Date: 2020-01-13T12:01:19+00:00

Actual source code: qarnoldi.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 quadratic eigensolver: "qarnoldi"

     13:    Method: Q-Arnoldi

     15:    Algorithm:

     17:        Quadratic Arnoldi with Krylov-Schur type restart.

     19:    References:

     21:        [1] K. Meerbergen, "The Quadratic Arnoldi method for the solution
     22:            of the quadratic eigenvalue problem", SIAM J. Matrix Anal.
     23:            Appl. 30(4):1462-1482, 2008.
     24: */

     26: #include <slepc/private/pepimpl.h>    /*I "slepcpep.h" I*/
     27: #include <petscblaslapack.h>

     29: typedef struct {
     30:   PetscReal keep;         /* restart parameter */
     31:   PetscBool lock;         /* locking/non-locking variant */
     32: } PEP_QARNOLDI;

     34: PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
     35: {
     37:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
     38:   PetscBool      shift,sinv,flg;

     41:   pep->lineariz = PETSC_TRUE;
     42:   PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
     43:   if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
     44:   if (!pep->max_it) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);

     46:   PetscObjectTypeCompare((PetscObject)pep->st,STSHIFT,&shift);
     47:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
     48:   if (!shift && !sinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only STSHIFT and STSINVERT spectral transformations can be used");
     49:   if (!pep->which) {
     50:     if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
     51:     else pep->which = PEP_LARGEST_MAGNITUDE;
     52:   }
     53:   if (pep->which==PEP_ALL) SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of pep->which");

     55:   if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver only available for quadratic problems");
     56:   if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver not implemented for non-monomial bases");
     57:   STGetTransform(pep->st,&flg);
     58:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");

     60:   /* set default extraction */
     61:   if (!pep->extract) {
     62:     pep->extract = PEP_EXTRACT_NONE;
     63:   }
     64:   if (pep->extract!=PEP_EXTRACT_NONE) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver does not support requested extraction");

     66:   if (!ctx->keep) ctx->keep = 0.5;

     68:   PEPAllocateSolution(pep,0);
     69:   PEPSetWorkVecs(pep,4);

     71:   DSSetType(pep->ds,DSNHEP);
     72:   DSSetExtraRow(pep->ds,PETSC_TRUE);
     73:   DSAllocate(pep->ds,pep->ncv+1);

     75:   return(0);
     76: }

     78: PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
     79: {
     81:   PetscInt       i,k=pep->nconv,ldds;
     82:   PetscScalar    *X,*pX0;
     83:   Mat            X0;

     86:   if (pep->nconv==0) return(0);
     87:   DSGetLeadingDimension(pep->ds,&ldds);
     88:   DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
     89:   DSGetArray(pep->ds,DS_MAT_X,&X);

     91:   /* update vectors V = V*X */
     92:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&X0);
     93:   MatDenseGetArray(X0,&pX0);
     94:   for (i=0;i<k;i++) {
     95:     PetscArraycpy(pX0+i*k,X+i*ldds,k);
     96:   }
     97:   MatDenseRestoreArray(X0,&pX0);
     98:   BVMultInPlace(pep->V,X0,0,k);
     99:   MatDestroy(&X0);
    100:   DSRestoreArray(pep->ds,DS_MAT_X,&X);
    101:   return(0);
    102: }

    104: /*
    105:   Compute a step of Classical Gram-Schmidt orthogonalization
    106: */
    107: static PetscErrorCode PEPQArnoldiCGS(PEP pep,PetscScalar *H,PetscBLASInt ldh,PetscScalar *h,PetscBLASInt j,BV V,Vec t,Vec v,Vec w,PetscReal *onorm,PetscReal *norm,PetscScalar *work)
    108: {
    110:   PetscBLASInt   ione = 1,j_1 = j+1;
    111:   PetscReal      x,y;
    112:   PetscScalar    dot,one = 1.0,zero = 0.0;

    115:   /* compute norm of v and w */
    116:   if (onorm) {
    117:     VecNorm(v,NORM_2,&x);
    118:     VecNorm(w,NORM_2,&y);
    119:     *onorm = PetscSqrtReal(x*x+y*y);
    120:   }

    122:   /* orthogonalize: compute h */
    123:   BVDotVec(V,v,h);
    124:   BVDotVec(V,w,work);
    125:   if (j>0)
    126:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
    127:   VecDot(w,t,&dot);
    128:   h[j] += dot;

    130:   /* orthogonalize: update v and w */
    131:   BVMultVec(V,-1.0,1.0,v,h);
    132:   if (j>0) {
    133:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
    134:     BVMultVec(V,-1.0,1.0,w,work);
    135:   }
    136:   VecAXPY(w,-h[j],t);

    138:   /* compute norm of v and w */
    139:   if (norm) {
    140:     VecNorm(v,NORM_2,&x);
    141:     VecNorm(w,NORM_2,&y);
    142:     *norm = PetscSqrtReal(x*x+y*y);
    143:   }
    144:   return(0);
    145: }

    147: /*
    148:   Compute a run of Q-Arnoldi iterations
    149: */
    150: static PetscErrorCode PEPQArnoldi(PEP pep,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
    151: {
    152:   PetscErrorCode     ierr;
    153:   PetscInt           i,j,l,m = *M;
    154:   Vec                t = pep->work[2],u = pep->work[3];
    155:   BVOrthogRefineType refinement;
    156:   PetscReal          norm=0.0,onorm,eta;
    157:   PetscScalar        *c = work + m;

    160:   BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL);
    161:   BVInsertVec(pep->V,k,v);
    162:   for (j=k;j<m;j++) {
    163:     /* apply operator */
    164:     VecCopy(w,t);
    165:     if (pep->Dr) {
    166:       VecPointwiseMult(v,v,pep->Dr);
    167:     }
    168:     STMatMult(pep->st,0,v,u);
    169:     VecCopy(t,v);
    170:     if (pep->Dr) {
    171:       VecPointwiseMult(t,t,pep->Dr);
    172:     }
    173:     STMatMult(pep->st,1,t,w);
    174:     VecAXPY(u,pep->sfactor,w);
    175:     STMatSolve(pep->st,u,w);
    176:     VecScale(w,-1.0/(pep->sfactor*pep->sfactor));
    177:     if (pep->Dr) {
    178:       VecPointwiseDivide(w,w,pep->Dr);
    179:     }
    180:     VecCopy(v,t);
    181:     BVSetActiveColumns(pep->V,0,j+1);

    183:     /* orthogonalize */
    184:     switch (refinement) {
    185:       case BV_ORTHOG_REFINE_NEVER:
    186:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work);
    187:         *breakdown = PETSC_FALSE;
    188:         break;
    189:       case BV_ORTHOG_REFINE_ALWAYS:
    190:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work);
    191:         PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work);
    192:         for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
    193:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
    194:         else *breakdown = PETSC_FALSE;
    195:         break;
    196:       case BV_ORTHOG_REFINE_IFNEEDED:
    197:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work);
    198:         /* ||q|| < eta ||h|| */
    199:         l = 1;
    200:         while (l<3 && norm < eta * onorm) {
    201:           l++;
    202:           onorm = norm;
    203:           PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work);
    204:           for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
    205:         }
    206:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
    207:         else *breakdown = PETSC_FALSE;
    208:         break;
    209:     }
    210:     VecScale(v,1.0/norm);
    211:     VecScale(w,1.0/norm);

    213:     H[j+1+ldh*j] = norm;
    214:     if (j<m-1) {
    215:       BVInsertVec(pep->V,j+1,v);
    216:     }
    217:   }
    218:   *beta = norm;
    219:   return(0);
    220: }

    222: PetscErrorCode PEPSolve_QArnoldi(PEP pep)
    223: {
    225:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
    226:   PetscInt       j,k,l,lwork,nv,ld,newn,nconv;
    227:   Vec            v=pep->work[0],w=pep->work[1];
    228:   Mat            Q;
    229:   PetscScalar    *S,*work;
    230:   PetscReal      beta=0.0,norm,x,y;
    231:   PetscBool      breakdown=PETSC_FALSE,sinv;

    234:   DSGetLeadingDimension(pep->ds,&ld);
    235:   lwork = 7*pep->ncv;
    236:   PetscMalloc1(lwork,&work);
    237:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
    238:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
    239:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

    241:   /* Get the starting Arnoldi vector */
    242:   for (j=0;j<2;j++) {
    243:     if (j>=pep->nini) {
    244:       BVSetRandomColumn(pep->V,j);
    245:     }
    246:   }
    247:   BVCopyVec(pep->V,0,v);
    248:   BVCopyVec(pep->V,1,w);
    249:   VecNorm(v,NORM_2,&x);
    250:   VecNorm(w,NORM_2,&y);
    251:   norm = PetscSqrtReal(x*x+y*y);
    252:   VecScale(v,1.0/norm);
    253:   VecScale(w,1.0/norm);

    255:   /* clean projected matrix (including the extra-arrow) */
    256:   DSGetArray(pep->ds,DS_MAT_A,&S);
    257:   PetscArrayzero(S,ld*ld);
    258:   DSRestoreArray(pep->ds,DS_MAT_A,&S);

    260:    /* Restart loop */
    261:   l = 0;
    262:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    263:     pep->its++;

    265:     /* Compute an nv-step Arnoldi factorization */
    266:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
    267:     DSGetArray(pep->ds,DS_MAT_A,&S);
    268:     PEPQArnoldi(pep,S,ld,pep->nconv+l,&nv,v,w,&beta,&breakdown,work);
    269:     DSRestoreArray(pep->ds,DS_MAT_A,&S);
    270:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
    271:     if (l==0) {
    272:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
    273:     } else {
    274:       DSSetState(pep->ds,DS_STATE_RAW);
    275:     }
    276:     BVSetActiveColumns(pep->V,pep->nconv,nv);

    278:     /* Solve projected problem */
    279:     DSSolve(pep->ds,pep->eigr,pep->eigi);
    280:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
    281:     DSUpdateExtraRow(pep->ds);
    282:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

    284:     /* Check convergence */
    285:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
    286:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
    287:     nconv = k;

    289:     /* Update l */
    290:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
    291:     else l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    292:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

    294:     if (pep->reason == PEP_CONVERGED_ITERATING) {
    295:       if (breakdown) {
    296:         /* Stop if breakdown */
    297:         PetscInfo2(pep,"Breakdown Quadratic Arnoldi method (it=%D norm=%g)\n",pep->its,(double)beta);
    298:         pep->reason = PEP_DIVERGED_BREAKDOWN;
    299:       } else {
    300:         /* Prepare the Rayleigh quotient for restart */
    301:         DSTruncate(pep->ds,k+l);
    302:         DSGetDimensions(pep->ds,&newn,NULL,NULL,NULL,NULL);
    303:         l = newn-k;
    304:       }
    305:     }
    306:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    307:     DSGetMat(pep->ds,DS_MAT_Q,&Q);
    308:     BVMultInPlace(pep->V,Q,pep->nconv,k+l);
    309:     MatDestroy(&Q);

    311:     pep->nconv = k;
    312:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
    313:   }
    314:   BVSetActiveColumns(pep->V,0,pep->nconv);
    315:   for (j=0;j<pep->nconv;j++) {
    316:     pep->eigr[j] *= pep->sfactor;
    317:     pep->eigi[j] *= pep->sfactor;
    318:   }

    320:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
    321:   RGPopScale(pep->rg);

    323:   /* truncate Schur decomposition and change the state to raw so that
    324:      DSVectors() computes eigenvectors from scratch */
    325:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
    326:   DSSetState(pep->ds,DS_STATE_RAW);
    327:   PetscFree(work);
    328:   return(0);
    329: }

    331: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
    332: {
    333:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    336:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
    337:   else {
    338:     if (keep<0.1 || keep>0.9) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
    339:     ctx->keep = keep;
    340:   }
    341:   return(0);
    342: }

    344: /*@
    345:    PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
    346:    method, in particular the proportion of basis vectors that must be kept
    347:    after restart.

    349:    Logically Collective on pep

    351:    Input Parameters:
    352: +  pep  - the eigenproblem solver context
    353: -  keep - the number of vectors to be kept at restart

    355:    Options Database Key:
    356: .  -pep_qarnoldi_restart - Sets the restart parameter

    358:    Notes:
    359:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

    361:    Level: advanced

    363: .seealso: PEPQArnoldiGetRestart()
    364: @*/
    365: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
    366: {

    372:   PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
    373:   return(0);
    374: }

    376: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
    377: {
    378:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    381:   *keep = ctx->keep;
    382:   return(0);
    383: }

    385: /*@
    386:    PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.

    388:    Not Collective

    390:    Input Parameter:
    391: .  pep - the eigenproblem solver context

    393:    Output Parameter:
    394: .  keep - the restart parameter

    396:    Level: advanced

    398: .seealso: PEPQArnoldiSetRestart()
    399: @*/
    400: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
    401: {

    407:   PetscUseMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
    408:   return(0);
    409: }

    411: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
    412: {
    413:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    416:   ctx->lock = lock;
    417:   return(0);
    418: }

    420: /*@
    421:    PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
    422:    the Q-Arnoldi method.

    424:    Logically Collective on pep

    426:    Input Parameters:
    427: +  pep  - the eigenproblem solver context
    428: -  lock - true if the locking variant must be selected

    430:    Options Database Key:
    431: .  -pep_qarnoldi_locking - Sets the locking flag

    433:    Notes:
    434:    The default is to keep all directions in the working subspace even if
    435:    already converged to working accuracy (the non-locking variant).
    436:    This behaviour can be changed so that converged eigenpairs are locked
    437:    when the method restarts.

    439:    Note that the default behaviour is the opposite to Krylov solvers in EPS.

    441:    Level: advanced

    443: .seealso: PEPQArnoldiGetLocking()
    444: @*/
    445: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
    446: {

    452:   PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
    453:   return(0);
    454: }

    456: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
    457: {
    458:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    461:   *lock = ctx->lock;
    462:   return(0);
    463: }

    465: /*@
    466:    PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.

    468:    Not Collective

    470:    Input Parameter:
    471: .  pep - the eigenproblem solver context

    473:    Output Parameter:
    474: .  lock - the locking flag

    476:    Level: advanced

    478: .seealso: PEPQArnoldiSetLocking()
    479: @*/
    480: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
    481: {

    487:   PetscUseMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
    488:   return(0);
    489: }

    491: PetscErrorCode PEPSetFromOptions_QArnoldi(PetscOptionItems *PetscOptionsObject,PEP pep)
    492: {
    494:   PetscBool      flg,lock;
    495:   PetscReal      keep;

    498:   PetscOptionsHead(PetscOptionsObject,"PEP Q-Arnoldi Options");

    500:     PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg);
    501:     if (flg) { PEPQArnoldiSetRestart(pep,keep); }

    503:     PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg);
    504:     if (flg) { PEPQArnoldiSetLocking(pep,lock); }

    506:   PetscOptionsTail();
    507:   return(0);
    508: }

    510: PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
    511: {
    513:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
    514:   PetscBool      isascii;

    517:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    518:   if (isascii) {
    519:     PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
    520:     PetscViewerASCIIPrintf(viewer,"  using the %slocking variant\n",ctx->lock?"":"non-");
    521:   }
    522:   return(0);
    523: }

    525: PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
    526: {

    530:   PetscFree(pep->data);
    531:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL);
    532:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL);
    533:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL);
    534:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL);
    535:   return(0);
    536: }

    538: SLEPC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
    539: {
    540:   PEP_QARNOLDI   *ctx;

    544:   PetscNewLog(pep,&ctx);
    545:   pep->data = (void*)ctx;
    546:   ctx->lock = PETSC_TRUE;

    548:   pep->ops->solve          = PEPSolve_QArnoldi;
    549:   pep->ops->setup          = PEPSetUp_QArnoldi;
    550:   pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
    551:   pep->ops->destroy        = PEPDestroy_QArnoldi;
    552:   pep->ops->view           = PEPView_QArnoldi;
    553:   pep->ops->backtransform  = PEPBackTransform_Default;
    554:   pep->ops->computevectors = PEPComputeVectors_Default;
    555:   pep->ops->extractvectors = PEPExtractVectors_QArnoldi;
    556:   pep->ops->setdefaultst   = PEPSetDefaultST_Transform;

    558:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi);
    559:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi);
    560:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi);
    561:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi);
    562:   return(0);
    563: }