive optimization for the Arnoldi
    182:    eigensolver than may provide better scalability, but sometimes makes the
    183:    solver converge less than the default algorithm.

    185:    Level: advanced

    187: .seealso: EPSArnoldiGetDelayed()
    188: @*/
    189: PetscErrorCode EPSArnoldiSetDelayed(EPS eps,PetscBool delayed)
    190: {

    196:   PetscTryMethod(eps,"EPSArnoldiSetDelayed_C",(EPS,PetscBool),(eps,delayed));
    197:   return(0);
    198: }

    200: static PetscErrorCode EPSArnoldiGetDelayed_Arnoldi(EPS eps,PetscBool *delayed)
    201: {
    202:   EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data;

    205:   *delayed = arnoldi->delayed;
    206:   return(0);
    207: }

    209: /*@
    210:    EPSArnoldiGetDelayed - Gets the type of reorthogonalization used during the Arnoldi
    211:    iteration.

    213:    Not Collective

    215:    Input Parameter:
    216: .  eps - the eigenproblem solver context

    218:    Input Parameter:
    219: .  delayed - boolean flag indicating if delayed reorthogonalization has been enabled

    221:    Level: advanced

    223: .seealso: EPSArnoldiSetDelayed()
    224: @*/
    225: PetscErrorCode EPSArnoldiGetDelayed(EPS eps,PetscBool *delayed)
    226: {

    232:   PetscUseMethod(eps,"EPSArnoldiGetDelayed_C",(EPS,PetscBool*),(eps,delayed));
    233:   return(0);
    234: }

    236: PetscErrorCode EPSDestroy_Arnoldi(EPS eps)
    237: {

    241:   PetscFree(eps->data);
    242:   PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",NULL);
    243:   PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",NULL);
    244:   return(0);
    245: }

    247: PetscErrorCode EPSView_Arnoldi(EPS eps,PetscViewer viewer)
    248: {
    250:   PetscBool      isascii;
    251:   EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI*)eps->data;

    254:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    255:   if (isascii && arnoldi->delayed) {
    256:     PetscViewerASCIIPrintf(viewer,"  using delayed reorthogonalization\n");
    257:   }
    258:   return(0);
    259: }

    261: SLEPC_EXTERN PetscErrorCode EPSCreate_Arnoldi(EPS eps)
    262: {
    263:   EPS_ARNOLDI    *ctx;

    267:   PetscNewLog(eps,&ctx);
    268:   eps->data = (void*)ctx;

    270:   eps->useds = PETSC_TRUE;

    272:   eps->ops->solve          = EPSSolve_Arnoldi;
    273:   eps->ops->setup          = EPSSetUp_Arnoldi;
    274:   eps->ops->setfromoptions = EPSSetFromOptions_Arnoldi;
    275:   eps->ops->destroy        = EPSDestroy_Arnoldi;
    276:   eps->ops->view           = EPSView_Arnoldi;
    277:   eps->ops->backtransform  = EPSBackTransform_Default;
    278:   eps->ops->computevectors = EPSComputeVectors_Schur;

    280:   PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",EPSArnoldiSetDelayed_Arnoldi);
    281:   PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",EPSArnoldiGetDelayed_Arnoldi);
    282:   return(0);
    283: }