Date: 2021-09-20T09:44:09+00:00

Actual source code: nleigs.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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: "nleigs"

     13:    Method: NLEIGS

     15:    Algorithm:

     17:        Fully rational Krylov method for nonlinear eigenvalue problems.

     19:    References:

     21:        [1] S. Guttel et al., "NLEIGS: A class of robust fully rational Krylov
     22:            method for nonlinear eigenvalue problems", SIAM J. Sci. Comput.
     23:            36(6):A2842-A2864, 2014.
     24: */

     26: #include <slepc/private/nepimpl.h>
     27: #include <slepcblaslapack.h>
     28: #include "nleigs.h"

     30: PetscErrorCode NEPNLEIGSBackTransform(PetscObject ob,PetscInt n,PetscScalar *valr,PetscScalar *vali)
     31: {
     32:   NEP         nep;
     33:   PetscInt    j;
     34: #if !defined(PETSC_USE_COMPLEX)
     35:   PetscScalar t;
     36: #endif

     39:   nep = (NEP)ob;
     40: #if !defined(PETSC_USE_COMPLEX)
     41:   for (j=0;j<n;j++) {
     42:     if (vali[j] == 0) valr[j] = 1.0 / valr[j] + nep->target;
     43:     else {
     44:       t = valr[j] * valr[j] + vali[j] * vali[j];
     45:       valr[j] = valr[j] / t + nep->target;
     46:       vali[j] = - vali[j] / t;
     47:     }
     48:   }
     49: #else
     50:   for (j=0;j<n;j++) {
     51:     valr[j] = 1.0 / valr[j] + nep->target;
     52:   }
     53: #endif
     54:   return(0);
     55: }

     57: /* Computes the roots of a polynomial */
     58: static PetscErrorCode NEPNLEIGSAuxiliarPRootFinder(PetscInt deg,PetscScalar *polcoeffs,PetscScalar *wr,PetscScalar *wi,PetscBool *avail)
     59: {
     61:   PetscScalar    *C;
     62:   PetscBLASInt   n_,lwork;
     63:   PetscInt       i;
     64: #if defined(PETSC_USE_COMPLEX) || defined(PETSC_HAVE_ESSL)
     65:   PetscReal      *rwork=NULL;
     66: #endif
     67: #if defined(PETSC_HAVE_ESSL)
     68:   PetscScalar    sdummy,*wri;
     69:   PetscBLASInt   idummy,io=0;
     70: #else
     71:   PetscScalar    *work;
     72:   PetscBLASInt   info;
     73: #endif

     76:   *avail = PETSC_TRUE;
     77:   if (deg>0) {
     78:     PetscCalloc1(deg*deg,&C);
     79:     PetscBLASIntCast(deg,&n_);
     80:     for (i=0;i<deg-1;i++) {
     81:       C[(deg+1)*i+1]   = 1.0;
     82:       C[(deg-1)*deg+i] = -polcoeffs[deg-i]/polcoeffs[0];
     83:     }
     84:     C[deg*deg+-1] = -polcoeffs[1]/polcoeffs[0];
     85:     PetscBLASIntCast(3*deg,&lwork);

     87:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     88: #if !defined(PETSC_HAVE_ESSL)
     89: #if !defined(PETSC_USE_COMPLEX)
     90:     PetscMalloc1(lwork,&work);
     91:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&n_,C,&n_,wr,wi,NULL,&n_,NULL,&n_,work,&lwork,&info));
     92:     if (info) *avail = PETSC_FALSE;
     93:     PetscFree(work);
     94: #else
     95:     PetscMalloc2(2*deg,&rwork,lwork,&work);
     96:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&n_,C,&n_,wr,NULL,&n_,NULL,&n_,work,&lwork,rwork,&info));
     97:     if (info) *avail = PETSC_FALSE;
     98:     PetscFree2(rwork,work);
     99: #endif
    100: #else /* defined(PETSC_HAVE_ESSL) */
    101:     PetscMalloc2(lwork,&rwork,2*deg,&wri);
    102:     PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_(&io,C,&n_,wri,&sdummy,&idummy,&idummy,&n_,rwork,&lwork));
    103: #if !defined(PETSC_USE_COMPLEX)
    104:     for (i=0;i<deg;i++) {
    105:       wr[i] = wri[2*i];
    106:       wi[i] = wri[2*i+1];
    107:     }
    108: #else
    109:     for (i=0;i<deg;i++) wr[i] = wri[i];
    110: #endif
    111:     PetscFree2(rwork,wri);
    112: #endif
    113:     PetscFPTrapPop();
    114:     PetscFree(C);
    115:   }
    116:   return(0);
    117: }

    119: static PetscErrorCode NEPNLEIGSAuxiliarRmDuplicates(PetscInt nin,PetscScalar *pin,PetscInt *nout,PetscScalar *pout,PetscInt max)
    120: {
    121:   PetscInt i,j;

    124:   for (i=0;i<nin;i++) {
    125:     if (max && *nout>=max) break;
    126:     pout[(*nout)++] = pin[i];
    127:     for (j=0;j<*nout-1;j++)
    128:       if (PetscAbsScalar(pin[i]-pout[j])<PETSC_MACHINE_EPSILON*100) {
    129:         (*nout)--;
    130:         break;
    131:       }
    132:   }
    133:   return(0);
    134: }

    136: static PetscErrorCode NEPNLEIGSFNSingularities(FN f,PetscInt *nisol,PetscScalar **isol,PetscBool *rational)
    137: {
    139:   FNCombineType  ctype;
    140:   FN             f1,f2;
    141:   PetscInt       i,nq,nisol1,nisol2;
    142:   PetscScalar    *qcoeff,*wr,*wi,*isol1,*isol2;
    143:   PetscBool      flg,avail,rat1,rat2;

    146:   *rational = PETSC_FALSE;
    147:   PetscObjectTypeCompare((PetscObject)f,FNRATIONAL,&flg);
    148:   if (flg) {
    149:     *rational = PETSC_TRUE;
    150:     FNRationalGetDenominator(f,&nq,&qcoeff);
    151:     if (nq>1) {
    152:       PetscMalloc2(nq-1,&wr,nq-1,&wi);
    153:       NEPNLEIGSAuxiliarPRootFinder(nq-1,qcoeff,wr,wi,&avail);
    154:       if (avail) {
    155:         PetscCalloc1(nq-1,isol);
    156:         *nisol = 0;
    157:         for (i=0;i<nq-1;i++)
    158: #if !defined(PETSC_USE_COMPLEX)
    159:           if (wi[i]==0)
    160: #endif
    161:             (*isol)[(*nisol)++] = wr[i];
    162:         nq = *nisol; *nisol = 0;
    163:         for (i=0;i<nq;i++) wr[i] = (*isol)[i];
    164:         NEPNLEIGSAuxiliarRmDuplicates(nq,wr,nisol,*isol,0);
    165:         PetscFree2(wr,wi);
    166:       } else { *nisol=0; *isol = NULL; }
    167:     } else { *nisol = 0; *isol = NULL; }
    168:     PetscFree(qcoeff);
    169:   }
    170:   PetscObjectTypeCompare((PetscObject)f,FNCOMBINE,&flg);
    171:   if (flg) {
    172:     FNCombineGetChildren(f,&ctype,&f1,&f2);
    173:     if (ctype != FN_COMBINE_COMPOSE && ctype != FN_COMBINE_DIVIDE) {
    174:       NEPNLEIGSFNSingularities(f1,&nisol1,&isol1,&rat1);
    175:       NEPNLEIGSFNSingularities(f2,&nisol2,&isol2,&rat2);
    176:       if (nisol1+nisol2>0) {
    177:         PetscCalloc1(nisol1+nisol2,isol);
    178:         *nisol = 0;
    179:         NEPNLEIGSAuxiliarRmDuplicates(nisol1,isol1,nisol,*isol,0);
    180:         NEPNLEIGSAuxiliarRmDuplicates(nisol2,isol2,nisol,*isol,0);
    181:       }
    182:       *rational = (rat1&&rat2)?PETSC_TRUE:PETSC_FALSE;
    183:       PetscFree(isol1);
    184:       PetscFree(isol2);
    185:     }
    186:   }
    187:   return(0);
    188: }

    190: static PetscErrorCode NEPNLEIGSRationalSingularities(NEP nep,PetscInt *ndptx,PetscScalar *dxi,PetscBool *rational)
    191: {
    193:   PetscInt       nt,i,nisol;
    194:   FN             f;
    195:   PetscScalar    *isol;
    196:   PetscBool      rat;

    199:   *rational = PETSC_TRUE;
    200:   *ndptx = 0;
    201:   NEPGetSplitOperatorInfo(nep,&nt,NULL);
    202:   for (i=0;i<nt;i++) {
    203:     NEPGetSplitOperatorTerm(nep,i,NULL,&f);
    204:     NEPNLEIGSFNSingularities(f,&nisol,&isol,&rat);
    205:     if (nisol) {
    206:       NEPNLEIGSAuxiliarRmDuplicates(nisol,isol,ndptx,dxi,0);
    207:       PetscFree(isol);
    208:     }
    209:     *rational = ((*rational)&&rat)?PETSC_TRUE:PETSC_FALSE;
    210:   }
    211:   return(0);
    212: }

    214: /*  Adaptive Anderson-Antoulas algorithm */
    215: static PetscErrorCode NEPNLEIGSAAAComputation(NEP nep,PetscInt ndpt,PetscScalar *ds,PetscScalar *F,PetscInt *ndptx,PetscScalar *dxi)
    216: {
    218:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    219:   PetscScalar    mean=0.0,*z,*f,*C,*A,*VT,*work,*ww,szero=0.0,sone=1.0;
    220:   PetscScalar    *N,*D;
    221:   PetscReal      *S,norm,err,*R;
    222:   PetscInt       i,k,j,idx=0,cont;
    223:   PetscBLASInt   n_,m_,lda_,lwork,info,one=1;
    224: #if defined(PETSC_USE_COMPLEX)
    225:   PetscReal      *rwork;
    226: #endif

    229:   PetscBLASIntCast(8*ndpt,&lwork);
    230:   PetscMalloc5(ndpt,&R,ndpt,&z,ndpt,&f,ndpt*ndpt,&C,ndpt,&ww);
    231:   PetscMalloc6(ndpt*ndpt,&A,ndpt,&S,ndpt*ndpt,&VT,lwork,&work,ndpt,&D,ndpt,&N);
    232: #if defined(PETSC_USE_COMPLEX)
    233:   PetscMalloc1(8*ndpt,&rwork);
    234: #endif
    235:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    236:   norm = 0.0;
    237:   for (i=0;i<ndpt;i++) {
    238:     mean += F[i];
    239:     norm = PetscMax(PetscAbsScalar(F[i]),norm);
    240:   }
    241:   mean /= ndpt;
    242:   PetscBLASIntCast(ndpt,&lda_);
    243:   for (i=0;i<ndpt;i++) R[i] = PetscAbsScalar(F[i]-mean);
    244:   /* next support point */
    245:   err = 0.0;
    246:   for (i=0;i<ndpt;i++) if (R[i]>=err) {idx = i; err = R[i];}
    247:   for (k=0;k<ndpt-1;k++) {
    248:     z[k] = ds[idx]; f[k] = F[idx]; R[idx] = -1.0;
    249:     /* next column of Cauchy matrix */
    250:     for (i=0;i<ndpt;i++) {
    251:       C[i+k*ndpt] = 1.0/(ds[i]-ds[idx]);
    252:     }

    254:     PetscArrayzero(A,ndpt*ndpt);
    255:     cont = 0;
    256:     for (i=0;i<ndpt;i++) {
    257:       if (R[i]!=-1.0) {
    258:         for (j=0;j<=k;j++)A[cont+j*ndpt] = C[i+j*ndpt]*F[i]-C[i+j*ndpt]*f[j];
    259:         cont++;
    260:       }
    261:     }
    262:     PetscBLASIntCast(cont,&m_);
    263:     PetscBLASIntCast(k+1,&n_);
    264: #if defined(PETSC_USE_COMPLEX)
    265:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","A",&m_,&n_,A,&lda_,S,NULL,&lda_,VT,&lda_,work,&lwork,rwork,&info));
    266: #else
    267:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","A",&m_,&n_,A,&lda_,S,NULL,&lda_,VT,&lda_,work,&lwork,&info));
    268: #endif
    269:     SlepcCheckLapackInfo("gesvd",info);
    270:     for (i=0;i<=k;i++) {
    271:       ww[i] = PetscConj(VT[i*ndpt+k]);
    272:       D[i] = ww[i]*f[i];
    273:     }
    274:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lda_,&n_,&sone,C,&lda_,D,&one,&szero,N,&one));
    275:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lda_,&n_,&sone,C,&lda_,ww,&one,&szero,D,&one));
    276:     for (i=0;i<ndpt;i++) if (R[i]>=0) R[i] = PetscAbsScalar(F[i]-N[i]/D[i]);
    277:     /* next support point */
    278:     err = 0.0;
    279:     for (i=0;i<ndpt;i++) if (R[i]>=err) {idx = i; err = R[i];}
    280:     if (err <= ctx->ddtol*norm) break;
    281:   }

    283:   if (k==ndpt-1) SETERRQ(PetscObjectComm((PetscObject)nep),1,"Failed to determine singularities automatically in general problem");
    284:   /* poles */
    285:   PetscArrayzero(C,ndpt*ndpt);
    286:   PetscArrayzero(A,ndpt*ndpt);
    287:   for (i=0;i<=k;i++) {
    288:     C[i+ndpt*i] = 1.0;
    289:     A[(i+1)*ndpt] = ww[i];
    290:     A[i+1] = 1.0;
    291:     A[i+1+(i+1)*ndpt] = z[i];
    292:   }
    293:   C[0] = 0.0; C[k+1+(k+1)*ndpt] = 1.0;
    294:   n_++;
    295: #if defined(PETSC_USE_COMPLEX)
    296:   PetscStackCallBLAS("LAPACKggev",LAPACKggev_("N","N",&n_,A,&lda_,C,&lda_,D,N,NULL,&lda_,NULL,&lda_,work,&lwork,rwork,&info));
    297: #else
    298:   PetscStackCallBLAS("LAPACKggev",LAPACKggev_("N","N",&n_,A,&lda_,C,&lda_,D,VT,N,NULL,&lda_,NULL,&lda_,work,&lwork,&info));
    299: #endif
    300:   SlepcCheckLapackInfo("ggev",info);
    301:   cont = 0.0;
    302:   for (i=0;i<n_;i++) if (N[i]!=0.0) {
    303:     dxi[cont++] = D[i]/N[i];
    304:   }
    305:   *ndptx = cont;
    306:   PetscFPTrapPop();
    307:   PetscFree5(R,z,f,C,ww);
    308:   PetscFree6(A,S,VT,work,D,N);
    309: #if defined(PETSC_USE_COMPLEX)
    310:   PetscFree(rwork);
    311: #endif
    312:   return(0);
    313: }

    315: /*  Singularities using Adaptive Anderson-Antoulas algorithm */
    316: static PetscErrorCode NEPNLEIGSAAASingularities(NEP nep,PetscInt ndpt,PetscScalar *ds,PetscInt *ndptx,PetscScalar *dxi)
    317: {
    319:   Vec            u,v,w;
    320:   PetscRandom    rand;
    321:   PetscScalar    *F,*isol;
    322:   PetscInt       i,k,nisol,nt;
    323:   Mat            T;
    324:   FN             f;

    327:   PetscMalloc1(ndpt,&F);
    328:   if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
    329:     PetscMalloc1(ndpt,&isol);
    330:     *ndptx = 0;
    331:     NEPGetSplitOperatorInfo(nep,&nt,NULL);
    332:     nisol = *ndptx;
    333:     for (k=0;k<nt;k++) {
    334:       NEPGetSplitOperatorTerm(nep,k,NULL,&f);
    335:       for (i=0;i<ndpt;i++) {
    336:         FNEvaluateFunction(f,ds[i],&F[i]);
    337:       }
    338:       NEPNLEIGSAAAComputation(nep,ndpt,ds,F,&nisol,isol);
    339:       if (nisol) {
    340:         NEPNLEIGSAuxiliarRmDuplicates(nisol,isol,ndptx,dxi,ndpt);
    341:       }
    342:     }
    343:     PetscFree(isol);
    344:   } else {
    345:     MatCreateVecs(nep->function,&u,NULL);
    346:     VecDuplicate(u,&v);
    347:     VecDuplicate(u,&w);
    348:     BVGetRandomContext(nep->V,&rand);
    349:     VecSetRandom(u,rand);
    350:     VecNormalize(u,NULL);
    351:     VecSetRandom(v,rand);
    352:     VecNormalize(v,NULL);
    353:     T = nep->function;
    354:     for (i=0;i<ndpt;i++) {
    355:       NEPComputeFunction(nep,ds[i],T,T);
    356:       MatMult(T,v,w);
    357:       VecDot(w,u,&F[i]);
    358:     }
    359:     NEPNLEIGSAAAComputation(nep,ndpt,ds,F,ndptx,dxi);
    360:     VecDestroy(&u);
    361:     VecDestroy(&v);
    362:     VecDestroy(&w);
    363:   }
    364:   PetscFree(F);
    365:   return(0);
    366: }

    368: static PetscErrorCode NEPNLEIGSLejaBagbyPoints(NEP nep)
    369: {
    371:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    372:   PetscInt       i,k,ndpt=NDPOINTS,ndptx=NDPOINTS;
    373:   PetscScalar    *ds,*dsi,*dxi,*nrs,*nrxi,*s=ctx->s,*xi=ctx->xi,*beta=ctx->beta;
    374:   PetscReal      maxnrs,minnrxi;
    375:   PetscBool      rational;
    376: #if !defined(PETSC_USE_COMPLEX)
    377:   PetscReal      a,b,h;
    378: #endif

    381:   if (!ctx->computesingularities && nep->problem_type!=NEP_RATIONAL) ndpt = ndptx = LBPOINTS;
    382:   PetscMalloc5(ndpt+1,&ds,ndpt+1,&dsi,ndpt,&dxi,ndpt+1,&nrs,ndpt,&nrxi);

    384:   /* Discretize the target region boundary */
    385:   RGComputeContour(nep->rg,ndpt,ds,dsi);
    386: #if !defined(PETSC_USE_COMPLEX)
    387:   for (i=0;i<ndpt;i++) if (dsi[i]!=0.0) break;
    388:   if (i<ndpt) {
    389:     if (nep->problem_type==NEP_RATIONAL) {
    390:       /* Select a segment in the real axis */
    391:       RGComputeBoundingBox(nep->rg,&a,&b,NULL,NULL);
    392:       if (a<=-PETSC_MAX_REAL || b>=PETSC_MAX_REAL) SETERRQ(PetscObjectComm((PetscObject)nep),1,"NLEIGS requires a bounded target set");
    393:       h = (b-a)/ndpt;
    394:       for (i=0;i<ndpt;i++) {ds[i] = a+h*i; dsi[i] = 0.0;}
    395:     } else SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NLEIGS with real arithmetic requires the target set to be included in the real axis");
    396:   }
    397: #endif
    398:   /* Discretize the singularity region */
    399:   if (ctx->computesingularities) {
    400:     (ctx->computesingularities)(nep,&ndptx,dxi,ctx->singularitiesctx);
    401:   } else {
    402:     if (nep->problem_type==NEP_RATIONAL) {
    403:       NEPNLEIGSRationalSingularities(nep,&ndptx,dxi,&rational);
    404:       if (!rational) SETERRQ(PetscObjectComm((PetscObject)nep),1,"Failed to determine singularities automatically in rational problem; consider solving the problem as general");
    405:     } else {
    406:       /* AAA algorithm */
    407:       NEPNLEIGSAAASingularities(nep,ndpt,ds,&ndptx,dxi);
    408:     }
    409:   }
    410:   /* Look for Leja-Bagby points in the discretization sets */
    411:   s[0]    = ds[0];
    412:   xi[0]   = (ndptx>0)?dxi[0]:PETSC_INFINITY;
    413:   if (PetscAbsScalar(xi[0])<10*PETSC_MACHINE_EPSILON) SETERRQ2(PetscObjectComm((PetscObject)nep),1,"Singularity point %D is nearly zero: %g; consider removing the singularity or shifting the problem",0,(double)PetscAbsScalar(xi[0]));
    414:   beta[0] = 1.0; /* scaling factors are also computed here */
    415:   for (i=0;i<ndpt;i++) {
    416:     nrs[i] = 1.0;
    417:     nrxi[i] = 1.0;
    418:   }
    419:   for (k=1;k<ctx->ddmaxit;k++) {
    420:     maxnrs = 0.0;
    421:     minnrxi = PETSC_MAX_REAL;
    422:     for (i=0;i<ndpt;i++) {
    423:       nrs[i] *= ((ds[i]-s[k-1])/(1.0-ds[i]/xi[k-1]))/beta[k-1];
    424:       if (PetscAbsScalar(nrs[i])>maxnrs) {maxnrs = PetscAbsScalar(nrs[i]); s[k] = ds[i];}
    425:     }
    426:     if (ndptx>k) {
    427:       for (i=1;i<ndptx;i++) {
    428:         nrxi[i] *= ((dxi[i]-s[k-1])/(1.0-dxi[i]/xi[k-1]))/beta[k-1];
    429:         if (PetscAbsScalar(nrxi[i])<minnrxi) {minnrxi = PetscAbsScalar(nrxi[i]); xi[k] = dxi[i];}
    430:       }
    431:       if (PetscAbsScalar(xi[k])<10*PETSC_MACHINE_EPSILON) SETERRQ2(PetscObjectComm((PetscObject)nep),1,"Singularity point %D is nearly zero: %g; consider removing the singularity or shifting the problem",k,(double)PetscAbsScalar(xi[k]));
    432:     } else xi[k] = PETSC_INFINITY;
    433:     beta[k] = maxnrs;
    434:   }
    435:   PetscFree5(ds,dsi,dxi,nrs,nrxi);
    436:   return(0);
    437: }

    439: PetscErrorCode NEPNLEIGSEvalNRTFunct(NEP nep,PetscInt k,PetscScalar sigma,PetscScalar *b)
    440: {
    441:   NEP_NLEIGS  *ctx=(NEP_NLEIGS*)nep->data;
    442:   PetscInt    i;
    443:   PetscScalar *beta=ctx->beta,*s=ctx->s,*xi=ctx->xi;

    446:   b[0] = 1.0/beta[0];
    447:   for (i=0;i<k;i++) {
    448:     b[i+1] = ((sigma-s[i])*b[i])/(beta[i+1]*(1.0-sigma/xi[i]));
    449:   }
    450:   return(0);
    451: }

    453: static PetscErrorCode MatMult_Fun(Mat A,Vec x,Vec y)
    454: {
    455:   PetscErrorCode      ierr;
    456:   NEP_NLEIGS_MATSHELL *ctx;
    457:   PetscInt            i;

    460:   MatShellGetContext(A,(void**)&ctx);
    461:   MatMult(ctx->A[0],x,y);
    462:   if (ctx->coeff[0]!=1.0) { VecScale(y,ctx->coeff[0]); }
    463:   for (i=1;i<ctx->nmat;i++) {
    464:     MatMult(ctx->A[i],x,ctx->t);
    465:     VecAXPY(y,ctx->coeff[i],ctx->t);
    466:   }
    467:   return(0);
    468: }

    470: static PetscErrorCode MatMultTranspose_Fun(Mat A,Vec x,Vec y)
    471: {
    472:   PetscErrorCode      ierr;
    473:   NEP_NLEIGS_MATSHELL *ctx;
    474:   PetscInt            i;

    477:   MatShellGetContext(A,(void**)&ctx);
    478:   MatMultTranspose(ctx->A[0],x,y);
    479:   if (ctx->coeff[0]!=1.0) { VecScale(y,ctx->coeff[0]); }
    480:   for (i=1;i<ctx->nmat;i++) {
    481:     MatMultTranspose(ctx->A[i],x,ctx->t);
    482:     VecAXPY(y,ctx->coeff[i],ctx->t);
    483:   }
    484:   return(0);
    485: }

    487: static PetscErrorCode MatGetDiagonal_Fun(Mat A,Vec diag)
    488: {
    489:   PetscErrorCode      ierr;
    490:   NEP_NLEIGS_MATSHELL *ctx;
    491:   PetscInt            i;

    494:   MatShellGetContext(A,(void**)&ctx);
    495:   MatGetDiagonal(ctx->A[0],diag);
    496:   if (ctx->coeff[0]!=1.0) { VecScale(diag,ctx->coeff[0]); }
    497:   for (i=1;i<ctx->nmat;i++) {
    498:     MatGetDiagonal(ctx->A[i],ctx->t);
    499:     VecAXPY(diag,ctx->coeff[i],ctx->t);
    500:   }
    501:   return(0);
    502: }

    504: static PetscErrorCode MatDuplicate_Fun(Mat A,MatDuplicateOption op,Mat *B)
    505: {
    506:   PetscInt            n,i;
    507:   NEP_NLEIGS_MATSHELL *ctxnew,*ctx;
    508:   void                (*fun)(void);
    509:   PetscErrorCode      ierr;

    512:   MatShellGetContext(A,(void**)&ctx);
    513:   PetscNew(&ctxnew);
    514:   ctxnew->nmat = ctx->nmat;
    515:   ctxnew->maxnmat = ctx->maxnmat;
    516:   PetscMalloc2(ctxnew->maxnmat,&ctxnew->A,ctxnew->maxnmat,&ctxnew->coeff);
    517:   for (i=0;i<ctx->nmat;i++) {
    518:     PetscObjectReference((PetscObject)ctx->A[i]);
    519:     ctxnew->A[i] = ctx->A[i];
    520:     ctxnew->coeff[i] = ctx->coeff[i];
    521:   }
    522:   MatGetSize(ctx->A[0],&n,NULL);
    523:   VecDuplicate(ctx->t,&ctxnew->t);
    524:   MatCreateShell(PetscObjectComm((PetscObject)A),n,n,n,n,(void*)ctxnew,B);
    525:   MatShellSetManageScalingShifts(*B);
    526:   MatShellGetOperation(A,MATOP_MULT,&fun);
    527:   MatShellSetOperation(*B,MATOP_MULT,fun);
    528:   MatShellGetOperation(A,MATOP_MULT_TRANSPOSE,&fun);
    529:   MatShellSetOperation(*B,MATOP_MULT_TRANSPOSE,fun);
    530:   MatShellGetOperation(A,MATOP_GET_DIAGONAL,&fun);
    531:   MatShellSetOperation(*B,MATOP_GET_DIAGONAL,fun);
    532:   MatShellGetOperation(A,MATOP_DUPLICATE,&fun);
    533:   MatShellSetOperation(*B,MATOP_DUPLICATE,fun);
    534:   MatShellGetOperation(A,MATOP_DESTROY,&fun);
    535:   MatShellSetOperation(*B,MATOP_DESTROY,fun);
    536:   MatShellGetOperation(A,MATOP_AXPY,&fun);
    537:   MatShellSetOperation(*B,MATOP_AXPY,fun);
    538:   return(0);
    539: }

    541: static PetscErrorCode MatDestroy_Fun(Mat A)
    542: {
    543:   NEP_NLEIGS_MATSHELL *ctx;
    544:   PetscErrorCode      ierr;
    545:   PetscInt            i;

    548:   if (A) {
    549:     MatShellGetContext(A,(void**)&ctx);
    550:     for (i=0;i<ctx->nmat;i++) {
    551:       MatDestroy(&ctx->A[i]);
    552:     }
    553:     VecDestroy(&ctx->t);
    554:     PetscFree2(ctx->A,ctx->coeff);
    555:     PetscFree(ctx);
    556:   }
    557:   return(0);
    558: }

    560: static PetscErrorCode MatAXPY_Fun(Mat Y,PetscScalar a,Mat X,MatStructure str)
    561: {
    562:   NEP_NLEIGS_MATSHELL *ctxY,*ctxX;
    563:   PetscErrorCode      ierr;
    564:   PetscInt            i,j;
    565:   PetscBool           found;

    568:   MatShellGetContext(Y,(void**)&ctxY);
    569:   MatShellGetContext(X,(void**)&ctxX);
    570:   for (i=0;i<ctxX->nmat;i++) {
    571:     found = PETSC_FALSE;
    572:     for (j=0;!found&&j<ctxY->nmat;j++) {
    573:       if (ctxX->A[i]==ctxY->A[j]) {
    574:         found = PETSC_TRUE;
    575:         ctxY->coeff[j] += a*ctxX->coeff[i];
    576:       }
    577:     }
    578:     if (!found) {
    579:       ctxY->coeff[ctxY->nmat] = a*ctxX->coeff[i];
    580:       ctxY->A[ctxY->nmat++] = ctxX->A[i];
    581:       PetscObjectReference((PetscObject)ctxX->A[i]);
    582:     }
    583:   }
    584:   return(0);
    585: }

    587: static PetscErrorCode MatScale_Fun(Mat M,PetscScalar a)
    588: {
    589:   NEP_NLEIGS_MATSHELL *ctx;
    590:   PetscErrorCode      ierr;
    591:   PetscInt            i;

    594:   MatShellGetContext(M,(void**)&ctx);
    595:   for (i=0;i<ctx->nmat;i++) ctx->coeff[i] *= a;
    596:   return(0);
    597: }

    599: static PetscErrorCode NLEIGSMatToMatShellArray(Mat M,Mat *Ms,PetscInt maxnmat)
    600: {
    601:   PetscErrorCode      ierr;
    602:   NEP_NLEIGS_MATSHELL *ctx;
    603:   PetscInt            n;
    604:   PetscBool           has;

    607:   MatHasOperation(M,MATOP_DUPLICATE,&has);
    608:   if (!has) SETERRQ(PetscObjectComm((PetscObject)M),1,"MatDuplicate operation required");
    609:   PetscNew(&ctx);
    610:   ctx->maxnmat = maxnmat;
    611:   PetscMalloc2(ctx->maxnmat,&ctx->A,ctx->maxnmat,&ctx->coeff);
    612:   MatDuplicate(M,MAT_COPY_VALUES,&ctx->A[0]);
    613:   ctx->nmat = 1;
    614:   ctx->coeff[0] = 1.0;
    615:   MatCreateVecs(M,&ctx->t,NULL);
    616:   MatGetSize(M,&n,NULL);
    617:   MatCreateShell(PetscObjectComm((PetscObject)M),n,n,n,n,(void*)ctx,Ms);
    618:   MatShellSetManageScalingShifts(*Ms);
    619:   MatShellSetOperation(*Ms,MATOP_MULT,(void(*)(void))MatMult_Fun);
    620:   MatShellSetOperation(*Ms,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Fun);
    621:   MatShellSetOperation(*Ms,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Fun);
    622:   MatShellSetOperation(*Ms,MATOP_DUPLICATE,(void(*)(void))MatDuplicate_Fun);
    623:   MatShellSetOperation(*Ms,MATOP_DESTROY,(void(*)(void))MatDestroy_Fun);
    624:   MatShellSetOperation(*Ms,MATOP_AXPY,(void(*)(void))MatAXPY_Fun);
    625:   MatShellSetOperation(*Ms,MATOP_SCALE,(void(*)(void))MatScale_Fun);
    626:   return(0);
    627: }

    629: static PetscErrorCode NEPNLEIGSDividedDifferences_split(NEP nep)
    630: {
    632:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    633:   PetscInt       k,j,i,maxnmat,nmax;
    634:   PetscReal      norm0,norm,*matnorm;
    635:   PetscScalar    *s=ctx->s,*beta=ctx->beta,*xi=ctx->xi,*b,alpha,*coeffs,*pK,*pH,sone=1.0;
    636:   Mat            T,Ts,K,H;
    637:   PetscBool      shell,hasmnorm=PETSC_FALSE,matrix=PETSC_TRUE;
    638:   PetscBLASInt   n_;

    641:   nmax = ctx->ddmaxit;
    642:   PetscMalloc1(nep->nt*nmax,&ctx->coeffD);
    643:   PetscMalloc3(nmax+1,&b,nmax+1,&coeffs,nep->nt,&matnorm);
    644:   for (j=0;j<nep->nt;j++) {
    645:     MatHasOperation(nep->A[j],MATOP_NORM,&hasmnorm);
    646:     if (!hasmnorm) break;
    647:     MatNorm(nep->A[j],NORM_INFINITY,matnorm+j);
    648:   }
    649:   /* Try matrix functions scheme */
    650:   PetscCalloc2(nmax*nmax,&pK,nmax*nmax,&pH);
    651:   for (i=0;i<nmax-1;i++) {
    652:     pK[(nmax+1)*i]   = 1.0;
    653:     pK[(nmax+1)*i+1] = beta[i+1]/xi[i];
    654:     pH[(nmax+1)*i]   = s[i];
    655:     pH[(nmax+1)*i+1] = beta[i+1];
    656:   }
    657:   pH[nmax*nmax-1] = s[nmax-1];
    658:   pK[nmax*nmax-1] = 1.0;
    659:   PetscBLASIntCast(nmax,&n_);
    660:   PetscStackCallBLAS("BLAStrsm",BLAStrsm_("R","L","N","U",&n_,&n_,&sone,pK,&n_,pH,&n_));
    661:   /* The matrix to be used is in H. K will be a work-space matrix */
    662:   MatCreateSeqDense(PETSC_COMM_SELF,nmax,nmax,pH,&H);
    663:   MatCreateSeqDense(PETSC_COMM_SELF,nmax,nmax,pK,&K);
    664:   for (j=0;matrix&&j<nep->nt;j++) {
    665:     PetscPushErrorHandler(PetscReturnErrorHandler,NULL);
    666:     FNEvaluateFunctionMat(nep->f[j],H,K);
    667:     PetscPopErrorHandler();
    668:     if (!ierr) {
    669:       for (i=0;i<nmax;i++) { ctx->coeffD[j+i*nep->nt] = pK[i]*beta[0]; }
    670:     } else {
    671:       matrix = PETSC_FALSE;
    672:       PetscFPTrapPop();
    673:     }
    674:   }
    675:   MatDestroy(&H);
    676:   MatDestroy(&K);
    677:   if (!matrix) {
    678:     for (j=0;j<nep->nt;j++) {
    679:       FNEvaluateFunction(nep->f[j],s[0],ctx->coeffD+j);
    680:       ctx->coeffD[j] *= beta[0];
    681:     }
    682:   }
    683:   if (hasmnorm) {
    684:     norm0 = 0.0;
    685:     for (j=0;j<nep->nt;j++) norm0 += matnorm[j]*PetscAbsScalar(ctx->coeffD[j]);
    686:   } else {
    687:     norm0 = 0.0;
    688:     for (j=0;j<nep->nt;j++) norm0 = PetscMax(PetscAbsScalar(ctx->coeffD[j]),norm0);
    689:   }
    690:   ctx->nmat = ctx->ddmaxit;
    691:   for (k=1;k<ctx->ddmaxit;k++) {
    692:     if (!matrix) {
    693:       NEPNLEIGSEvalNRTFunct(nep,k,s[k],b);
    694:       for (i=0;i<nep->nt;i++) {
    695:         FNEvaluateFunction(nep->f[i],s[k],ctx->coeffD+k*nep->nt+i);
    696:         for (j=0;j<k;j++) {
    697:           ctx->coeffD[k*nep->nt+i] -= b[j]*ctx->coeffD[i+nep->nt*j];
    698:         }
    699:         ctx->coeffD[k*nep->nt+i] /= b[k];
    700:       }
    701:     }
    702:     if (hasmnorm) {
    703:       norm = 0.0;
    704:       for (j=0;j<nep->nt;j++) norm += matnorm[j]*PetscAbsScalar(ctx->coeffD[k*nep->nt+j]);
    705:     } else {
    706:       norm = 0.0;
    707:       for (j=0;j<nep->nt;j++) norm = PetscMax(PetscAbsScalar(ctx->coeffD[k*nep->nt+j]),norm);
    708:     }
    709:     if (k>1 && norm/norm0 < ctx->ddtol) {
    710:       ctx->nmat = k+1;
    711:       break;
    712:     }
    713:   }
    714:   if (!ctx->ksp) { NEPNLEIGSGetKSPs(nep,&ctx->nshiftsw,&ctx->ksp); }
    715:   MatIsShell(nep->A[0],&shell);
    716:   maxnmat = PetscMax(ctx->ddmaxit,nep->nt);
    717:   for (i=0;i<ctx->nshiftsw;i++) {
    718:     NEPNLEIGSEvalNRTFunct(nep,ctx->nmat-1,ctx->shifts[i],coeffs);
    719:     if (!shell) {
    720:       MatDuplicate(nep->A[0],MAT_COPY_VALUES,&T);
    721:     } else {
    722:       NLEIGSMatToMatShellArray(nep->A[0],&T,maxnmat);
    723:     }
    724:     alpha = 0.0;
    725:     for (j=0;j<ctx->nmat;j++) alpha += coeffs[j]*ctx->coeffD[j*nep->nt];
    726:     MatScale(T,alpha);
    727:     for (k=1;k<nep->nt;k++) {
    728:       alpha = 0.0;
    729:       for (j=0;j<ctx->nmat;j++) alpha += coeffs[j]*ctx->coeffD[j*nep->nt+k];
    730:       if (shell) {
    731:         NLEIGSMatToMatShellArray(nep->A[k],&Ts,maxnmat);
    732:       }
    733:       MatAXPY(T,alpha,shell?Ts:nep->A[k],nep->mstr);
    734:       if (shell) {
    735:         MatDestroy(&Ts);
    736:       }
    737:     }
    738:     KSPSetOperators(ctx->ksp[i],T,T);
    739:     KSPSetUp(ctx->ksp[i]);
    740:     MatDestroy(&T);
    741:   }
    742:   PetscFree3(b,coeffs,matnorm);
    743:   PetscFree2(pK,pH);
    744:   return(0);
    745: }

    747: static PetscErrorCode NEPNLEIGSDividedDifferences_callback(NEP nep)
    748: {
    750:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    751:   PetscInt       k,j,i,maxnmat;
    752:   PetscReal      norm0,norm;
    753:   PetscScalar    *s=ctx->s,*beta=ctx->beta,*b,*coeffs;
    754:   Mat            *D=ctx->D,T;
    755:   PetscBool      shell,has,vec=PETSC_FALSE;
    756:   PetscRandom    rand;
    757:   Vec            w[2];

    760:   PetscMalloc2(ctx->ddmaxit+1,&b,ctx->ddmaxit+1,&coeffs);
    761:   BVGetRandomContext(nep->V,&rand);
    762:   T = nep->function;
    763:   NEPComputeFunction(nep,s[0],T,T);
    764:   MatIsShell(T,&shell);
    765:   maxnmat = PetscMax(ctx->ddmaxit,nep->nt);
    766:   if (!shell) {
    767:     MatDuplicate(T,MAT_COPY_VALUES,&D[0]);
    768:   } else {
    769:     NLEIGSMatToMatShellArray(T,&D[0],maxnmat);
    770:   }
    771:   if (beta[0]!=1.0) {
    772:     MatScale(D[0],1.0/beta[0]);
    773:   }
    774:   MatHasOperation(D[0],MATOP_NORM,&has);
    775:   if (has) {
    776:     MatNorm(D[0],NORM_FROBENIUS,&norm0);
    777:   } else {
    778:     MatCreateVecs(D[0],NULL,&w[0]);
    779:     VecDuplicate(w[0],&w[1]);
    780:     VecDuplicate(w[0],&ctx->vrn);
    781:     VecSetRandomNormal(ctx->vrn,rand,w[0],w[1]);
    782:     VecNormalize(ctx->vrn,NULL);
    783:     vec = PETSC_TRUE;
    784:     MatNormEstimate(D[0],ctx->vrn,w[0],&norm0);
    785:   }
    786:   ctx->nmat = ctx->ddmaxit;
    787:   for (k=1;k<ctx->ddmaxit;k++) {
    788:     NEPNLEIGSEvalNRTFunct(nep,k,s[k],b);
    789:     NEPComputeFunction(nep,s[k],T,T);
    790:     if (!shell) {
    791:       MatDuplicate(T,MAT_COPY_VALUES,&D[k]);
    792:     } else {
    793:       NLEIGSMatToMatShellArray(T,&D[k],maxnmat);
    794:     }
    795:     for (j=0;j<k;j++) {
    796:       MatAXPY(D[k],-b[j],D[j],nep->mstr);
    797:     }
    798:     MatScale(D[k],1.0/b[k]);
    799:     MatHasOperation(D[k],MATOP_NORM,&has);
    800:     if (has) {
    801:       MatNorm(D[k],NORM_FROBENIUS,&norm);
    802:     } else {
    803:       if (!vec) {
    804:         MatCreateVecs(D[k],NULL,&w[0]);
    805:         VecDuplicate(w[0],&w[1]);
    806:         VecDuplicate(w[0],&ctx->vrn);
    807:         VecSetRandomNormal(ctx->vrn,rand,w[0],w[1]);
    808:         VecNormalize(ctx->vrn,NULL);
    809:         vec = PETSC_TRUE;
    810:       }
    811:       MatNormEstimate(D[k],ctx->vrn,w[0],&norm);
    812:     }
    813:     if (k>1 && norm/norm0 < ctx->ddtol && k>1) {
    814:       ctx->nmat = k+1;
    815:       break;
    816:     }
    817:   }
    818:   if (!ctx->ksp) { NEPNLEIGSGetKSPs(nep,&ctx->nshiftsw,&ctx->ksp); }
    819:   for (i=0;i<ctx->nshiftsw;i++) {
    820:     NEPNLEIGSEvalNRTFunct(nep,ctx->nmat-1,ctx->shifts[i],coeffs);
    821:     MatDuplicate(ctx->D[0],MAT_COPY_VALUES,&T);
    822:     if (coeffs[0]!=1.0) { MatScale(T,coeffs[0]); }
    823:     for (j=1;j<ctx->nmat;j++) {
    824:       MatAXPY(T,coeffs[j],ctx->D[j],nep->mstr);
    825:     }
    826:     KSPSetOperators(ctx->ksp[i],T,T);
    827:     KSPSetUp(ctx->ksp[i]);
    828:     MatDestroy(&T);
    829:   }
    830:   PetscFree2(b,coeffs);
    831:   if (vec) {
    832:     VecDestroy(&w[0]);
    833:     VecDestroy(&w[1]);
    834:   }
    835:   return(0);
    836: }

    838: /*
    839:    NEPKrylovConvergence - This is the analogue to EPSKrylovConvergence.
    840: */
    841: PetscErrorCode NEPNLEIGSKrylovConvergence(NEP nep,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal betah,PetscScalar betak,PetscInt *kout,Vec *w)
    842: {
    844:   PetscInt       k,newk,marker,inside;
    845:   PetscScalar    re,im;
    846:   PetscReal      resnorm,tt;
    847:   PetscBool      istrivial;
    848:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;

    851:   RGIsTrivial(nep->rg,&istrivial);
    852:   marker = -1;
    853:   if (nep->trackall) getall = PETSC_TRUE;
    854:   for (k=kini;k<kini+nits;k++) {
    855:     /* eigenvalue */
    856:     re = nep->eigr[k];
    857:     im = nep->eigi[k];
    858:     if (!istrivial) {
    859:       if (!ctx->nshifts) {
    860:         NEPNLEIGSBackTransform((PetscObject)nep,1,&re,&im);
    861:       }
    862:       RGCheckInside(nep->rg,1,&re,&im,&inside);
    863:       if (marker==-1 && inside<0) marker = k;
    864:     }
    865:     newk = k;
    866:     DSVectors(nep->ds,DS_MAT_X,&newk,&resnorm);
    867:     tt = (ctx->nshifts)?SlepcAbsEigenvalue(betak-nep->eigr[k]*betah,nep->eigi[k]*betah):betah;
    868:     resnorm *=  PetscAbsReal(tt);
    869:     /* error estimate */
    870:     (*nep->converged)(nep,nep->eigr[k],nep->eigi[k],resnorm,&nep->errest[k],nep->convergedctx);
    871:     if (marker==-1 && nep->errest[k] >= nep->tol) marker = k;
    872:     if (newk==k+1) {
    873:       nep->errest[k+1] = nep->errest[k];
    874:       k++;
    875:     }
    876:     if (marker!=-1 && !getall) break;
    877:   }
    878:   if (marker!=-1) k = marker;
    879:   *kout = k;
    880:   return(0);
    881: }

    883: PetscErrorCode NEPSetUp_NLEIGS(NEP nep)
    884: {
    886:   PetscInt       k,in;
    887:   PetscScalar    zero=0.0;
    888:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    889:   SlepcSC        sc;
    890:   PetscBool      istrivial;

    893:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
    894:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
    895:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
    896:   if (!ctx->ddmaxit) ctx->ddmaxit = LBPOINTS;
    897:   RGIsTrivial(nep->rg,&istrivial);
    898:   if (istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPNLEIGS requires a nontrivial region defining the target set");
    899:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
    900:   if (nep->which!=NEP_TARGET_MAGNITUDE && nep->which!=NEP_TARGET_REAL && nep->which!=NEP_TARGET_IMAGINARY && nep->which!=NEP_WHICH_USER) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only target selection of eigenvalues");

    902:   /* Initialize the NLEIGS context structure */
    903:   k = ctx->ddmaxit;
    904:   PetscMalloc4(k,&ctx->s,k,&ctx->xi,k,&ctx->beta,k,&ctx->D);
    905:   nep->data = ctx;
    906:   if (nep->tol==PETSC_DEFAULT) nep->tol = SLEPC_DEFAULT_TOL;
    907:   if (ctx->ddtol==PETSC_DEFAULT) ctx->ddtol = nep->tol/10.0;
    908:   if (!ctx->keep) ctx->keep = 0.5;

    910:   /* Compute Leja-Bagby points and scaling values */
    911:   NEPNLEIGSLejaBagbyPoints(nep);
    912:   if (nep->problem_type!=NEP_RATIONAL) {
    913:     RGCheckInside(nep->rg,1,&nep->target,&zero,&in);
    914:     if (in<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"The target is not inside the target set");
    915:   }

    917:   /* Compute the divided difference matrices */
    918:   if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
    919:     NEPNLEIGSDividedDifferences_split(nep);
    920:   } else {
    921:     NEPNLEIGSDividedDifferences_callback(nep);
    922:   }
    923:   NEPAllocateSolution(nep,ctx->nmat-1);
    924:   NEPSetWorkVecs(nep,4);
    925:   if (!ctx->fullbasis) {
    926:     if (nep->twosided) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Two-sided variant requires the full-basis option, rerun with -nep_nleigs_full_basis");
    927:     /* set-up DS and transfer split operator functions */
    928:     DSSetType(nep->ds,ctx->nshifts?DSGNHEP:DSNHEP);
    929:     DSAllocate(nep->ds,nep->ncv+1);
    930:     DSGetSlepcSC(nep->ds,&sc);
    931:     if (!ctx->nshifts) sc->map = NEPNLEIGSBackTransform;
    932:     DSSetExtraRow(nep->ds,PETSC_TRUE);
    933:     sc->mapobj        = (PetscObject)nep;
    934:     sc->rg            = nep->rg;
    935:     sc->comparison    = nep->sc->comparison;
    936:     sc->comparisonctx = nep->sc->comparisonctx;
    937:     BVDestroy(&ctx->V);
    938:     BVCreateTensor(nep->V,ctx->nmat-1,&ctx->V);
    939:     nep->ops->solve          = NEPSolve_NLEIGS;
    940:     nep->ops->computevectors = NEPComputeVectors_Schur;
    941:   } else {
    942:     NEPSetUp_NLEIGS_FullBasis(nep);
    943:     nep->ops->solve          = NEPSolve_NLEIGS_FullBasis;
    944:     nep->ops->computevectors = NULL;
    945:   }
    946:   return(0);
    947: }

    949: /*
    950:   Extend the TOAR basis by applying the the matrix operator
    951:   over a vector which is decomposed on the TOAR way
    952:   Input:
    953:     - S,V: define the latest Arnoldi vector (nv vectors in V)
    954:   Output:
    955:     - t: new vector extending the TOAR basis
    956:     - r: temporally coefficients to compute the TOAR coefficients
    957:          for the new Arnoldi vector
    958:   Workspace: t_ (two vectors)
    959: */
    960: static PetscErrorCode NEPTOARExtendBasis(NEP nep,PetscInt idxrktg,PetscScalar *S,PetscInt ls,PetscInt nv,BV W,BV V,Vec t,PetscScalar *r,PetscInt lr,Vec *t_)
    961: {
    963:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    964:   PetscInt       deg=ctx->nmat-1,k,j;
    965:   Vec            v=t_[0],q=t_[1],w;
    966:   PetscScalar    *beta=ctx->beta,*s=ctx->s,*xi=ctx->xi,*coeffs,sigma;

    969:   if (!ctx->ksp) { NEPNLEIGSGetKSPs(nep,&ctx->nshiftsw,&ctx->ksp); }
    970:   sigma = ctx->shifts[idxrktg];
    971:   BVSetActiveColumns(nep->V,0,nv);
    972:   PetscMalloc1(ctx->nmat,&coeffs);
    973:   if (PetscAbsScalar(s[deg-2]-sigma)<100*PETSC_MACHINE_EPSILON) SETERRQ(PETSC_COMM_SELF,1,"Breakdown in NLEIGS");
    974:   /* i-part stored in (i-1) position */
    975:   for (j=0;j<nv;j++) {
    976:     r[(deg-2)*lr+j] = (S[(deg-2)*ls+j]+(beta[deg-1]/xi[deg-2])*S[(deg-1)*ls+j])/(s[deg-2]-sigma);
    977:   }
    978:   BVSetActiveColumns(W,0,deg);
    979:   BVGetColumn(W,deg-1,&w);
    980:   BVMultVec(V,1.0/beta[deg],0,w,S+(deg-1)*ls);
    981:   BVRestoreColumn(W,deg-1,&w);
    982:   BVGetColumn(W,deg-2,&w);
    983:   BVMultVec(V,1.0,0.0,w,r+(deg-2)*lr);
    984:   BVRestoreColumn(W,deg-2,&w);
    985:   for (k=deg-2;k>0;k--) {
    986:     if (PetscAbsScalar(s[k-1]-sigma)<100*PETSC_MACHINE_EPSILON) SETERRQ(PETSC_COMM_SELF,1,"Breakdown in NLEIGS");
    987:     for (j=0;j<nv;j++) r[(k-1)*lr+j] = (S[(k-1)*ls+j]+(beta[k]/xi[k-1])*S[k*ls+j]-beta[k]*(1.0-sigma/xi[k-1])*r[(k)*lr+j])/(s[k-1]-sigma);
    988:     BVGetColumn(W,k-1,&w);
    989:     BVMultVec(V,1.0,0.0,w,r+(k-1)*lr);
    990:     BVRestoreColumn(W,k-1,&w);
    991:   }
    992:   if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
    993:     for (j=0;j<ctx->nmat-2;j++) coeffs[j] = ctx->coeffD[nep->nt*j];
    994:     coeffs[ctx->nmat-2] = ctx->coeffD[nep->nt*(ctx->nmat-1)];
    995:     BVMultVec(W,1.0,0.0,v,coeffs);
    996:     MatMult(nep->A[0],v,q);
    997:     for (k=1;k<nep->nt;k++) {
    998:       for (j=0;j<ctx->nmat-2;j++) coeffs[j] = ctx->coeffD[nep->nt*j+k];
    999:       coeffs[ctx->nmat-2] = ctx->coeffD[nep->nt*(ctx->nmat-1)+k];
    1000:       BVMultVec(W,1.0,0,v,coeffs);
    1001:       MatMult(nep->A[k],v,t);
    1002:       VecAXPY(q,1.0,t);
    1003:     }
    1004:     KSPSolve(ctx->ksp[idxrktg],q,t);
    1005:     VecScale(t,-1.0);
    1006:   } else {
    1007:     for (k=0;k<deg-1;k++) {
    1008:       BVGetColumn(W,k,&w);
    1009:       MatMult(ctx->D[k],w,q);
    1010:       BVRestoreColumn(W,k,&w);
    1011:       BVInsertVec(W,k,q);
    1012:     }
    1013:     BVGetColumn(W,deg-1,&w);
    1014:     MatMult(ctx->D[deg],w,q);
    1015:     BVRestoreColumn(W,k,&w);
    1016:     BVInsertVec(W,k,q);
    1017:     for (j=0;j<ctx->nmat-1;j++) coeffs[j] = 1.0;
    1018:     BVMultVec(W,1.0,0.0,q,coeffs);
    1019:     KSPSolve(ctx->ksp[idxrktg],q,t);
    1020:     VecScale(t,-1.0);
    1021:   }
    1022:   PetscFree(coeffs);
    1023:   return(0);
    1024: }

    1026: /*
    1027:   Compute TOAR coefficients of the blocks of the new Arnoldi vector computed
    1028: */
    1029: static PetscErrorCode NEPTOARCoefficients(NEP nep,PetscScalar sigma,PetscInt nv,PetscScalar *S,PetscInt ls,PetscScalar *r,PetscInt lr,PetscScalar *x,PetscScalar *work)
    1030: {
    1032:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    1033:   PetscInt       k,j,d=ctx->nmat-1;
    1034:   PetscScalar    *t=work;

    1037:   NEPNLEIGSEvalNRTFunct(nep,d-1,sigma,t);
    1038:   for (k=0;k<d-1;k++) {
    1039:     for (j=0;j<=nv;j++) r[k*lr+j] += t[k]*x[j];
    1040:   }
    1041:   for (j=0;j<=nv;j++) r[(d-1)*lr+j] = t[d-1]*x[j];
    1042:   return(0);
    1043: }

    1045: /*
    1046:   Compute continuation vector coefficients for the Rational-Krylov run.
    1047:   dim(work) >= (end-ini)*(end-ini+1) + end+1 + 2*(end-ini+1), dim(t) = end.
    1048: */
    1049: static PetscErrorCode NEPNLEIGS_RKcontinuation(NEP nep,PetscInt ini,PetscInt end,PetscScalar *K,PetscScalar *H,PetscInt ld,PetscScalar sigma,PetscScalar *S,PetscInt lds,PetscScalar *cont,PetscScalar *t,PetscScalar *work)
    1050: {
    1052:   PetscScalar    *x,*W,*tau,sone=1.0,szero=0.0;
    1053:   PetscInt       i,j,n1,n,nwu=0;
    1054:   PetscBLASInt   info,n_,n1_,one=1,dim,lds_;
    1055:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;

    1058:   if (!ctx->nshifts || !end) {
    1059:     t[0] = 1;
    1060:     PetscArraycpy(cont,S+end*lds,lds);
    1061:   } else {
    1062:     n   = end-ini;
    1063:     n1  = n+1;
    1064:     x   = work+nwu;
    1065:     nwu += end+1;
    1066:     tau = work+nwu;
    1067:     nwu += n;
    1068:     W   = work+nwu;
    1069:     nwu += n1*n;
    1070:     for (j=ini;j<end;j++) {
    1071:       for (i=ini;i<=end;i++) W[(j-ini)*n1+i-ini] = K[j*ld+i] -H[j*ld+i]*sigma;
    1072:     }
    1073:     PetscBLASIntCast(n,&n_);
    1074:     PetscBLASIntCast(n1,&n1_);
    1075:     PetscBLASIntCast(end+1,&dim);
    1076:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    1077:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&n1_,&n_,W,&n1_,tau,work+nwu,&n1_,&info));
    1078:     SlepcCheckLapackInfo("geqrf",info);
    1079:     for (i=0;i<end;i++) t[i] = 0.0;
    1080:     t[end] = 1.0;
    1081:     for (j=n-1;j>=0;j--) {
    1082:       for (i=0;i<ini+j;i++) x[i] = 0.0;
    1083:       x[ini+j] = 1.0;
    1084:       for (i=j+1;i<n1;i++) x[i+ini] = W[i+n1*j];
    1085:       tau[j] = PetscConj(tau[j]);
    1086:       PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&dim,&one,x,&one,tau+j,t,&dim,work+nwu));
    1087:     }
    1088:     PetscBLASIntCast(lds,&lds_);
    1089:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&n1_,&sone,S,&lds_,t,&one,&szero,cont,&one));
    1090:     PetscFPTrapPop();
    1091:   }
    1092:   return(0);
    1093: }

    1095: /*
    1096:   Compute a run of Arnoldi iterations
    1097: */
    1098: PetscErrorCode NEPNLEIGSTOARrun(NEP nep,PetscScalar *K,PetscScalar *H,PetscInt ldh,BV W,PetscInt k,PetscInt *M,PetscBool *breakdown,Vec *t_)
    1099: {
    1101:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;
    1102:   PetscInt       i,j,m=*M,lwa,deg=ctx->nmat-1,lds,nqt,ld,l;
    1103:   Vec            t;
    1104:   PetscReal      norm;
    1105:   PetscScalar    *x,*work,*tt,sigma,*cont,*S;
    1106:   PetscBool      lindep;
    1107:   Mat            MS;

    1110:   BVTensorGetFactors(ctx->V,NULL,&MS);
    1111:   MatDenseGetArray(MS,&S);
    1112:   BVGetSizes(nep->V,NULL,NULL,&ld);
    1113:   lds = ld*deg;
    1114:   BVGetActiveColumns(nep->V,&l,&nqt);
    1115:   lwa = PetscMax(ld,deg)+(m+1)*(m+1)+4*(m+1);
    1116:   PetscMalloc4(ld,&x,lwa,&work,m+1,&tt,lds,&cont);
    1117:   BVSetActiveColumns(ctx->V,0,m);
    1118:   for (j=k;j<m;j++) {
    1119:     sigma = ctx->shifts[(++(ctx->idxrk))%ctx->nshiftsw];

    1121:     /* Continuation vector */
    1122:     NEPNLEIGS_RKcontinuation(nep,0,j,K,H,ldh,sigma,S,lds,cont,tt,work);

    1124:     /* apply operator */
    1125:     BVGetColumn(nep->V,nqt,&t);
    1126:     NEPTOARExtendBasis(nep,(ctx->idxrk)%ctx->nshiftsw,cont,ld,nqt,W,nep->V,t,S+(j+1)*lds,ld,t_);
    1127:     BVRestoreColumn(nep->V,nqt,&t);

    1129:     /* orthogonalize */
    1130:     BVOrthogonalizeColumn(nep->V,nqt,x,&norm,&lindep);
    1131:     if (!lindep) {
    1132:       x[nqt] = norm;
    1133:       BVScaleColumn(nep->V,nqt,1.0/norm);
    1134:       nqt++;
    1135:     } else x[nqt] = 0.0;

    1137:     NEPTOARCoefficients(nep,sigma,nqt-1,cont,ld,S+(j+1)*lds,ld,x,work);

    1139:     /* Level-2 orthogonalization */
    1140:     BVOrthogonalizeColumn(ctx->V,j+1,H+j*ldh,&norm,breakdown);
    1141:     H[j+1+ldh*j] = norm;
    1142:     if (ctx->nshifts) {
    1143:       for (i=0;i<=j;i++) K[i+ldh*j] = sigma*H[i+ldh*j] + tt[i];
    1144:       K[j+1+ldh*j] = sigma*H[j+1+ldh*j];
    1145:     }
    1146:     if (*breakdown) {
    1147:       *M = j+1;
    1148:       break;
    1149:     }
    1150:     BVScaleColumn(ctx->V,j+1,1.0/norm);
    1151:     BVSetActiveColumns(nep->V,l,nqt);
    1152:   }
    1153:   PetscFree4(x,work,tt,cont);
    1154:   MatDenseRestoreArray(MS,&S);
    1155:   BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1156:   return(0);
    1157: }

    1159: PetscErrorCode NEPSolve_NLEIGS(NEP nep)
    1160: {
    1161:   PetscErrorCode    ierr;
    1162:   NEP_NLEIGS        *ctx = (NEP_NLEIGS*)nep->data;
    1163:   PetscInt          i,k=0,l,nv=0,ld,lds,ldds,nq;
    1164:   PetscInt          deg=ctx->nmat-1,nconv=0,dsn,dsk;
    1165:   PetscScalar       *H,*pU,*K,betak=0,*eigr,*eigi;
    1166:   const PetscScalar *S;
    1167:   PetscReal         betah;
    1168:   PetscBool         falselock=PETSC_FALSE,breakdown=PETSC_FALSE;
    1169:   BV                W;
    1170:   Mat               MS,MQ,U;

    1173:   if (ctx->lock) {
    1174:     /* undocumented option to use a cheaper locking instead of the true locking */
    1175:     PetscOptionsGetBool(NULL,NULL,"-nep_nleigs_falselocking",&falselock,NULL);
    1176:   }

    1178:   BVGetSizes(nep->V,NULL,NULL,&ld);
    1179:   lds = deg*ld;
    1180:   DSGetLeadingDimension(nep->ds,&ldds);
    1181:   if (!ctx->nshifts) {
    1182:     PetscMalloc2(nep->ncv,&eigr,nep->ncv,&eigi);
    1183:   } else { eigr = nep->eigr; eigi = nep->eigi; }
    1184:   BVDuplicateResize(nep->V,PetscMax(nep->nt-1,ctx->nmat-1),&W);

    1187:   /* clean projected matrix (including the extra-arrow) */
    1188:   DSGetArray(nep->ds,DS_MAT_A,&H);
    1189:   PetscArrayzero(H,ldds*ldds);
    1190:   DSRestoreArray(nep->ds,DS_MAT_A,&H);
    1191:   if (ctx->nshifts) {
    1192:     DSGetArray(nep->ds,DS_MAT_B,&H);
    1193:     PetscArrayzero(H,ldds*ldds);
    1194:     DSRestoreArray(nep->ds,DS_MAT_B,&H);
    1195:   }

    1197:   /* Get the starting Arnoldi vector */
    1198:   BVTensorBuildFirstColumn(ctx->V,nep->nini);

    1200:   /* Restart loop */
    1201:   l = 0;
    1202:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    1203:     nep->its++;

    1205:     /* Compute an nv-step Krylov relation */
    1206:     nv = PetscMin(nep->nconv+nep->mpd,nep->ncv);
    1207:     if (ctx->nshifts) { DSGetArray(nep->ds,DS_MAT_A,&K); }
    1208:     DSGetArray(nep->ds,ctx->nshifts?DS_MAT_B:DS_MAT_A,&H);
    1209:     NEPNLEIGSTOARrun(nep,K,H,ldds,W,nep->nconv+l,&nv,&breakdown,nep->work);
    1210:     betah = PetscAbsScalar(H[(nv-1)*ldds+nv]);
    1211:     DSRestoreArray(nep->ds,ctx->nshifts?DS_MAT_B:DS_MAT_A,&H);
    1212:     if (ctx->nshifts) {
    1213:       betak = K[(nv-1)*ldds+nv];
    1214:       DSRestoreArray(nep->ds,DS_MAT_A,&K);
    1215:     }
    1216:     DSSetDimensions(nep->ds,nv,0,nep->nconv,nep->nconv+l);
    1217:     if (l==0) {
    1218:       DSSetState(nep->ds,DS_STATE_INTERMEDIATE);
    1219:     } else {
    1220:       DSSetState(nep->ds,DS_STATE_RAW);
    1221:     }

    1223:     /* Solve projected problem */
    1224:     DSSolve(nep->ds,nep->eigr,nep->eigi);
    1225:     DSSort(nep->ds,nep->eigr,nep->eigi,NULL,NULL,NULL);
    1226:     DSUpdateExtraRow(nep->ds);
    1227:     DSSynchronize(nep->ds,nep->eigr,nep->eigi);

    1229:     /* Check convergence */
    1230:     NEPNLEIGSKrylovConvergence(nep,PETSC_FALSE,nep->nconv,nv-nep->nconv,betah,betak,&k,nep->work);
    1231:     (*nep->stopping)(nep,nep->its,nep->max_it,k,nep->nev,&nep->reason,nep->stoppingctx);

    1233:     /* Update l */
    1234:     if (nep->reason != NEP_CONVERGED_ITERATING || breakdown) l = 0;
    1235:     else {
    1236:       l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    1237:       DSGetTruncateSize(nep->ds,k,nv,&l);
    1238:       if (!breakdown) {
    1239:         /* Prepare the Rayleigh quotient for restart */
    1240:         DSGetDimensions(nep->ds,&dsn,NULL,NULL,&dsk,NULL);
    1241:         DSSetDimensions(nep->ds,dsn,0,k,dsk);
    1242:         DSTruncate(nep->ds,k+l,PETSC_FALSE);
    1243:       }
    1244:     }
    1245:     nconv = k;
    1246:     if (!ctx->lock && nep->reason == NEP_CONVERGED_ITERATING && !breakdown) { l += k; k = 0; }
    1247:     if (l) { PetscInfo1(nep,"Preparing to restart keeping l=%D vectors\n",l); }

    1249:     /* Update S */
    1250:     DSGetMat(nep->ds,ctx->nshifts?DS_MAT_Z:DS_MAT_Q,&MQ);
    1251:     BVMultInPlace(ctx->V,MQ,nep->nconv,k+l);
    1252:     MatDestroy(&MQ);

    1254:     /* Copy last column of S */
    1255:     BVCopyColumn(ctx->V,nv,k+l);

    1257:     if (breakdown && nep->reason == NEP_CONVERGED_ITERATING) {
    1258:       /* Stop if breakdown */
    1259:       PetscInfo2(nep,"Breakdown (it=%D norm=%g)\n",nep->its,(double)betah);
    1260:       nep->reason = NEP_DIVERGED_BREAKDOWN;
    1261:     }
    1262:     if (nep->reason != NEP_CONVERGED_ITERATING) l--;
    1263:     /* truncate S */
    1264:     BVGetActiveColumns(nep->V,NULL,&nq);
    1265:     if (k+l+deg<=nq) {
    1266:       BVSetActiveColumns(ctx->V,nep->nconv,k+l+1);
    1267:       if (!falselock && ctx->lock) {
    1268:         BVTensorCompress(ctx->V,k-nep->nconv);
    1269:       } else {
    1270:         BVTensorCompress(ctx->V,0);
    1271:       }
    1272:     }
    1273:     nep->nconv = k;
    1274:     if (!ctx->nshifts) {
    1275:       for (i=0;i<nv;i++) { eigr[i] = nep->eigr[i]; eigi[i] = nep->eigi[i]; }
    1276:       NEPNLEIGSBackTransform((PetscObject)nep,nv,eigr,eigi);
    1277:     }
    1278:     NEPMonitor(nep,nep->its,nconv,eigr,eigi,nep->errest,nv);
    1279:   }
    1280:   nep->nconv = nconv;
    1281:   if (nep->nconv>0) {
    1282:     BVSetActiveColumns(ctx->V,0,nep->nconv);
    1283:     BVGetActiveColumns(nep->V,NULL,&nq);
    1284:     BVSetActiveColumns(nep->V,0,nq);
    1285:     if (nq>nep->nconv) {
    1286:       BVTensorCompress(ctx->V,nep->nconv);
    1287:       BVSetActiveColumns(nep->V,0,nep->nconv);
    1288:       nq = nep->nconv;
    1289:     }
    1290:     if (ctx->nshifts) {
    1291:       DSGetMat(nep->ds,DS_MAT_B,&MQ);
    1292:       BVMultInPlace(ctx->V,MQ,0,nep->nconv);
    1293:       MatDestroy(&MQ);
    1294:     }
    1295:     BVTensorGetFactors(ctx->V,NULL,&MS);
    1296:     MatDenseGetArrayRead(MS,&S);
    1297:     PetscMalloc1(nq*nep->nconv,&pU);
    1298:     for (i=0;i<nep->nconv;i++) {
    1299:       PetscArraycpy(pU+i*nq,S+i*lds,nq);
    1300:     }
    1301:     MatDenseRestoreArrayRead(MS,&S);
    1302:     BVTensorRestoreFactors(ctx->V,NULL,&MS);
    1303:     MatCreateSeqDense(PETSC_COMM_SELF,nq,nep->nconv,pU,&U);
    1304:     BVSetActiveColumns(nep->V,0,nq);
    1305:     BVMultInPlace(nep->V,U,0,nep->nconv);
    1306:     BVSetActiveColumns(nep->V,0,nep->nconv);
    1307:     MatDestroy(&U);
    1308:     PetscFree(pU);
    1309:     DSTruncate(nep->ds,nep->nconv,PETSC_TRUE);
    1310:   }

    1312:   /* Map eigenvalues back to the original problem */
    1313:   if (!ctx->nshifts) {
    1314:     NEPNLEIGSBackTransform((PetscObject)nep,nep->nconv,nep->eigr,nep->eigi);
    1315:     PetscFree2(eigr,eigi);
    1316:   }
    1317:   BVDestroy(&W);
    1318:   return(0);
    1319: }

    1321: static PetscErrorCode NEPNLEIGSSetSingularitiesFunction_NLEIGS(NEP nep,PetscErrorCode (*fun)(NEP,PetscInt*,PetscScalar*,void*),void *ctx)
    1322: {
    1323:   NEP_NLEIGS *nepctx=(NEP_NLEIGS*)nep->data;

    1326:   if (fun) nepctx->computesingularities = fun;
    1327:   if (ctx) nepctx->singularitiesctx     = ctx;
    1328:   nep->state = NEP_STATE_INITIAL;
    1329:   return(0);
    1330: }

    1332: /*@C
    1333:    NEPNLEIGSSetSingularitiesFunction - Sets a user function to compute a discretization
    1334:    of the singularity set (where T(.) is not analytic).

    1336:    Logically Collective on nep

    1338:    Input Parameters:
    1339: +  nep - the NEP context
    1340: .  fun - user function (if NULL then NEP retains any previously set value)
    1341: -  ctx - [optional] user-defined context for private data for the function
    1342:          (may be NULL, in which case NEP retains any previously set value)

    1344:    Calling Sequence of fun:
    1345: $   fun(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *ctx)

    1347: +   nep   - the NEP context
    1348: .   maxnp - on input number of requested points in the discretization (can be set)
    1349: .   xi    - computed values of the discretization
    1350: -   ctx   - optional context, as set by NEPNLEIGSSetSingularitiesFunction()

    1352:    Notes:
    1353:    The user-defined function can set a smaller value of maxnp if necessary.
    1354:    It is wrong to return a larger value.

    1356:    If the problem type has been set to rational with NEPSetProblemType(),
    1357:    then it is not necessary to set the singularities explicitly since the
    1358:    solver will try to determine them automatically.

    1360:    Level: intermediate

    1362: .seealso: NEPNLEIGSGetSingularitiesFunction(), NEPSetProblemType()
    1363: @*/
    1364: PetscErrorCode NEPNLEIGSSetSingularitiesFunction(NEP nep,PetscErrorCode (*fun)(NEP,PetscInt*,PetscScalar*,void*),void *ctx)
    1365: {

    1370:   PetscTryMethod(nep,"NEPNLEIGSSetSingularitiesFunction_C",(NEP,PetscErrorCode(*)(NEP,PetscInt*,PetscScalar*,void*),void*),(nep,fun,ctx));
    1371:   return(0);
    1372: }

    1374: static PetscErrorCode NEPNLEIGSGetSingularitiesFunction_NLEIGS(NEP nep,PetscErrorCode (**fun)(NEP,PetscInt*,PetscScalar*,void*),void **ctx)
    1375: {
    1376:   NEP_NLEIGS *nepctx=(NEP_NLEIGS*)nep->data;

    1379:   if (fun) *fun = nepctx->computesingularities;
    1380:   if (ctx) *ctx = nepctx->singularitiesctx;
    1381:   return(0);
    1382: }

    1384: /*@C
    1385:    NEPNLEIGSGetSingularitiesFunction - Returns the Function and optionally the user
    1386:    provided context for computing a discretization of the singularity set.

    1388:    Not Collective

    1390:    Input Parameter:
    1391: .  nep - the nonlinear eigensolver context

    1393:    Output Parameters:
    1394: +  fun - location to put the function (or NULL)
    1395: -  ctx - location to stash the function context (or NULL)

    1397:    Level: advanced

    1399: .seealso: NEPNLEIGSSetSingularitiesFunction()
    1400: @*/
    1401: PetscErrorCode NEPNLEIGSGetSingularitiesFunction(NEP nep,PetscErrorCode (**fun)(NEP,PetscInt*,PetscScalar*,void*),void **ctx)
    1402: {

    1407:   PetscUseMethod(nep,"NEPNLEIGSGetSingularitiesFunction_C",(NEP,PetscErrorCode(**)(NEP,PetscInt*,PetscScalar*,void*),void**),(nep,fun,ctx));
    1408:   return(0);
    1409: }

    1411: static PetscErrorCode NEPNLEIGSSetRestart_NLEIGS(NEP nep,PetscReal keep)
    1412: {
    1413:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1416:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
    1417:   else {
    1418:     if (keep<0.1 || keep>0.9) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
    1419:     ctx->keep = keep;
    1420:   }
    1421:   return(0);
    1422: }

    1424: /*@
    1425:    NEPNLEIGSSetRestart - Sets the restart parameter for the NLEIGS
    1426:    method, in particular the proportion of basis vectors that must be kept
    1427:    after restart.

    1429:    Logically Collective on nep

    1431:    Input Parameters:
    1432: +  nep  - the nonlinear eigensolver context
    1433: -  keep - the number of vectors to be kept at restart

    1435:    Options Database Key:
    1436: .  -nep_nleigs_restart - Sets the restart parameter

    1438:    Notes:
    1439:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

    1441:    Level: advanced

    1443: .seealso: NEPNLEIGSGetRestart()
    1444: @*/
    1445: PetscErrorCode NEPNLEIGSSetRestart(NEP nep,PetscReal keep)
    1446: {

    1452:   PetscTryMethod(nep,"NEPNLEIGSSetRestart_C",(NEP,PetscReal),(nep,keep));
    1453:   return(0);
    1454: }

    1456: static PetscErrorCode NEPNLEIGSGetRestart_NLEIGS(NEP nep,PetscReal *keep)
    1457: {
    1458:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1461:   *keep = ctx->keep;
    1462:   return(0);
    1463: }

    1465: /*@
    1466:    NEPNLEIGSGetRestart - Gets the restart parameter used in the NLEIGS method.

    1468:    Not Collective

    1470:    Input Parameter:
    1471: .  nep - the nonlinear eigensolver context

    1473:    Output Parameter:
    1474: .  keep - the restart parameter

    1476:    Level: advanced

    1478: .seealso: NEPNLEIGSSetRestart()
    1479: @*/
    1480: PetscErrorCode NEPNLEIGSGetRestart(NEP nep,PetscReal *keep)
    1481: {

    1487:   PetscUseMethod(nep,"NEPNLEIGSGetRestart_C",(NEP,PetscReal*),(nep,keep));
    1488:   return(0);
    1489: }

    1491: static PetscErrorCode NEPNLEIGSSetLocking_NLEIGS(NEP nep,PetscBool lock)
    1492: {
    1493:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1496:   ctx->lock = lock;
    1497:   return(0);
    1498: }

    1500: /*@
    1501:    NEPNLEIGSSetLocking - Choose between locking and non-locking variants of
    1502:    the NLEIGS method.

    1504:    Logically Collective on nep

    1506:    Input Parameters:
    1507: +  nep  - the nonlinear eigensolver context
    1508: -  lock - true if the locking variant must be selected

    1510:    Options Database Key:
    1511: .  -nep_nleigs_locking - Sets the locking flag

    1513:    Notes:
    1514:    The default is to lock converged eigenpairs when the method restarts.
    1515:    This behaviour can be changed so that all directions are kept in the
    1516:    working subspace even if already converged to working accuracy (the
    1517:    non-locking variant).

    1519:    Level: advanced

    1521: .seealso: NEPNLEIGSGetLocking()
    1522: @*/
    1523: PetscErrorCode NEPNLEIGSSetLocking(NEP nep,PetscBool lock)
    1524: {

    1530:   PetscTryMethod(nep,"NEPNLEIGSSetLocking_C",(NEP,PetscBool),(nep,lock));
    1531:   return(0);
    1532: }

    1534: static PetscErrorCode NEPNLEIGSGetLocking_NLEIGS(NEP nep,PetscBool *lock)
    1535: {
    1536:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1539:   *lock = ctx->lock;
    1540:   return(0);
    1541: }

    1543: /*@
    1544:    NEPNLEIGSGetLocking - Gets the locking flag used in the NLEIGS method.

    1546:    Not Collective

    1548:    Input Parameter:
    1549: .  nep - the nonlinear eigensolver context

    1551:    Output Parameter:
    1552: .  lock - the locking flag

    1554:    Level: advanced

    1556: .seealso: NEPNLEIGSSetLocking()
    1557: @*/
    1558: PetscErrorCode NEPNLEIGSGetLocking(NEP nep,PetscBool *lock)
    1559: {

    1565:   PetscUseMethod(nep,"NEPNLEIGSGetLocking_C",(NEP,PetscBool*),(nep,lock));
    1566:   return(0);
    1567: }

    1569: static PetscErrorCode NEPNLEIGSSetInterpolation_NLEIGS(NEP nep,PetscReal tol,PetscInt degree)
    1570: {
    1572:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;

    1575:   if (tol == PETSC_DEFAULT) {
    1576:     ctx->ddtol = PETSC_DEFAULT;
    1577:     nep->state = NEP_STATE_INITIAL;
    1578:   } else {
    1579:     if (tol <= 0.0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of tol. Must be > 0");
    1580:     ctx->ddtol = tol;
    1581:   }
    1582:   if (degree == PETSC_DEFAULT || degree == PETSC_DECIDE) {
    1583:     ctx->ddmaxit = 0;
    1584:     if (nep->state) { NEPReset(nep); }
    1585:     nep->state = NEP_STATE_INITIAL;
    1586:   } else {
    1587:     if (degree <= 0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of degree. Must be > 0");
    1588:     if (ctx->ddmaxit != degree) {
    1589:       ctx->ddmaxit = degree;
    1590:       if (nep->state) { NEPReset(nep); }
    1591:       nep->state = NEP_STATE_INITIAL;
    1592:     }
    1593:   }
    1594:   return(0);
    1595: }

    1597: /*@
    1598:    NEPNLEIGSSetInterpolation - Sets the tolerance and maximum degree
    1599:    when building the interpolation via divided differences.

    1601:    Logically Collective on nep

    1603:    Input Parameters:
    1604: +  nep    - the nonlinear eigensolver context
    1605: .  tol    - tolerance to stop computing divided differences
    1606: -  degree - maximum degree of interpolation

    1608:    Options Database Key:
    1609: +  -nep_nleigs_interpolation_tol <tol> - Sets the tolerance to stop computing divided differences
    1610: -  -nep_nleigs_interpolation_degree <degree> - Sets the maximum degree of interpolation

    1612:    Notes:
    1613:    Use PETSC_DEFAULT for either argument to assign a reasonably good value.

    1615:    Level: advanced

    1617: .seealso: NEPNLEIGSGetInterpolation()
    1618: @*/
    1619: PetscErrorCode NEPNLEIGSSetInterpolation(NEP nep,PetscReal tol,PetscInt degree)
    1620: {

    1627:   PetscTryMethod(nep,"NEPNLEIGSSetInterpolation_C",(NEP,PetscReal,PetscInt),(nep,tol,degree));
    1628:   return(0);
    1629: }

    1631: static PetscErrorCode NEPNLEIGSGetInterpolation_NLEIGS(NEP nep,PetscReal *tol,PetscInt *degree)
    1632: {
    1633:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1636:   if (tol)    *tol    = ctx->ddtol;
    1637:   if (degree) *degree = ctx->ddmaxit;
    1638:   return(0);
    1639: }

    1641: /*@
    1642:    NEPNLEIGSGetInterpolation - Gets the tolerance and maximum degree
    1643:    when building the interpolation via divided differences.

    1645:    Not Collective

    1647:    Input Parameter:
    1648: .  nep - the nonlinear eigensolver context

    1650:    Output Parameter:
    1651: +  tol    - tolerance to stop computing divided differences
    1652: -  degree - maximum degree of interpolation

    1654:    Level: advanced

    1656: .seealso: NEPNLEIGSSetInterpolation()
    1657: @*/
    1658: PetscErrorCode NEPNLEIGSGetInterpolation(NEP nep,PetscReal *tol,PetscInt *degree)
    1659: {

    1664:   PetscTryMethod(nep,"NEPNLEIGSGetInterpolation_C",(NEP,PetscReal*,PetscInt*),(nep,tol,degree));
    1665:   return(0);
    1666: }

    1668: static PetscErrorCode NEPNLEIGSSetRKShifts_NLEIGS(NEP nep,PetscInt ns,PetscScalar *shifts)
    1669: {
    1671:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    1672:   PetscInt       i;

    1675:   if (ns<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_WRONG,"Number of shifts must be non-negative");
    1676:   if (ctx->nshifts) { PetscFree(ctx->shifts); }
    1677:   for (i=0;i<ctx->nshiftsw;i++) { KSPDestroy(&ctx->ksp[i]); }
    1678:   PetscFree(ctx->ksp);
    1679:   ctx->ksp = NULL;
    1680:   if (ns) {
    1681:     PetscMalloc1(ns,&ctx->shifts);
    1682:     for (i=0;i<ns;i++) ctx->shifts[i] = shifts[i];
    1683:   }
    1684:   ctx->nshifts = ns;
    1685:   nep->state   = NEP_STATE_INITIAL;
    1686:   return(0);
    1687: }

    1689: /*@
    1690:    NEPNLEIGSSetRKShifts - Sets a list of shifts to be used in the Rational
    1691:    Krylov method.

    1693:    Logically Collective on nep

    1695:    Input Parameters:
    1696: +  nep    - the nonlinear eigensolver context
    1697: .  ns     - number of shifts
    1698: -  shifts - array of scalar values specifying the shifts

    1700:    Options Database Key:
    1701: .  -nep_nleigs_rk_shifts - Sets the list of shifts

    1703:    Notes:
    1704:    If only one shift is provided, the built subspace built is equivalent to
    1705:    shift-and-invert Krylov-Schur (provided that the absolute convergence
    1706:    criterion is used).

    1708:    In the case of real scalars, complex shifts are not allowed. In the
    1709:    command line, a comma-separated list of complex values can be provided with
    1710:    the format [+/-][realnumber][+/-]realnumberi with no spaces, e.g.
    1711:    -nep_nleigs_rk_shifts 1.0+2.0i,1.5+2.0i,1.0+1.5i

    1713:    Use ns=0 to remove previously set shifts.

    1715:    Level: advanced

    1717: .seealso: NEPNLEIGSGetRKShifts()
    1718: @*/
    1719: PetscErrorCode NEPNLEIGSSetRKShifts(NEP nep,PetscInt ns,PetscScalar shifts[])
    1720: {

    1727:   PetscTryMethod(nep,"NEPNLEIGSSetRKShifts_C",(NEP,PetscInt,PetscScalar*),(nep,ns,shifts));
    1728:   return(0);
    1729: }

    1731: static PetscErrorCode NEPNLEIGSGetRKShifts_NLEIGS(NEP nep,PetscInt *ns,PetscScalar **shifts)
    1732: {
    1734:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    1735:   PetscInt       i;

    1738:   *ns = ctx->nshifts;
    1739:   if (ctx->nshifts) {
    1740:     PetscMalloc1(ctx->nshifts,shifts);
    1741:     for (i=0;i<ctx->nshifts;i++) (*shifts)[i] = ctx->shifts[i];
    1742:   }
    1743:   return(0);
    1744: }

    1746: /*@C
    1747:    NEPNLEIGSGetRKShifts - Gets the list of shifts used in the Rational
    1748:    Krylov method.

    1750:    Not Collective

    1752:    Input Parameter:
    1753: .  nep - the nonlinear eigensolver context

    1755:    Output Parameter:
    1756: +  ns     - number of shifts
    1757: -  shifts - array of shifts

    1759:    Note:
    1760:    The user is responsible for deallocating the returned array.

    1762:    Level: advanced

    1764: .seealso: NEPNLEIGSSetRKShifts()
    1765: @*/
    1766: PetscErrorCode NEPNLEIGSGetRKShifts(NEP nep,PetscInt *ns,PetscScalar *shifts[])
    1767: {

    1774:   PetscTryMethod(nep,"NEPNLEIGSGetRKShifts_C",(NEP,PetscInt*,PetscScalar**),(nep,ns,shifts));
    1775:   return(0);
    1776: }

    1778: static PetscErrorCode NEPNLEIGSGetKSPs_NLEIGS(NEP nep,PetscInt *nsolve,KSP **ksp)
    1779: {
    1781:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;
    1782:   PetscInt       i;
    1783:   PC             pc;

    1786:   if (!ctx->ksp) {
    1787:     NEPNLEIGSSetShifts(nep,&ctx->nshiftsw);
    1788:     PetscMalloc1(ctx->nshiftsw,&ctx->ksp);
    1789:     for (i=0;i<ctx->nshiftsw;i++) {
    1790:       KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp[i]);
    1791:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp[i],(PetscObject)nep,1);
    1792:       KSPSetOptionsPrefix(ctx->ksp[i],((PetscObject)nep)->prefix);
    1793:       KSPAppendOptionsPrefix(ctx->ksp[i],"nep_nleigs_");
    1794:       PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp[i]);
    1795:       PetscObjectSetOptions((PetscObject)ctx->ksp[i],((PetscObject)nep)->options);
    1796:       KSPSetErrorIfNotConverged(ctx->ksp[i],PETSC_TRUE);
    1797:       KSPSetTolerances(ctx->ksp[i],SLEPC_DEFAULT_TOL,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    1798:       KSPGetPC(ctx->ksp[i],&pc);
    1799:       KSPSetType(ctx->ksp[i],KSPPREONLY);
    1800:       PCSetType(pc,PCLU);
    1801:     }
    1802:   }
    1803:   if (nsolve) *nsolve = ctx->nshiftsw;
    1804:   if (ksp)    *ksp    = ctx->ksp;
    1805:   return(0);
    1806: }

    1808: /*@C
    1809:    NEPNLEIGSGetKSPs - Retrieve the array of linear solver objects associated with
    1810:    the nonlinear eigenvalue solver.

    1812:    Not Collective

    1814:    Input Parameter:
    1815: .  nep - nonlinear eigenvalue solver

    1817:    Output Parameters:
    1818: +  nsolve - number of returned KSP objects
    1819: -  ksp - array of linear solver object

    1821:    Notes:
    1822:    The number of KSP objects is equal to the number of shifts provided by the user,
    1823:    or 1 if the user did not provide shifts.

    1825:    Level: advanced

    1827: .seealso: NEPNLEIGSSetRKShifts()
    1828: @*/
    1829: PetscErrorCode NEPNLEIGSGetKSPs(NEP nep,PetscInt *nsolve,KSP **ksp)
    1830: {

    1835:   PetscUseMethod(nep,"NEPNLEIGSGetKSPs_C",(NEP,PetscInt*,KSP**),(nep,nsolve,ksp));
    1836:   return(0);
    1837: }

    1839: static PetscErrorCode NEPNLEIGSSetFullBasis_NLEIGS(NEP nep,PetscBool fullbasis)
    1840: {
    1841:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1844:   if (fullbasis!=ctx->fullbasis) {
    1845:     ctx->fullbasis = fullbasis;
    1846:     nep->state     = NEP_STATE_INITIAL;
    1847:     nep->useds     = PetscNot(fullbasis);
    1848:   }
    1849:   return(0);
    1850: }

    1852: /*@
    1853:    NEPNLEIGSSetFullBasis - Choose between TOAR-basis (default) and full-basis
    1854:    variants of the NLEIGS method.

    1856:    Logically Collective on nep

    1858:    Input Parameters:
    1859: +  nep  - the nonlinear eigensolver context
    1860: -  fullbasis - true if the full-basis variant must be selected

    1862:    Options Database Key:
    1863: .  -nep_nleigs_full_basis - Sets the full-basis flag

    1865:    Notes:
    1866:    The default is to use a compact representation of the Krylov basis, that is,
    1867:    V = (I otimes U) S, with a tensor BV. This behaviour can be changed so that
    1868:    the full basis V is explicitly stored and operated with. This variant is more
    1869:    expensive in terms of memory and computation, but is necessary in some cases,
    1870:    particularly for two-sided computations, see NEPSetTwoSided().

    1872:    In the full-basis variant, the NLEIGS solver uses an EPS object to explicitly
    1873:    solve the linearized eigenproblem, see NEPNLEIGSGetEPS().

    1875:    Level: advanced

    1877: .seealso: NEPNLEIGSGetFullBasis(), NEPNLEIGSGetEPS(), NEPSetTwoSided(), BVCreateTensor()
    1878: @*/
    1879: PetscErrorCode NEPNLEIGSSetFullBasis(NEP nep,PetscBool fullbasis)
    1880: {

    1886:   PetscTryMethod(nep,"NEPNLEIGSSetFullBasis_C",(NEP,PetscBool),(nep,fullbasis));
    1887:   return(0);
    1888: }

    1890: static PetscErrorCode NEPNLEIGSGetFullBasis_NLEIGS(NEP nep,PetscBool *fullbasis)
    1891: {
    1892:   NEP_NLEIGS *ctx=(NEP_NLEIGS*)nep->data;

    1895:   *fullbasis = ctx->fullbasis;
    1896:   return(0);
    1897: }

    1899: /*@
    1900:    NEPNLEIGSGetFullBasis - Gets the flag that indicates if NLEIGS is using the
    1901:    full-basis variant.

    1903:    Not Collective

    1905:    Input Parameter:
    1906: .  nep - the nonlinear eigensolver context

    1908:    Output Parameter:
    1909: .  fullbasis - the flag

    1911:    Level: advanced

    1913: .seealso: NEPNLEIGSSetFullBasis()
    1914: @*/
    1915: PetscErrorCode NEPNLEIGSGetFullBasis(NEP nep,PetscBool *fullbasis)
    1916: {

    1922:   PetscUseMethod(nep,"NEPNLEIGSGetFullBasis_C",(NEP,PetscBool*),(nep,fullbasis));
    1923:   return(0);
    1924: }

    1926: #define SHIFTMAX 30

    1928: PetscErrorCode NEPSetFromOptions_NLEIGS(PetscOptionItems *PetscOptionsObject,NEP nep)
    1929: {
    1931:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;
    1932:   PetscInt       i=0,k;
    1933:   PetscBool      flg1,flg2,b;
    1934:   PetscReal      r;
    1935:   PetscScalar    array[SHIFTMAX];

    1938:   PetscOptionsHead(PetscOptionsObject,"NEP NLEIGS Options");

    1940:     PetscOptionsReal("-nep_nleigs_restart","Proportion of vectors kept after restart","NEPNLEIGSSetRestart",0.5,&r,&flg1);
    1941:     if (flg1) { NEPNLEIGSSetRestart(nep,r); }

    1943:     PetscOptionsBool("-nep_nleigs_locking","Choose between locking and non-locking variants","NEPNLEIGSSetLocking",PETSC_FALSE,&b,&flg1);
    1944:     if (flg1) { NEPNLEIGSSetLocking(nep,b); }

    1946:     PetscOptionsBool("-nep_nleigs_full_basis","Choose between TOAR and full-basis variants","NEPNLEIGSSetFullBasis",PETSC_FALSE,&b,&flg1);
    1947:     if (flg1) { NEPNLEIGSSetFullBasis(nep,b); }

    1949:     NEPNLEIGSGetInterpolation(nep,&r,&i);
    1950:     if (!i) i = PETSC_DEFAULT;
    1951:     PetscOptionsInt("-nep_nleigs_interpolation_degree","Maximum number of terms for interpolation via divided differences","NEPNLEIGSSetInterpolation",i,&i,&flg1);
    1952:     PetscOptionsReal("-nep_nleigs_interpolation_tol","Tolerance for interpolation via divided differences","NEPNLEIGSSetInterpolation",r,&r,&flg2);
    1953:     if (flg1 || flg2) { NEPNLEIGSSetInterpolation(nep,r,i); }

    1955:     k = SHIFTMAX;
    1956:     for (i=0;i<k;i++) array[i] = 0;
    1957:     PetscOptionsScalarArray("-nep_nleigs_rk_shifts","Shifts for Rational Krylov","NEPNLEIGSSetRKShifts",array,&k,&flg1);
    1958:     if (flg1) { NEPNLEIGSSetRKShifts(nep,k,array); }

    1960:   PetscOptionsTail();

    1962:   if (!ctx->ksp) { NEPNLEIGSGetKSPs(nep,&ctx->nshiftsw,&ctx->ksp); }
    1963:   for (i=0;i<ctx->nshiftsw;i++) {
    1964:     KSPSetFromOptions(ctx->ksp[i]);
    1965:   }

    1967:   if (ctx->fullbasis) {
    1968:     if (!ctx->eps) { NEPNLEIGSGetEPS(nep,&ctx->eps); }
    1969:     EPSSetFromOptions(ctx->eps);
    1970:   }
    1971:   return(0);
    1972: }

    1974: PetscErrorCode NEPView_NLEIGS(NEP nep,PetscViewer viewer)
    1975: {
    1977:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;
    1978:   PetscBool      isascii;
    1979:   PetscInt       i;
    1980:   char           str[50];

    1983:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1984:   if (isascii) {
    1985:     PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
    1986:     if (ctx->fullbasis) {
    1987:       PetscViewerASCIIPrintf(viewer,"  using the full-basis variant\n");
    1988:     } else {
    1989:       PetscViewerASCIIPrintf(viewer,"  using the %slocking variant\n",ctx->lock?"":"non-");
    1990:     }
    1991:     PetscViewerASCIIPrintf(viewer,"  divided difference terms: used=%D, max=%D\n",ctx->nmat,ctx->ddmaxit);
    1992:     PetscViewerASCIIPrintf(viewer,"  tolerance for divided difference convergence: %g\n",(double)ctx->ddtol);
    1993:     if (ctx->nshifts) {
    1994:       PetscViewerASCIIPrintf(viewer,"  RK shifts: ");
    1995:       PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    1996:       for (i=0;i<ctx->nshifts;i++) {
    1997:         SlepcSNPrintfScalar(str,sizeof(str),ctx->shifts[i],PETSC_FALSE);
    1998:         PetscViewerASCIIPrintf(viewer,"%s%s",str,(i<ctx->nshifts-1)?",":"");
    1999:       }
    2000:       PetscViewerASCIIPrintf(viewer,"\n");
    2001:       PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    2002:     }
    2003:     if (!ctx->ksp) { NEPNLEIGSGetKSPs(nep,&ctx->nshiftsw,&ctx->ksp); }
    2004:     PetscViewerASCIIPushTab(viewer);
    2005:     KSPView(ctx->ksp[0],viewer);
    2006:     PetscViewerASCIIPopTab(viewer);
    2007:     if (ctx->fullbasis) {
    2008:       if (!ctx->eps) { NEPNLEIGSGetEPS(nep,&ctx->eps); }
    2009:       PetscViewerASCIIPushTab(viewer);
    2010:       EPSView(ctx->eps,viewer);
    2011:       PetscViewerASCIIPopTab(viewer);
    2012:     }
    2013:   }
    2014:   return(0);
    2015: }

    2017: PetscErrorCode NEPReset_NLEIGS(NEP nep)
    2018: {
    2020:   PetscInt       k;
    2021:   NEP_NLEIGS     *ctx=(NEP_NLEIGS*)nep->data;

    2024:   if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
    2025:     PetscFree(ctx->coeffD);
    2026:   } else {
    2027:     for (k=0;k<ctx->nmat;k++) { MatDestroy(&ctx->D[k]); }
    2028:   }
    2029:   PetscFree4(ctx->s,ctx->xi,ctx->beta,ctx->D);
    2030:   for (k=0;k<ctx->nshiftsw;k++) { KSPReset(ctx->ksp[k]); }
    2031:   if (ctx->vrn) {
    2032:     VecDestroy(&ctx->vrn);
    2033:   }
    2034:   if (ctx->fullbasis) {
    2035:     MatDestroy(&ctx->A);
    2036:     EPSReset(ctx->eps);
    2037:     for (k=0;k<4;k++) { VecDestroy(&ctx->w[k]); }
    2038:   }
    2039:   return(0);
    2040: }

    2042: PetscErrorCode NEPDestroy_NLEIGS(NEP nep)
    2043: {
    2045:   PetscInt       k;
    2046:   NEP_NLEIGS     *ctx = (NEP_NLEIGS*)nep->data;

    2049:   BVDestroy(&ctx->V);
    2050:   for (k=0;k<ctx->nshiftsw;k++) { KSPDestroy(&ctx->ksp[k]); }
    2051:   PetscFree(ctx->ksp);
    2052:   if (ctx->nshifts) { PetscFree(ctx->shifts); }
    2053:   if (ctx->fullbasis) { EPSDestroy(&ctx->eps); }
    2054:   PetscFree(nep->data);
    2055:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetSingularitiesFunction_C",NULL);
    2056:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetSingularitiesFunction_C",NULL);
    2057:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetRestart_C",NULL);
    2058:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetRestart_C",NULL);
    2059:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetLocking_C",NULL);
    2060:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetLocking_C",NULL);
    2061:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetInterpolation_C",NULL);
    2062:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetInterpolation_C",NULL);
    2063:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetRKShifts_C",NULL);
    2064:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetRKShifts_C",NULL);
    2065:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetKSPs_C",NULL);
    2066:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetFullBasis_C",NULL);
    2067:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetFullBasis_C",NULL);
    2068:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetEPS_C",NULL);
    2069:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetEPS_C",NULL);
    2070:   return(0);
    2071: }

    2073: SLEPC_EXTERN PetscErrorCode NEPCreate_NLEIGS(NEP nep)
    2074: {
    2076:   NEP_NLEIGS     *ctx;

    2079:   PetscNewLog(nep,&ctx);
    2080:   nep->data  = (void*)ctx;
    2081:   ctx->lock  = PETSC_TRUE;
    2082:   ctx->ddtol = PETSC_DEFAULT;

    2084:   nep->useds = PETSC_TRUE;

    2086:   nep->ops->setup          = NEPSetUp_NLEIGS;
    2087:   nep->ops->setfromoptions = NEPSetFromOptions_NLEIGS;
    2088:   nep->ops->view           = NEPView_NLEIGS;
    2089:   nep->ops->destroy        = NEPDestroy_NLEIGS;
    2090:   nep->ops->reset          = NEPReset_NLEIGS;

    2092:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetSingularitiesFunction_C",NEPNLEIGSSetSingularitiesFunction_NLEIGS);
    2093:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetSingularitiesFunction_C",NEPNLEIGSGetSingularitiesFunction_NLEIGS);
    2094:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetRestart_C",NEPNLEIGSSetRestart_NLEIGS);
    2095:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetRestart_C",NEPNLEIGSGetRestart_NLEIGS);
    2096:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetLocking_C",NEPNLEIGSSetLocking_NLEIGS);
    2097:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetLocking_C",NEPNLEIGSGetLocking_NLEIGS);
    2098:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetInterpolation_C",NEPNLEIGSSetInterpolation_NLEIGS);
    2099:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetInterpolation_C",NEPNLEIGSGetInterpolation_NLEIGS);
    2100:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetRKShifts_C",NEPNLEIGSSetRKShifts_NLEIGS);
    2101:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetRKShifts_C",NEPNLEIGSGetRKShifts_NLEIGS);
    2102:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetKSPs_C",NEPNLEIGSGetKSPs_NLEIGS);
    2103:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetFullBasis_C",NEPNLEIGSSetFullBasis_NLEIGS);
    2104:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetFullBasis_C",NEPNLEIGSGetFullBasis_NLEIGS);
    2105:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSSetEPS_C",NEPNLEIGSSetEPS_NLEIGS);
    2106:   PetscObjectComposeFunction((PetscObject)nep,"NEPNLEIGSGetEPS_C",NEPNLEIGSGetEPS_NLEIGS);
    2107:   return(0);
    2108: }