Date: 2026-01-20T11:35:27+00:00

Actual source code: dsnep.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: typedef struct {
     15:   PetscInt       nf;                 /* number of functions in f[] */
     16:   FN             f[DS_NUM_EXTRA];    /* functions defining the nonlinear operator */
     17:   PetscInt       max_mid;            /* maximum minimality index */
     18:   PetscInt       nnod;               /* number of nodes for quadrature rules */
     19:   PetscInt       spls;               /* number of sampling columns for quadrature rules */
     20:   PetscInt       Nit;                /* number of refinement iterations */
     21:   PetscReal      rtol;               /* tolerance of Newton refinement */
     22:   RG             rg;                 /* region for contour integral */
     23:   PetscLayout    map;                /* used to distribute work among MPI processes */
     24:   void           *computematrixctx;
     25:   DSNEPMatrixFunctionFn *computematrix;
     26: } DS_NEP;

     28: /*
     29:    DSNEPComputeMatrix - Build the matrix associated with a nonlinear operator
     30:    T(lambda) or its derivative T'(lambda), given the parameter lambda, where
     31:    T(lambda) = sum_i E_i*f_i(lambda). The result is written in mat.
     32: */
     33: static PetscErrorCode DSNEPComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat)
     34: {
     35:   DS_NEP            *ctx = (DS_NEP*)ds->data;
     36:   PetscScalar       *T,alpha;
     37:   const PetscScalar *E;
     38:   PetscInt          i,ld,n;
     39:   PetscBLASInt      k,inc=1;

     41:   PetscFunctionBegin;
     42:   PetscCall(PetscLogEventBegin(DS_Other,ds,0,0,0));
     43:   if (ctx->computematrix) PetscCall((*ctx->computematrix)(ds,lambda,deriv,mat,ctx->computematrixctx));
     44:   else {
     45:     PetscCall(DSGetDimensions(ds,&n,NULL,NULL,NULL));
     46:     PetscCall(DSGetLeadingDimension(ds,&ld));
     47:     PetscCall(PetscBLASIntCast(ld*n,&k));
     48:     PetscCall(MatDenseGetArray(ds->omat[mat],&T));
     49:     PetscCall(PetscArrayzero(T,k));
     50:     for (i=0;i<ctx->nf;i++) {
     51:       if (deriv) PetscCall(FNEvaluateDerivative(ctx->f[i],lambda,&alpha));
     52:       else PetscCall(FNEvaluateFunction(ctx->f[i],lambda,&alpha));
     53:       PetscCall(MatDenseGetArrayRead(ds->omat[DSMatExtra[i]],&E));
     54:       PetscCallBLAS("BLASaxpy",BLASaxpy_(&k,&alpha,E,&inc,T,&inc));
     55:       PetscCall(MatDenseRestoreArrayRead(ds->omat[DSMatExtra[i]],&E));
     56:     }
     57:     PetscCall(MatDenseRestoreArray(ds->omat[mat],&T));
     58:   }
     59:   PetscCall(PetscLogEventEnd(DS_Other,ds,0,0,0));
     60:   PetscFunctionReturn(PETSC_SUCCESS);
     61: }

     63: static PetscErrorCode DSAllocate_NEP(DS ds,PetscInt ld)
     64: {
     65:   DS_NEP         *ctx = (DS_NEP*)ds->data;
     66:   PetscInt       i;

     68:   PetscFunctionBegin;
     69:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
     70:   for (i=0;i<ctx->nf;i++) PetscCall(DSAllocateMat_Private(ds,DSMatExtra[i]));
     71:   PetscCall(PetscFree(ds->perm));
     72:   PetscCall(PetscMalloc1(ld*ctx->max_mid,&ds->perm));
     73:   PetscFunctionReturn(PETSC_SUCCESS);
     74: }

     76: static PetscErrorCode DSView_NEP(DS ds,PetscViewer viewer)
     77: {
     78:   DS_NEP            *ctx = (DS_NEP*)ds->data;
     79:   PetscViewerFormat format;
     80:   PetscInt          i;
     81:   const char        *methodname[] = {
     82:                      "Successive Linear Problems",
     83:                      "Contour Integral"
     84:   };
     85:   const int         nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);

     87:   PetscFunctionBegin;
     88:   PetscCall(PetscViewerGetFormat(viewer,&format));
     89:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
     90:     if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
     91: #if defined(PETSC_USE_COMPLEX)
     92:     if (ds->method==1) {  /* contour integral method */
     93:       PetscCall(PetscViewerASCIIPrintf(viewer,"number of integration points: %" PetscInt_FMT "\n",ctx->nnod));
     94:       PetscCall(PetscViewerASCIIPrintf(viewer,"maximum minimality index: %" PetscInt_FMT "\n",ctx->max_mid));
     95:       if (ctx->spls) PetscCall(PetscViewerASCIIPrintf(viewer,"number of sampling columns for quadrature: %" PetscInt_FMT "\n",ctx->spls));
     96:       if (ctx->Nit) PetscCall(PetscViewerASCIIPrintf(viewer,"doing iterative refinement (%" PetscInt_FMT " its, tolerance %g)\n",ctx->Nit,(double)ctx->rtol));
     97:       PetscCall(RGView(ctx->rg,viewer));
     98:     }
     99: #endif
    100:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPrintf(viewer,"number of functions: %" PetscInt_FMT "\n",ctx->nf));
    101:     PetscFunctionReturn(PETSC_SUCCESS);
    102:   }
    103:   for (i=0;i<ctx->nf;i++) {
    104:     PetscCall(FNView(ctx->f[i],viewer));
    105:     PetscCall(DSViewMat(ds,viewer,DSMatExtra[i]));
    106:   }
    107:   if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
    108:   PetscFunctionReturn(PETSC_SUCCESS);
    109: }

    111: static PetscErrorCode DSVectors_NEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    112: {
    113:   PetscFunctionBegin;
    114:   PetscCheck(!rnorm,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    115:   switch (mat) {
    116:     case DS_MAT_X:
    117:       break;
    118:     case DS_MAT_Y:
    119:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    120:     default:
    121:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    122:   }
    123:   PetscFunctionReturn(PETSC_SUCCESS);
    124: }

    126: static PetscErrorCode DSSort_NEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *dummy)
    127: {
    128:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    129:   PetscInt       n,l,i,*perm,lds;
    130:   PetscScalar    *Q;

    132:   PetscFunctionBegin;
    133:   if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
    134:   if (!ds->method) PetscFunctionReturn(PETSC_SUCCESS);  /* SLP computes just one eigenvalue */
    135:   n = ds->n*ctx->max_mid;
    136:   lds = ds->ld*ctx->max_mid;
    137:   l = ds->l;
    138:   perm = ds->perm;
    139:   for (i=0;i<n;i++) perm[i] = i;
    140:   if (rr) PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE));
    141:   else PetscCall(DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE));
    142:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    143:   for (i=l;i<ds->t;i++) Q[i+i*lds] = wr[perm[i]];
    144:   for (i=l;i<ds->t;i++) wr[i] = Q[i+i*lds];
    145:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    146:   /* n != ds->n */
    147:   PetscCall(DSPermuteColumns_Private(ds,0,ds->t,ds->n,DS_MAT_X,perm));
    148:   PetscFunctionReturn(PETSC_SUCCESS);
    149: }

    151: #if defined(SLEPC_MISSING_LAPACK_GGEV3)
    152: #define LAPGEEV "ggev"
    153: #else
    154: #define LAPGEEV "ggev3"
    155: #endif

    157: static PetscErrorCode DSSolve_NEP_SLP(DS ds,PetscScalar *wr,PetscScalar *wi)
    158: {
    159:   PetscScalar    *A,*B,*W,*X,*work,*alpha,*beta,a;
    160:   PetscScalar    sigma,lambda,mu,re,re2,sone=1.0,szero=0.0;
    161:   PetscBLASInt   info,n,ld,lwork,one=1,zero=0;
    162:   PetscInt       it,pos,j,maxit=100,result;
    163:   PetscReal      norm,tol,done=1.0;
    164: #if !defined(PETSC_USE_COMPLEX)
    165:   PetscReal      *alphai,im,im2;
    166: #endif

    168:   PetscFunctionBegin;
    169:   PetscCall(PetscBLASIntCast(ds->n,&n));
    170:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    171:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
    172:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
    173:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
    174:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    175:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
    176:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
    177:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));

    179:   /* workspace query and memory allocation */
    180:   lwork = -1;
    181: #if defined(PETSC_USE_COMPLEX)
    182:   PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,NULL,NULL,NULL,&ld,W,&ld,&a,&lwork,NULL,&info));
    183:   PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
    184:   PetscCall(DSAllocateWork_Private(ds,lwork+2*ds->n,8*ds->n,0));
    185:   alpha = ds->work;
    186:   beta  = ds->work + ds->n;
    187:   work  = ds->work + 2*ds->n;
    188: #else
    189:   PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,NULL,NULL,NULL,NULL,&ld,W,&ld,&a,&lwork,&info));
    190:   PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
    191:   PetscCall(DSAllocateWork_Private(ds,lwork+3*ds->n,0,0));
    192:   alpha  = ds->work;
    193:   beta   = ds->work + ds->n;
    194:   alphai = ds->work + 2*ds->n;
    195:   work   = ds->work + 3*ds->n;
    196: #endif

    198:   sigma = 0.0;
    199:   if (ds->sc->comparison==SlepcCompareTargetMagnitude || ds->sc->comparison==SlepcCompareTargetReal) sigma = *(PetscScalar*)ds->sc->comparisonctx;
    200:   lambda = sigma;
    201:   tol = n*PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);

    203:   for (it=0;it<maxit;it++) {

    205:     /* evaluate T and T' */
    206:     PetscCall(DSNEPComputeMatrix(ds,lambda,PETSC_FALSE,DS_MAT_A));
    207:     if (it) {
    208:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,A,&ld,X,&one,&szero,X+ld,&one));
    209:       norm = BLASnrm2_(&n,X+ld,&one);
    210:       if (norm/PetscAbsScalar(lambda)<=tol) break;
    211:     }
    212:     PetscCall(DSNEPComputeMatrix(ds,lambda,PETSC_TRUE,DS_MAT_B));

    214:     /* compute eigenvalue correction mu and eigenvector u */
    215: #if defined(PETSC_USE_COMPLEX)
    216:     PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,alpha,beta,NULL,&ld,W,&ld,work,&lwork,ds->rwork,&info));
    217: #else
    218:     PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&n,A,&ld,B,&ld,alpha,alphai,beta,NULL,&ld,W,&ld,work,&lwork,&info));
    219: #endif
    220:     SlepcCheckLapackInfo(LAPGEEV,info);

    222:     /* find smallest eigenvalue */
    223:     j = 0;
    224:     if (beta[j]==0.0) re = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    225:     else re = alpha[j]/beta[j];
    226: #if !defined(PETSC_USE_COMPLEX)
    227:     if (beta[j]==0.0) im = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    228:     else im = alphai[j]/beta[j];
    229: #endif
    230:     pos = 0;
    231:     for (j=1;j<n;j++) {
    232:       if (beta[j]==0.0) re2 = (PetscRealPart(alpha[j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    233:       else re2 = alpha[j]/beta[j];
    234: #if !defined(PETSC_USE_COMPLEX)
    235:       if (beta[j]==0.0) im2 = (alphai[j]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    236:       else im2 = alphai[j]/beta[j];
    237:       PetscCall(SlepcCompareSmallestMagnitude(re,im,re2,im2,&result,NULL));
    238: #else
    239:       PetscCall(SlepcCompareSmallestMagnitude(re,0.0,re2,0.0,&result,NULL));
    240: #endif
    241:       if (result > 0) {
    242:         re = re2;
    243: #if !defined(PETSC_USE_COMPLEX)
    244:         im = im2;
    245: #endif
    246:         pos = j;
    247:       }
    248:     }

    250: #if !defined(PETSC_USE_COMPLEX)
    251:     PetscCheck(im==0.0,PETSC_COMM_SELF,PETSC_ERR_SUP,"DSNEP found a complex eigenvalue; try rerunning with complex scalars");
    252: #endif
    253:     mu = alpha[pos]/beta[pos];
    254:     PetscCall(PetscArraycpy(X,W+pos*ld,n));
    255:     norm = BLASnrm2_(&n,X,&one);
    256:     PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&one,X,&n,&info));
    257:     SlepcCheckLapackInfo("lascl",info);

    259:     /* correct eigenvalue approximation */
    260:     lambda = lambda - mu;
    261:   }
    262:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    263:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
    264:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
    265:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));

    267:   PetscCheck(it<maxit,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"DSNEP did not converge");
    268:   ds->t = 1;
    269:   wr[0] = lambda;
    270:   if (wi) wi[0] = 0.0;
    271:   PetscFunctionReturn(PETSC_SUCCESS);
    272: }

    274: #if defined(PETSC_USE_COMPLEX)
    275: /*
    276:   Newton refinement for eigenpairs computed with contour integral.
    277:   k  - number of eigenpairs to refine
    278:   wr - eigenvalues (eigenvectors are stored in DS_MAT_X)
    279: */
    280: static PetscErrorCode DSNEPNewtonRefine(DS ds,PetscInt k,PetscScalar *wr)
    281: {
    282:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    283:   PetscScalar    *X,*W,*U,*R,sone=1.0,szero=0.0;
    284:   PetscReal      norm;
    285:   PetscInt       i,j,ii,nwu=0,*p,jstart=0,jend=k;
    286:   const PetscInt *range;
    287:   PetscBLASInt   n,*perm,info,ld,one=1,n1;
    288:   PetscMPIInt    len,size,root;
    289:   PetscLayout    map;

    291:   PetscFunctionBegin;
    292:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
    293:   PetscCall(PetscBLASIntCast(ds->n,&n));
    294:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    295:   n1 = n+1;
    296:   p  = ds->perm;
    297:   PetscCall(PetscArrayzero(p,k));
    298:   PetscCall(DSAllocateWork_Private(ds,(n+2)*(n+1),0,n+1));
    299:   U    = ds->work+nwu;    nwu += (n+1)*(n+1);
    300:   R    = ds->work+nwu;    /*nwu += n+1;*/
    301:   perm = ds->iwork;
    302:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
    303:     PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,k,1,&map));
    304:     PetscCall(PetscLayoutGetRange(map,&jstart,&jend));
    305:   }
    306:   for (ii=0;ii<ctx->Nit;ii++) {
    307:     for (j=jstart;j<jend;j++) {
    308:       if (p[j]<2) {
    309:         PetscCall(DSNEPComputeMatrix(ds,wr[j],PETSC_FALSE,DS_MAT_W));
    310:         PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
    311:         PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,R,&one));
    312:         PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
    313:         norm = BLASnrm2_(&n,R,&one);
    314:         if (norm/PetscAbsScalar(wr[j]) > ctx->rtol) {
    315:           PetscCall(PetscInfo(NULL,"Refining eigenpair %" PetscInt_FMT ", residual=%g\n",j,(double)(norm/PetscAbsScalar(wr[j]))));
    316:           p[j] = 1;
    317:           R[n] = 0.0;
    318:           PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
    319:           for (i=0;i<n;i++) {
    320:             PetscCall(PetscArraycpy(U+i*n1,W+i*ld,n));
    321:             U[n+i*n1] = PetscConj(X[j*ld+i]);
    322:           }
    323:           PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
    324:           U[n+n*n1] = 0.0;
    325:           PetscCall(DSNEPComputeMatrix(ds,wr[j],PETSC_TRUE,DS_MAT_W));
    326:           PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
    327:           PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,W,&ld,X+ld*j,&one,&szero,U+n*(n+1),&one));
    328:           PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));
    329:           /* solve system  */
    330:           PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n1,&n1,U,&n1,perm,&info));
    331:           SlepcCheckLapackInfo("getrf",info);
    332:           PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n1,&one,U,&n1,perm,R,&n1,&info));
    333:           SlepcCheckLapackInfo("getrs",info);
    334:           wr[j] -= R[n];
    335:           for (i=0;i<n;i++) X[j*ld+i] -= R[i];
    336:           /* normalization */
    337:           norm = BLASnrm2_(&n,X+ld*j,&one);
    338:           for (i=0;i<n;i++) X[ld*j+i] /= norm;
    339:         } else p[j] = 2;
    340:       }
    341:     }
    342:   }
    343:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {  /* communicate results */
    344:     PetscCall(PetscMPIIntCast(k,&len));
    345:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE,p,len,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)ds)));
    346:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ds),&size));
    347:     PetscCall(PetscLayoutGetRanges(map,&range));
    348:     for (j=0;j<k;j++) {
    349:       if (p[j]) {  /* j-th eigenpair has been refined */
    350:         for (root=0;root<size;root++) if (range[root+1]>j) break;
    351:         PetscCall(PetscMPIIntCast(1,&len));
    352:         PetscCallMPI(MPI_Bcast(wr+j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds)));
    353:         PetscCall(PetscMPIIntCast(n,&len));
    354:         PetscCallMPI(MPI_Bcast(X+ld*j,len,MPIU_SCALAR,root,PetscObjectComm((PetscObject)ds)));
    355:       }
    356:     }
    357:     PetscCall(PetscLayoutDestroy(&map));
    358:   }
    359:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
    360:   PetscFunctionReturn(PETSC_SUCCESS);
    361: }

    363: PetscErrorCode DSSolve_NEP_Contour(DS ds,PetscScalar *wr,PetscScalar *wi)
    364: {
    365:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    366:   PetscScalar    *alpha,*beta,*Q,*Z,*X,*U,*V,*W,*work,*Rc,*R,*w,*z,*zn,*S;
    367:   PetscScalar    sone=1.0,szero=0.0,center,a;
    368:   PetscReal      *rwork,norm,radius,vscale,rgscale,*sigma;
    369:   PetscBLASInt   info,n,*perm,p,pp,ld,lwork,k_,rk_,colA,rowA,one=1;
    370:   PetscInt       mid,lds,nnod=ctx->nnod,k,i,ii,jj,j,s,off,rk,nwu=0,nw,lrwork,*inside,kstart=0,kend=nnod;
    371:   PetscMPIInt    len;
    372:   PetscBool      isellipse;
    373:   PetscRandom    rand;

    375:   PetscFunctionBegin;
    376:   PetscCheck(ctx->rg,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"The contour solver requires a region passed with DSNEPSetRG()");
    377:   /* Contour parameters */
    378:   PetscCall(PetscObjectTypeCompare((PetscObject)ctx->rg,RGELLIPSE,&isellipse));
    379:   PetscCheck(isellipse,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Region must be Ellipse");
    380:   PetscCall(RGEllipseGetParameters(ctx->rg,&center,&radius,&vscale));
    381:   PetscCall(RGGetScale(ctx->rg,&rgscale));
    382:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {
    383:     if (!ctx->map) PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)ds),PETSC_DECIDE,ctx->nnod,1,&ctx->map));
    384:     PetscCall(PetscLayoutGetRange(ctx->map,&kstart,&kend));
    385:   }

    387:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_W)); /* size n */
    388:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q)); /* size mid*n */
    389:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Z)); /* size mid*n */
    390:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_U)); /* size mid*n */
    391:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_V)); /* size mid*n */
    392:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    393:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
    394:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_U],&U));
    395:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_V],&V));
    396:   mid  = ctx->max_mid;
    397:   PetscCall(PetscBLASIntCast(ds->n,&n));
    398:   p    = n;   /* maximum number of columns for the probing matrix */
    399:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    400:   PetscCall(PetscBLASIntCast(mid*n,&rowA));
    401:   nw     = 2*n*(p+mid)+3*nnod+2*mid*n*p;
    402:   lrwork = 9*mid*n;

    404:   /* workspace query and memory allocation */
    405:   lwork = -1;
    406:   PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&rowA,Q,&rowA,Z,&rowA,NULL,NULL,NULL,&ld,V,&rowA,&a,&lwork,NULL,&info));
    407:   PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
    408:   PetscCall(DSAllocateWork_Private(ds,lwork+nw,lrwork,n+1));

    410:   sigma = ds->rwork;
    411:   rwork = ds->rwork+mid*n;
    412:   perm  = ds->iwork;
    413:   z     = ds->work+nwu;    nwu += nnod;         /* quadrature points */
    414:   zn    = ds->work+nwu;    nwu += nnod;         /* normalized quadrature points */
    415:   w     = ds->work+nwu;    nwu += nnod;         /* quadrature weights */
    416:   Rc    = ds->work+nwu;    nwu += n*p;
    417:   R     = ds->work+nwu;    nwu += n*p;
    418:   alpha = ds->work+nwu;    nwu += mid*n;
    419:   beta  = ds->work+nwu;    nwu += mid*n;
    420:   S     = ds->work+nwu;    nwu += 2*mid*n*p;
    421:   work  = ds->work+nwu;

    423:   /* Compute quadrature parameters */
    424:   PetscCall(RGComputeQuadrature(ctx->rg,RG_QUADRULE_TRAPEZOIDAL,nnod,z,zn,w));

    426:   /* Set random matrix */
    427:   PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)ds),&rand));
    428:   PetscCall(PetscRandomSetSeed(rand,0x12345678));
    429:   PetscCall(PetscRandomSeed(rand));
    430:   for (j=0;j<p;j++)
    431:     for (i=0;i<n;i++) PetscCall(PetscRandomGetValue(rand,Rc+i+j*n));
    432:   PetscCall(PetscArrayzero(S,2*mid*n*p));
    433:   /* Loop of integration points */
    434:   for (k=kstart;k<kend;k++) {
    435:     PetscCall(PetscInfo(NULL,"Solving integration point %" PetscInt_FMT "\n",k));
    436:     PetscCall(PetscArraycpy(R,Rc,p*n));
    437:     PetscCall(DSNEPComputeMatrix(ds,z[k],PETSC_FALSE,DS_MAT_W));

    439:     /* LU factorization */
    440:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_W],&W));
    441:     PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,W,&ld,perm,&info));
    442:     SlepcCheckLapackInfo("getrf",info);
    443:     PetscCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n,&p,W,&ld,perm,R,&n,&info));
    444:     SlepcCheckLapackInfo("getrs",info);
    445:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_W],&W));

    447:     /* Moments computation */
    448:     for (s=0;s<2*ctx->max_mid;s++) {
    449:       off = s*n*p;
    450:       for (j=0;j<p;j++)
    451:         for (i=0;i<n;i++) S[off+i+j*n] += w[k]*R[j*n+i];
    452:       w[k] *= zn[k];
    453:     }
    454:   }

    456:   if (ds->pmode==DS_PARALLEL_DISTRIBUTED) {  /* compute final S via reduction */
    457:     PetscCall(PetscMPIIntCast(2*mid*n*p,&len));
    458:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE,S,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ds)));
    459:   }
    460:   PetscCall(PetscBLASIntCast(ctx->spls?PetscMin(ctx->spls,n):n,&p));
    461:   pp = p;
    462:   do {
    463:     p = pp;
    464:     PetscCall(PetscBLASIntCast(mid*p,&colA));

    466:     PetscCall(PetscInfo(ds,"Computing SVD of size %" PetscBLASInt_FMT "x%" PetscBLASInt_FMT "\n",rowA,colA));
    467:     for (jj=0;jj<mid;jj++) {
    468:       for (ii=0;ii<mid;ii++) {
    469:         off = jj*p*rowA+ii*n;
    470:         for (j=0;j<p;j++)
    471:           for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii)*n+j)*n+i];
    472:       }
    473:     }
    474:     PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&rowA,&colA,Q,&rowA,sigma,U,&rowA,V,&colA,work,&lwork,rwork,&info));
    475:     SlepcCheckLapackInfo("gesvd",info);

    477:     rk = colA;
    478:     for (i=1;i<colA;i++) if (sigma[i]/sigma[0]<PETSC_MACHINE_EPSILON*1e4) {rk = i; break;}
    479:     if (rk<colA || p==n) break;
    480:     pp *= 2;
    481:   } while (pp<=n);
    482:   PetscCall(PetscInfo(ds,"Solving generalized eigenproblem of size %" PetscInt_FMT "\n",rk));
    483:   for (jj=0;jj<mid;jj++) {
    484:     for (ii=0;ii<mid;ii++) {
    485:       off = jj*p*rowA+ii*n;
    486:       for (j=0;j<p;j++)
    487:         for (i=0;i<n;i++) Q[off+j*rowA+i] = S[((jj+ii+1)*n+j)*n+i];
    488:     }
    489:   }
    490:   PetscCall(PetscBLASIntCast(rk,&rk_));
    491:   PetscCallBLAS("BLASgemm",BLASgemm_("N","C",&rowA,&rk_,&colA,&sone,Q,&rowA,V,&colA,&szero,Z,&rowA));
    492:   PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rowA,&sone,U,&rowA,Z,&rowA,&szero,Q,&rk_));
    493:   PetscCall(PetscArrayzero(Z,n*mid*n*mid));
    494:   for (j=0;j<rk;j++) Z[j+j*rk_] = sigma[j];
    495:   PetscCallBLAS("LAPACK" LAPGEEV,LAPACKggevalt_("N","V",&rk_,Q,&rk_,Z,&rk_,alpha,beta,NULL,&ld,V,&rk_,work,&lwork,rwork,&info));
    496:   SlepcCheckLapackInfo(LAPGEEV,info);
    497:   for (i=0;i<rk;i++) wr[i] = (center+alpha[i]*radius/beta[i])*rgscale;
    498:   PetscCall(PetscMalloc1(rk,&inside));
    499:   PetscCall(RGCheckInside(ctx->rg,rk,wr,wi,inside));
    500:   k=0;
    501:   for (i=0;i<rk;i++)
    502:     if (inside[i]==1) inside[k++] = i;
    503:   /* Discard values outside region */
    504:   lds = ld*mid;
    505:   PetscCall(PetscArrayzero(Q,lds*lds));
    506:   PetscCall(PetscArrayzero(Z,lds*lds));
    507:   for (i=0;i<k;i++) Q[i+i*lds] = (center*beta[inside[i]]+radius*alpha[inside[i]])*rgscale;
    508:   for (i=0;i<k;i++) Z[i+i*lds] = beta[inside[i]];
    509:   for (i=0;i<k;i++) wr[i] = Q[i+i*lds]/Z[i+i*lds];
    510:   for (j=0;j<k;j++) for (i=0;i<rk;i++) V[j*rk+i] = sigma[i]*V[inside[j]*rk+i];
    511:   PetscCall(PetscBLASIntCast(k,&k_));
    512:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
    513:   PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&k_,&rk_,&sone,U,&rowA,V,&rk_,&szero,X,&ld));
    514:   /* Normalize */
    515:   for (j=0;j<k;j++) {
    516:     norm = BLASnrm2_(&n,X+ld*j,&one);
    517:     for (i=0;i<n;i++) X[ld*j+i] /= norm;
    518:   }
    519:   PetscCall(PetscFree(inside));
    520:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
    521:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    522:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
    523:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_U],&U));
    524:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_V],&V));

    526:   /* Newton refinement */
    527:   if (ctx->Nit) PetscCall(DSNEPNewtonRefine(ds,k,wr));
    528:   ds->t = k;
    529:   PetscCall(PetscRandomDestroy(&rand));
    530:   PetscFunctionReturn(PETSC_SUCCESS);
    531: }
    532: #endif

    534: #if !defined(PETSC_HAVE_MPIUNI)
    535: static PetscErrorCode DSSynchronize_NEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    536: {
    537:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    538:   PetscInt       ld=ds->ld,k=0;
    539:   PetscMPIInt    n,n2,rank,size,off=0;
    540:   PetscScalar    *X;

    542:   PetscFunctionBegin;
    543:   if (!ds->method) { /* SLP */
    544:     if (ds->state>=DS_STATE_CONDENSED) k += ds->n;
    545:     if (eigr) k += 1;
    546:     if (eigi) k += 1;
    547:     PetscCall(PetscMPIIntCast(1,&n));
    548:     PetscCall(PetscMPIIntCast(ds->n,&n2));
    549:   } else { /* Contour */
    550:     if (ds->state>=DS_STATE_CONDENSED) k += ctx->max_mid*ds->n*ld;
    551:     if (eigr) k += ctx->max_mid*ds->n;
    552:     if (eigi) k += ctx->max_mid*ds->n;
    553:     PetscCall(PetscMPIIntCast(ctx->max_mid*ds->n,&n));
    554:     PetscCall(PetscMPIIntCast(ctx->max_mid*ds->n*ld,&n2));
    555:   }
    556:   PetscCall(DSAllocateWork_Private(ds,k,0,0));
    557:   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
    558:   if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
    559:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
    560:   if (!rank) {
    561:     if (ds->state>=DS_STATE_CONDENSED) PetscCallMPI(MPI_Pack(X,n2,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    562:     if (eigr) PetscCallMPI(MPI_Pack(eigr,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    563: #if !defined(PETSC_USE_COMPLEX)
    564:     if (eigi) PetscCallMPI(MPI_Pack(eigi,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    565: #endif
    566:   }
    567:   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
    568:   if (rank) {
    569:     if (ds->state>=DS_STATE_CONDENSED) PetscCallMPI(MPI_Unpack(ds->work,size,&off,X,n2,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    570:     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    571: #if !defined(PETSC_USE_COMPLEX)
    572:     if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    573: #endif
    574:   }
    575:   if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
    576:   PetscFunctionReturn(PETSC_SUCCESS);
    577: }
    578: #endif

    580: static PetscErrorCode DSNEPSetFN_NEP(DS ds,PetscInt n,FN fn[])
    581: {
    582:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    583:   PetscInt       i;

    585:   PetscFunctionBegin;
    586:   PetscCheck(n>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more functions, you have %" PetscInt_FMT,n);
    587:   PetscCheck(n<=DS_NUM_EXTRA,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Too many functions, you specified %" PetscInt_FMT " but the limit is %d",n,DS_NUM_EXTRA);
    588:   if (ds->ld) PetscCall(PetscInfo(ds,"DSNEPSetFN() called after DSAllocate()\n"));
    589:   for (i=0;i<n;i++) PetscCall(PetscObjectReference((PetscObject)fn[i]));
    590:   for (i=0;i<ctx->nf;i++) PetscCall(FNDestroy(&ctx->f[i]));
    591:   for (i=0;i<n;i++) ctx->f[i] = fn[i];
    592:   ctx->nf = n;
    593:   PetscFunctionReturn(PETSC_SUCCESS);
    594: }

    596: /*@
    597:    DSNEPSetFN - Sets a number of functions that define the nonlinear
    598:    eigenproblem.

    600:    Collective

    602:    Input Parameters:
    603: +  ds - the direct solver context
    604: .  n  - number of functions
    605: -  fn - array of functions

    607:    Notes:
    608:    The nonlinear eigenproblem is defined in terms of the split nonlinear
    609:    operator $T(\lambda) = \sum_i E_i f_i(\lambda)$.

    611:    This function must be called before `DSAllocate()`. Then `DSAllocate()`
    612:    will allocate an extra matrix $E_i$ per each function, that can be
    613:    filled in the usual way.

    615:    Level: advanced

    617: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetFN()`, `DSAllocate()`
    618: @*/
    619: PetscErrorCode DSNEPSetFN(DS ds,PetscInt n,FN fn[])
    620: {
    621:   PetscInt       i;

    623:   PetscFunctionBegin;
    626:   PetscAssertPointer(fn,3);
    627:   for (i=0;i<n;i++) {
    629:     PetscCheckSameComm(ds,1,fn[i],3);
    630:   }
    631:   PetscTryMethod(ds,"DSNEPSetFN_C",(DS,PetscInt,FN[]),(ds,n,fn));
    632:   PetscFunctionReturn(PETSC_SUCCESS);
    633: }

    635: static PetscErrorCode DSNEPGetFN_NEP(DS ds,PetscInt k,FN *fn)
    636: {
    637:   DS_NEP *ctx = (DS_NEP*)ds->data;

    639:   PetscFunctionBegin;
    640:   PetscCheck(k>=0 && k<ctx->nf,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"k must be between 0 and %" PetscInt_FMT,ctx->nf-1);
    641:   *fn = ctx->f[k];
    642:   PetscFunctionReturn(PETSC_SUCCESS);
    643: }

    645: /*@
    646:    DSNEPGetFN - Gets the functions associated with the nonlinear `DS`.

    648:    Not Collective

    650:    Input Parameters:
    651: +  ds - the direct solver context
    652: -  k  - the index of the requested function (starting in 0)

    654:    Output Parameter:
    655: .  fn - the function

    657:    Level: advanced

    659: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetFN()`
    660: @*/
    661: PetscErrorCode DSNEPGetFN(DS ds,PetscInt k,FN *fn)
    662: {
    663:   PetscFunctionBegin;
    665:   PetscAssertPointer(fn,3);
    666:   PetscUseMethod(ds,"DSNEPGetFN_C",(DS,PetscInt,FN*),(ds,k,fn));
    667:   PetscFunctionReturn(PETSC_SUCCESS);
    668: }

    670: static PetscErrorCode DSNEPGetNumFN_NEP(DS ds,PetscInt *n)
    671: {
    672:   DS_NEP *ctx = (DS_NEP*)ds->data;

    674:   PetscFunctionBegin;
    675:   *n = ctx->nf;
    676:   PetscFunctionReturn(PETSC_SUCCESS);
    677: }

    679: /*@
    680:    DSNEPGetNumFN - Returns the number of functions stored internally by
    681:    the `DS`.

    683:    Not Collective

    685:    Input Parameter:
    686: .  ds - the direct solver context

    688:    Output Parameter:
    689: .  n - the number of functions passed in `DSNEPSetFN()`

    691:    Level: advanced

    693: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetFN()`
    694: @*/
    695: PetscErrorCode DSNEPGetNumFN(DS ds,PetscInt *n)
    696: {
    697:   PetscFunctionBegin;
    699:   PetscAssertPointer(n,2);
    700:   PetscUseMethod(ds,"DSNEPGetNumFN_C",(DS,PetscInt*),(ds,n));
    701:   PetscFunctionReturn(PETSC_SUCCESS);
    702: }

    704: static PetscErrorCode DSNEPSetMinimality_NEP(DS ds,PetscInt n)
    705: {
    706:   DS_NEP *ctx = (DS_NEP*)ds->data;

    708:   PetscFunctionBegin;
    709:   if (n == PETSC_DECIDE || n == PETSC_DEFAULT) ctx->max_mid = 4;
    710:   else {
    711:     PetscCheck(n>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The minimality value must be > 0");
    712:     ctx->max_mid = n;
    713:   }
    714:   PetscFunctionReturn(PETSC_SUCCESS);
    715: }

    717: /*@
    718:    DSNEPSetMinimality - Sets the maximum minimality index used internally by
    719:    the `DSNEP`.

    721:    Logically Collective

    723:    Input Parameters:
    724: +  ds - the direct solver context
    725: -  n  - the maximum minimality index

    727:    Options Database Key:
    728: .  -ds_nep_minimality \<n\> - sets the maximum minimality index

    730:    Notes:
    731:    The maximum minimality index is used only in the contour integral method,
    732:    and is related to the highest moments used in the method. The default
    733:    value is 1, a larger value might give better accuracy in some cases, but
    734:    at a higher cost.

    736:    Level: advanced

    738: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetMinimality()`
    739: @*/
    740: PetscErrorCode DSNEPSetMinimality(DS ds,PetscInt n)
    741: {
    742:   PetscFunctionBegin;
    745:   PetscTryMethod(ds,"DSNEPSetMinimality_C",(DS,PetscInt),(ds,n));
    746:   PetscFunctionReturn(PETSC_SUCCESS);
    747: }

    749: static PetscErrorCode DSNEPGetMinimality_NEP(DS ds,PetscInt *n)
    750: {
    751:   DS_NEP *ctx = (DS_NEP*)ds->data;

    753:   PetscFunctionBegin;
    754:   *n = ctx->max_mid;
    755:   PetscFunctionReturn(PETSC_SUCCESS);
    756: }

    758: /*@
    759:    DSNEPGetMinimality - Returns the maximum minimality index used internally by
    760:    the `DSNEP`.

    762:    Not Collective

    764:    Input Parameter:
    765: .  ds - the direct solver context

    767:    Output Parameter:
    768: .  n - the maximum minimality index passed in `DSNEPSetMinimality()`

    770:    Level: advanced

    772: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetMinimality()`
    773: @*/
    774: PetscErrorCode DSNEPGetMinimality(DS ds,PetscInt *n)
    775: {
    776:   PetscFunctionBegin;
    778:   PetscAssertPointer(n,2);
    779:   PetscUseMethod(ds,"DSNEPGetMinimality_C",(DS,PetscInt*),(ds,n));
    780:   PetscFunctionReturn(PETSC_SUCCESS);
    781: }

    783: static PetscErrorCode DSNEPSetRefine_NEP(DS ds,PetscReal tol,PetscInt its)
    784: {
    785:   DS_NEP *ctx = (DS_NEP*)ds->data;

    787:   PetscFunctionBegin;
    788:   if (tol == (PetscReal)PETSC_DETERMINE) {
    789:     ctx->rtol = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);
    790:   } else if (tol != (PetscReal)PETSC_CURRENT) {
    791:     PetscCheck(tol>0.0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The tolerance must be > 0");
    792:     ctx->rtol = tol;
    793:   }
    794:   if (its == PETSC_DETERMINE) {
    795:     ctx->Nit = 3;
    796:   } else if (its != PETSC_CURRENT) {
    797:     PetscCheck(its>=0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The number of iterations must be >= 0");
    798:     ctx->Nit = its;
    799:   }
    800:   PetscFunctionReturn(PETSC_SUCCESS);
    801: }

    803: /*@
    804:    DSNEPSetRefine - Sets the tolerance and the number of iterations of Newton iterative
    805:    refinement for eigenpairs when solving a `DSNEP`.

    807:    Logically Collective

    809:    Input Parameters:
    810: +  ds  - the direct solver context
    811: .  tol - the tolerance
    812: -  its - the number of iterations

    814:    Options Database Keys:
    815: +  -ds_nep_refine_tol \<tol\> - sets the tolerance
    816: -  -ds_nep_refine_its \<its\> - sets the number of Newton iterations

    818:    Notes:
    819:    Iterative refinement of eigenpairs is currently used only in the contour
    820:    integral method.

    822:    Use `PETSC_CURRENT` to retain the current value of any of the parameters.
    823:    Use `PETSC_DETERMINE` for either argument to assign a default value computed
    824:    internally.

    826:    Level: advanced

    828: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetRefine()`
    829: @*/
    830: PetscErrorCode DSNEPSetRefine(DS ds,PetscReal tol,PetscInt its)
    831: {
    832:   PetscFunctionBegin;
    836:   PetscTryMethod(ds,"DSNEPSetRefine_C",(DS,PetscReal,PetscInt),(ds,tol,its));
    837:   PetscFunctionReturn(PETSC_SUCCESS);
    838: }

    840: static PetscErrorCode DSNEPGetRefine_NEP(DS ds,PetscReal *tol,PetscInt *its)
    841: {
    842:   DS_NEP *ctx = (DS_NEP*)ds->data;

    844:   PetscFunctionBegin;
    845:   if (tol) *tol = ctx->rtol;
    846:   if (its) *its = ctx->Nit;
    847:   PetscFunctionReturn(PETSC_SUCCESS);
    848: }

    850: /*@
    851:    DSNEPGetRefine - Returns the tolerance and the number of iterations of Newton iterative
    852:    refinement for eigenpairs.

    854:    Not Collective

    856:    Input Parameter:
    857: .  ds - the direct solver context

    859:    Output Parameters:
    860: +  tol - the tolerance
    861: -  its - the number of iterations

    863:    Level: advanced

    865: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetRefine()`
    866: @*/
    867: PetscErrorCode DSNEPGetRefine(DS ds,PetscReal *tol,PetscInt *its)
    868: {
    869:   PetscFunctionBegin;
    871:   PetscUseMethod(ds,"DSNEPGetRefine_C",(DS,PetscReal*,PetscInt*),(ds,tol,its));
    872:   PetscFunctionReturn(PETSC_SUCCESS);
    873: }

    875: static PetscErrorCode DSNEPSetIntegrationPoints_NEP(DS ds,PetscInt ip)
    876: {
    877:   DS_NEP         *ctx = (DS_NEP*)ds->data;

    879:   PetscFunctionBegin;
    880:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) ctx->nnod = 64;
    881:   else {
    882:     PetscCheck(ip>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The number of integration points must be > 0");
    883:     ctx->nnod = ip;
    884:   }
    885:   PetscCall(PetscLayoutDestroy(&ctx->map));  /* need to redistribute at next solve */
    886:   PetscFunctionReturn(PETSC_SUCCESS);
    887: }

    889: /*@
    890:    DSNEPSetIntegrationPoints - Sets the number of integration points to be
    891:    used in the contour integral method when solving a `DSNEP`.

    893:    Logically Collective

    895:    Input Parameters:
    896: +  ds - the direct solver context
    897: -  ip - the number of integration points

    899:    Options Database Key:
    900: .  -ds_nep_integration_points \<ip\> - sets the number of integration points

    902:    Notes:
    903:    This parameter is relevant only in the contour integral method.

    905:    Level: advanced

    907: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetIntegrationPoints()`
    908: @*/
    909: PetscErrorCode DSNEPSetIntegrationPoints(DS ds,PetscInt ip)
    910: {
    911:   PetscFunctionBegin;
    914:   PetscTryMethod(ds,"DSNEPSetIntegrationPoints_C",(DS,PetscInt),(ds,ip));
    915:   PetscFunctionReturn(PETSC_SUCCESS);
    916: }

    918: static PetscErrorCode DSNEPGetIntegrationPoints_NEP(DS ds,PetscInt *ip)
    919: {
    920:   DS_NEP *ctx = (DS_NEP*)ds->data;

    922:   PetscFunctionBegin;
    923:   *ip = ctx->nnod;
    924:   PetscFunctionReturn(PETSC_SUCCESS);
    925: }

    927: /*@
    928:    DSNEPGetIntegrationPoints - Returns the number of integration points used
    929:    in the contour integral method.

    931:    Not Collective

    933:    Input Parameter:
    934: .  ds - the direct solver context

    936:    Output Parameter:
    937: .  ip - the number of integration points

    939:    Level: advanced

    941: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetIntegrationPoints()`
    942: @*/
    943: PetscErrorCode DSNEPGetIntegrationPoints(DS ds,PetscInt *ip)
    944: {
    945:   PetscFunctionBegin;
    947:   PetscAssertPointer(ip,2);
    948:   PetscUseMethod(ds,"DSNEPGetIntegrationPoints_C",(DS,PetscInt*),(ds,ip));
    949:   PetscFunctionReturn(PETSC_SUCCESS);
    950: }

    952: static PetscErrorCode DSNEPSetSamplingSize_NEP(DS ds,PetscInt p)
    953: {
    954:   DS_NEP *ctx = (DS_NEP*)ds->data;

    956:   PetscFunctionBegin;
    957:   if (p == PETSC_DECIDE || p == PETSC_DEFAULT) ctx->spls = 0;
    958:   else {
    959:     PetscCheck(p>0,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The sample size must be > 0");
    960:     PetscCheck(p>=20,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"The sample size cannot be smaller than 20");
    961:     ctx->spls = p;
    962:   }
    963:   PetscFunctionReturn(PETSC_SUCCESS);
    964: }

    966: /*@
    967:    DSNEPSetSamplingSize - Sets the number of sampling columns to be
    968:    used in the contour integral method when solving a `DSNEP`.

    970:    Logically Collective

    972:    Input Parameters:
    973: +  ds - the direct solver context
    974: -  p  - the number of columns for the sampling matrix

    976:    Options Database Key:
    977: .  -ds_nep_sampling_size \<p\> - the number of sampling columns

    979:    Note:
    980:    This parameter is relevant only in the contour integral method.

    982:    Level: advanced

    984: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetSamplingSize()`
    985: @*/
    986: PetscErrorCode DSNEPSetSamplingSize(DS ds,PetscInt p)
    987: {
    988:   PetscFunctionBegin;
    991:   PetscTryMethod(ds,"DSNEPSetSamplingSize_C",(DS,PetscInt),(ds,p));
    992:   PetscFunctionReturn(PETSC_SUCCESS);
    993: }

    995: static PetscErrorCode DSNEPGetSamplingSize_NEP(DS ds,PetscInt *p)
    996: {
    997:   DS_NEP *ctx = (DS_NEP*)ds->data;

    999:   PetscFunctionBegin;
    1000:   *p = ctx->spls;
    1001:   PetscFunctionReturn(PETSC_SUCCESS);
    1002: }

    1004: /*@
    1005:    DSNEPGetSamplingSize - Returns the number of sampling columns used
    1006:    in the contour integral method.

    1008:    Not Collective

    1010:    Input Parameter:
    1011: .  ds - the direct solver context

    1013:    Output Parameter:
    1014: .  p -  the number of columns for the sampling matrix

    1016:    Level: advanced

    1018: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetSamplingSize()`
    1019: @*/
    1020: PetscErrorCode DSNEPGetSamplingSize(DS ds,PetscInt *p)
    1021: {
    1022:   PetscFunctionBegin;
    1024:   PetscAssertPointer(p,2);
    1025:   PetscUseMethod(ds,"DSNEPGetSamplingSize_C",(DS,PetscInt*),(ds,p));
    1026:   PetscFunctionReturn(PETSC_SUCCESS);
    1027: }

    1029: static PetscErrorCode DSNEPSetComputeMatrixFunction_NEP(DS ds,DSNEPMatrixFunctionFn *fun,void *ctx)
    1030: {
    1031:   DS_NEP *dsctx = (DS_NEP*)ds->data;

    1033:   PetscFunctionBegin;
    1034:   dsctx->computematrix    = fun;
    1035:   dsctx->computematrixctx = ctx;
    1036:   PetscFunctionReturn(PETSC_SUCCESS);
    1037: }

    1039: /*@C
    1040:    DSNEPSetComputeMatrixFunction - Sets a user-provided subroutine to compute
    1041:    the matrices $T(\lambda)$ or $T'(\lambda)$.

    1043:    Logically Collective

    1045:    Input Parameters:
    1046: +  ds  - the direct solver context
    1047: .  fun - matrix function evaluation routine, see `DSNEPMatrixFunctionFn` for the calling sequence
    1048: -  ctx - a context pointer (the last parameter to the user function)

    1050:    Note:
    1051:    The result is computed as $T(\lambda) = \sum_i E_i f_i(\lambda)$, and similarly
    1052:    for the derivative, where $E_i$ are the extra matrices, see `DSMatType`.

    1054:    Level: developer

    1056: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetComputeMatrixFunction()`
    1057: @*/
    1058: PetscErrorCode DSNEPSetComputeMatrixFunction(DS ds,DSNEPMatrixFunctionFn *fun,void *ctx)
    1059: {
    1060:   PetscFunctionBegin;
    1062:   PetscTryMethod(ds,"DSNEPSetComputeMatrixFunction_C",(DS,DSNEPMatrixFunctionFn*,void*),(ds,fun,ctx));
    1063:   PetscFunctionReturn(PETSC_SUCCESS);
    1064: }

    1066: static PetscErrorCode DSNEPGetComputeMatrixFunction_NEP(DS ds,DSNEPMatrixFunctionFn **fun,void *ctx)
    1067: {
    1068:   DS_NEP *dsctx = (DS_NEP*)ds->data;

    1070:   PetscFunctionBegin;
    1071:   if (fun) *fun = dsctx->computematrix;
    1072:   if (ctx) *(void**)ctx = dsctx->computematrixctx;
    1073:   PetscFunctionReturn(PETSC_SUCCESS);
    1074: }

    1076: /*@C
    1077:    DSNEPGetComputeMatrixFunction - Returns the user-provided callback function
    1078:    set in `DSNEPSetComputeMatrixFunction()`.

    1080:    Not Collective

    1082:    Input Parameter:
    1083: .  ds  - the direct solver context

    1085:    Output Parameters:
    1086: +  fun - the pointer to the user function
    1087: -  ctx - the context pointer

    1089:    Level: developer

    1091: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetComputeMatrixFunction()`
    1092: @*/
    1093: PetscErrorCode DSNEPGetComputeMatrixFunction(DS ds,DSNEPMatrixFunctionFn **fun,void *ctx)
    1094: {
    1095:   PetscFunctionBegin;
    1097:   PetscUseMethod(ds,"DSNEPGetComputeMatrixFunction_C",(DS,DSNEPMatrixFunctionFn**,void*),(ds,fun,ctx));
    1098:   PetscFunctionReturn(PETSC_SUCCESS);
    1099: }

    1101: static PetscErrorCode DSNEPSetRG_NEP(DS ds,RG rg)
    1102: {
    1103:   DS_NEP         *dsctx = (DS_NEP*)ds->data;

    1105:   PetscFunctionBegin;
    1106:   PetscCall(PetscObjectReference((PetscObject)rg));
    1107:   PetscCall(RGDestroy(&dsctx->rg));
    1108:   dsctx->rg = rg;
    1109:   PetscFunctionReturn(PETSC_SUCCESS);
    1110: }

    1112: /*@
    1113:    DSNEPSetRG - Associates a region object to the `DSNEP` solver.

    1115:    Collective

    1117:    Input Parameters:
    1118: +  ds  - the direct solver context
    1119: -  rg  - the region context

    1121:    Notes:
    1122:    The region is used only in the contour integral method, and
    1123:    should enclose the wanted eigenvalues.

    1125:    Level: developer

    1127: .seealso: [](sec:ds), `DSNEP`, `DSNEPGetRG()`
    1128: @*/
    1129: PetscErrorCode DSNEPSetRG(DS ds,RG rg)
    1130: {
    1131:   PetscFunctionBegin;
    1133:   if (rg) {
    1135:     PetscCheckSameComm(ds,1,rg,2);
    1136:   }
    1137:   PetscTryMethod(ds,"DSNEPSetRG_C",(DS,RG),(ds,rg));
    1138:   PetscFunctionReturn(PETSC_SUCCESS);
    1139: }

    1141: static PetscErrorCode DSNEPGetRG_NEP(DS ds,RG *rg)
    1142: {
    1143:   DS_NEP         *ctx = (DS_NEP*)ds->data;

    1145:   PetscFunctionBegin;
    1146:   if (!ctx->rg) {
    1147:     PetscCall(RGCreate(PetscObjectComm((PetscObject)ds),&ctx->rg));
    1148:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->rg,(PetscObject)ds,1));
    1149:     PetscCall(RGSetOptionsPrefix(ctx->rg,((PetscObject)ds)->prefix));
    1150:     PetscCall(RGAppendOptionsPrefix(ctx->rg,"ds_nep_"));
    1151:     PetscCall(PetscObjectSetOptions((PetscObject)ctx->rg,((PetscObject)ds)->options));
    1152:   }
    1153:   *rg = ctx->rg;
    1154:   PetscFunctionReturn(PETSC_SUCCESS);
    1155: }

    1157: /*@
    1158:    DSNEPGetRG - Obtain the region object associated to the `DSNEP` solver.

    1160:    Collective

    1162:    Input Parameter:
    1163: .  ds  - the direct solver context

    1165:    Output Parameter:
    1166: .  rg  - the region context

    1168:    Level: developer

    1170: .seealso: [](sec:ds), `DSNEP`, `DSNEPSetRG()`
    1171: @*/
    1172: PetscErrorCode DSNEPGetRG(DS ds,RG *rg)
    1173: {
    1174:   PetscFunctionBegin;
    1176:   PetscAssertPointer(rg,2);
    1177:   PetscUseMethod(ds,"DSNEPGetRG_C",(DS,RG*),(ds,rg));
    1178:   PetscFunctionReturn(PETSC_SUCCESS);
    1179: }

    1181: static PetscErrorCode DSSetFromOptions_NEP(DS ds,PetscOptionItems PetscOptionsObject)
    1182: {
    1183:   PetscInt       k;
    1184:   PetscBool      flg;
    1185: #if defined(PETSC_USE_COMPLEX)
    1186:   PetscReal      r;
    1187:   PetscBool      flg1;
    1188:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    1189: #endif

    1191:   PetscFunctionBegin;
    1192:   PetscOptionsHeadBegin(PetscOptionsObject,"DS NEP Options");

    1194:     PetscCall(PetscOptionsInt("-ds_nep_minimality","Maximum minimality index","DSNEPSetMinimality",4,&k,&flg));
    1195:     if (flg) PetscCall(DSNEPSetMinimality(ds,k));

    1197:     PetscCall(PetscOptionsInt("-ds_nep_integration_points","Number of integration points","DSNEPSetIntegrationPoints",64,&k,&flg));
    1198:     if (flg) PetscCall(DSNEPSetIntegrationPoints(ds,k));

    1200:     PetscCall(PetscOptionsInt("-ds_nep_sampling_size","Number of sampling columns","DSNEPSetSamplingSize",0,&k,&flg));
    1201:     if (flg) PetscCall(DSNEPSetSamplingSize(ds,k));

    1203: #if defined(PETSC_USE_COMPLEX)
    1204:     r = ctx->rtol;
    1205:     PetscCall(PetscOptionsReal("-ds_nep_refine_tol","Refinement tolerance","DSNEPSetRefine",ctx->rtol,&r,&flg1));
    1206:     k = ctx->Nit;
    1207:     PetscCall(PetscOptionsInt("-ds_nep_refine_its","Number of iterative refinement iterations","DSNEPSetRefine",ctx->Nit,&k,&flg));
    1208:     if (flg1||flg) PetscCall(DSNEPSetRefine(ds,r,k));

    1210:     if (ds->method==1) {
    1211:       if (!ctx->rg) PetscCall(DSNEPGetRG(ds,&ctx->rg));
    1212:       PetscCall(RGSetFromOptions(ctx->rg));
    1213:     }
    1214: #endif

    1216:   PetscOptionsHeadEnd();
    1217:   PetscFunctionReturn(PETSC_SUCCESS);
    1218: }

    1220: static PetscErrorCode DSDestroy_NEP(DS ds)
    1221: {
    1222:   DS_NEP         *ctx = (DS_NEP*)ds->data;
    1223:   PetscInt       i;

    1225:   PetscFunctionBegin;
    1226:   for (i=0;i<ctx->nf;i++) PetscCall(FNDestroy(&ctx->f[i]));
    1227:   PetscCall(RGDestroy(&ctx->rg));
    1228:   PetscCall(PetscLayoutDestroy(&ctx->map));
    1229:   PetscCall(PetscFree(ds->data));
    1230:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",NULL));
    1231:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",NULL));
    1232:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",NULL));
    1233:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",NULL));
    1234:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",NULL));
    1235:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",NULL));
    1236:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",NULL));
    1237:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",NULL));
    1238:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",NULL));
    1239:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",NULL));
    1240:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",NULL));
    1241:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",NULL));
    1242:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",NULL));
    1243:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",NULL));
    1244:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",NULL));
    1245:   PetscFunctionReturn(PETSC_SUCCESS);
    1246: }

    1248: static PetscErrorCode DSMatGetSize_NEP(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
    1249: {
    1250:   DS_NEP *ctx = (DS_NEP*)ds->data;

    1252:   PetscFunctionBegin;
    1253:   *rows = ds->n;
    1254:   if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V) *rows *= ctx->max_mid;
    1255:   *cols = ds->n;
    1256:   if (t==DS_MAT_Q || t==DS_MAT_Z || t==DS_MAT_U || t==DS_MAT_V || t==DS_MAT_X || t==DS_MAT_Y) *cols *= ctx->max_mid;
    1257:   PetscFunctionReturn(PETSC_SUCCESS);
    1258: }

    1260: /*MC
    1261:    DSNEP - Dense Nonlinear Eigenvalue Problem.

    1263:    Notes:
    1264:    The problem is expressed as $T(\lambda)x = 0$, where $T(\lambda)$ is a
    1265:    parameter-dependent matrix written as $T(\lambda) = \sum_i E_i f_i(\lambda)$.
    1266:    The eigenvalues $\lambda$ are the arguments returned by `DSSolve()`.

    1268:    The coefficient matrices $E_i$ are the extra matrices of the `DS`, and
    1269:    the scalar functions $f_i$ are passed via `DSNEPSetFN()`. Optionally, a
    1270:    callback function to fill the $E_i$ matrices can be set with
    1271:    `DSNEPSetComputeMatrixFunction()`.

    1273:    Used DS matrices:
    1274: +  `DS_MAT_E0` to `DS_MAT_E9` - coefficient matrices of the split form of $T(\lambda)$
    1275: .  `DS_MAT_X`  - eigenvectors
    1276: .  `DS_MAT_A`  - (workspace) $T(\lambda)$ evaluated at a given $\lambda$ (SLP only)
    1277: .  `DS_MAT_B`  - (workspace) $T'(\lambda)$ evaluated at a given $\lambda$ (SLP only)
    1278: .  `DS_MAT_Q`  - (workspace) left Hankel matrix (contour only)
    1279: .  `DS_MAT_Z`  - (workspace) right Hankel matrix (contour only)
    1280: .  `DS_MAT_U`  - (workspace) left singular vectors (contour only)
    1281: .  `DS_MAT_V`  - (workspace) right singular vectors (contour only)
    1282: -  `DS_MAT_W`  - (workspace) auxiliary matrix of size $n\times n$

    1284:    Implemented methods:
    1285: +  0 - Successive Linear Problems (SLP), computes just one eigenpair
    1286: -  1 - Contour integral, computes all eigenvalues inside a region

    1288:    Level: beginner

    1290: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`, `DSNEPSetFN()`, `DSNEPSetComputeMatrixFunction()`
    1291: M*/
    1292: SLEPC_EXTERN PetscErrorCode DSCreate_NEP(DS ds)
    1293: {
    1294:   DS_NEP         *ctx;

    1296:   PetscFunctionBegin;
    1297:   PetscCall(PetscNew(&ctx));
    1298:   ds->data = (void*)ctx;
    1299:   ctx->max_mid = 4;
    1300:   ctx->nnod    = 64;
    1301:   ctx->Nit     = 3;
    1302:   ctx->rtol    = PETSC_MACHINE_EPSILON/PetscSqrtReal(PETSC_SQRT_MACHINE_EPSILON);

    1304:   ds->ops->allocate       = DSAllocate_NEP;
    1305:   ds->ops->setfromoptions = DSSetFromOptions_NEP;
    1306:   ds->ops->view           = DSView_NEP;
    1307:   ds->ops->vectors        = DSVectors_NEP;
    1308:   ds->ops->solve[0]       = DSSolve_NEP_SLP;
    1309: #if defined(PETSC_USE_COMPLEX)
    1310:   ds->ops->solve[1]       = DSSolve_NEP_Contour;
    1311: #endif
    1312:   ds->ops->sort           = DSSort_NEP;
    1313: #if !defined(PETSC_HAVE_MPIUNI)
    1314:   ds->ops->synchronize    = DSSynchronize_NEP;
    1315: #endif
    1316:   ds->ops->destroy        = DSDestroy_NEP;
    1317:   ds->ops->matgetsize     = DSMatGetSize_NEP;

    1319:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetFN_C",DSNEPSetFN_NEP));
    1320:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetFN_C",DSNEPGetFN_NEP));
    1321:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetNumFN_C",DSNEPGetNumFN_NEP));
    1322:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetMinimality_C",DSNEPGetMinimality_NEP));
    1323:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetMinimality_C",DSNEPSetMinimality_NEP));
    1324:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRefine_C",DSNEPGetRefine_NEP));
    1325:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRefine_C",DSNEPSetRefine_NEP));
    1326:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetIntegrationPoints_C",DSNEPGetIntegrationPoints_NEP));
    1327:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetIntegrationPoints_C",DSNEPSetIntegrationPoints_NEP));
    1328:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetSamplingSize_C",DSNEPGetSamplingSize_NEP));
    1329:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetSamplingSize_C",DSNEPSetSamplingSize_NEP));
    1330:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetRG_C",DSNEPSetRG_NEP));
    1331:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetRG_C",DSNEPGetRG_NEP));
    1332:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPSetComputeMatrixFunction_C",DSNEPSetComputeMatrixFunction_NEP));
    1333:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSNEPGetComputeMatrixFunction_C",DSNEPGetComputeMatrixFunction_NEP));
    1334:   PetscFunctionReturn(PETSC_SUCCESS);
    1335: }