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

   This file is part of SLEPc.
   SLEPc is distributed under a 2-clause BSD license (see LICENSE).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
/*
   SLEPc eigensolver: "ciss"

   Method: Contour Integral Spectral Slicing

   Algorithm:

       Contour integral based on Sakurai-Sugiura method to construct a
       subspace, with various eigenpair extractions (Rayleigh-Ritz,
       explicit moment).

   Based on code contributed by Y. Maeda, T. Sakurai.

   References:

       [1] J. Asakura, T. Sakurai, H. Tadano, T. Ikegami, K. Kimura, "A
           numerical method for nonlinear eigenvalue problems using contour
           integrals", JSIAM Lett. 1:52-55, 2009.

       [2] S. Yokota and T. Sakurai, "A projection method for nonlinear
           eigenvalue problems using contour integrals", JSIAM Lett.
           5:41-44, 2013.
*/

#include <slepc/private/nepimpl.h>         /*I "slepcnep.h" I*/
#include <slepc/private/slepccontour.h>

typedef struct _n_nep_ciss_project *NEP_CISS_PROJECT;
typedef struct {
  /* parameters */
  PetscInt          N;             /* number of integration points (32) */
  PetscInt          L;             /* block size (16) */
  PetscInt          M;             /* moment degree (N/4 = 4) */
  PetscReal         delta;         /* threshold of singular value (1e-12) */
  PetscInt          L_max;         /* maximum number of columns of the source matrix V */
  PetscReal         spurious_threshold; /* discard spurious eigenpairs */
  PetscBool         isreal;        /* T(z) is real for real z */
  PetscInt          npart;         /* number of partitions */
  PetscInt          refine_inner;
  PetscInt          refine_blocksize;
  NEPCISSExtraction extraction;
  /* private data */
  SlepcContourData  contour;
  PetscReal         *sigma;        /* threshold for numerical rank */
  PetscScalar       *weight;
  PetscScalar       *omega;
  PetscScalar       *pp;
  BV                V;
  BV                S;
  BV                Y;
  PetscBool         useconj;
  Mat               J;             /* auxiliary matrix when using subcomm */
  BV                pV;
  PetscObjectId     rgid;
  PetscObjectState  rgstate;
} NEP_CISS;

struct _n_nep_ciss_project {
  NEP  nep;
  BV   Q;
};

static PetscErrorCode NEPContourDSComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat,void *ctx)
{
  NEP_CISS_PROJECT proj = (NEP_CISS_PROJECT)ctx;
  Mat              M,fun;

  PetscFunctionBegin;
  if (!deriv) {
    PetscCall(NEPComputeFunction(proj->nep,lambda,proj->nep->function,proj->nep->function));
    fun = proj->nep->function;
  } else {
    PetscCall(NEPComputeJacobian(proj->nep,lambda,proj->nep->jacobian));
    fun = proj->nep->jacobian;
  }
  PetscCall(DSGetMat(ds,mat,&M));
  PetscCall(BVMatProject(proj->Q,fun,proj->Q,M));
  PetscCall(DSRestoreMat(ds,mat,&M));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPComputeFunctionSubcomm(NEP nep,PetscScalar lambda,Mat T,Mat P,PetscBool deriv)
{
  PetscInt       i;
  PetscScalar    alpha;
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  PetscAssert(nep->fui!=NEP_USER_INTERFACE_CALLBACK,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_WRONGSTATE,"Should not arrive here with callbacks");
  PetscCall(MatZeroEntries(T));
  if (!deriv && T != P) PetscCall(MatZeroEntries(P));
  for (i=0;i<nep->nt;i++) {
    if (!deriv) PetscCall(FNEvaluateFunction(nep->f[i],lambda,&alpha));
    else PetscCall(FNEvaluateDerivative(nep->f[i],lambda,&alpha));
    PetscCall(MatAXPY(T,alpha,ctx->contour->pA[i],nep->mstr));
    if (!deriv && T != P) PetscCall(MatAXPY(P,alpha,ctx->contour->pP[i],nep->mstrp));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Set up KSP solvers for every integration point
*/
static PetscErrorCode NEPCISSSetUp(NEP nep,Mat T,Mat P)
{
  NEP_CISS         *ctx = (NEP_CISS*)nep->data;
  SlepcContourData contour;
  PetscInt         i,p_id;
  Mat              Amat,Pmat;

  PetscFunctionBegin;
  if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
  contour = ctx->contour;
  PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
  for (i=0;i<contour->npoints;i++) {
    p_id = i*contour->subcomm->n + contour->subcomm->color;
    PetscCall(MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&Amat));
    if (T != P) PetscCall(MatDuplicate(P,MAT_DO_NOT_COPY_VALUES,&Pmat)); else Pmat = Amat;
    if (contour->subcomm->n == 1 || nep->fui==NEP_USER_INTERFACE_CALLBACK) PetscCall(NEPComputeFunction(nep,ctx->omega[p_id],Amat,Pmat));
    else PetscCall(NEPComputeFunctionSubcomm(nep,ctx->omega[p_id],Amat,Pmat,PETSC_FALSE));
    PetscCall(NEP_KSPSetOperators(contour->ksp[i],Amat,Pmat));
    PetscCall(MatDestroy(&Amat));
    if (T != P) PetscCall(MatDestroy(&Pmat));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Y_i = F(z_i)^{-1}Fp(z_i)V for every integration point, Y=[Y_i] is in the context
*/
static PetscErrorCode NEPCISSSolve(NEP nep,Mat dT,BV V,PetscInt L_start,PetscInt L_end)
{
  NEP_CISS         *ctx = (NEP_CISS*)nep->data;
  SlepcContourData contour = ctx->contour;
  PetscInt         i,p_id;
  Mat              MV,BMV=NULL,MC;

  PetscFunctionBegin;
  PetscCall(BVSetActiveColumns(V,L_start,L_end));
  PetscCall(BVGetMat(V,&MV));
  for (i=0;i<contour->npoints;i++) {
    p_id = i*contour->subcomm->n + contour->subcomm->color;
    if (contour->subcomm->n==1 || nep->fui==NEP_USER_INTERFACE_CALLBACK) PetscCall(NEPComputeJacobian(nep,ctx->omega[p_id],dT));
    else PetscCall(NEPComputeFunctionSubcomm(nep,ctx->omega[p_id],dT,NULL,PETSC_TRUE));
    PetscCall(BVSetActiveColumns(ctx->Y,i*ctx->L+L_start,i*ctx->L+L_end));
    PetscCall(BVGetMat(ctx->Y,&MC));
    if (!i) {
      PetscCall(MatProductCreate(dT,MV,NULL,&BMV));
      PetscCall(MatProductSetType(BMV,MATPRODUCT_AB));
      PetscCall(MatProductSetFromOptions(BMV));
      PetscCall(MatProductSymbolic(BMV));
    }
    PetscCall(MatProductNumeric(BMV));
    PetscCall(KSPMatSolve(contour->ksp[i],BMV,MC));
    PetscCall(BVRestoreMat(ctx->Y,&MC));
  }
  PetscCall(MatDestroy(&BMV));
  PetscCall(BVRestoreMat(V,&MV));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPSetUp_CISS(NEP nep)
{
  NEP_CISS         *ctx = (NEP_CISS*)nep->data;
  SlepcContourData contour;
  PetscInt         nwork;
  PetscBool        istrivial,isellipse,flg;
  NEP_CISS_PROJECT dsctxf;
  PetscObjectId    id;
  PetscObjectState state;
  Vec              v0;

  PetscFunctionBegin;
  if (nep->ncv==PETSC_DETERMINE) nep->ncv = ctx->L_max*ctx->M;
  else {
    ctx->L_max = nep->ncv/ctx->M;
    if (!ctx->L_max) {
      ctx->L_max = 1;
      nep->ncv = ctx->L_max*ctx->M;
    }
  }
  ctx->L = PetscMin(ctx->L,ctx->L_max);
  if (nep->max_it==PETSC_DETERMINE) nep->max_it = 5;
  if (nep->mpd==PETSC_DETERMINE) nep->mpd = nep->ncv;
  if (!nep->which) nep->which = NEP_ALL;
  PetscCheck(nep->which==NEP_ALL,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only computing all eigenvalues");
  NEPCheckUnsupported(nep,NEP_FEATURE_STOPPING | NEP_FEATURE_TWOSIDED);

  /* check region */
  PetscCall(RGIsTrivial(nep->rg,&istrivial));
  PetscCheck(!istrivial,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
  PetscCall(RGGetComplement(nep->rg,&flg));
  PetscCheck(!flg,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
  PetscCall(PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse));
  PetscCheck(isellipse,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Currently only implemented for elliptic regions");

  /* if the region has changed, then reset contour data */
  PetscCall(PetscObjectGetId((PetscObject)nep->rg,&id));
  PetscCall(PetscObjectStateGet((PetscObject)nep->rg,&state));
  if (ctx->rgid && (id != ctx->rgid || state != ctx->rgstate)) {
    PetscCall(SlepcContourDataDestroy(&ctx->contour));
    PetscCall(PetscInfo(nep,"Resetting the contour data structure due to a change of region\n"));
    ctx->rgid = id; ctx->rgstate = state;
  }

  /* create contour data structure */
  if (!ctx->contour) {
    PetscCall(RGCanUseConjugates(nep->rg,ctx->isreal,&ctx->useconj));
    PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)nep,&ctx->contour));
  }

  PetscCall(NEPAllocateSolution(nep,0));
  if (ctx->weight) PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
  PetscCall(PetscMalloc4(ctx->N,&ctx->weight,ctx->N,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma));

  /* allocate basis vectors */
  PetscCall(BVDestroy(&ctx->S));
  PetscCall(BVDuplicateResize(nep->V,ctx->L*ctx->M,&ctx->S));
  PetscCall(BVDestroy(&ctx->V));
  PetscCall(BVDuplicateResize(nep->V,ctx->L,&ctx->V));

  contour = ctx->contour;
  if (contour->subcomm && contour->subcomm->n != 1 && nep->fui==NEP_USER_INTERFACE_CALLBACK) {
    PetscCall(NEPComputeFunction(nep,0,nep->function,nep->function_pre));
    PetscCall(SlepcContourRedundantMat(contour,1,&nep->function,(nep->function!=nep->function_pre)?&nep->function_pre:NULL));
  } else PetscCall(SlepcContourRedundantMat(contour,nep->nt,nep->A,nep->P));
  if (contour->pA) {
    if (!ctx->J) PetscCall(MatDuplicate(contour->pA[0],MAT_DO_NOT_COPY_VALUES,&ctx->J));
    PetscCall(BVGetColumn(ctx->V,0,&v0));
    PetscCall(SlepcContourScatterCreate(contour,v0));
    PetscCall(BVRestoreColumn(ctx->V,0,&v0));
    PetscCall(BVDestroy(&ctx->pV));
    PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->pV));
    PetscCall(BVSetSizesFromVec(ctx->pV,contour->xsub,nep->n));
    PetscCall(BVSetFromOptions(ctx->pV));
    PetscCall(BVResize(ctx->pV,ctx->L,PETSC_FALSE));
  }

  PetscCall(BVDestroy(&ctx->Y));
  if (contour->pA) {
    PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->Y));
    PetscCall(BVSetSizesFromVec(ctx->Y,contour->xsub,nep->n));
    PetscCall(BVSetFromOptions(ctx->Y));
    PetscCall(BVResize(ctx->Y,contour->npoints*ctx->L,PETSC_FALSE));
  } else PetscCall(BVDuplicateResize(nep->V,contour->npoints*ctx->L,&ctx->Y));

  if (ctx->extraction == NEP_CISS_EXTRACTION_RITZ)  {
    PetscCall(DSSetMethod(nep->ds,1));
    PetscCall(DSNEPSetRG(nep->ds,nep->rg));
    if (nep->fui==NEP_USER_INTERFACE_SPLIT) PetscCall(DSNEPSetFN(nep->ds,nep->nt,nep->f));
    else {
      PetscCall(PetscNew(&dsctxf));
      dsctxf->nep = nep;
      PetscCall(DSNEPSetComputeMatrixFunction(nep->ds,NEPContourDSComputeMatrix,dsctxf,PetscCtxDestroyDefault));
    }
  }
  PetscCall(DSAllocate(nep->ds,nep->ncv));
  nwork = (nep->fui==NEP_USER_INTERFACE_SPLIT)? 2: 1;
  PetscCall(NEPSetWorkVecs(nep,nwork));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPSolve_CISS(NEP nep)
{
  NEP_CISS         *ctx = (NEP_CISS*)nep->data;
  SlepcContourData contour = ctx->contour;
  Mat              X,M,E,T,P,J;
  BV               V;
  PetscInt         i,j,ld,L_add=0,nv=0,L_base=ctx->L,inner,*inside;
  PetscScalar      *Mu,*H0,*H1,*rr,*temp,center;
  PetscReal        error,max_error,radius,rgscale,est_eig,eta;
  PetscBool        isellipse,*fl1;
  Vec              si;
  SlepcSC          sc;
  PetscRandom      rand;
  NEP_CISS_PROJECT dsctxf;

  PetscFunctionBegin;
  PetscCall(DSGetSlepcSC(nep->ds,&sc));
  sc->comparison    = SlepcCompareLargestMagnitude;
  sc->comparisonctx = NULL;
  sc->map           = NULL;
  sc->mapobj        = NULL;
  PetscCall(DSGetLeadingDimension(nep->ds,&ld));
  PetscCall(RGComputeQuadrature(nep->rg,RG_QUADRULE_TRAPEZOIDAL,ctx->N,ctx->omega,ctx->pp,ctx->weight));
  if (contour->pA) {
    T = contour->pA[0];
    P = ((nep->fui==NEP_USER_INTERFACE_SPLIT && nep->P) || (nep->fui==NEP_USER_INTERFACE_CALLBACK && contour->pP))? contour->pP[0]: T;
  } else {
    T = nep->function;
    P = nep->function_pre? nep->function_pre: nep->function;
  }
  PetscCall(NEPCISSSetUp(nep,T,P));
  PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
  PetscCall(BVSetRandomSign(ctx->V));
  PetscCall(BVGetRandomContext(ctx->V,&rand));
  if (contour->pA) {
    J = ctx->J;
    V = ctx->pV;
    PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
  } else {
    J = nep->jacobian;
    V = ctx->V;
  }
  PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
  PetscCall(PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse));
  if (isellipse) {
    PetscCall(BVTraceQuadrature(ctx->Y,ctx->V,ctx->L,ctx->L,ctx->weight,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj,&est_eig));
    PetscCall(PetscInfo(nep,"Estimated eigenvalue count: %f\n",(double)est_eig));
    eta = PetscPowReal(10.0,-PetscLog10Real(nep->tol)/ctx->N);
    L_add = PetscMax(0,(PetscInt)PetscCeilReal((est_eig*eta)/ctx->M)-ctx->L);
    if (L_add>ctx->L_max-ctx->L) {
      PetscCall(PetscInfo(nep,"Number of eigenvalues inside the contour path may be too large\n"));
      L_add = ctx->L_max-ctx->L;
    }
  }
  /* Updates L after estimate the number of eigenvalue */
  if (L_add>0) {
    PetscCall(PetscInfo(nep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by Estimate #Eig\n",ctx->L,ctx->L+L_add));
    PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    PetscCall(BVSetRandomSign(ctx->V));
    if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    ctx->L += L_add;
    PetscCall(NEPCISSSolve(nep,J,V,ctx->L-L_add,ctx->L));
  }

  PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
  for (i=0;i<ctx->refine_blocksize;i++) {
    PetscCall(BVDotQuadrature(ctx->Y,V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
    PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    PetscCall(PetscLogEventBegin(NEP_CISS_SVD,nep,0,0,0));
    PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
    PetscCall(PetscLogEventEnd(NEP_CISS_SVD,nep,0,0,0));
    if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    L_add = L_base;
    if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    PetscCall(PetscInfo(nep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by SVD(H0)\n",ctx->L,ctx->L+L_add));
    PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    PetscCall(BVSetRandomSign(ctx->V));
    if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    ctx->L += L_add;
    PetscCall(NEPCISSSolve(nep,J,V,ctx->L-L_add,ctx->L));
    if (L_add) {
      PetscCall(PetscFree2(Mu,H0));
      PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
    }
  }

  PetscCall(RGGetScale(nep->rg,&rgscale));
  PetscCall(RGEllipseGetParameters(nep->rg,&center,&radius,NULL));

  if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) PetscCall(PetscMalloc1(ctx->L*ctx->M*ctx->L*ctx->M,&H1));

  while (nep->reason == NEP_CONVERGED_ITERATING) {
    nep->its++;
    for (inner=0;inner<=ctx->refine_inner;inner++) {
      if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
        PetscCall(BVDotQuadrature(ctx->Y,V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
        PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
        PetscCall(PetscLogEventBegin(NEP_CISS_SVD,nep,0,0,0));
        PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
        PetscCall(PetscLogEventEnd(NEP_CISS_SVD,nep,0,0,0));
      } else {
        PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
        /* compute SVD of S */
        PetscCall(BVSVDAndRank(ctx->S,ctx->M,ctx->L,ctx->delta,(ctx->extraction==NEP_CISS_EXTRACTION_CAA)?BV_SVD_METHOD_QR_CAA:BV_SVD_METHOD_QR,H0,ctx->sigma,&nv));
      }
      PetscCall(PetscInfo(nep,"Estimated rank: nv = %" PetscInt_FMT "\n",nv));
      if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
        PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
        PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
        PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
        PetscCall(BVCopy(ctx->S,ctx->V));
        if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
        PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
      } else break;
    }
    nep->nconv = 0;
    if (nv == 0) { nep->reason = NEP_CONVERGED_TOL; break; }
    else {
      /* Extracting eigenpairs */
      PetscCall(DSSetDimensions(nep->ds,nv,0,0));
      PetscCall(DSSetState(nep->ds,DS_STATE_RAW));
      if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
        PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
        PetscCall(CISS_BlockHankel(Mu,1,ctx->L,ctx->M,H1));
        PetscCall(DSGetArray(nep->ds,DS_MAT_A,&temp));
        for (j=0;j<nv;j++)
          for (i=0;i<nv;i++)
            temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
        PetscCall(DSRestoreArray(nep->ds,DS_MAT_A,&temp));
        PetscCall(DSGetArray(nep->ds,DS_MAT_B,&temp));
        for (j=0;j<nv;j++)
          for (i=0;i<nv;i++)
            temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
        PetscCall(DSRestoreArray(nep->ds,DS_MAT_B,&temp));
      } else if (ctx->extraction == NEP_CISS_EXTRACTION_CAA) {
        PetscCall(BVSetActiveColumns(ctx->S,0,nv));
        PetscCall(DSGetArray(nep->ds,DS_MAT_A,&temp));
        for (i=0;i<nv;i++) PetscCall(PetscArraycpy(temp+i*ld,H0+i*nv,nv));
        PetscCall(DSRestoreArray(nep->ds,DS_MAT_A,&temp));
      } else {
        PetscCall(BVSetActiveColumns(ctx->S,0,nv));
        if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
          for (i=0;i<nep->nt;i++) {
            PetscCall(DSGetMat(nep->ds,DSMatExtra[i],&E));
            PetscCall(BVMatProject(ctx->S,nep->A[i],ctx->S,E));
            PetscCall(DSRestoreMat(nep->ds,DSMatExtra[i],&E));
          }
        } else {
          PetscCall(DSNEPGetComputeMatrixFunction(nep->ds,NULL,(PetscCtxRt)&dsctxf,NULL));
          dsctxf->Q = ctx->S;
        }
      }
      PetscCall(DSSolve(nep->ds,nep->eigr,nep->eigi));
      PetscCall(DSSynchronize(nep->ds,nep->eigr,nep->eigi));
      PetscCall(DSGetDimensions(nep->ds,NULL,NULL,NULL,&nv));
      if (ctx->extraction == NEP_CISS_EXTRACTION_CAA || ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
        for (i=0;i<nv;i++) {
          nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
        }
      }
      PetscCall(PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr));
      PetscCall(DSVectors(nep->ds,DS_MAT_X,NULL,NULL));
      PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
      PetscCall(SlepcCISS_isGhost(X,nv,ctx->sigma,ctx->spurious_threshold,fl1));
      PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
      PetscCall(RGCheckInside(nep->rg,nv,nep->eigr,nep->eigi,inside));
      for (i=0;i<nv;i++) {
        if (fl1[i] && inside[i]>=0) {
          rr[i] = 1.0;
          nep->nconv++;
        } else rr[i] = 0.0;
      }
      PetscCall(DSSort(nep->ds,nep->eigr,nep->eigi,rr,NULL,&nep->nconv));
      PetscCall(DSSynchronize(nep->ds,nep->eigr,nep->eigi));
      if (ctx->extraction == NEP_CISS_EXTRACTION_CAA || ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
        for (i=0;i<nv;i++) nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
      }
      PetscCall(PetscFree3(fl1,inside,rr));
      PetscCall(BVSetActiveColumns(nep->V,0,nv));
      PetscCall(DSVectors(nep->ds,DS_MAT_X,NULL,NULL));
      if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
        PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
        PetscCall(BVSetActiveColumns(ctx->S,0,nv));
        PetscCall(BVCopy(ctx->S,nep->V));
        PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
        PetscCall(BVMultInPlace(ctx->S,X,0,nep->nconv));
        PetscCall(BVMultInPlace(nep->V,X,0,nep->nconv));
        PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
      } else {
        PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
        PetscCall(BVMultInPlace(ctx->S,X,0,nep->nconv));
        PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
        PetscCall(BVSetActiveColumns(ctx->S,0,nep->nconv));
        PetscCall(BVCopy(ctx->S,nep->V));
      }
      max_error = 0.0;
      for (i=0;i<nep->nconv;i++) {
        PetscCall(BVGetColumn(nep->V,i,&si));
        PetscCall(VecNormalize(si,NULL));
        PetscCall(NEPComputeResidualNorm_Private(nep,PETSC_FALSE,nep->eigr[i],si,nep->work,&error));
        PetscCall((*nep->converged)(nep,nep->eigr[i],0,error,&error,nep->convergedctx));
        PetscCall(BVRestoreColumn(nep->V,i,&si));
        max_error = PetscMax(max_error,error);
      }
      if (max_error <= nep->tol) nep->reason = NEP_CONVERGED_TOL;
      else if (nep->its > nep->max_it) nep->reason = NEP_DIVERGED_ITS;
      else {
        if (nep->nconv > ctx->L) nv = nep->nconv;
        else if (ctx->L > nv) nv = ctx->L;
        nv = PetscMin(nv,ctx->L*ctx->M);
        PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M));
        PetscCall(MatSetRandom(M,rand));
        PetscCall(BVSetActiveColumns(ctx->S,0,nv));
        PetscCall(BVMultInPlace(ctx->S,M,0,ctx->L));
        PetscCall(MatDestroy(&M));
        PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
        PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
        PetscCall(BVCopy(ctx->S,ctx->V));
        if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
        PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
      }
    }
  }
  PetscCall(PetscFree2(Mu,H0));
  if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) PetscCall(PetscFree(H1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSSetSizes_CISS(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;
  PetscInt       oN,oL,oM,oLmax,onpart;
  PetscMPIInt    size;

  PetscFunctionBegin;
  oN = ctx->N;
  if (ip == PETSC_DETERMINE) {
    if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
  } else if (ip != PETSC_CURRENT) {
    PetscCheck(ip>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    PetscCheck(ip%2==0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
  }
  oL = ctx->L;
  if (bs == PETSC_DETERMINE) {
    ctx->L = 16;
  } else if (bs != PETSC_CURRENT) {
    PetscCheck(bs>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    ctx->L = bs;
  }
  oM = ctx->M;
  if (ms == PETSC_DETERMINE) {
    ctx->M = ctx->N/4;
  } else if (ms != PETSC_CURRENT) {
    PetscCheck(ms>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    PetscCheck(ms<=ctx->N,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
    ctx->M = ms;
  }
  onpart = ctx->npart;
  if (npart == PETSC_DETERMINE) {
    ctx->npart = 1;
  } else if (npart != PETSC_CURRENT) {
    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)nep),&size));
    PetscCheck(npart>0 && npart<=size,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of npart");
    ctx->npart = npart;
  }
  oLmax = ctx->L_max;
  if (bsmax == PETSC_DETERMINE) {
    ctx->L_max = 64;
  } else if (bsmax != PETSC_CURRENT) {
    PetscCheck(bsmax>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    ctx->L_max = PetscMax(bsmax,ctx->L);
  }
  if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) {
    PetscCall(SlepcContourDataDestroy(&ctx->contour));
    PetscCall(PetscInfo(nep,"Resetting the contour data structure due to a change of parameters\n"));
    nep->state = NEP_STATE_INITIAL;
  }
  ctx->isreal = realmats;
  if (oL != ctx->L || oM != ctx->M || oLmax != ctx->L_max) nep->state = NEP_STATE_INITIAL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSSetSizes - Sets the values of various size parameters in the CISS solver.

   Logically Collective

   Input Parameters:
+  nep      - the nonlinear eigensolver context
.  ip       - number of integration points
.  bs       - block size
.  ms       - moment size
.  npart    - number of partitions when splitting the communicator
.  bsmax    - max block size
-  realmats - $T(z)$ is real for real $z$

   Options Database Keys:
+  -nep_ciss_integration_points ip - sets the number of integration points
.  -nep_ciss_blocksize bs          - sets the block size
.  -nep_ciss_moments ms            - sets the moment size
.  -nep_ciss_partitions npart      - sets the number of partitions
.  -nep_ciss_maxblocksize bsmax    - sets the maximum block size
-  -nep_ciss_realmats (true|false) - $T(z)$ is real for real $z$

   Notes:
   For all integer arguments, you can use `PETSC_CURRENT` to keep the current value, and
   `PETSC_DETERMINE` to set them to a default value.

   The default number of partitions is 1. This means the internal `KSP` object is shared
   among all processes of the `NEP` communicator. Otherwise, the communicator is split
   into `npart` communicators, so that `npart` `KSP` solves proceed simultaneously.

   The `realmats` flag can be set to `PETSC_TRUE` when $T(\cdot)$ is guaranteed to be real
   when the argument is a real value, for example, when all matrices in
   the split form are real. When set to `PETSC_TRUE`, the solver avoids some computations.

   For a detailed description of the parameters see {cite:p}`Mae16`.

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetSizes()`
@*/
PetscErrorCode NEPCISSSetSizes(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscValidLogicalCollectiveInt(nep,ip,2);
  PetscValidLogicalCollectiveInt(nep,bs,3);
  PetscValidLogicalCollectiveInt(nep,ms,4);
  PetscValidLogicalCollectiveInt(nep,npart,5);
  PetscValidLogicalCollectiveInt(nep,bsmax,6);
  PetscValidLogicalCollectiveBool(nep,realmats,7);
  PetscTryMethod(nep,"NEPCISSSetSizes_C",(NEP,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(nep,ip,bs,ms,npart,bsmax,realmats));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSGetSizes_CISS(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (ip) *ip = ctx->N;
  if (bs) *bs = ctx->L;
  if (ms) *ms = ctx->M;
  if (npart) *npart = ctx->npart;
  if (bsmax) *bsmax = ctx->L_max;
  if (realmats) *realmats = ctx->isreal;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSGetSizes - Gets the values of various size parameters in the CISS solver.

   Not Collective

   Input Parameter:
.  nep - the nonlinear eigensolver context

   Output Parameters:
+  ip       - number of integration points
.  bs       - block size
.  ms       - moment size
.  npart    - number of partitions when splitting the communicator
.  bsmax    - max block size
-  realmats - $T(z)$ is real for real $z$

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetSizes()`
@*/
PetscErrorCode NEPCISSGetSizes(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscUseMethod(nep,"NEPCISSGetSizes_C",(NEP,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(nep,ip,bs,ms,npart,bsmax,realmats));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSSetThreshold_CISS(NEP nep,PetscReal delta,PetscReal spur)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (delta == (PetscReal)PETSC_DETERMINE) {
    ctx->delta = SLEPC_DEFAULT_TOL*1e-4;
  } else if (delta != (PetscReal)PETSC_CURRENT) {
    PetscCheck(delta>0.0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    ctx->delta = delta;
  }
  if (spur == (PetscReal)PETSC_DETERMINE) {
    ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
  } else if (spur != (PetscReal)PETSC_CURRENT) {
    PetscCheck(spur>0.0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    ctx->spurious_threshold = spur;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSSetThreshold - Sets the values of various threshold parameters in
   the CISS solver.

   Logically Collective

   Input Parameters:
+  nep   - the nonlinear eigensolver context
.  delta - threshold for numerical rank
-  spur  - spurious threshold (to discard spurious eigenpairs)

   Options Database Keys:
+  -nep_ciss_delta delta             - sets the delta
-  -nep_ciss_spurious_threshold spur - sets the spurious threshold

   Notes:
   `PETSC_CURRENT` can be used to preserve the current value of any of the
   arguments, and `PETSC_DETERMINE` to set them to a default value.

   For a detailed description of the parameters see {cite:p}`Mae16`.

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetThreshold()`
@*/
PetscErrorCode NEPCISSSetThreshold(NEP nep,PetscReal delta,PetscReal spur)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscValidLogicalCollectiveReal(nep,delta,2);
  PetscValidLogicalCollectiveReal(nep,spur,3);
  PetscTryMethod(nep,"NEPCISSSetThreshold_C",(NEP,PetscReal,PetscReal),(nep,delta,spur));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSGetThreshold_CISS(NEP nep,PetscReal *delta,PetscReal *spur)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (delta) *delta = ctx->delta;
  if (spur)  *spur = ctx->spurious_threshold;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSGetThreshold - Gets the values of various threshold parameters in
   the CISS solver.

   Not Collective

   Input Parameter:
.  nep - the nonlinear eigensolver context

   Output Parameters:
+  delta - threshold for numerical rank
-  spur  - spurious threshold (to discard spurious eigenpairs)

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetThreshold()`
@*/
PetscErrorCode NEPCISSGetThreshold(NEP nep,PetscReal *delta,PetscReal *spur)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscUseMethod(nep,"NEPCISSGetThreshold_C",(NEP,PetscReal*,PetscReal*),(nep,delta,spur));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSSetRefinement_CISS(NEP nep,PetscInt inner,PetscInt blsize)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (inner == PETSC_DETERMINE) {
    ctx->refine_inner = 0;
  } else if (inner != PETSC_CURRENT) {
    PetscCheck(inner>=0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    ctx->refine_inner = inner;
  }
  if (blsize == PETSC_DETERMINE) {
    ctx->refine_blocksize = 0;
  } else if (blsize != PETSC_CURRENT) {
    PetscCheck(blsize>=0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    ctx->refine_blocksize = blsize;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSSetRefinement - Sets the values of various refinement parameters
   in the CISS solver.

   Logically Collective

   Input Parameters:
+  nep    - the nonlinear eigensolver context
.  inner  - number of iterative refinement iterations (inner loop)
-  blsize - number of iterative refinement iterations (blocksize loop)

   Options Database Keys:
+  -nep_ciss_refine_inner inner      - sets number of inner iterations
-  -nep_ciss_refine_blocksize blsize - sets number of blocksize iterations

   Note:
   `PETSC_CURRENT` can be used to preserve the current value of any of the
   arguments, and `PETSC_DETERMINE` to set them to a default of 0 (no refinement).

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetRefinement()`
@*/
PetscErrorCode NEPCISSSetRefinement(NEP nep,PetscInt inner,PetscInt blsize)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscValidLogicalCollectiveInt(nep,inner,2);
  PetscValidLogicalCollectiveInt(nep,blsize,3);
  PetscTryMethod(nep,"NEPCISSSetRefinement_C",(NEP,PetscInt,PetscInt),(nep,inner,blsize));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSGetRefinement_CISS(NEP nep,PetscInt *inner,PetscInt *blsize)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (inner)  *inner = ctx->refine_inner;
  if (blsize) *blsize = ctx->refine_blocksize;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSGetRefinement - Gets the values of various refinement parameters
   in the CISS solver.

   Not Collective

   Input Parameter:
.  nep - the nonlinear eigensolver context

   Output Parameters:
+  inner  - number of iterative refinement iterations (inner loop)
-  blsize - number of iterative refinement iterations (blocksize loop)

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetRefinement()`
@*/
PetscErrorCode NEPCISSGetRefinement(NEP nep, PetscInt *inner, PetscInt *blsize)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscUseMethod(nep,"NEPCISSGetRefinement_C",(NEP,PetscInt*,PetscInt*),(nep,inner,blsize));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSSetExtraction_CISS(NEP nep,NEPCISSExtraction extraction)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  if (ctx->extraction != extraction) {
    ctx->extraction = extraction;
    nep->state      = NEP_STATE_INITIAL;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSSetExtraction - Sets the extraction technique used in the CISS solver.

   Logically Collective

   Input Parameters:
+  nep        - the nonlinear eigensolver context
-  extraction - the extraction technique, see `NEPCISSExtraction` for possible values

   Options Database Key:
.  -nep_ciss_extraction (ritz|hankel|caa) - sets the extraction technique

   Notes:
   By default, the Rayleigh-Ritz extraction is used (`NEP_CISS_EXTRACTION_RITZ`).

   If the `hankel` or the `caa` option is specified (`NEP_CISS_EXTRACTION_HANKEL` or
   `NEP_CISS_EXTRACTION_CAA`), then the block Hankel method, or the communication-avoiding
   Arnoldi method, respectively, is used for extracting eigenpairs.

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetExtraction()`, `NEPCISSExtraction`
@*/
PetscErrorCode NEPCISSSetExtraction(NEP nep,NEPCISSExtraction extraction)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscValidLogicalCollectiveEnum(nep,extraction,2);
  PetscTryMethod(nep,"NEPCISSSetExtraction_C",(NEP,NEPCISSExtraction),(nep,extraction));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSGetExtraction_CISS(NEP nep,NEPCISSExtraction *extraction)
{
  NEP_CISS *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  *extraction = ctx->extraction;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   NEPCISSGetExtraction - Gets the extraction technique used in the CISS solver.

   Not Collective

   Input Parameter:
.  nep - the nonlinear eigensolver context

   Output Parameter:
.  extraction - extraction technique

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetExtraction()`, `NEPCISSExtraction`
@*/
PetscErrorCode NEPCISSGetExtraction(NEP nep,NEPCISSExtraction *extraction)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscAssertPointer(extraction,2);
  PetscUseMethod(nep,"NEPCISSGetExtraction_C",(NEP,NEPCISSExtraction*),(nep,extraction));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPCISSGetKSPs_CISS(NEP nep,PetscInt *nsolve,KSP **ksp)
{
  NEP_CISS         *ctx = (NEP_CISS*)nep->data;
  SlepcContourData contour;
  PetscInt         i;
  PC               pc;
  MPI_Comm         child;

  PetscFunctionBegin;
  if (!ctx->contour) {  /* initialize contour data structure first */
    PetscCall(RGCanUseConjugates(nep->rg,ctx->isreal,&ctx->useconj));
    PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)nep,&ctx->contour));
  }
  contour = ctx->contour;
  if (!contour->ksp) {
    PetscCall(PetscMalloc1(contour->npoints,&contour->ksp));
    PetscCall(PetscSubcommGetChild(contour->subcomm,&child));
    for (i=0;i<contour->npoints;i++) {
      PetscCall(KSPCreate(child,&contour->ksp[i]));
      PetscCall(PetscObjectIncrementTabLevel((PetscObject)contour->ksp[i],(PetscObject)nep,1));
      PetscCall(KSPSetOptionsPrefix(contour->ksp[i],((PetscObject)nep)->prefix));
      PetscCall(KSPAppendOptionsPrefix(contour->ksp[i],"nep_ciss_"));
      PetscCall(PetscObjectSetOptions((PetscObject)contour->ksp[i],((PetscObject)nep)->options));
      PetscCall(KSPSetErrorIfNotConverged(contour->ksp[i],PETSC_TRUE));
      PetscCall(KSPSetTolerances(contour->ksp[i],SlepcDefaultTol(nep->tol),PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
      PetscCall(KSPGetPC(contour->ksp[i],&pc));
      if ((nep->fui==NEP_USER_INTERFACE_SPLIT && nep->P) || (nep->fui==NEP_USER_INTERFACE_CALLBACK && nep->function_pre!=nep->function)) {
        PetscCall(KSPSetType(contour->ksp[i],KSPBCGS));
        PetscCall(PCSetType(pc,PCBJACOBI));
      } else {
        PetscCall(KSPSetType(contour->ksp[i],KSPPREONLY));
        PetscCall(PCSetType(pc,PCLU));
      }
    }
  }
  if (nsolve) *nsolve = contour->npoints;
  if (ksp)    *ksp    = contour->ksp;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   NEPCISSGetKSPs - Retrieve the array of linear solver objects associated with
   the CISS solver.

   Collective

   Input Parameter:
.  nep - the nonlinear eigensolver context

   Output Parameters:
+  nsolve - number of solver objects
-  ksp - array of linear solver object

   Notes:
   The number of `KSP` solvers is equal to the number of integration points divided by
   the number of partitions. This value is halved in the case of real matrices with
   a region centered at the real axis.

   Level: advanced

.seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetSizes()`
@*/
PetscErrorCode NEPCISSGetKSPs(NEP nep,PetscInt *nsolve,KSP **ksp)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(nep,NEP_CLASSID,1);
  PetscUseMethod(nep,"NEPCISSGetKSPs_C",(NEP,PetscInt*,KSP**),(nep,nsolve,ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPReset_CISS(NEP nep)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  PetscCall(BVDestroy(&ctx->S));
  PetscCall(BVDestroy(&ctx->V));
  PetscCall(BVDestroy(&ctx->Y));
  PetscCall(SlepcContourDataReset(ctx->contour));
  PetscCall(MatDestroy(&ctx->J));
  PetscCall(BVDestroy(&ctx->pV));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPSetFromOptions_CISS(NEP nep,PetscOptionItems PetscOptionsObject)
{
  NEP_CISS          *ctx = (NEP_CISS*)nep->data;
  PetscReal         r1,r2;
  PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
  PetscBool         b1,flg,flg2,flg3,flg4,flg5,flg6;
  NEPCISSExtraction extraction;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject,"NEP CISS Options");

    PetscCall(NEPCISSGetSizes(nep,&i1,&i2,&i3,&i4,&i5,&b1));
    PetscCall(PetscOptionsInt("-nep_ciss_integration_points","Number of integration points","NEPCISSSetSizes",i1,&i1,&flg));
    PetscCall(PetscOptionsInt("-nep_ciss_blocksize","Block size","NEPCISSSetSizes",i2,&i2,&flg2));
    PetscCall(PetscOptionsInt("-nep_ciss_moments","Moment size","NEPCISSSetSizes",i3,&i3,&flg3));
    PetscCall(PetscOptionsInt("-nep_ciss_partitions","Number of partitions","NEPCISSSetSizes",i4,&i4,&flg4));
    PetscCall(PetscOptionsInt("-nep_ciss_maxblocksize","Maximum block size","NEPCISSSetSizes",i5,&i5,&flg5));
    PetscCall(PetscOptionsBool("-nep_ciss_realmats","True if T(z) is real for real z","NEPCISSSetSizes",b1,&b1,&flg6));
    if (flg || flg2 || flg3 || flg4 || flg5 || flg6) PetscCall(NEPCISSSetSizes(nep,i1,i2,i3,i4,i5,b1));

    PetscCall(NEPCISSGetThreshold(nep,&r1,&r2));
    PetscCall(PetscOptionsReal("-nep_ciss_delta","Threshold for numerical rank","NEPCISSSetThreshold",r1,&r1,&flg));
    PetscCall(PetscOptionsReal("-nep_ciss_spurious_threshold","Threshold for the spurious eigenpairs","NEPCISSSetThreshold",r2,&r2,&flg2));
    if (flg || flg2) PetscCall(NEPCISSSetThreshold(nep,r1,r2));

    PetscCall(NEPCISSGetRefinement(nep,&i6,&i7));
    PetscCall(PetscOptionsInt("-nep_ciss_refine_inner","Number of inner iterative refinement iterations","NEPCISSSetRefinement",i6,&i6,&flg));
    PetscCall(PetscOptionsInt("-nep_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","NEPCISSSetRefinement",i7,&i7,&flg2));
    if (flg || flg2) PetscCall(NEPCISSSetRefinement(nep,i6,i7));

    PetscCall(PetscOptionsEnum("-nep_ciss_extraction","Extraction technique","NEPCISSSetExtraction",NEPCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg));
    if (flg) PetscCall(NEPCISSSetExtraction(nep,extraction));

  PetscOptionsHeadEnd();

  if (!nep->rg) PetscCall(NEPGetRG(nep,&nep->rg));
  PetscCall(RGSetFromOptions(nep->rg)); /* this is necessary here to set useconj */
  if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
  PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
  for (i=0;i<ctx->contour->npoints;i++) PetscCall(KSPSetFromOptions(ctx->contour->ksp[i]));
  PetscCall(PetscSubcommSetFromOptions(ctx->contour->subcomm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPDestroy_CISS(NEP nep)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  PetscCall(SlepcContourDataDestroy(&ctx->contour));
  PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
  PetscCall(PetscFree(nep->data));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetExtraction_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetExtraction_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetKSPs_C",NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPView_CISS(NEP nep,PetscViewer viewer)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;
  PetscBool      isascii;
  PetscViewer    sviewer;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
  if (isascii) {
    PetscCall(PetscViewerASCIIPrintf(viewer,"  sizes { integration points: %" PetscInt_FMT ", block size: %" PetscInt_FMT ", moment size: %" PetscInt_FMT ", partitions: %" PetscInt_FMT ", maximum block size: %" PetscInt_FMT " }\n",ctx->N,ctx->L,ctx->M,ctx->npart,ctx->L_max));
    if (ctx->isreal) PetscCall(PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n"));
    PetscCall(PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold));
    PetscCall(PetscViewerASCIIPrintf(viewer,"  iterative refinement  { inner: %" PetscInt_FMT ", blocksize: %" PetscInt_FMT " }\n",ctx->refine_inner, ctx->refine_blocksize));
    PetscCall(PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",NEPCISSExtractions[ctx->extraction]));
    if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
    PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
    PetscCall(PetscViewerASCIIPushTab(viewer));
    if (ctx->npart>1 && ctx->contour->subcomm) {
      PetscCall(PetscViewerGetSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
      if (!ctx->contour->subcomm->color) PetscCall(KSPView(ctx->contour->ksp[0],sviewer));
      PetscCall(PetscViewerFlush(sviewer));
      PetscCall(PetscViewerRestoreSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
      /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
      PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    } else PetscCall(KSPView(ctx->contour->ksp[0],viewer));
    PetscCall(PetscViewerASCIIPopTab(viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode NEPSetDSType_CISS(NEP nep)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  switch (ctx->extraction) {
    case NEP_CISS_EXTRACTION_RITZ:   PetscCall(DSSetType(nep->ds,DSNEP)); break;
    case NEP_CISS_EXTRACTION_HANKEL: PetscCall(DSSetType(nep->ds,DSGNHEP)); break;
    case NEP_CISS_EXTRACTION_CAA:    PetscCall(DSSetType(nep->ds,DSNHEP)); break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   NEPCISS - NEPCISS = "ciss" - A contour integral eigensolver based on the
   Sakurai-Sugiura scheme.

   Notes:
   This solver is based on the numerical contour integration idea
   proposed initially for linear problems by {cite:t}`Sak03`. In nonlinear
   eigenproblems, a Rayleigh-Ritz projection is done, resulting in
   a small dense nonlinear eigenproblem {cite:p}`Asa09,Yok13`.

   Contour integral methods are able to compute all eigenvalues
   lying inside a region of the complex plane. Use `NEPGetRG()` to
   specify the region. However, the computational cost is usually high
   because multiple linear systems must be solved. Use `NEPCISSGetKSPs()`
   to configure the `KSP` objects for this.

   Details of the implementation in SLEPc can be found in {cite:p}`Mae16`.

   Level: beginner

.seealso: [](ch:nep), `NEP`, `NEPType`, `NEPSetType()`, `NEPGetRG()`
M*/
SLEPC_EXTERN PetscErrorCode NEPCreate_CISS(NEP nep)
{
  NEP_CISS       *ctx = (NEP_CISS*)nep->data;

  PetscFunctionBegin;
  PetscCall(PetscNew(&ctx));
  nep->data = ctx;
  /* set default values of parameters */
  ctx->N                  = 32;
  ctx->L                  = 16;
  ctx->M                  = ctx->N/4;
  ctx->delta              = SLEPC_DEFAULT_TOL*1e-4;
  ctx->L_max              = 64;
  ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
  ctx->isreal             = PETSC_FALSE;
  ctx->npart              = 1;

  nep->useds = PETSC_TRUE;

  nep->ops->solve          = NEPSolve_CISS;
  nep->ops->setup          = NEPSetUp_CISS;
  nep->ops->setfromoptions = NEPSetFromOptions_CISS;
  nep->ops->reset          = NEPReset_CISS;
  nep->ops->destroy        = NEPDestroy_CISS;
  nep->ops->view           = NEPView_CISS;
  nep->ops->setdstype      = NEPSetDSType_CISS;

  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NEPCISSSetSizes_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NEPCISSGetSizes_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NEPCISSSetThreshold_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NEPCISSGetThreshold_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NEPCISSSetRefinement_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NEPCISSGetRefinement_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetExtraction_C",NEPCISSSetExtraction_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetExtraction_C",NEPCISSGetExtraction_CISS));
  PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetKSPs_C",NEPCISSGetKSPs_CISS));
  PetscFunctionReturn(PETSC_SUCCESS);
}
