Date: 2016-03-29T14:58:59+00:00

Actual source code: qarnoldi.c
slepc-3.6.3 2016-03-29
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      1: /*

      3:    SLEPc quadratic eigensolver: "qarnoldi"

      5:    Method: Q-Arnoldi

      7:    Algorithm:

      9:        Quadratic Arnoldi with Krylov-Schur type restart.

     11:    References:

     13:        [1] K. Meerbergen, "The Quadratic Arnoldi method for the solution
     14:            of the quadratic eigenvalue problem", SIAM J. Matrix Anal.
     15:            Appl. 30(4):1462-1482, 2008.

     17:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     18:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     19:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

     21:    This file is part of SLEPc.

     23:    SLEPc is free software: you can redistribute it and/or modify it under  the
     24:    terms of version 3 of the GNU Lesser General Public License as published by
     25:    the Free Software Foundation.

     27:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     28:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     29:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     30:    more details.

     32:    You  should have received a copy of the GNU Lesser General  Public  License
     33:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     34:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35: */

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

     40: typedef struct {
     41:   PetscReal keep;         /* restart parameter */
     42:   PetscBool lock;         /* locking/non-locking variant */
     43: } PEP_QARNOLDI;

     47: PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
     48: {
     50:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
     51:   PetscBool      sinv,flg;

     54:   pep->lineariz = PETSC_TRUE;
     55:   PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
     56:   if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
     57:   if (!pep->max_it) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);
     58:   if (!pep->which) {
     59:     PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
     60:     if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
     61:     else pep->which = PEP_LARGEST_MAGNITUDE;
     62:   }

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

     69:   /* set default extraction */
     70:   if (!pep->extract) {
     71:     pep->extract = PEP_EXTRACT_NONE;
     72:   }
     73:   if (pep->extract!=PEP_EXTRACT_NONE) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver does not support requested extraction");
     74:
     75:   if (!ctx->keep) ctx->keep = 0.5;

     77:   PEPAllocateSolution(pep,0);
     78:   PEPSetWorkVecs(pep,4);

     80:   DSSetType(pep->ds,DSNHEP);
     81:   DSSetExtraRow(pep->ds,PETSC_TRUE);
     82:   DSAllocate(pep->ds,pep->ncv+1);

     84:   /* process starting vector */
     85:   if (pep->nini>-2) {
     86:     BVSetRandomColumn(pep->V,0,pep->rand);
     87:     BVSetRandomColumn(pep->V,1,pep->rand);
     88:   } else {
     89:     BVInsertVec(pep->V,0,pep->IS[0]);
     90:     BVInsertVec(pep->V,1,pep->IS[1]);
     91:   }
     92:   if (pep->nini<0) {
     93:     SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
     94:   }
     95:   return(0);
     96: }

    100: PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
    101: {
    103:   PetscInt       i,k=pep->nconv,ldds;
    104:   PetscScalar    *X,*pX0;
    105:   Mat            X0;

    108:   if (pep->nconv==0) return(0);
    109:   DSGetLeadingDimension(pep->ds,&ldds);
    110:   DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
    111:   DSGetArray(pep->ds,DS_MAT_X,&X);

    113:   /* update vectors V = V*X */
    114:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&X0);
    115:   MatDenseGetArray(X0,&pX0);
    116:   for (i=0;i<k;i++) {
    117:     PetscMemcpy(pX0+i*k,X+i*ldds,k*sizeof(PetscScalar));
    118:   }
    119:   MatDenseRestoreArray(X0,&pX0);
    120:   BVSetActiveColumns(pep->V,0,k);
    121:   BVMultInPlace(pep->V,X0,0,k);
    122:   MatDestroy(&X0);
    123:   BVSetActiveColumns(pep->V,0,k);
    124:   DSRestoreArray(pep->ds,DS_MAT_X,&X);
    125:   return(0);
    126: }

    130: /*
    131:   Compute a step of Classical Gram-Schmidt orthogonalization
    132: */
    133: 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)
    134: {
    136:   PetscBLASInt   ione = 1,j_1 = j+1;
    137:   PetscReal      x,y;
    138:   PetscScalar    dot,one = 1.0,zero = 0.0;

    141:   /* compute norm of v and w */
    142:   if (onorm) {
    143:     VecNorm(v,NORM_2,&x);
    144:     VecNorm(w,NORM_2,&y);
    145:     *onorm = PetscSqrtReal(x*x+y*y);
    146:   }

    148:   /* orthogonalize: compute h */
    149:   BVDotVec(V,v,h);
    150:   BVDotVec(V,w,work);
    151:   if (j>0)
    152:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
    153:   VecDot(w,t,&dot);
    154:   h[j] += dot;

    156:   /* orthogonalize: update v and w */
    157:   BVMultVec(V,-1.0,1.0,v,h);
    158:   if (j>0) {
    159:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
    160:     BVMultVec(V,-1.0,1.0,w,work);
    161:   }
    162:   VecAXPY(w,-h[j],t);

    164:   /* compute norm of v and w */
    165:   if (norm) {
    166:     VecNorm(v,NORM_2,&x);
    167:     VecNorm(w,NORM_2,&y);
    168:     *norm = PetscSqrtReal(x*x+y*y);
    169:   }
    170:   return(0);
    171: }

    175: /*
    176:   Compute a run of Q-Arnoldi iterations
    177: */
    178: static PetscErrorCode PEPQArnoldi(PEP pep,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
    179: {
    180:   PetscErrorCode     ierr;
    181:   PetscInt           i,j,l,m = *M;
    182:   Vec                t = pep->work[2],u = pep->work[3];
    183:   BVOrthogRefineType refinement;
    184:   PetscReal          norm,onorm,eta;
    185:   PetscScalar        *c = work + m;

    188:   BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL);
    189:   BVInsertVec(pep->V,k,v);
    190:   for (j=k;j<m;j++) {
    191:     /* apply operator */
    192:     VecCopy(w,t);
    193:     if (pep->Dr) {
    194:       VecPointwiseMult(v,v,pep->Dr);
    195:     }
    196:     STMatMult(pep->st,0,v,u);
    197:     VecCopy(t,v);
    198:     if (pep->Dr) {
    199:       VecPointwiseMult(t,t,pep->Dr);
    200:     }
    201:     STMatMult(pep->st,1,t,w);
    202:     VecAXPY(u,pep->sfactor,w);
    203:     STMatSolve(pep->st,u,w);
    204:     VecScale(w,-1.0/(pep->sfactor*pep->sfactor));
    205:     if (pep->Dr) {
    206:       VecPointwiseDivide(w,w,pep->Dr);
    207:     }
    208:     VecCopy(v,t);
    209:     BVSetActiveColumns(pep->V,0,j+1);

    211:     /* orthogonalize */
    212:     switch (refinement) {
    213:       case BV_ORTHOG_REFINE_NEVER:
    214:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work);
    215:         *breakdown = PETSC_FALSE;
    216:         break;
    217:       case BV_ORTHOG_REFINE_ALWAYS:
    218:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work);
    219:         PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work);
    220:         for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
    221:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
    222:         else *breakdown = PETSC_FALSE;
    223:         break;
    224:       case BV_ORTHOG_REFINE_IFNEEDED:
    225:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work);
    226:         /* ||q|| < eta ||h|| */
    227:         l = 1;
    228:         while (l<3 && norm < eta * onorm) {
    229:           l++;
    230:           onorm = norm;
    231:           PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work);
    232:           for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
    233:         }
    234:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
    235:         else *breakdown = PETSC_FALSE;
    236:         break;
    237:       default: SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of ip->orth_ref");
    238:     }
    239:     VecScale(v,1.0/norm);
    240:     VecScale(w,1.0/norm);

    242:     H[j+1+ldh*j] = norm;
    243:     if (j<m-1) {
    244:       BVInsertVec(pep->V,j+1,v);
    245:     }
    246:   }
    247:   *beta = norm;
    248:   return(0);
    249: }

    253: PetscErrorCode PEPSolve_QArnoldi(PEP pep)
    254: {
    256:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
    257:   PetscInt       j,k,l,lwork,nv,ld,newn,nconv;
    258:   Vec            v=pep->work[0],w=pep->work[1];
    259:   Mat            Q;
    260:   PetscScalar    *S,*work;
    261:   PetscReal      beta=0.0,norm,x,y;
    262:   PetscBool      breakdown=PETSC_FALSE,sinv;

    265:   DSGetLeadingDimension(pep->ds,&ld);
    266:   lwork = 7*pep->ncv;
    267:   PetscMalloc1(lwork,&work);
    268:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
    269:   RGSetScale(pep->rg,sinv?1.0/pep->sfactor:pep->sfactor);
    270:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

    272:   /* Get the starting Arnoldi vector */
    273:   BVCopyVec(pep->V,0,v);
    274:   BVCopyVec(pep->V,1,w);
    275:   VecNorm(v,NORM_2,&x);
    276:   VecNorm(w,NORM_2,&y);
    277:   norm = PetscSqrtReal(x*x+y*y);
    278:   VecScale(v,1.0/norm);
    279:   VecScale(w,1.0/norm);

    281:    /* Restart loop */
    282:   l = 0;
    283:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    284:     pep->its++;

    286:     /* Compute an nv-step Arnoldi factorization */
    287:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
    288:     DSGetArray(pep->ds,DS_MAT_A,&S);
    289:     PEPQArnoldi(pep,S,ld,pep->nconv+l,&nv,v,w,&beta,&breakdown,work);
    290:     DSRestoreArray(pep->ds,DS_MAT_A,&S);
    291:     DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
    292:     if (l==0) {
    293:       DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
    294:     } else {
    295:       DSSetState(pep->ds,DS_STATE_RAW);
    296:     }
    297:     BVSetActiveColumns(pep->V,pep->nconv,nv);

    299:     /* Solve projected problem */
    300:     DSSolve(pep->ds,pep->eigr,pep->eigi);
    301:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
    302:     DSUpdateExtraRow(pep->ds);

    304:     /* Check convergence */
    305:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
    306:     if (pep->its >= pep->max_it) pep->reason = PEP_DIVERGED_ITS;
    307:     if (k >= pep->nev) pep->reason = PEP_CONVERGED_TOL;
    308:     nconv = k;

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

    315:     if (pep->reason == PEP_CONVERGED_ITERATING) {
    316:       if (breakdown) {
    317:         /* Stop if breakdown */
    318:         PetscInfo2(pep,"Breakdown Quadratic Arnoldi method (it=%D norm=%g)\n",pep->its,(double)beta);
    319:         pep->reason = PEP_DIVERGED_BREAKDOWN;
    320:       } else {
    321:         /* Prepare the Rayleigh quotient for restart */
    322:         DSTruncate(pep->ds,k+l);
    323:         DSGetDimensions(pep->ds,&newn,NULL,NULL,NULL,NULL);
    324:         l = newn-k;
    325:       }
    326:     }
    327:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    328:     DSGetMat(pep->ds,DS_MAT_Q,&Q);
    329:     BVMultInPlace(pep->V,Q,pep->nconv,k+l);
    330:     MatDestroy(&Q);

    332:     pep->nconv = k;
    333:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
    334:   }

    336:   for (j=0;j<pep->nconv;j++) {
    337:     pep->eigr[j] *= pep->sfactor;
    338:     pep->eigi[j] *= pep->sfactor;
    339:   }

    341:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
    342:   RGSetScale(pep->rg,1.0);

    344:   /* truncate Schur decomposition and change the state to raw so that
    345:      DSVectors() computes eigenvectors from scratch */
    346:   DSSetDimensions(pep->ds,pep->nconv,0,0,0);
    347:   DSSetState(pep->ds,DS_STATE_RAW);
    348:   PetscFree(work);
    349:   return(0);
    350: }

    354: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
    355: {
    356:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    359:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
    360:   else {
    361:     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]");
    362:     ctx->keep = keep;
    363:   }
    364:   return(0);
    365: }

    369: /*@
    370:    PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
    371:    method, in particular the proportion of basis vectors that must be kept
    372:    after restart.

    374:    Logically Collective on PEP

    376:    Input Parameters:
    377: +  pep  - the eigenproblem solver context
    378: -  keep - the number of vectors to be kept at restart

    380:    Options Database Key:
    381: .  -pep_qarnoldi_restart - Sets the restart parameter

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

    386:    Level: advanced

    388: .seealso: PEPQArnoldiGetRestart()
    389: @*/
    390: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
    391: {

    397:   PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
    398:   return(0);
    399: }

    403: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
    404: {
    405:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    408:   *keep = ctx->keep;
    409:   return(0);
    410: }

    414: /*@
    415:    PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.

    417:    Not Collective

    419:    Input Parameter:
    420: .  pep - the eigenproblem solver context

    422:    Output Parameter:
    423: .  keep - the restart parameter

    425:    Level: advanced

    427: .seealso: PEPQArnoldiSetRestart()
    428: @*/
    429: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
    430: {

    436:   PetscTryMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
    437:   return(0);
    438: }

    442: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
    443: {
    444:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    447:   ctx->lock = lock;
    448:   return(0);
    449: }

    453: /*@
    454:    PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
    455:    the Q-Arnoldi method.

    457:    Logically Collective on PEP

    459:    Input Parameters:
    460: +  pep  - the eigenproblem solver context
    461: -  lock - true if the locking variant must be selected

    463:    Options Database Key:
    464: .  -pep_qarnoldi_locking - Sets the locking flag

    466:    Notes:
    467:    The default is to keep all directions in the working subspace even if
    468:    already converged to working accuracy (the non-locking variant).
    469:    This behaviour can be changed so that converged eigenpairs are locked
    470:    when the method restarts.

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

    474:    Level: advanced

    476: .seealso: PEPQArnoldiGetLocking()
    477: @*/
    478: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
    479: {

    485:   PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
    486:   return(0);
    487: }

    491: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
    492: {
    493:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

    496:   *lock = ctx->lock;
    497:   return(0);
    498: }

    502: /*@
    503:    PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.

    505:    Not Collective

    507:    Input Parameter:
    508: .  pep - the eigenproblem solver context

    510:    Output Parameter:
    511: .  lock - the locking flag

    513:    Level: advanced

    515: .seealso: PEPQArnoldiSetLocking()
    516: @*/
    517: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
    518: {

    524:   PetscTryMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
    525:   return(0);
    526: }

    530: PetscErrorCode PEPSetFromOptions_QArnoldi(PetscOptions *PetscOptionsObject,PEP pep)
    531: {
    533:   PetscBool      flg,lock;
    534:   PetscReal      keep;

    537:   PetscOptionsHead(PetscOptionsObject,"PEP Q-Arnoldi Options");
    538:   PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg);
    539:   if (flg) {
    540:     PEPQArnoldiSetRestart(pep,keep);
    541:   }
    542:   PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg);
    543:   if (flg) {
    544:     PEPQArnoldiSetLocking(pep,lock);
    545:   }
    546:   PetscOptionsTail();
    547:   return(0);
    548: }

    552: PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
    553: {
    555:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
    556:   PetscBool      isascii;

    559:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    560:   if (isascii) {
    561:     PetscViewerASCIIPrintf(viewer,"  Q-Arnoldi: %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
    562:     PetscViewerASCIIPrintf(viewer,"  Q-Arnoldi: using the %slocking variant\n",ctx->lock?"":"non-");
    563:   }
    564:   return(0);
    565: }

    569: PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
    570: {

    574:   PetscFree(pep->data);
    575:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL);
    576:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL);
    577:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL);
    578:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL);
    579:   return(0);
    580: }

    584: PETSC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
    585: {
    586:   PEP_QARNOLDI   *ctx;

    590:   PetscNewLog(pep,&ctx);
    591:   pep->data = (void*)ctx;
    592:   ctx->lock = PETSC_TRUE;

    594:   pep->ops->solve          = PEPSolve_QArnoldi;
    595:   pep->ops->setup          = PEPSetUp_QArnoldi;
    596:   pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
    597:   pep->ops->destroy        = PEPDestroy_QArnoldi;
    598:   pep->ops->view           = PEPView_QArnoldi;
    599:   pep->ops->backtransform  = PEPBackTransform_Default;
    600:   pep->ops->computevectors = PEPComputeVectors_Default;
    601:   pep->ops->computevectors = PEPExtractVectors_QArnoldi;
    602:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi);
    603:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi);
    604:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi);
    605:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi);
    606:   return(0);
    607: }