pvfmm-static-build/include/fmm_pts.txx

/**
 * \file fmm_pts.txx
 * \author Dhairya Malhotra, dhairya.malhotra@gmail.com
 * \date 3-07-2011
 * \brief This file contains the implementation of the FMM_Pts class.
 */

#include <omp.h>
#include <cmath>
#include <cstdlib>
#include <cassert>
#include <sstream>
#include <iostream>
#include <stdint.h>
#include <set>
#ifdef PVFMM_HAVE_SYS_STAT_H
#include <sys/stat.h>
#endif

#ifdef __SSE__
#include <xmmintrin.h>
#endif
#ifdef __SSE2__
#include <emmintrin.h>
#endif
#ifdef __SSE3__
#include <pmmintrin.h>
#endif
#ifdef __AVX__
#include <immintrin.h>
#endif
#if defined(__MIC__)
#include <immintrin.h>
#endif

#include <profile.hpp>

namespace pvfmm{

/**
 * \brief Returns the coordinates of points on the surface of a cube.
 * \param[in] p Number of points on an edge of the cube is (n+1)
 * \param[in] c Coordinates to the centre of the cube (3D array).
 * \param[in] alpha Scaling factor for the size of the cube.
 * \param[in] depth Depth of the cube in the octree.
 * \return Vector with coordinates of points on the surface of the cube in the
 * format [x0 y0 z0 x1 y1 z1 .... ].
 */
template <class Real_t>
std::vector<Real_t> surface(int p, Real_t* c, Real_t alpha, int depth){
  size_t n_=(6*(p-1)*(p-1)+2);  //Total number of points.

  std::vector<Real_t> coord(n_*3);
  coord[0]=coord[1]=coord[2]=-1.0;
  size_t cnt=1;
  for(int i=0;i<p-1;i++)
    for(int j=0;j<p-1;j++){
      coord[cnt*3  ]=-1.0;
      coord[cnt*3+1]=(2.0*(i+1)-p+1)/(p-1);
      coord[cnt*3+2]=(2.0*j-p+1)/(p-1);
      cnt++;
    }
  for(int i=0;i<p-1;i++)
    for(int j=0;j<p-1;j++){
      coord[cnt*3  ]=(2.0*i-p+1)/(p-1);
      coord[cnt*3+1]=-1.0;
      coord[cnt*3+2]=(2.0*(j+1)-p+1)/(p-1);
      cnt++;
    }
  for(int i=0;i<p-1;i++)
    for(int j=0;j<p-1;j++){
      coord[cnt*3  ]=(2.0*(i+1)-p+1)/(p-1);
      coord[cnt*3+1]=(2.0*j-p+1)/(p-1);
      coord[cnt*3+2]=-1.0;
      cnt++;
    }
  for(size_t i=0;i<(n_/2)*3;i++)
    coord[cnt*3+i]=-coord[i];

  Real_t r = 0.5*pow(0.5,depth);
  Real_t b = alpha*r;
  for(size_t i=0;i<n_;i++){
    coord[i*3+0]=(coord[i*3+0]+1.0)*b+c[0];
    coord[i*3+1]=(coord[i*3+1]+1.0)*b+c[1];
    coord[i*3+2]=(coord[i*3+2]+1.0)*b+c[2];
  }
  return coord;
}

/**
 * \brief Returns the coordinates of points on the upward check surface of cube.
 * \see surface()
 */
template <class Real_t>
std::vector<Real_t> u_check_surf(int p, Real_t* c, int depth){
  Real_t r=0.5*pow(0.5,depth);
  Real_t coord[3]={c[0]-r*(RAD1-1.0),c[1]-r*(RAD1-1.0),c[2]-r*(RAD1-1.0)};
  return surface(p,coord,(Real_t)RAD1,depth);
}

/**
 * \brief Returns the coordinates of points on the upward equivalent surface of cube.
 * \see surface()
 */
template <class Real_t>
std::vector<Real_t> u_equiv_surf(int p, Real_t* c, int depth){
  Real_t r=0.5*pow(0.5,depth);
  Real_t coord[3]={c[0]-r*(RAD0-1.0),c[1]-r*(RAD0-1.0),c[2]-r*(RAD0-1.0)};
  return surface(p,coord,(Real_t)RAD0,depth);
}

/**
 * \brief Returns the coordinates of points on the downward check surface of cube.
 * \see surface()
 */
template <class Real_t>
std::vector<Real_t> d_check_surf(int p, Real_t* c, int depth){
  Real_t r=0.5*pow(0.5,depth);
  Real_t coord[3]={c[0]-r*(RAD0-1.0),c[1]-r*(RAD0-1.0),c[2]-r*(RAD0-1.0)};
  return surface(p,coord,(Real_t)RAD0,depth);
}

/**
 * \brief Returns the coordinates of points on the downward equivalent surface of cube.
 * \see surface()
 */
template <class Real_t>
std::vector<Real_t> d_equiv_surf(int p, Real_t* c, int depth){
  Real_t r=0.5*pow(0.5,depth);
  Real_t coord[3]={c[0]-r*(RAD1-1.0),c[1]-r*(RAD1-1.0),c[2]-r*(RAD1-1.0)};
  return surface(p,coord,(Real_t)RAD1,depth);
}

/**
 * \brief Defines the 3D grid for convolution in FFT acceleration of V-list.
 * \see surface()
 */
template <class Real_t>
std::vector<Real_t> conv_grid(int p, Real_t* c, int depth){
  Real_t r=pow(0.5,depth);
  Real_t a=r*RAD0;
  Real_t coord[3]={c[0],c[1],c[2]};
  int n1=p*2;
  int n2=(int)pow((Real_t)n1,2);
  int n3=(int)pow((Real_t)n1,3);
  std::vector<Real_t> grid(n3*3);
  for(int i=0;i<n1;i++)
  for(int j=0;j<n1;j++)
  for(int k=0;k<n1;k++){
    grid[(i+n1*j+n2*k)*3+0]=(i-p)*a/(p-1)+coord[0];
    grid[(i+n1*j+n2*k)*3+1]=(j-p)*a/(p-1)+coord[1];
    grid[(i+n1*j+n2*k)*3+2]=(k-p)*a/(p-1)+coord[2];
  }
  return grid;
}

template <class Real_t>
void FMM_Data<Real_t>::Clear(){
  upward_equiv.Resize(0);
}

template <class Real_t>
PackedData FMM_Data<Real_t>::PackMultipole(void* buff_ptr){
  PackedData p0; p0.data=buff_ptr;
  p0.length=upward_equiv.Dim()*sizeof(Real_t);
  if(p0.length==0) return p0;

  if(p0.data==NULL) p0.data=(char*)&upward_equiv[0];
  else mem::memcopy(p0.data,&upward_equiv[0],p0.length);
  return p0;
}

template <class Real_t>
void FMM_Data<Real_t>::AddMultipole(PackedData p0){
  Real_t* data=(Real_t*)p0.data;
  size_t n=p0.length/sizeof(Real_t);
  assert(upward_equiv.Dim()==n);
  Matrix<Real_t> v0(1,n,&upward_equiv[0],false);
  Matrix<Real_t> v1(1,n,data,false);
  v0+=v1;
}

template <class Real_t>
void FMM_Data<Real_t>::InitMultipole(PackedData p0, bool own_data){
  Real_t* data=(Real_t*)p0.data;
  size_t n=p0.length/sizeof(Real_t);
  if(n==0) return;
  if(own_data){
    upward_equiv=Vector<Real_t>(n, &data[0], false);
  }else{
    upward_equiv.ReInit(n, &data[0], false);
  }
}

template <class FMMNode>
FMM_Pts<FMMNode>::~FMM_Pts() {
  if(mat!=NULL){
//    int rank;
//    MPI_Comm_rank(comm,&rank);
//    if(rank==0) mat->Save2File("Precomp.data");
    delete mat;
    mat=NULL;
  }
  if(vprecomp_fft_flag) FFTW_t<Real_t>::fft_destroy_plan(vprecomp_fftplan);
  #ifdef __INTEL_OFFLOAD0
  #pragma offload target(mic:0)
  #endif
  {
    if(vlist_fft_flag ) FFTW_t<Real_t>::fft_destroy_plan(vlist_fftplan );
    if(vlist_ifft_flag) FFTW_t<Real_t>::fft_destroy_plan(vlist_ifftplan);
    vlist_fft_flag =false;
    vlist_ifft_flag=false;
  }
}



template <class FMMNode>
void FMM_Pts<FMMNode>::Initialize(int mult_order, const MPI_Comm& comm_, const Kernel<Real_t>* kernel_, const Kernel<Real_t>* aux_kernel_){
  Profile::Tic("InitFMM_Pts",&comm_,true);{

  bool verbose=false;
  #ifndef NDEBUG
  #ifdef __VERBOSE__
  int rank;
  MPI_Comm_rank(comm_,&rank);
  if(!rank) verbose=true;
  #endif
  #endif
  if(    kernel_)     kernel_->Initialize(verbose);
  if(aux_kernel_) aux_kernel_->Initialize(verbose);

  multipole_order=mult_order;
  comm=comm_;
  kernel=kernel_;
  assert(kernel!=NULL);
  aux_kernel=(aux_kernel_?aux_kernel_:kernel_);
  assert(kernel->ker_dim[0]==aux_kernel->ker_dim[0]);

  mat=new PrecompMat<Real_t>(Homogen(), MAX_DEPTH+1);
  if(this->mat_fname.size()==0){
    std::stringstream st;
    st<<PVFMM_PRECOMP_DATA_PATH;

    if(!st.str().size()){ // look in PVFMM_DIR
      char* pvfmm_dir = getenv ("PVFMM_DIR");
      if(pvfmm_dir) st<<pvfmm_dir<<'/';
    }

    #ifndef STAT_MACROS_BROKEN
    if(st.str().size()){ // check if the path is a directory
      struct stat stat_buff;
      if(stat(st.str().c_str(), &stat_buff) || !S_ISDIR(stat_buff.st_mode)){
        std::cout<<"error: path not found: "<<st.str()<<'\n';
        exit(0);
      }
    }
    #endif

    st<<"Precomp_"<<kernel->ker_name.c_str()<<"_m"<<mult_order;
    if(sizeof(Real_t)==8) st<<"";
    else if(sizeof(Real_t)==4) st<<"_f";
    else st<<"_t"<<sizeof(Real_t);
    st<<".data";
    this->mat_fname=st.str();
  }
  this->mat->LoadFile(mat_fname.c_str(), this->comm);

  interac_list.Initialize(COORD_DIM, this->mat);

  Profile::Tic("PrecompUC2UE",&comm,false,4);
  this->PrecompAll(UC2UE_Type);
  Profile::Toc();

  Profile::Tic("PrecompDC2DE",&comm,false,4);
  this->PrecompAll(DC2DE_Type);
  Profile::Toc();

  Profile::Tic("PrecompBC",&comm,false,4);
  { /*
    int type=BC_Type;
    for(int l=0;l<MAX_DEPTH;l++)
    for(size_t indx=0;indx<this->interac_list.ListCount((Mat_Type)type);indx++){
      Matrix<Real_t>& M=this->mat->Mat(l, (Mat_Type)type, indx);
      M.Resize(0,0);
    } // */
  }
  this->PrecompAll(BC_Type,0);
  Profile::Toc();

  Profile::Tic("PrecompU2U",&comm,false,4);
  this->PrecompAll(U2U_Type);
  Profile::Toc();

  Profile::Tic("PrecompD2D",&comm,false,4);
  this->PrecompAll(D2D_Type);
  Profile::Toc();

  Profile::Tic("PrecompV",&comm,false,4);
  this->PrecompAll(V_Type);
  Profile::Toc();
  Profile::Tic("PrecompV1",&comm,false,4);
  this->PrecompAll(V1_Type);
  Profile::Toc();

  }Profile::Toc();
}

template <class FMMNode>
Permutation<typename FMMNode::Real_t>& FMM_Pts<FMMNode>::PrecompPerm(Mat_Type type, Perm_Type perm_indx){

  //Check if the matrix already exists.
  Permutation<Real_t>& P_ = mat->Perm((Mat_Type)type, perm_indx);
  if(P_.Dim()!=0) return P_;

  //Compute the matrix.
  Permutation<Real_t> P;
  switch (type){

    case UC2UE_Type:
    {
      break;
    }
    case DC2DE_Type:
    {
      break;
    }
    case S2U_Type:
    {
      break;
    }
    case U2U_Type:
    {
      P=PrecompPerm(D2D_Type, perm_indx);
      break;
    }
    case D2D_Type:
    {
      Real_t eps=1e-10;
      int dof=kernel->ker_dim[0];
      size_t p_indx=perm_indx % C_Perm;
      Permutation<Real_t>& ker_perm=kernel->perm_vec[p_indx];
      assert(dof==ker_perm.Dim());

      Real_t c[3]={-0.5,-0.5,-0.5};
      std::vector<Real_t> trg_coord=d_check_surf(this->MultipoleOrder(),c,0);
      int n_trg=trg_coord.size()/3;

      P=Permutation<Real_t>(n_trg*dof);
      if(p_indx==ReflecX || p_indx==ReflecY || p_indx==ReflecZ){ // Set P.perm
        for(int i=0;i<n_trg;i++)
        for(int j=0;j<n_trg;j++){
          if(fabs(trg_coord[i*3+0]-trg_coord[j*3+0]*(p_indx==ReflecX?-1.0:1.0))<eps)
          if(fabs(trg_coord[i*3+1]-trg_coord[j*3+1]*(p_indx==ReflecY?-1.0:1.0))<eps)
          if(fabs(trg_coord[i*3+2]-trg_coord[j*3+2]*(p_indx==ReflecZ?-1.0:1.0))<eps){
            for(int k=0;k<dof;k++){
              P.perm[j*dof+k]=i*dof+ker_perm.perm[k];
            }
          }
        }
      }else if(p_indx==SwapXY || p_indx==SwapXZ){
        for(int i=0;i<n_trg;i++)
        for(int j=0;j<n_trg;j++){
          if(fabs(trg_coord[i*3+0]-trg_coord[j*3+(p_indx==SwapXY?1:2)])<eps)
          if(fabs(trg_coord[i*3+1]-trg_coord[j*3+(p_indx==SwapXY?0:1)])<eps)
          if(fabs(trg_coord[i*3+2]-trg_coord[j*3+(p_indx==SwapXY?2:0)])<eps){
            for(int k=0;k<dof;k++){
              P.perm[j*dof+k]=i*dof+ker_perm.perm[k];
            }
          }
        }
      }else{
        for(int j=0;j<n_trg;j++){
          for(int k=0;k<dof;k++){
            P.perm[j*dof+k]=j*dof+ker_perm.perm[k];
          }
        }
      }

      if(p_indx==Scaling && this->Homogen()){ // Set level-by-level scaling
        const Vector<Real_t>& scal_exp=kernel->src_scal;
        assert(dof==scal_exp.Dim());

        Vector<Real_t> scal(scal_exp.Dim());
        for(size_t i=0;i<scal_exp.Dim();i++){
          scal[i]=pow(2.0,(perm_indx<C_Perm?1.0:-1.0)*scal_exp[i]);
        }
        for(int j=0;j<n_trg;j++){
          for(int i=0;i<dof;i++){
            P.scal[j*dof+i]*=scal[i];
          }
        }
      }
      { // Set P.scal
        for(int j=0;j<n_trg;j++){
          for(int i=0;i<dof;i++){
            P.scal[j*dof+i]*=ker_perm.scal[i];
          }
        }
      }
      break;
    }
    case D2T_Type:
    {
      break;
    }
    case U0_Type:
    {
      break;
    }
    case U1_Type:
    {
      break;
    }
    case U2_Type:
    {
      break;
    }
    case V_Type:
    {
      break;
    }
    case V1_Type:
    {
      break;
    }
    case W_Type:
    {
      break;
    }
    case X_Type:
    {
      break;
    }
    case BC_Type:
    {
      break;
    }
    default:
      break;
  }

  //Save the matrix for future use.
  #pragma omp critical (PRECOMP_MATRIX_PTS)
  {
    if(P_.Dim()==0) P_=P;
  }

  return P_;
}

template <class FMMNode>
Matrix<typename FMMNode::Real_t>& FMM_Pts<FMMNode>::Precomp(int level, Mat_Type type, size_t mat_indx){
  if(this->Homogen()) level=0;

  //Check if the matrix already exists.
  Matrix<Real_t>& M_ = this->mat->Mat(level, type, mat_indx);
  if(M_.Dim(0)!=0 && M_.Dim(1)!=0) return M_;
  else{ //Compute matrix from symmetry class (if possible).
    size_t class_indx = this->interac_list.InteracClass(type, mat_indx);
    if(class_indx!=mat_indx){
      Matrix<Real_t>& M0 = this->Precomp(level, type, class_indx);
      Permutation<Real_t>& Pr = this->interac_list.Perm_R(level, type, mat_indx);
      Permutation<Real_t>& Pc = this->interac_list.Perm_C(level, type, mat_indx);
      if(Pr.Dim()>0 && Pc.Dim()>0 && M0.Dim(0)>0 && M0.Dim(1)>0) return M_;
    }
  }

  //Compute the matrix.
  Matrix<Real_t> M;
  const int* ker_dim=kernel->ker_dim;
  const int* aux_ker_dim=aux_kernel->ker_dim;
  //int omp_p=omp_get_max_threads();
  switch (type){

    case UC2UE_Type:
    {
      if(MultipoleOrder()==0) break;
      // Coord of upward check surface
      Real_t c[3]={0,0,0};
      std::vector<Real_t> uc_coord=u_check_surf(MultipoleOrder(),c,level);
      size_t n_uc=uc_coord.size()/3;

      // Coord of upward equivalent surface
      std::vector<Real_t> ue_coord=u_equiv_surf(MultipoleOrder(),c,level);
      size_t n_ue=ue_coord.size()/3;

      // Evaluate potential at check surface due to equivalent surface.
      Matrix<Real_t> M_e2c(n_ue*aux_ker_dim[0],n_uc*aux_ker_dim[1]);
      aux_kernel->BuildMatrix(&ue_coord[0], n_ue,
                             &uc_coord[0], n_uc, &(M_e2c[0][0]));

      Real_t eps=1.0;
      while(eps+(Real_t)1.0>1.0) eps*=0.5;
      M=M_e2c.pinv(sqrt(eps)); //check 2 equivalent
      break;
    }
    case DC2DE_Type:
    {
      if(MultipoleOrder()==0) break;
      // Coord of downward check surface
      Real_t c[3]={0,0,0};
      std::vector<Real_t> check_surf=d_check_surf(MultipoleOrder(),c,level);
      size_t n_ch=check_surf.size()/3;

      // Coord of downward equivalent surface
      std::vector<Real_t> equiv_surf=d_equiv_surf(MultipoleOrder(),c,level);
      size_t n_eq=equiv_surf.size()/3;

      // Evaluate potential at check surface due to equivalent surface.
      Matrix<Real_t> M_e2c(n_eq*aux_ker_dim[0],n_ch*aux_ker_dim[1]);
      aux_kernel->BuildMatrix(&equiv_surf[0], n_eq,
                             &check_surf[0], n_ch, &(M_e2c[0][0]));

      Real_t eps=1.0;
      while(eps+(Real_t)1.0>1.0) eps*=0.5;
      M=M_e2c.pinv(sqrt(eps)); //check 2 equivalent
      break;
    }
    case S2U_Type:
    {
      break;
    }
    case U2U_Type:
    {
      if(MultipoleOrder()==0) break;
      // Coord of upward check surface
      Real_t c[3]={0,0,0};
      std::vector<Real_t> check_surf=u_check_surf(MultipoleOrder(),c,level);
      size_t n_uc=check_surf.size()/3;

      // Coord of child's upward equivalent surface
      Real_t s=pow(0.5,(level+2));
      int* coord=interac_list.RelativeCoord(type,mat_indx);
      Real_t child_coord[3]={(coord[0]+1)*s,(coord[1]+1)*s,(coord[2]+1)*s};
      std::vector<Real_t> equiv_surf=u_equiv_surf(MultipoleOrder(),child_coord,level+1);
      size_t n_ue=equiv_surf.size()/3;

      // Evaluate potential at check surface due to equivalent surface.
      Matrix<Real_t> M_ce2c(n_ue*aux_ker_dim[0],n_uc*aux_ker_dim[1]);
      aux_kernel->BuildMatrix(&equiv_surf[0], n_ue,
                             &check_surf[0], n_uc, &(M_ce2c[0][0]));
      Matrix<Real_t>& M_c2e = Precomp(level, UC2UE_Type, 0);
      M=M_ce2c*M_c2e;
      break;
    }
    case D2D_Type:
    {
      if(MultipoleOrder()==0) break;
      // Coord of downward check surface
      Real_t s=pow(0.5,level+1);
      int* coord=interac_list.RelativeCoord(type,mat_indx);
      Real_t c[3]={(coord[0]+1)*s,(coord[1]+1)*s,(coord[2]+1)*s};
      std::vector<Real_t> check_surf=d_check_surf(MultipoleOrder(),c,level);
      size_t n_dc=check_surf.size()/3;

      // Coord of parent's downward equivalent surface
      Real_t parent_coord[3]={0,0,0};
      std::vector<Real_t> equiv_surf=d_equiv_surf(MultipoleOrder(),parent_coord,level-1);
      size_t n_de=equiv_surf.size()/3;

      // Evaluate potential at check surface due to equivalent surface.
      Matrix<Real_t> M_pe2c(n_de*aux_ker_dim[0],n_dc*aux_ker_dim[1]);
      aux_kernel->BuildMatrix(&equiv_surf[0], n_de,
                             &check_surf[0], n_dc, &(M_pe2c[0][0]));
      Matrix<Real_t>& M_c2e=Precomp(level,DC2DE_Type,0);
      M=M_pe2c*M_c2e;
      break;
    }
    case D2T_Type:
    {
      if(MultipoleOrder()==0) break;
      std::vector<Real_t>& rel_trg_coord=mat->RelativeTrgCoord();

      // Coord of target points
      Real_t r=pow(0.5,level);
      size_t n_trg=rel_trg_coord.size()/3;
      std::vector<Real_t> trg_coord(n_trg*3);
      for(size_t i=0;i<n_trg*COORD_DIM;i++) trg_coord[i]=rel_trg_coord[i]*r;

      // Coord of downward equivalent surface
      Real_t c[3]={0,0,0};
      std::vector<Real_t> equiv_surf=d_equiv_surf(MultipoleOrder(),c,level);
      size_t n_eq=equiv_surf.size()/3;

      // Evaluate potential at target points due to equivalent surface.
      {
        M     .Resize(n_eq*ker_dim [0], n_trg*ker_dim [1]);
        kernel->BuildMatrix(&equiv_surf[0], n_eq, &trg_coord[0], n_trg, &(M     [0][0]));
      }
      break;
    }
    case U0_Type:
    {
      break;
    }
    case U1_Type:
    {
      break;
    }
    case U2_Type:
    {
      break;
    }
    case V_Type:
    {
      if(MultipoleOrder()==0) break;
      int n1=MultipoleOrder()*2;
      int n3 =n1*n1*n1;
      int n3_=n1*n1*(n1/2+1);

      //Compute the matrix.
      Real_t s=pow(0.5,level);
      int* coord2=interac_list.RelativeCoord(type,mat_indx);
      Real_t coord_diff[3]={coord2[0]*s,coord2[1]*s,coord2[2]*s};

      //Evaluate potential.
      std::vector<Real_t> r_trg(COORD_DIM,0.0);
      std::vector<Real_t> conv_poten(n3*aux_ker_dim[0]*aux_ker_dim[1]);
      std::vector<Real_t> conv_coord=conv_grid(MultipoleOrder(),coord_diff,level);
      aux_kernel->BuildMatrix(&conv_coord[0],n3,&r_trg[0],1,&conv_poten[0]);

      //Rearrange data.
      Matrix<Real_t> M_conv(n3,aux_ker_dim[0]*aux_ker_dim[1],&conv_poten[0],false);
      M_conv=M_conv.Transpose();

      //Compute FFTW plan.
      int nnn[3]={n1,n1,n1};
      Real_t *fftw_in, *fftw_out;
      fftw_in  = mem::aligned_new<Real_t>(  n3 *aux_ker_dim[0]*aux_ker_dim[1]*sizeof(Real_t));
      fftw_out = mem::aligned_new<Real_t>(2*n3_*aux_ker_dim[0]*aux_ker_dim[1]*sizeof(Real_t));
      #pragma omp critical (FFTW_PLAN)
      {
        if (!vprecomp_fft_flag){
          vprecomp_fftplan = FFTW_t<Real_t>::fft_plan_many_dft_r2c(COORD_DIM, nnn, aux_ker_dim[0]*aux_ker_dim[1],
              (Real_t*)fftw_in, NULL, 1, n3, (typename FFTW_t<Real_t>::cplx*) fftw_out, NULL, 1, n3_, FFTW_ESTIMATE);
          vprecomp_fft_flag=true;
        }
      }

      //Compute FFT.
      mem::memcopy(fftw_in, &conv_poten[0], n3*aux_ker_dim[0]*aux_ker_dim[1]*sizeof(Real_t));
      FFTW_t<Real_t>::fft_execute_dft_r2c(vprecomp_fftplan, (Real_t*)fftw_in, (typename FFTW_t<Real_t>::cplx*)(fftw_out));
      Matrix<Real_t> M_(2*n3_*aux_ker_dim[0]*aux_ker_dim[1],1,(Real_t*)fftw_out,false);
      M=M_;

      //Free memory.
      mem::aligned_delete<Real_t>(fftw_in);
      mem::aligned_delete<Real_t>(fftw_out);
      break;
    }
    case V1_Type:
    {
      if(MultipoleOrder()==0) break;
      size_t mat_cnt =interac_list.ListCount( V_Type);
      for(size_t k=0;k<mat_cnt;k++) Precomp(level, V_Type, k);

      const size_t chld_cnt=1UL<<COORD_DIM;
      size_t n1=MultipoleOrder()*2;
      size_t M_dim=n1*n1*(n1/2+1);
      size_t n3=n1*n1*n1;

      Vector<Real_t> zero_vec(M_dim*aux_ker_dim[0]*aux_ker_dim[1]*2);
      zero_vec.SetZero();

      Vector<Real_t*> M_ptr(chld_cnt*chld_cnt);
      for(size_t i=0;i<chld_cnt*chld_cnt;i++) M_ptr[i]=&zero_vec[0];

      int* rel_coord_=interac_list.RelativeCoord(V1_Type, mat_indx);
      for(int j1=0;j1<chld_cnt;j1++)
      for(int j2=0;j2<chld_cnt;j2++){
        int rel_coord[3]={rel_coord_[0]*2-(j1/1)%2+(j2/1)%2,
                          rel_coord_[1]*2-(j1/2)%2+(j2/2)%2,
                          rel_coord_[2]*2-(j1/4)%2+(j2/4)%2};
        for(size_t k=0;k<mat_cnt;k++){
          int* ref_coord=interac_list.RelativeCoord(V_Type, k);
          if(ref_coord[0]==rel_coord[0] &&
             ref_coord[1]==rel_coord[1] &&
             ref_coord[2]==rel_coord[2]){
            Matrix<Real_t>& M = this->mat->Mat(level, V_Type, k);
            M_ptr[j2*chld_cnt+j1]=&M[0][0];
            break;
          }
        }
      }

      // Build matrix aux_ker_dim0 x aux_ker_dim1 x M_dim x 8 x 8
      M.Resize(aux_ker_dim[0]*aux_ker_dim[1]*M_dim, 2*chld_cnt*chld_cnt);
      for(int j=0;j<aux_ker_dim[0]*aux_ker_dim[1]*M_dim;j++){
        for(size_t k=0;k<chld_cnt*chld_cnt;k++){
          M[j][k*2+0]=M_ptr[k][j*2+0]/n3;
          M[j][k*2+1]=M_ptr[k][j*2+1]/n3;
        }
      }
      break;
    }
    case W_Type:
    {
      if(MultipoleOrder()==0) break;
      std::vector<Real_t>& rel_trg_coord=mat->RelativeTrgCoord();

      // Coord of target points
      Real_t s=pow(0.5,level);
      size_t n_trg=rel_trg_coord.size()/3;
      std::vector<Real_t> trg_coord(n_trg*3);
      for(size_t j=0;j<n_trg*COORD_DIM;j++) trg_coord[j]=rel_trg_coord[j]*s;

      // Coord of downward equivalent surface
      int* coord2=interac_list.RelativeCoord(type,mat_indx);
      Real_t c[3]={(coord2[0]+1)*s*0.25,(coord2[1]+1)*s*0.25,(coord2[2]+1)*s*0.25};
      std::vector<Real_t> equiv_surf=u_equiv_surf(MultipoleOrder(),c,level+1);
      size_t n_eq=equiv_surf.size()/3;

      // Evaluate potential at target points due to equivalent surface.
      {
        M     .Resize(n_eq*ker_dim [0],n_trg*ker_dim [1]);
        kernel->BuildMatrix(&equiv_surf[0], n_eq, &trg_coord[0], n_trg, &(M     [0][0]));
      }
      break;
    }
    case X_Type:
    {
      break;
    }
    case BC_Type:
    {
      if(MultipoleOrder()==0) break;
      size_t mat_cnt_m2m=interac_list.ListCount(U2U_Type);
      size_t n_surf=(6*(MultipoleOrder()-1)*(MultipoleOrder()-1)+2);  //Total number of points.
      if((M.Dim(0)!=n_surf*aux_ker_dim[0] || M.Dim(1)!=n_surf*aux_ker_dim[1]) && level==0){
        Matrix<Real_t> M_m2m[BC_LEVELS+1];
        Matrix<Real_t> M_m2l[BC_LEVELS+1];
        Matrix<Real_t> M_l2l[BC_LEVELS+1];
        Matrix<Real_t> M_zero_avg(n_surf*aux_ker_dim[0],n_surf*aux_ker_dim[0]);
        { // Set average multipole charge to zero. (improves stability for large BC_LEVELS)
          M_zero_avg.SetZero();
          for(size_t i=0;i<n_surf*aux_ker_dim[0];i++)
            M_zero_avg[i][i]+=1;
          for(size_t i=0;i<n_surf;i++)
            for(size_t j=0;j<n_surf;j++)
              for(size_t k=0;k<aux_ker_dim[0];k++)
                M_zero_avg[i*aux_ker_dim[0]+k][j*aux_ker_dim[0]+k]-=1.0/n_surf;
        }
        for(int level=0; level>=-BC_LEVELS; level--){
          // Compute M_l2l
          M_l2l[-level] = this->Precomp(level, D2D_Type, 0);
          assert(M_l2l[-level].Dim(0)>0 && M_l2l[-level].Dim(1)>0);

          // Compute M_m2m
          for(size_t mat_indx=0; mat_indx<mat_cnt_m2m; mat_indx++){
            Matrix<Real_t> M=this->Precomp(level, U2U_Type, mat_indx);
            assert(M.Dim(0)>0 && M_m2m>0);
            if(mat_indx==0) M_m2m[-level] = M_zero_avg*M;
            else M_m2m[-level] += M_zero_avg*M;
          }

          // Compute M_m2l
          if(!Homogen() || level==0){
            Real_t s=(1UL<<(-level));
            Real_t ue_coord[3]={0,0,0};
            Real_t dc_coord[3]={0,0,0};
            std::vector<Real_t> src_coord=u_equiv_surf(MultipoleOrder(), ue_coord, level);
            std::vector<Real_t> trg_coord=d_check_surf(MultipoleOrder(), dc_coord, level);
            Matrix<Real_t> M_ue2dc(n_surf*aux_ker_dim[0], n_surf*aux_ker_dim[1]);
            M_ue2dc.SetZero();

            for(int x0=-2;x0<4;x0++)
            for(int x1=-2;x1<4;x1++)
            for(int x2=-2;x2<4;x2++)
            if(abs(x0)>1 || abs(x1)>1 || abs(x2)>1){
              ue_coord[0]=x0*s; ue_coord[1]=x1*s; ue_coord[2]=x2*s;
              std::vector<Real_t> src_coord=u_equiv_surf(MultipoleOrder(), ue_coord, level);
              Matrix<Real_t> M_tmp(n_surf*aux_ker_dim[0], n_surf*aux_ker_dim[1]);
              aux_kernel->BuildMatrix(&src_coord[0], n_surf,
                                     &trg_coord[0], n_surf, &(M_tmp[0][0]));
              M_ue2dc+=M_tmp;
            }

            // Shift by constant.
            for(size_t i=0;i<M_ue2dc.Dim(0);i++){
              std::vector<Real_t> avg(aux_ker_dim[1],0);
              for(size_t j=0; j<M_ue2dc.Dim(1); j+=aux_ker_dim[1])
                for(int k=0; k<aux_ker_dim[1]; k++) avg[k]+=M_ue2dc[i][j+k];
              for(int k=0; k<aux_ker_dim[1]; k++) avg[k]/=n_surf;
              for(size_t j=0; j<M_ue2dc.Dim(1); j+=aux_ker_dim[1])
                for(int k=0; k<aux_ker_dim[1]; k++) M_ue2dc[i][j+k]-=avg[k];
            }

            Matrix<Real_t>& M_dc2de = Precomp(level, DC2DE_Type, 0);
            M_m2l[-level]=M_ue2dc*M_dc2de;
          }else M_m2l[-level]=M_m2l[-level-1];
        }

        for(int level=-BC_LEVELS;level<=0;level++){
          if(level==-BC_LEVELS) M = M_m2l[-level];
          else                  M = M_m2l[-level] + M_m2m[-level]*M*M_l2l[-level];

          { // Shift by constant. (improves stability for large BC_LEVELS)
            Matrix<Real_t> M_de2dc(n_surf*aux_ker_dim[0], n_surf*aux_ker_dim[1]);
            { // M_de2dc TODO: For homogeneous kernels, compute only once.
              // Coord of downward check surface
              Real_t c[3]={0,0,0};
              int level_=(Homogen()?0:level);
              std::vector<Real_t> check_surf=d_check_surf(MultipoleOrder(),c,level_);
              size_t n_ch=check_surf.size()/3;

              // Coord of downward equivalent surface
              std::vector<Real_t> equiv_surf=d_equiv_surf(MultipoleOrder(),c,level_);
              size_t n_eq=equiv_surf.size()/3;

              // Evaluate potential at check surface due to equivalent surface.
              aux_kernel->BuildMatrix(&equiv_surf[0], n_eq,
                                     &check_surf[0], n_ch, &(M_de2dc[0][0]));
            }
            Matrix<Real_t> M_ue2dc=M*M_de2dc;

            for(size_t i=0;i<M_ue2dc.Dim(0);i++){
              std::vector<Real_t> avg(aux_ker_dim[1],0);
              for(size_t j=0; j<M_ue2dc.Dim(1); j+=aux_ker_dim[1])
                for(int k=0; k<aux_ker_dim[1]; k++) avg[k]+=M_ue2dc[i][j+k];
              for(int k=0; k<aux_ker_dim[1]; k++) avg[k]/=n_surf;
              for(size_t j=0; j<M_ue2dc.Dim(1); j+=aux_ker_dim[1])
                for(int k=0; k<aux_ker_dim[1]; k++) M_ue2dc[i][j+k]-=avg[k];
            }

            Matrix<Real_t>& M_dc2de = Precomp(level, DC2DE_Type, 0);
            M=M_ue2dc*M_dc2de;
          }
        }

        { // ax+by+cz+d correction.
          std::vector<Real_t> corner_pts;
          corner_pts.push_back(0); corner_pts.push_back(0); corner_pts.push_back(0);
          corner_pts.push_back(1); corner_pts.push_back(0); corner_pts.push_back(0);
          corner_pts.push_back(0); corner_pts.push_back(1); corner_pts.push_back(0);
          corner_pts.push_back(0); corner_pts.push_back(0); corner_pts.push_back(1);
          size_t n_corner=corner_pts.size()/3;

          // Coord of downward equivalent surface
          Real_t c[3]={0,0,0};
          std::vector<Real_t> up_equiv_surf=u_equiv_surf(MultipoleOrder(),c,0);
          std::vector<Real_t> dn_equiv_surf=d_equiv_surf(MultipoleOrder(),c,0);
          std::vector<Real_t> dn_check_surf=d_check_surf(MultipoleOrder(),c,0);

          Matrix<Real_t> M_err;
          { // Evaluate potential at corner due to upward and dnward equivalent surface.
            { // Error from local expansion.
              Matrix<Real_t> M_e2pt(n_surf*aux_ker_dim[0],n_corner*aux_ker_dim[1]);
              aux_kernel->BuildMatrix(&dn_equiv_surf[0], n_surf,
                                     &corner_pts[0], n_corner, &(M_e2pt[0][0]));
              M_err=M*M_e2pt;
            }
            for(size_t k=0;k<4;k++){ // Error from colleagues of root.
              for(int j0=-1;j0<=1;j0++)
              for(int j1=-1;j1<=1;j1++)
              for(int j2=-1;j2<=1;j2++){
                Real_t pt_coord[3]={corner_pts[k*COORD_DIM+0]-j0,
                                    corner_pts[k*COORD_DIM+1]-j1,
                                    corner_pts[k*COORD_DIM+2]-j2};
                if(fabs(pt_coord[0]-0.5)>1.0 || fabs(pt_coord[1]-0.5)>1.0 || fabs(pt_coord[2]-0.5)>1.0){
                  Matrix<Real_t> M_e2pt(n_surf*aux_ker_dim[0],aux_ker_dim[1]);
                  aux_kernel->BuildMatrix(&up_equiv_surf[0], n_surf,
                                         &pt_coord[0], 1, &(M_e2pt[0][0]));
                  for(size_t i=0;i<M_e2pt.Dim(0);i++)
                    for(size_t j=0;j<M_e2pt.Dim(1);j++)
                      M_err[i][k*aux_ker_dim[1]+j]+=M_e2pt[i][j];
                }
              }
            }
          }

          Matrix<Real_t> M_grad(M_err.Dim(0),n_surf*aux_ker_dim[1]);
          for(size_t i=0;i<M_err.Dim(0);i++)
          for(size_t k=0;k<aux_ker_dim[1];k++)
          for(size_t j=0;j<n_surf;j++){
            M_grad[i][j*aux_ker_dim[1]+k]=(M_err[i][0*aux_ker_dim[1]+k]                         )*1.0                         +
                                          (M_err[i][1*aux_ker_dim[1]+k]-M_err[i][0*aux_ker_dim[1]+k])*dn_check_surf[j*COORD_DIM+0]+
                                          (M_err[i][2*aux_ker_dim[1]+k]-M_err[i][0*aux_ker_dim[1]+k])*dn_check_surf[j*COORD_DIM+1]+
                                          (M_err[i][3*aux_ker_dim[1]+k]-M_err[i][0*aux_ker_dim[1]+k])*dn_check_surf[j*COORD_DIM+2];
          }

          Matrix<Real_t>& M_dc2de = Precomp(0, DC2DE_Type, 0);
          M-=M_grad*M_dc2de;
        }
        { // Free memory
          Mat_Type type=D2D_Type;
          for(int l=-BC_LEVELS;l<0;l++)
          for(size_t indx=0;indx<this->interac_list.ListCount(type);indx++){
            Matrix<Real_t>& M=this->mat->Mat(l, type, indx);
            M.Resize(0,0);
          }
          type=U2U_Type;
          for(int l=-BC_LEVELS;l<0;l++)
          for(size_t indx=0;indx<this->interac_list.ListCount(type);indx++){
            Matrix<Real_t>& M=this->mat->Mat(l, type, indx);
            M.Resize(0,0);
          }
          type=DC2DE_Type;
          for(int l=-BC_LEVELS;l<0;l++)
          for(size_t indx=0;indx<this->interac_list.ListCount(type);indx++){
            Matrix<Real_t>& M=this->mat->Mat(l, type, indx);
            M.Resize(0,0);
          }
          type=UC2UE_Type;
          for(int l=-BC_LEVELS;l<0;l++)
          for(size_t indx=0;indx<this->interac_list.ListCount(type);indx++){
            Matrix<Real_t>& M=this->mat->Mat(l, type, indx);
            M.Resize(0,0);
          }
        }
      }
      break;
    }
    default:
      break;
  }

  //Save the matrix for future use.
  #pragma omp critical (PRECOMP_MATRIX_PTS)
  if(M_.Dim(0)==0 && M_.Dim(1)==0){
    M_=M;
    /*
    M_.Resize(M.Dim(0),M.Dim(1));
    int dof=aux_ker_dim[0]*aux_ker_dim[1];
    for(int j=0;j<dof;j++){
      size_t a=(M.Dim(0)*M.Dim(1)* j   )/dof;
      size_t b=(M.Dim(0)*M.Dim(1)*(j+1))/dof;
      #pragma omp parallel for // NUMA
      for(int tid=0;tid<omp_p;tid++){
        size_t a_=a+((b-a)* tid   )/omp_p;
        size_t b_=a+((b-a)*(tid+1))/omp_p;
        mem::memcopy(&M_[0][a_], &M[0][a_], (b_-a_)*sizeof(Real_t));
      }
    }
    */
  }

  return M_;
}

template <class FMMNode>
void FMM_Pts<FMMNode>::PrecompAll(Mat_Type type, int level){
  if(level==-1){
    for(int l=0;l<MAX_DEPTH;l++){
      PrecompAll(type, l);
    }
    return;
  }

  //Compute basic permutations.
  for(size_t i=0;i<Perm_Count;i++)
    this->PrecompPerm(type, (Perm_Type) i);

  {
    //Allocate matrices.
    size_t mat_cnt=interac_list.ListCount((Mat_Type)type);
    mat->Mat(level, (Mat_Type)type, mat_cnt-1);

    { // Compute InteracClass matrices.
      std::vector<size_t> indx_lst;
      for(size_t i=0; i<mat_cnt; i++){
        if(interac_list.InteracClass((Mat_Type)type,i)==i)
          indx_lst.push_back(i);
      }

      //Compute Transformations.
      //#pragma omp parallel for //lets use fine grained parallelism
      for(size_t i=0; i<indx_lst.size(); i++){
        Precomp(level, (Mat_Type)type, indx_lst[i]);
      }
    }

    //#pragma omp parallel for //lets use fine grained parallelism
    for(size_t mat_indx=0;mat_indx<mat_cnt;mat_indx++){
      Matrix<Real_t>& M0=interac_list.ClassMat(level,(Mat_Type)type,mat_indx);
      Permutation<Real_t>& pr=interac_list.Perm_R(level, (Mat_Type)type, mat_indx);
      Permutation<Real_t>& pc=interac_list.Perm_C(level, (Mat_Type)type, mat_indx);
      if(pr.Dim()!=M0.Dim(0) || pc.Dim()!=M0.Dim(1)) Precomp(level, (Mat_Type)type, mat_indx);
    }
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::CollectNodeData(std::vector<FMMNode*>& node, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, std::vector<size_t> extra_size){
  if(      buff.size()<7)       buff.resize(7);
  if(    n_list.size()<7)     n_list.resize(7);

  if(node.size()==0) return;
  {// 0. upward_equiv
    int indx=0;
    Matrix<Real_t>& M_uc2ue = this->interac_list.ClassMat(0, UC2UE_Type, 0);
    size_t vec_sz=M_uc2ue.Dim(1);
    std::vector< FMMNode* > node_lst;
    {
      std::vector<std::vector< FMMNode* > > node_lst_(MAX_DEPTH+1);
      FMMNode_t* r_node=NULL;
      for(size_t i=0;i<node.size();i++){
        if(!node[i]->IsLeaf())
          node_lst_[node[i]->Depth()].push_back(node[i]);
        if(node[i]->Depth()==0) r_node=node[i];
      }
      size_t chld_cnt=1UL<<COORD_DIM;
      for(int i=0;i<=MAX_DEPTH;i++)
        for(size_t j=0;j<node_lst_[i].size();j++)
          for(size_t k=0;k<chld_cnt;k++)
            node_lst.push_back((FMMNode_t*)node_lst_[i][j]->Child(k));
      if(r_node!=NULL) node_lst.push_back(r_node);
    }
    n_list[indx]=node_lst;
    size_t buff_size=node_lst.size()*vec_sz;
    buff_size+=(extra_size.size()>indx?extra_size[indx]:0);
    #pragma omp parallel for
    for(size_t i=0;i<node.size();i++){ // Clear data
      Vector<Real_t>& upward_equiv=node[i]->FMMData()->upward_equiv;
      upward_equiv.ReInit(0);
    }
    buff[indx].Resize(1,buff_size);
    #pragma omp parallel for
    for(size_t i=0;i<node_lst.size();i++){
      Vector<Real_t>& upward_equiv=node_lst[i]->FMMData()->upward_equiv;
      upward_equiv.ReInit(vec_sz, buff[indx][0]+i*vec_sz, false);
      upward_equiv.SetZero();
    }
    buff[indx].AllocDevice(true);
  }
  {// 1. dnward_equiv
    int indx=1;
    Matrix<Real_t>& M_dc2de = this->interac_list.ClassMat(0, DC2DE_Type, 0);
    size_t vec_sz=M_dc2de.Dim(1);
    std::vector< FMMNode* > node_lst;
    {
      std::vector<std::vector< FMMNode* > > node_lst_(MAX_DEPTH+1);
      FMMNode_t* r_node=NULL;
      for(size_t i=0;i<node.size();i++){
        if(!node[i]->IsLeaf() && !node[i]->IsGhost())
          node_lst_[node[i]->Depth()].push_back(node[i]);
        if(node[i]->Depth()==0) r_node=node[i];
      }
      size_t chld_cnt=1UL<<COORD_DIM;
      for(int i=0;i<=MAX_DEPTH;i++)
        for(size_t j=0;j<node_lst_[i].size();j++)
          for(size_t k=0;k<chld_cnt;k++)
            node_lst.push_back((FMMNode_t*)node_lst_[i][j]->Child(k));
      if(r_node!=NULL) node_lst.push_back(r_node);
    }
    n_list[indx]=node_lst;
    size_t buff_size=node_lst.size()*vec_sz;
    buff_size+=(extra_size.size()>indx?extra_size[indx]:0);
    #pragma omp parallel for
    for(size_t i=0;i<node.size();i++){ // Clear data
      Vector<Real_t>& dnward_equiv=node[i]->FMMData()->dnward_equiv;
      dnward_equiv.ReInit(0);
    }
    buff[indx].Resize(1,buff_size);
    #pragma omp parallel for
    for(size_t i=0;i<node_lst.size();i++){
      Vector<Real_t>& dnward_equiv=node_lst[i]->FMMData()->dnward_equiv;
      dnward_equiv.ReInit(vec_sz, buff[indx][0]+i*vec_sz, false);
      dnward_equiv.SetZero();
    }
    buff[indx].AllocDevice(true);
  }
  {// 2. upward_equiv_fft
    int indx=2;
    std::vector< FMMNode* > node_lst;
    {
      std::vector<std::vector< FMMNode* > > node_lst_(MAX_DEPTH+1);
      for(size_t i=0;i<node.size();i++)
        if(!node[i]->IsLeaf())
          node_lst_[node[i]->Depth()].push_back(node[i]);
      for(int i=0;i<=MAX_DEPTH;i++)
        for(size_t j=0;j<node_lst_[i].size();j++)
          node_lst.push_back(node_lst_[i][j]);
    }
    n_list[indx]=node_lst;
    buff[indx].AllocDevice(true);
  }
  {// 3. dnward_check_fft
    int indx=3;
    std::vector< FMMNode* > node_lst;
    {
      std::vector<std::vector< FMMNode* > > node_lst_(MAX_DEPTH+1);
      for(size_t i=0;i<node.size();i++)
        if(!node[i]->IsLeaf() && !node[i]->IsGhost())
          node_lst_[node[i]->Depth()].push_back(node[i]);
      for(int i=0;i<=MAX_DEPTH;i++)
        for(size_t j=0;j<node_lst_[i].size();j++)
          node_lst.push_back(node_lst_[i][j]);
    }
    n_list[indx]=node_lst;
    buff[indx].AllocDevice(true);
  }
  {// 4. src_val
    int indx=4;
    int src_dof=kernel->ker_dim[0];
    int surf_dof=COORD_DIM+src_dof;
    std::vector< FMMNode* > node_lst;
    size_t buff_size=0;
    for(size_t i=0;i<node.size();i++)
      if(node[i]->IsLeaf()){
        node_lst.push_back(node[i]);
        buff_size+=(node[i]->src_coord.Dim()/COORD_DIM)*src_dof;
        buff_size+=(node[i]->surf_coord.Dim()/COORD_DIM)*surf_dof;
      }
    n_list[indx]=node_lst;

    #pragma omp parallel for
    for(size_t i=0;i<node.size();i++){ // Move data before resizing buff[indx]
      { // src_value
        Vector<Real_t>& src_value=node[i]->src_value;
        Vector<Real_t> new_buff=src_value;
        src_value.Swap(new_buff);
      }
      { // surf_value
        Vector<Real_t>& surf_value=node[i]->surf_value;
        Vector<Real_t> new_buff=surf_value;
        surf_value.Swap(new_buff);
      }
    }

    buff[indx].Resize(1,buff_size+(extra_size.size()>indx?extra_size[indx]:0));
    Real_t* buff_ptr=&buff[indx][0][0];
    for(size_t i=0;i<node_lst.size();i++){
      { // src_value
        Vector<Real_t>& src_value=node_lst[i]->src_value;
        mem::memcopy(buff_ptr,&src_value[0],src_value.Dim()*sizeof(Real_t));
        src_value.ReInit((node_lst[i]->src_coord.Dim()/COORD_DIM)*src_dof, buff_ptr, false);
        buff_ptr+=(node_lst[i]->src_coord.Dim()/COORD_DIM)*src_dof;
      }
      { // surf_value
        Vector<Real_t>& surf_value=node_lst[i]->surf_value;
        mem::memcopy(buff_ptr,&surf_value[0],surf_value.Dim()*sizeof(Real_t));
        surf_value.ReInit((node_lst[i]->surf_coord.Dim()/COORD_DIM)*surf_dof, buff_ptr, false);
        buff_ptr+=(node_lst[i]->surf_coord.Dim()/COORD_DIM)*surf_dof;
      }
    }
    buff[indx].AllocDevice(true);
  }
  {// 5. trg_val
    int indx=5;
    int trg_dof=kernel->ker_dim[1];
    std::vector< FMMNode* > node_lst;
    size_t buff_size=0;
    for(size_t i=0;i<node.size();i++)
      if(node[i]->IsLeaf() && !node[i]->IsGhost()){
        node_lst.push_back(node[i]);
        buff_size+=(node[i]->trg_coord.Dim()/COORD_DIM)*trg_dof;
      }
    n_list[indx]=node_lst;

    #pragma omp parallel for
    for(size_t i=0;i<node.size();i++){ // Clear data
      { // trg_value
        Vector<Real_t>& trg_value=node[i]->trg_value;
        trg_value.ReInit(0);
      }
    }
    buff[indx].Resize(1,buff_size+(extra_size.size()>indx?extra_size[indx]:0));
    Real_t* buff_ptr=&buff[indx][0][0];
    for(size_t i=0;i<node_lst.size();i++){
      { // trg_value
        Vector<Real_t>& trg_value=node_lst[i]->trg_value;
        trg_value.ReInit((node_lst[i]->trg_coord.Dim()/COORD_DIM)*trg_dof, buff_ptr, false);
        buff_ptr+=(node_lst[i]->trg_coord.Dim()/COORD_DIM)*trg_dof;
      }
    }
    #pragma omp parallel for
    for(size_t i=0;i<node_lst.size();i++){
      Vector<Real_t>& trg_value=node_lst[i]->trg_value;
      trg_value.SetZero();
    }
    buff[indx].AllocDevice(true);
  }
  {// 6. pts_coord
    int indx=6;
    size_t m=MultipoleOrder();
    std::vector< FMMNode* > node_lst;
    size_t buff_size=0;
    for(size_t i=0;i<node.size();i++)
      if(node[i]->IsLeaf()){
        node_lst.push_back(node[i]);
        buff_size+=node[i]->src_coord.Dim();
        buff_size+=node[i]->surf_coord.Dim();
        buff_size+=node[i]->trg_coord.Dim();
      }
    n_list[indx]=node_lst;

    #pragma omp parallel for
    for(size_t i=0;i<node.size();i++){ // Move data before resizing buff[indx]
      { // src_coord
        Vector<Real_t>& src_coord=node[i]->src_coord;
        Vector<Real_t> new_buff=src_coord;
        src_coord.Swap(new_buff);
      }
      { // surf_coord
        Vector<Real_t>& surf_coord=node[i]->surf_coord;
        Vector<Real_t> new_buff=surf_coord;
        surf_coord.Swap(new_buff);
      }
      { // trg_coord
        Vector<Real_t>& trg_coord=node[i]->trg_coord;
        Vector<Real_t> new_buff=trg_coord;
        trg_coord.Swap(new_buff);
      }
    }

    buff_size+=(extra_size.size()>indx?extra_size[indx]:0);
    buff_size+=4*MAX_DEPTH*(6*(m-1)*(m-1)+2)*COORD_DIM;
    buff[indx].Resize(1,buff_size);

    Real_t* buff_ptr=&buff[indx][0][0];
    for(size_t i=0;i<node_lst.size();i++){
      { // src_coord
        Vector<Real_t>& src_coord=node_lst[i]->src_coord;
        mem::memcopy(buff_ptr,&src_coord[0],src_coord.Dim()*sizeof(Real_t));
        src_coord.ReInit(node_lst[i]->src_coord.Dim(), buff_ptr, false);
        buff_ptr+=node_lst[i]->src_coord.Dim();
      }
      { // surf_coord
        Vector<Real_t>& surf_coord=node_lst[i]->surf_coord;
        mem::memcopy(buff_ptr,&surf_coord[0],surf_coord.Dim()*sizeof(Real_t));
        surf_coord.ReInit(node_lst[i]->surf_coord.Dim(), buff_ptr, false);
        buff_ptr+=node_lst[i]->surf_coord.Dim();
      }
      { // trg_coord
        Vector<Real_t>& trg_coord=node_lst[i]->trg_coord;
        mem::memcopy(buff_ptr,&trg_coord[0],trg_coord.Dim()*sizeof(Real_t));
        trg_coord.ReInit(node_lst[i]->trg_coord.Dim(), buff_ptr, false);
        buff_ptr+=node_lst[i]->trg_coord.Dim();
      }
    }

    { // check and equiv surfaces.
      upwd_check_surf.resize(MAX_DEPTH);
      upwd_equiv_surf.resize(MAX_DEPTH);
      dnwd_check_surf.resize(MAX_DEPTH);
      dnwd_equiv_surf.resize(MAX_DEPTH);
      for(size_t depth=0;depth<MAX_DEPTH;depth++){
        Real_t c[3]={0.0,0.0,0.0};
        upwd_check_surf[depth].ReInit((6*(m-1)*(m-1)+2)*COORD_DIM, buff_ptr, false); buff_ptr+=(6*(m-1)*(m-1)+2)*COORD_DIM;
        upwd_equiv_surf[depth].ReInit((6*(m-1)*(m-1)+2)*COORD_DIM, buff_ptr, false); buff_ptr+=(6*(m-1)*(m-1)+2)*COORD_DIM;
        dnwd_check_surf[depth].ReInit((6*(m-1)*(m-1)+2)*COORD_DIM, buff_ptr, false); buff_ptr+=(6*(m-1)*(m-1)+2)*COORD_DIM;
        dnwd_equiv_surf[depth].ReInit((6*(m-1)*(m-1)+2)*COORD_DIM, buff_ptr, false); buff_ptr+=(6*(m-1)*(m-1)+2)*COORD_DIM;
        upwd_check_surf[depth]=u_check_surf(m,c,depth);
        upwd_equiv_surf[depth]=u_equiv_surf(m,c,depth);
        dnwd_check_surf[depth]=d_check_surf(m,c,depth);
        dnwd_equiv_surf[depth]=d_equiv_surf(m,c,depth);
      }
    }

    buff[indx].AllocDevice(true);
  }
}



template <class FMMNode>
void FMM_Pts<FMMNode>::SetupPrecomp(SetupData<Real_t>& setup_data, bool device){
  if(setup_data.precomp_data==NULL || setup_data.level>MAX_DEPTH) return;

  Profile::Tic("SetupPrecomp",&this->comm,true,25);
  { // Build precomp_data
    size_t precomp_offset=0;
    int level=setup_data.level;
    Matrix<char>& precomp_data=*setup_data.precomp_data;
    std::vector<Mat_Type>& interac_type_lst=setup_data.interac_type;
    for(size_t type_indx=0; type_indx<interac_type_lst.size(); type_indx++){
      Mat_Type& interac_type=interac_type_lst[type_indx];
      this->PrecompAll(interac_type, level); // Compute matrices.
      precomp_offset=this->mat->CompactData(level, interac_type, precomp_data, precomp_offset);
    }
  }
  Profile::Toc();

  if(device){ // Host2Device
    Profile::Tic("Host2Device",&this->comm,false,25);
    setup_data.precomp_data->AllocDevice(true);
    Profile::Toc();
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::SetupInterac(SetupData<Real_t>& setup_data, bool device){
  int level=setup_data.level;
  std::vector<Mat_Type>& interac_type_lst=setup_data.interac_type;

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  Matrix<Real_t>&  input_data=*setup_data. input_data;
  Matrix<Real_t>& output_data=*setup_data.output_data;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector;

  size_t n_in =nodes_in .size();
  size_t n_out=nodes_out.size();

  // Setup precomputed data.
  SetupPrecomp(setup_data,device);

  // Build interac_data
  Profile::Tic("Interac-Data",&this->comm,true,25);
  Matrix<char>& interac_data=setup_data.interac_data;
  if(n_out>0 && n_in >0){ // Build precomp_data, interac_data
    std::vector<size_t> interac_mat;
    std::vector<size_t> interac_cnt;
    std::vector<size_t> interac_blk;
    std::vector<size_t>  input_perm;
    std::vector<size_t> output_perm;
    size_t dof=0, M_dim0=0, M_dim1=0;

    size_t precomp_offset=0;
    size_t buff_size=DEVICE_BUFFER_SIZE*1024l*1024l;
    for(size_t type_indx=0; type_indx<interac_type_lst.size(); type_indx++){

      Mat_Type& interac_type=interac_type_lst[type_indx];
      size_t mat_cnt=this->interac_list.ListCount(interac_type);
      Matrix<size_t> precomp_data_offset;
      { // Load precomp_data for interac_type.
        Matrix<char>& precomp_data=*setup_data.precomp_data;
        char* indx_ptr=precomp_data[0]+precomp_offset;
        size_t total_size=((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
        size_t mat_cnt_  =((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
        size_t max_depth =((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
        precomp_data_offset.ReInit(mat_cnt_,(1+(2+2)*max_depth), (size_t*)indx_ptr, false);
        precomp_offset+=total_size;
      }

      Matrix<FMMNode*> src_interac_list(n_in ,mat_cnt); src_interac_list.SetZero();
      Matrix<FMMNode*> trg_interac_list(n_out,mat_cnt); trg_interac_list.SetZero();
      { // Build trg_interac_list
        for(size_t i=0;i<n_out;i++){
          if(!((FMMNode*)nodes_out[i])->IsGhost() && (level==-1 || ((FMMNode*)nodes_out[i])->Depth()==level)){
            std::vector<FMMNode*>& lst=((FMMNode*)nodes_out[i])->interac_list[interac_type];
            mem::memcopy(&trg_interac_list[i][0], &lst[0], lst.size()*sizeof(FMMNode*));
            assert(lst.size()==mat_cnt);
          }
        }
      }
      { // Build src_interac_list
        for(size_t i=0;i<n_in ;i++) ((FMMNode*)nodes_in [i])->node_id=i;
        for(size_t i=0;i<n_out;i++){
          for(size_t j=0;j<mat_cnt;j++)
          if(trg_interac_list[i][j]!=NULL){
            src_interac_list[trg_interac_list[i][j]->node_id][j]=(FMMNode*)nodes_out[i];
          }
        }
      }

      Matrix<size_t> interac_dsp(n_out,mat_cnt);
      std::vector<size_t> interac_blk_dsp(1,0);
      { // Determine dof, M_dim0, M_dim1
        dof=1;
        Matrix<Real_t>& M0 = this->interac_list.ClassMat(level, interac_type_lst[0], 0);
        M_dim0=M0.Dim(0); M_dim1=M0.Dim(1);
      }
      { // Determine interaction blocks which fit in memory.
        size_t vec_size=(M_dim0+M_dim1)*sizeof(Real_t)*dof;
        for(size_t j=0;j<mat_cnt;j++){// Determine minimum buff_size
          size_t vec_cnt=0;
          for(size_t i=0;i<n_out;i++){
            if(trg_interac_list[i][j]!=NULL) vec_cnt++;
          }
          if(buff_size<vec_cnt*vec_size)
            buff_size=vec_cnt*vec_size;
        }

        size_t interac_dsp_=0;
        for(size_t j=0;j<mat_cnt;j++){
          for(size_t i=0;i<n_out;i++){
            interac_dsp[i][j]=interac_dsp_;
            if(trg_interac_list[i][j]!=NULL) interac_dsp_++;
          }
          if(interac_dsp_*vec_size>buff_size) // Comment to disable symmetries.
          {
            interac_blk.push_back(j-interac_blk_dsp.back());
            interac_blk_dsp.push_back(j);

            size_t offset=interac_dsp[0][j];
            for(size_t i=0;i<n_out;i++) interac_dsp[i][j]-=offset;
            interac_dsp_-=offset;

            assert(interac_dsp_*vec_size<=buff_size); // Problem too big for buff_size.
          }
          interac_mat.push_back(precomp_data_offset[this->interac_list.InteracClass(interac_type,j)][0]);
          interac_cnt.push_back(interac_dsp_-interac_dsp[0][j]);
        }
        interac_blk.push_back(mat_cnt-interac_blk_dsp.back());
        interac_blk_dsp.push_back(mat_cnt);
      }

      { // Determine input_perm.
        size_t vec_size=M_dim0*dof;
        for(size_t i=0;i<n_out;i++) ((FMMNode*)nodes_out[i])->node_id=i;
        for(size_t k=1;k<interac_blk_dsp.size();k++){
          for(size_t i=0;i<n_in ;i++){
            for(size_t j=interac_blk_dsp[k-1];j<interac_blk_dsp[k];j++){
              FMMNode_t* trg_node=src_interac_list[i][j];
              if(trg_node!=NULL){
                size_t depth=trg_node->Depth();
                input_perm .push_back(precomp_data_offset[j][1+4*depth+0]); // prem
                input_perm .push_back(precomp_data_offset[j][1+4*depth+1]); // scal
                input_perm .push_back(interac_dsp[trg_node->node_id][j]*vec_size*sizeof(Real_t)); // trg_ptr
                input_perm .push_back((size_t)(& input_vector[i][0][0]- input_data[0])); // src_ptr
                assert(input_vector[i]->Dim()==vec_size);
              }
            }
          }
        }
      }
      { // Determine output_perm
        size_t vec_size=M_dim1*dof;
        for(size_t k=1;k<interac_blk_dsp.size();k++){
          for(size_t i=0;i<n_out;i++){
            for(size_t j=interac_blk_dsp[k-1];j<interac_blk_dsp[k];j++){
              if(trg_interac_list[i][j]!=NULL){
                size_t depth=((FMMNode*)nodes_out[i])->Depth();
                output_perm.push_back(precomp_data_offset[j][1+4*depth+2]); // prem
                output_perm.push_back(precomp_data_offset[j][1+4*depth+3]); // scal
                output_perm.push_back(interac_dsp[               i ][j]*vec_size*sizeof(Real_t)); // src_ptr
                output_perm.push_back((size_t)(&output_vector[i][0][0]-output_data[0])); // trg_ptr
                assert(output_vector[i]->Dim()==vec_size);
              }
            }
          }
        }
      }
    }
    if(this->dev_buffer.Dim()<buff_size) this->dev_buffer.Resize(buff_size);
    if(this->cpu_buffer.Dim()<buff_size) this->cpu_buffer.Resize(buff_size);

    { // Set interac_data.
      size_t data_size=sizeof(size_t)*4;
      data_size+=sizeof(size_t)+interac_blk.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+interac_cnt.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+interac_mat.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+ input_perm.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+output_perm.size()*sizeof(size_t);
      if(interac_data.Dim(0)*interac_data.Dim(1)<sizeof(size_t)){
        data_size+=sizeof(size_t);
        interac_data.Resize(1,data_size);
        ((size_t*)&interac_data[0][0])[0]=sizeof(size_t);
      }else{
        size_t pts_data_size=*((size_t*)&interac_data[0][0]);
        assert(interac_data.Dim(0)*interac_data.Dim(1)>=pts_data_size);
        data_size+=pts_data_size;
        if(data_size>interac_data.Dim(0)*interac_data.Dim(1)){ //Resize and copy interac_data.
          Matrix< char> pts_interac_data=interac_data;
          interac_data.Resize(1,data_size);
          mem::memcopy(&interac_data[0][0],&pts_interac_data[0][0],pts_data_size);
        }
      }
      char* data_ptr=&interac_data[0][0];
      data_ptr+=((size_t*)data_ptr)[0];

      ((size_t*)data_ptr)[0]=data_size; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=   M_dim0; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=   M_dim1; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=      dof; data_ptr+=sizeof(size_t);

      ((size_t*)data_ptr)[0]=interac_blk.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &interac_blk[0], interac_blk.size()*sizeof(size_t));
      data_ptr+=interac_blk.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=interac_cnt.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &interac_cnt[0], interac_cnt.size()*sizeof(size_t));
      data_ptr+=interac_cnt.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=interac_mat.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &interac_mat[0], interac_mat.size()*sizeof(size_t));
      data_ptr+=interac_mat.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]= input_perm.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, & input_perm[0],  input_perm.size()*sizeof(size_t));
      data_ptr+= input_perm.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=output_perm.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &output_perm[0], output_perm.size()*sizeof(size_t));
      data_ptr+=output_perm.size()*sizeof(size_t);
    }
  }
  Profile::Toc();

  if(device){ // Host2Device
    Profile::Tic("Host2Device",&this->comm,false,25);
    setup_data.interac_data .AllocDevice(true);
    Profile::Toc();
  }
}

#if defined(PVFMM_HAVE_CUDA)
#include <cuda_func.hpp>

template <class Real_t, int SYNC>
void EvalListGPU(SetupData<Real_t>& setup_data, Vector<char>& dev_buffer, MPI_Comm& comm) {
  cudaStream_t* stream = pvfmm::CUDA_Lock::acquire_stream();

  Profile::Tic("Host2Device",&comm,false,25);
  typename Matrix<char>::Device    interac_data;
  typename Vector<char>::Device            buff;
  typename Matrix<char>::Device  precomp_data_d;
  typename Matrix<char>::Device  interac_data_d;
  typename Matrix<Real_t>::Device  input_data_d;
  typename Matrix<Real_t>::Device output_data_d;

  interac_data  = setup_data.interac_data;
  buff          =              dev_buffer. AllocDevice(false);
  precomp_data_d= setup_data.precomp_data->AllocDevice(false);
  interac_data_d= setup_data.interac_data. AllocDevice(false);
  input_data_d  = setup_data.  input_data->AllocDevice(false);
  output_data_d = setup_data. output_data->AllocDevice(false);
  Profile::Toc();

  { // Set interac_data.
    size_t data_size, M_dim0, M_dim1, dof;
    Vector<size_t> interac_blk;
    Vector<size_t> interac_cnt;
    Vector<size_t> interac_mat;
    Vector<size_t> input_perm_d;
    Vector<size_t> output_perm_d;

    { // Set interac_data.
      char* data_ptr=&interac_data  [0][0];
      char*  dev_ptr=&interac_data_d[0][0];

      data_size=((size_t*)data_ptr)[0]; data_ptr+=data_size;      dev_ptr += data_size;
      data_size=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t); dev_ptr += sizeof(size_t);
      M_dim0   =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t); dev_ptr += sizeof(size_t);
      M_dim1   =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t); dev_ptr += sizeof(size_t);
      dof      =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t); dev_ptr += sizeof(size_t);

      interac_blk.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr += sizeof(size_t) + sizeof(size_t)*interac_blk.Dim();
      dev_ptr  += sizeof(size_t) + sizeof(size_t)*interac_blk.Dim();

      interac_cnt.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr += sizeof(size_t) + sizeof(size_t)*interac_cnt.Dim();
      dev_ptr  += sizeof(size_t) + sizeof(size_t)*interac_cnt.Dim();

      interac_mat.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr += sizeof(size_t) + sizeof(size_t)*interac_mat.Dim();
      dev_ptr  += sizeof(size_t) + sizeof(size_t)*interac_mat.Dim();

      input_perm_d.ReInit(((size_t*)data_ptr)[0],(size_t*)(dev_ptr+sizeof(size_t)),false);
      data_ptr += sizeof(size_t) + sizeof(size_t)*input_perm_d.Dim();
      dev_ptr  += sizeof(size_t) + sizeof(size_t)*input_perm_d.Dim();

      output_perm_d.ReInit(((size_t*)data_ptr)[0],(size_t*)(dev_ptr+sizeof(size_t)),false);
      data_ptr += sizeof(size_t) + sizeof(size_t)*output_perm_d.Dim();
      dev_ptr  += sizeof(size_t) + sizeof(size_t)*output_perm_d.Dim();
    }

    { // interactions
      size_t interac_indx = 0;
      size_t interac_blk_dsp = 0;
      cudaError_t error;
      for (size_t k = 0; k < interac_blk.Dim(); k++) {
        size_t vec_cnt=0;
        for(size_t j=interac_blk_dsp;j<interac_blk_dsp+interac_blk[k];j++) vec_cnt+=interac_cnt[j];

        char *buff_in_d  =&buff[0];
        char *buff_out_d =&buff[vec_cnt*dof*M_dim0*sizeof(Real_t)];

        { // Input permutation.
          in_perm_gpu<Real_t>(&precomp_data_d[0][0], &input_data_d[0][0], buff_in_d,
                              &input_perm_d[interac_indx*4], vec_cnt, M_dim0, stream);
        }

        size_t vec_cnt0 = 0;
        for (size_t j = interac_blk_dsp; j < interac_blk_dsp + interac_blk[k];) {
          size_t vec_cnt1 = 0;
          size_t interac_mat0 = interac_mat[j];
          for (; j < interac_blk_dsp + interac_blk[k] && interac_mat[j] == interac_mat0; j++) vec_cnt1 += interac_cnt[j];
          Matrix<Real_t> M_d(M_dim0, M_dim1, (Real_t*)(precomp_data_d.dev_ptr + interac_mat0), false);
          Matrix<Real_t> Ms_d(dof*vec_cnt1, M_dim0, (Real_t*)(buff_in_d +  M_dim0*vec_cnt0*dof*sizeof(Real_t)), false);
          Matrix<Real_t> Mt_d(dof*vec_cnt1, M_dim1, (Real_t*)(buff_out_d + M_dim1*vec_cnt0*dof*sizeof(Real_t)), false);
          Matrix<Real_t>::CUBLASGEMM(Mt_d, Ms_d, M_d);
          vec_cnt0 += vec_cnt1;
        }

        { // Input permutation.
          out_perm_gpu<Real_t>(&precomp_data_d[0][0], &output_data_d[0][0], buff_out_d,
                               &output_perm_d[interac_indx*4], vec_cnt, M_dim1, stream);
        }

        interac_indx += vec_cnt;
        interac_blk_dsp += interac_blk[k];
      }
    }
  }

	if(SYNC) CUDA_Lock::wait();
}
#endif

template <class FMMNode>
template <int SYNC>
void FMM_Pts<FMMNode>::EvalList(SetupData<Real_t>& setup_data, bool device){
  if(setup_data.interac_data.Dim(0)==0 || setup_data.interac_data.Dim(1)==0){
    Profile::Tic("Host2Device",&this->comm,false,25);
    Profile::Toc();
    Profile::Tic("DeviceComp",&this->comm,false,20);
    Profile::Toc();
    return;
  }

#if defined(PVFMM_HAVE_CUDA)
  if (device) {
    EvalListGPU<Real_t, SYNC>(setup_data, this->dev_buffer, this->comm);
    return;
  }
#endif

  Profile::Tic("Host2Device",&this->comm,false,25);
  typename Vector<char>::Device          buff;
  typename Matrix<char>::Device  precomp_data;
  typename Matrix<char>::Device  interac_data;
  typename Matrix<Real_t>::Device  input_data;
  typename Matrix<Real_t>::Device output_data;
  if(device){
    buff        =       this-> dev_buffer. AllocDevice(false);
    precomp_data= setup_data.precomp_data->AllocDevice(false);
    interac_data= setup_data.interac_data. AllocDevice(false);
    input_data  = setup_data.  input_data->AllocDevice(false);
    output_data = setup_data. output_data->AllocDevice(false);
  }else{
    buff        =       this-> cpu_buffer;
    precomp_data=*setup_data.precomp_data;
    interac_data= setup_data.interac_data;
    input_data  =*setup_data.  input_data;
    output_data =*setup_data. output_data;
  }
  Profile::Toc();

  Profile::Tic("DeviceComp",&this->comm,false,20);
  int lock_idx=-1;
  int wait_lock_idx=-1;
  if(device) wait_lock_idx=MIC_Lock::curr_lock();
  if(device) lock_idx=MIC_Lock::get_lock();
  #ifdef __INTEL_OFFLOAD
  #pragma offload if(device) target(mic:0) signal(&MIC_Lock::lock_vec[device?lock_idx:0])
  #endif
  { // Offloaded computation.

    // Set interac_data.
    size_t data_size, M_dim0, M_dim1, dof;
    Vector<size_t> interac_blk;
    Vector<size_t> interac_cnt;
    Vector<size_t> interac_mat;
    Vector<size_t>  input_perm;
    Vector<size_t> output_perm;
    { // Set interac_data.
      char* data_ptr=&interac_data[0][0];

      data_size=((size_t*)data_ptr)[0]; data_ptr+=data_size;
      data_size=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      M_dim0   =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      M_dim1   =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      dof      =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);

      interac_blk.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+interac_blk.Dim()*sizeof(size_t);

      interac_cnt.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+interac_cnt.Dim()*sizeof(size_t);

      interac_mat.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+interac_mat.Dim()*sizeof(size_t);

      input_perm .ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+ input_perm.Dim()*sizeof(size_t);

      output_perm.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+output_perm.Dim()*sizeof(size_t);
    }

    if(device) MIC_Lock::wait_lock(wait_lock_idx);

    //Compute interaction from Chebyshev source density.
    { // interactions
      int omp_p=omp_get_max_threads();
      size_t interac_indx=0;
      size_t interac_blk_dsp=0;
      for(size_t k=0;k<interac_blk.Dim();k++){
        size_t vec_cnt=0;
        for(size_t j=interac_blk_dsp;j<interac_blk_dsp+interac_blk[k];j++) vec_cnt+=interac_cnt[j];

        char* buff_in =&buff[0];
        char* buff_out=&buff[vec_cnt*dof*M_dim0*sizeof(Real_t)];

        // Input permutation.
        #pragma omp parallel for
        for(int tid=0;tid<omp_p;tid++){
          size_t a=( tid   *vec_cnt)/omp_p;
          size_t b=((tid+1)*vec_cnt)/omp_p;

          for(size_t i=a;i<b;i++){
            const PERM_INT_T*  perm=(PERM_INT_T*)(precomp_data[0]+input_perm[(interac_indx+i)*4+0]);
            const     Real_t*  scal=(    Real_t*)(precomp_data[0]+input_perm[(interac_indx+i)*4+1]);
            const     Real_t* v_in =(    Real_t*)(  input_data[0]+input_perm[(interac_indx+i)*4+3]);
            Real_t*           v_out=(    Real_t*)(     buff_in   +input_perm[(interac_indx+i)*4+2]);

            // TODO: Fix for dof>1
            #ifdef __MIC__
            {
              __m512d v8;
              size_t j_start=(((uintptr_t)(v_out       ) + (uintptr_t)(MEM_ALIGN-1)) & ~ (uintptr_t)(MEM_ALIGN-1))-((uintptr_t)v_out);
              size_t j_end  =(((uintptr_t)(v_out+M_dim0)                           ) & ~ (uintptr_t)(MEM_ALIGN-1))-((uintptr_t)v_out);
              j_start/=sizeof(Real_t);
              j_end  /=sizeof(Real_t);
              assert(((uintptr_t)(v_out))%sizeof(Real_t)==0);
              assert(((uintptr_t)(v_out+j_start))%64==0);
              assert(((uintptr_t)(v_out+j_end  ))%64==0);
              size_t j=0;
              for(;j<j_start;j++ ){
                v_out[j]=v_in[perm[j]]*scal[j];
              }
              for(;j<j_end  ;j+=8){
                v8=_mm512_setr_pd(
                    v_in[perm[j+0]]*scal[j+0],
                    v_in[perm[j+1]]*scal[j+1],
                    v_in[perm[j+2]]*scal[j+2],
                    v_in[perm[j+3]]*scal[j+3],
                    v_in[perm[j+4]]*scal[j+4],
                    v_in[perm[j+5]]*scal[j+5],
                    v_in[perm[j+6]]*scal[j+6],
                    v_in[perm[j+7]]*scal[j+7]);
                _mm512_storenrngo_pd(v_out+j,v8);
              }
              for(;j<M_dim0 ;j++ ){
                v_out[j]=v_in[perm[j]]*scal[j];
              }
            }
            #else
            for(size_t j=0;j<M_dim0;j++ ){
              v_out[j]=v_in[perm[j]]*scal[j];
            }
            #endif
          }
        }

        size_t vec_cnt0=0;
        for(size_t j=interac_blk_dsp;j<interac_blk_dsp+interac_blk[k];){
          size_t vec_cnt1=0;
          size_t interac_mat0=interac_mat[j];
          for(;j<interac_blk_dsp+interac_blk[k] && interac_mat[j]==interac_mat0;j++) vec_cnt1+=interac_cnt[j];
          Matrix<Real_t> M(M_dim0, M_dim1, (Real_t*)(precomp_data[0]+interac_mat0), false);
          #ifdef __MIC__
          {
            Matrix<Real_t> Ms(dof*vec_cnt1, M_dim0, (Real_t*)(buff_in +M_dim0*vec_cnt0*dof*sizeof(Real_t)), false);
            Matrix<Real_t> Mt(dof*vec_cnt1, M_dim1, (Real_t*)(buff_out+M_dim1*vec_cnt0*dof*sizeof(Real_t)), false);
            Matrix<Real_t>::GEMM(Mt,Ms,M);
          }
          #else
          #pragma omp parallel for
          for(int tid=0;tid<omp_p;tid++){
            size_t a=(dof*vec_cnt1*(tid  ))/omp_p;
            size_t b=(dof*vec_cnt1*(tid+1))/omp_p;
            Matrix<Real_t> Ms(b-a, M_dim0, (Real_t*)(buff_in +M_dim0*vec_cnt0*dof*sizeof(Real_t))+M_dim0*a, false);
            Matrix<Real_t> Mt(b-a, M_dim1, (Real_t*)(buff_out+M_dim1*vec_cnt0*dof*sizeof(Real_t))+M_dim1*a, false);
            Matrix<Real_t>::GEMM(Mt,Ms,M);
          }
          #endif
          vec_cnt0+=vec_cnt1;
        }

        // Output permutation.
        #pragma omp parallel for
        for(int tid=0;tid<omp_p;tid++){
          size_t a=( tid   *vec_cnt)/omp_p;
          size_t b=((tid+1)*vec_cnt)/omp_p;

          if(tid>      0 && a<vec_cnt){ // Find 'a' independent of other threads.
            size_t out_ptr=output_perm[(interac_indx+a)*4+3];
            if(tid>      0) while(a<vec_cnt && out_ptr==output_perm[(interac_indx+a)*4+3]) a++;
          }
          if(tid<omp_p-1 && b<vec_cnt){ // Find 'b' independent of other threads.
            size_t out_ptr=output_perm[(interac_indx+b)*4+3];
            if(tid<omp_p-1) while(b<vec_cnt && out_ptr==output_perm[(interac_indx+b)*4+3]) b++;
          }
          for(size_t i=a;i<b;i++){ // Compute permutations.
            const PERM_INT_T*  perm=(PERM_INT_T*)(precomp_data[0]+output_perm[(interac_indx+i)*4+0]);
            const     Real_t*  scal=(    Real_t*)(precomp_data[0]+output_perm[(interac_indx+i)*4+1]);
            const     Real_t* v_in =(    Real_t*)(    buff_out   +output_perm[(interac_indx+i)*4+2]);
            Real_t*           v_out=(    Real_t*)( output_data[0]+output_perm[(interac_indx+i)*4+3]);

            // TODO: Fix for dof>1
            #ifdef __MIC__
            {
              __m512d v8;
              __m512d v_old;
              size_t j_start=(((uintptr_t)(v_out       ) + (uintptr_t)(MEM_ALIGN-1)) & ~ (uintptr_t)(MEM_ALIGN-1))-((uintptr_t)v_out);
              size_t j_end  =(((uintptr_t)(v_out+M_dim1)                           ) & ~ (uintptr_t)(MEM_ALIGN-1))-((uintptr_t)v_out);
              j_start/=sizeof(Real_t);
              j_end  /=sizeof(Real_t);
              assert(((uintptr_t)(v_out))%sizeof(Real_t)==0);
              assert(((uintptr_t)(v_out+j_start))%64==0);
              assert(((uintptr_t)(v_out+j_end  ))%64==0);
              size_t j=0;
              for(;j<j_start;j++ ){
                v_out[j]+=v_in[perm[j]]*scal[j];
              }
              for(;j<j_end  ;j+=8){
                v_old=_mm512_load_pd(v_out+j);
                v8=_mm512_setr_pd(
                    v_in[perm[j+0]]*scal[j+0],
                    v_in[perm[j+1]]*scal[j+1],
                    v_in[perm[j+2]]*scal[j+2],
                    v_in[perm[j+3]]*scal[j+3],
                    v_in[perm[j+4]]*scal[j+4],
                    v_in[perm[j+5]]*scal[j+5],
                    v_in[perm[j+6]]*scal[j+6],
                    v_in[perm[j+7]]*scal[j+7]);
                v_old=_mm512_add_pd(v_old, v8);
                _mm512_storenrngo_pd(v_out+j,v_old);
              }
              for(;j<M_dim1 ;j++ ){
                v_out[j]+=v_in[perm[j]]*scal[j];
              }
            }
            #else
            for(size_t j=0;j<M_dim1;j++ ){
              v_out[j]+=v_in[perm[j]]*scal[j];
            }
            #endif
          }
        }

        interac_indx+=vec_cnt;
        interac_blk_dsp+=interac_blk[k];
      }
    }

    if(device) MIC_Lock::release_lock(lock_idx);
  }

  #ifdef __INTEL_OFFLOAD
  if(SYNC){
    #pragma offload if(device) target(mic:0)
    {if(device) MIC_Lock::wait_lock(lock_idx);}
  }
  #endif

  Profile::Toc();
}



template <class FMMNode>
void FMM_Pts<FMMNode>::Source2UpSetup(SetupData<Real_t>&  setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=aux_kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=S2U_Type;

    setup_data. input_data=&buff[4];
    setup_data.output_data=&buff[0];
    setup_data. coord_data=&buff[6];
    Vector<FMMNode_t*>& nodes_in =n_list[4];
    Vector<FMMNode_t*>& nodes_out=n_list[0];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level   || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level   || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++){
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_value);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_value);
  }
  for(size_t i=0;i<nodes_out.size();i++){
    output_vector.push_back(&upwd_check_surf[((FMMNode*)nodes_out[i])->Depth()]);
    output_vector.push_back(&((FMMData*)((FMMNode*)nodes_out[i])->FMMData())->upward_equiv);
  }

  //Upward check to upward equivalent matrix.
  Matrix<Real_t>& M_uc2ue = this->mat->Mat(level, UC2UE_Type, 0);
  this->SetupInteracPts(setup_data, false, true, &M_uc2ue,device);
  { // Resize device buffer
    size_t n=setup_data.output_data->Dim(0)*setup_data.output_data->Dim(1)*sizeof(Real_t);
    if(this->dev_buffer.Dim()<n) this->dev_buffer.Resize(n);
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::Source2Up(SetupData<Real_t>&  setup_data, bool device){
  //Add Source2Up contribution.
  this->EvalListPts(setup_data, device);
}


template <class FMMNode>
void FMM_Pts<FMMNode>::Up2UpSetup(SetupData<Real_t>& setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=aux_kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=U2U_Type;

    setup_data. input_data=&buff[0];
    setup_data.output_data=&buff[0];
    Vector<FMMNode_t*>& nodes_in =n_list[0];
    Vector<FMMNode_t*>& nodes_out=n_list[0];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level+1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level  ) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++)  input_vector.push_back(&((FMMData*)((FMMNode*)nodes_in [i])->FMMData())->upward_equiv);
  for(size_t i=0;i<nodes_out.size();i++) output_vector.push_back(&((FMMData*)((FMMNode*)nodes_out[i])->FMMData())->upward_equiv);

  SetupInterac(setup_data,device);
}

template <class FMMNode>
void FMM_Pts<FMMNode>::Up2Up     (SetupData<Real_t>& setup_data, bool device){
  //Add Up2Up contribution.
  EvalList(setup_data, device);
}



template <class FMMNode>
void FMM_Pts<FMMNode>::PeriodicBC(FMMNode* node){
  if(this->MultipoleOrder()==0) return;
  Matrix<Real_t>& M = Precomp(0, BC_Type, 0);

  assert(node->FMMData()->upward_equiv.Dim()>0);
  int dof=1;

  Vector<Real_t>& upward_equiv=node->FMMData()->upward_equiv;
  Vector<Real_t>& dnward_equiv=node->FMMData()->dnward_equiv;
  assert(upward_equiv.Dim()==M.Dim(0)*dof);
  assert(dnward_equiv.Dim()==M.Dim(1)*dof);
  Matrix<Real_t> d_equiv(dof,M.Dim(0),&dnward_equiv[0],false);
  Matrix<Real_t> u_equiv(dof,M.Dim(1),&upward_equiv[0],false);
  Matrix<Real_t>::GEMM(d_equiv,u_equiv,M);
}



template <class FMMNode>
void FMM_Pts<FMMNode>::FFT_UpEquiv(size_t dof, size_t m, size_t ker_dim0, Vector<size_t>& fft_vec,
    Vector<Real_t>& input_data, Vector<Real_t>& output_data, Vector<Real_t>& buffer_){

  size_t n1=m*2;
  size_t n2=n1*n1;
  size_t n3=n1*n2;
  size_t n3_=n2*(n1/2+1);
  size_t chld_cnt=1UL<<COORD_DIM;
  size_t fftsize_in =2*n3_*chld_cnt*ker_dim0*dof;
  int omp_p=omp_get_max_threads();

  //Load permutation map.
  size_t n=6*(m-1)*(m-1)+2;
  static Vector<size_t> map;
  { // Build map to reorder upward_equiv
    size_t n_old=map.Dim();
    if(n_old!=n){
      Real_t c[3]={0,0,0};
      Vector<Real_t> surf=surface(m, c, (Real_t)(m-1), 0);
      map.Resize(surf.Dim()/COORD_DIM);
      for(size_t i=0;i<map.Dim();i++)
        map[i]=((size_t)(m-1-surf[i*3]+0.5))+((size_t)(m-1-surf[i*3+1]+0.5))*n1+((size_t)(m-1-surf[i*3+2]+0.5))*n2;
    }
  }
  { // Build FFTW plan.
    if(!vlist_fft_flag){
      int nnn[3]={(int)n1,(int)n1,(int)n1};
      void *fftw_in, *fftw_out;
      fftw_in  = mem::aligned_new<Real_t>(  n3 *ker_dim0*chld_cnt);
      fftw_out = mem::aligned_new<Real_t>(2*n3_*ker_dim0*chld_cnt);
      vlist_fftplan = FFTW_t<Real_t>::fft_plan_many_dft_r2c(COORD_DIM,nnn,ker_dim0*chld_cnt,
          (Real_t*)fftw_in, NULL, 1, n3, (typename FFTW_t<Real_t>::cplx*)(fftw_out),NULL, 1, n3_, FFTW_ESTIMATE);
      mem::aligned_delete<Real_t>((Real_t*)fftw_in );
      mem::aligned_delete<Real_t>((Real_t*)fftw_out);
      vlist_fft_flag=true;
    }
  }

  { // Offload section
    size_t n_in = fft_vec.Dim();
    #pragma omp parallel for
    for(int pid=0; pid<omp_p; pid++){
      size_t node_start=(n_in*(pid  ))/omp_p;
      size_t node_end  =(n_in*(pid+1))/omp_p;
      Vector<Real_t> buffer(fftsize_in, &buffer_[fftsize_in*pid], false);
      for(size_t node_idx=node_start; node_idx<node_end; node_idx++){
        Vector<Real_t*>  upward_equiv(chld_cnt);
        for(size_t i=0;i<chld_cnt;i++) upward_equiv[i]=&input_data[0] + fft_vec[node_idx] + n*ker_dim0*dof*i;
        Vector<Real_t> upward_equiv_fft(fftsize_in, &output_data[fftsize_in *node_idx], false);
        upward_equiv_fft.SetZero();

        // Rearrange upward equivalent data.
        for(size_t k=0;k<n;k++){
          size_t idx=map[k];
          for(int j1=0;j1<dof;j1++)
          for(int j0=0;j0<(int)chld_cnt;j0++)
          for(int i=0;i<ker_dim0;i++)
            upward_equiv_fft[idx+(j0+(i+j1*ker_dim0)*chld_cnt)*n3]=upward_equiv[j0][ker_dim0*(n*j1+k)+i];
        }

        // Compute FFT.
        for(int i=0;i<dof;i++)
          FFTW_t<Real_t>::fft_execute_dft_r2c(vlist_fftplan, (Real_t*)&upward_equiv_fft[i*  n3 *ker_dim0*chld_cnt],
                                      (typename FFTW_t<Real_t>::cplx*)&buffer          [i*2*n3_*ker_dim0*chld_cnt]);

        //Compute flops.
        #ifndef FFTW3_MKL
        double add, mul, fma;
        FFTW_t<Real_t>::fftw_flops(vlist_fftplan, &add, &mul, &fma);
        #ifndef __INTEL_OFFLOAD0
        Profile::Add_FLOP((long long)(add+mul+2*fma));
        #endif
        #endif

        for(int i=0;i<ker_dim0*dof;i++)
        for(size_t j=0;j<n3_;j++)
        for(size_t k=0;k<chld_cnt;k++){
          upward_equiv_fft[2*(chld_cnt*(n3_*i+j)+k)+0]=buffer[2*(n3_*(chld_cnt*i+k)+j)+0];
          upward_equiv_fft[2*(chld_cnt*(n3_*i+j)+k)+1]=buffer[2*(n3_*(chld_cnt*i+k)+j)+1];
        }
      }
    }
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::FFT_Check2Equiv(size_t dof, size_t m, size_t ker_dim1, Vector<size_t>& ifft_vec,
    Vector<Real_t>& input_data, Vector<Real_t>& output_data, Vector<Real_t>& buffer_, Matrix<Real_t>& M){

  size_t n1=m*2;
  size_t n2=n1*n1;
  size_t n3=n1*n2;
  size_t n3_=n2*(n1/2+1);
  size_t chld_cnt=1UL<<COORD_DIM;
  size_t fftsize_out=2*n3_*dof*ker_dim1*chld_cnt;
  int omp_p=omp_get_max_threads();

  //Load permutation map.
  size_t n=6*(m-1)*(m-1)+2;
  static Vector<size_t> map;
  { // Build map to reorder dnward_check
    size_t n_old=map.Dim();
    if(n_old!=n){
      Real_t c[3]={0,0,0};
      Vector<Real_t> surf=surface(m, c, (Real_t)(m-1), 0);
      map.Resize(surf.Dim()/COORD_DIM);
      for(size_t i=0;i<map.Dim();i++)
        map[i]=((size_t)(m*2-0.5-surf[i*3]))+((size_t)(m*2-0.5-surf[i*3+1]))*n1+((size_t)(m*2-0.5-surf[i*3+2]))*n2;
      //map;//.AllocDevice(true);
    }
  }
  { // Build FFTW plan.
    if(!vlist_ifft_flag){
      //Build FFTW plan.
      int nnn[3]={(int)n1,(int)n1,(int)n1};
      Real_t *fftw_in, *fftw_out;
      fftw_in  = mem::aligned_new<Real_t>(2*n3_*ker_dim1*chld_cnt);
      fftw_out = mem::aligned_new<Real_t>(  n3 *ker_dim1*chld_cnt);
      vlist_ifftplan = FFTW_t<Real_t>::fft_plan_many_dft_c2r(COORD_DIM,nnn,ker_dim1*chld_cnt,
          (typename FFTW_t<Real_t>::cplx*)fftw_in, NULL, 1, n3_, (Real_t*)(fftw_out),NULL, 1, n3, FFTW_ESTIMATE);
      mem::aligned_delete<Real_t>(fftw_in);
      mem::aligned_delete<Real_t>(fftw_out);
      vlist_ifft_flag=true;
    }
  }

  { // Offload section
    size_t n_out=ifft_vec.Dim();
    #pragma omp parallel for
    for(int pid=0; pid<omp_p; pid++){
      size_t node_start=(n_out*(pid  ))/omp_p;
      size_t node_end  =(n_out*(pid+1))/omp_p;
      Vector<Real_t> buffer(fftsize_out, &buffer_[fftsize_out*pid], false);
      for(size_t node_idx=node_start; node_idx<node_end; node_idx++){
        Vector<Real_t> dnward_check_fft(fftsize_out, &input_data[fftsize_out*node_idx], false);

        //De-interleave data.
        for(int i=0;i<ker_dim1*dof;i++)
        for(size_t j=0;j<n3_;j++)
        for(size_t k=0;k<chld_cnt;k++){
          buffer[2*(n3_*(ker_dim1*dof*k+i)+j)+0]=dnward_check_fft[2*(chld_cnt*(n3_*i+j)+k)+0];
          buffer[2*(n3_*(ker_dim1*dof*k+i)+j)+1]=dnward_check_fft[2*(chld_cnt*(n3_*i+j)+k)+1];
        }

        // Compute FFT.
        for(int i=0;i<dof;i++)
          FFTW_t<Real_t>::fft_execute_dft_c2r(vlist_ifftplan, (typename FFTW_t<Real_t>::cplx*)&buffer          [i*2*n3_*ker_dim1*chld_cnt],
                                                                                     (Real_t*)&dnward_check_fft[i*  n3 *ker_dim1*chld_cnt]);
        //Compute flops.
        #ifndef FFTW3_MKL
        double add, mul, fma;
        FFTW_t<Real_t>::fftw_flops(vlist_ifftplan, &add, &mul, &fma);
        #ifndef __INTEL_OFFLOAD0
        Profile::Add_FLOP((long long)(add+mul+2*fma));
        #endif
        #endif

        // Rearrange downward check data.
        for(size_t k=0;k<n;k++){
          size_t idx=map[k];
          for(int j1=0;j1<dof;j1++)
          for(int j0=0;j0<(int)chld_cnt;j0++)
          for(int i=0;i<ker_dim1;i++)
            buffer[ker_dim1*(n*(dof*j0+j1)+k)+i]=dnward_check_fft[idx+(j1+(i+j0*ker_dim1)*dof)*n3];
        }

        // Compute check to equiv.
        for(size_t j=0;j<chld_cnt;j++){
          Matrix<Real_t> d_check(dof,M.Dim(0),&buffer[n*ker_dim1*dof*j],false);
          Matrix<Real_t> d_equiv(dof,M.Dim(1),&output_data[0] + ifft_vec[node_idx] + M.Dim(1)*dof*j,false);
          Matrix<Real_t>::GEMM(d_equiv,d_check,M,1.0);
        }
      }
    }
  }
}

template<class Real_t>
inline void matmult_8x8x2(Real_t*& M_, Real_t*& IN0, Real_t*& IN1, Real_t*& OUT0, Real_t*& OUT1){
  // Generic code.
  Real_t out_reg000, out_reg001, out_reg010, out_reg011;
  Real_t out_reg100, out_reg101, out_reg110, out_reg111;
  Real_t  in_reg000,  in_reg001,  in_reg010,  in_reg011;
  Real_t  in_reg100,  in_reg101,  in_reg110,  in_reg111;
  Real_t   m_reg000,   m_reg001,   m_reg010,   m_reg011;
  Real_t   m_reg100,   m_reg101,   m_reg110,   m_reg111;
  //#pragma unroll
  for(int i1=0;i1<8;i1+=2){
    Real_t* IN0_=IN0;
    Real_t* IN1_=IN1;

    out_reg000=OUT0[ 0]; out_reg001=OUT0[ 1];
    out_reg010=OUT0[ 2]; out_reg011=OUT0[ 3];
    out_reg100=OUT1[ 0]; out_reg101=OUT1[ 1];
    out_reg110=OUT1[ 2]; out_reg111=OUT1[ 3];
    //#pragma unroll
    for(int i2=0;i2<8;i2+=2){
      m_reg000=M_[ 0]; m_reg001=M_[ 1];
      m_reg010=M_[ 2]; m_reg011=M_[ 3];
      m_reg100=M_[16]; m_reg101=M_[17];
      m_reg110=M_[18]; m_reg111=M_[19];

      in_reg000=IN0_[0]; in_reg001=IN0_[1];
      in_reg010=IN0_[2]; in_reg011=IN0_[3];
      in_reg100=IN1_[0]; in_reg101=IN1_[1];
      in_reg110=IN1_[2]; in_reg111=IN1_[3];

      out_reg000 += m_reg000*in_reg000 - m_reg001*in_reg001;
      out_reg001 += m_reg000*in_reg001 + m_reg001*in_reg000;
      out_reg010 += m_reg010*in_reg000 - m_reg011*in_reg001;
      out_reg011 += m_reg010*in_reg001 + m_reg011*in_reg000;

      out_reg000 += m_reg100*in_reg010 - m_reg101*in_reg011;
      out_reg001 += m_reg100*in_reg011 + m_reg101*in_reg010;
      out_reg010 += m_reg110*in_reg010 - m_reg111*in_reg011;
      out_reg011 += m_reg110*in_reg011 + m_reg111*in_reg010;

      out_reg100 += m_reg000*in_reg100 - m_reg001*in_reg101;
      out_reg101 += m_reg000*in_reg101 + m_reg001*in_reg100;
      out_reg110 += m_reg010*in_reg100 - m_reg011*in_reg101;
      out_reg111 += m_reg010*in_reg101 + m_reg011*in_reg100;

      out_reg100 += m_reg100*in_reg110 - m_reg101*in_reg111;
      out_reg101 += m_reg100*in_reg111 + m_reg101*in_reg110;
      out_reg110 += m_reg110*in_reg110 - m_reg111*in_reg111;
      out_reg111 += m_reg110*in_reg111 + m_reg111*in_reg110;

      M_+=32; // Jump to (column+2).
      IN0_+=4;
      IN1_+=4;
    }
    OUT0[ 0]=out_reg000; OUT0[ 1]=out_reg001;
    OUT0[ 2]=out_reg010; OUT0[ 3]=out_reg011;
    OUT1[ 0]=out_reg100; OUT1[ 1]=out_reg101;
    OUT1[ 2]=out_reg110; OUT1[ 3]=out_reg111;
    M_+=4-64*2; // Jump back to first column (row+2).
    OUT0+=4;
    OUT1+=4;
  }
}

#if defined(__AVX__) || defined(__SSE3__)
template<>
inline void matmult_8x8x2<double>(double*& M_, double*& IN0, double*& IN1, double*& OUT0, double*& OUT1){
#ifdef __AVX__ //AVX code.
  __m256d out00,out01,out10,out11;
  __m256d out20,out21,out30,out31;
  double* in0__ = IN0;
  double* in1__ = IN1;

  out00 = _mm256_load_pd(OUT0);
  out01 = _mm256_load_pd(OUT1);
  out10 = _mm256_load_pd(OUT0+4);
  out11 = _mm256_load_pd(OUT1+4);
  out20 = _mm256_load_pd(OUT0+8);
  out21 = _mm256_load_pd(OUT1+8);
  out30 = _mm256_load_pd(OUT0+12);
  out31 = _mm256_load_pd(OUT1+12);
  for(int i2=0;i2<8;i2+=2){
    __m256d m00;
    __m256d ot00;
    __m256d mt0,mtt0;
    __m256d in00,in00_r,in01,in01_r;
    in00 = _mm256_broadcast_pd((const __m128d*)in0__);
    in00_r = _mm256_permute_pd(in00,5);
    in01 = _mm256_broadcast_pd((const __m128d*)in1__);
    in01_r = _mm256_permute_pd(in01,5);

    m00 = _mm256_load_pd(M_);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out00 = _mm256_add_pd(out00,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out01 = _mm256_add_pd(out01,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+4);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out10 = _mm256_add_pd(out10,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out11 = _mm256_add_pd(out11,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+8);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out20 = _mm256_add_pd(out20,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out21 = _mm256_add_pd(out21,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+12);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out30 = _mm256_add_pd(out30,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out31 = _mm256_add_pd(out31,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));


    in00 = _mm256_broadcast_pd((const __m128d*) (in0__+2));
    in00_r = _mm256_permute_pd(in00,5);
    in01 = _mm256_broadcast_pd((const __m128d*) (in1__+2));
    in01_r = _mm256_permute_pd(in01,5);

    m00 = _mm256_load_pd(M_+16);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out00 = _mm256_add_pd(out00,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out01 = _mm256_add_pd(out01,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+20);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out10 = _mm256_add_pd(out10,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out11 = _mm256_add_pd(out11,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+24);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out20 = _mm256_add_pd(out20,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out21 = _mm256_add_pd(out21,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    m00 = _mm256_load_pd(M_+28);

    mt0 = _mm256_unpacklo_pd(m00,m00);
    ot00 = _mm256_mul_pd(mt0,in00);
    mtt0 = _mm256_unpackhi_pd(m00,m00);
    out30 = _mm256_add_pd(out30,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in00_r)));

    ot00 = _mm256_mul_pd(mt0,in01);
    out31 = _mm256_add_pd(out31,_mm256_addsub_pd(ot00,_mm256_mul_pd(mtt0,in01_r)));

    M_ += 32;
    in0__ += 4;
    in1__ += 4;
  }
  _mm256_store_pd(OUT0,out00);
  _mm256_store_pd(OUT1,out01);
  _mm256_store_pd(OUT0+4,out10);
  _mm256_store_pd(OUT1+4,out11);
  _mm256_store_pd(OUT0+8,out20);
  _mm256_store_pd(OUT1+8,out21);
  _mm256_store_pd(OUT0+12,out30);
  _mm256_store_pd(OUT1+12,out31);
#elif defined __SSE3__ // SSE code.
  __m128d out00, out01, out10, out11;
  __m128d in00, in01, in10, in11;
  __m128d m00, m01, m10, m11;
  //#pragma unroll
  for(int i1=0;i1<8;i1+=2){
    double* IN0_=IN0;
    double* IN1_=IN1;

    out00 =_mm_load_pd (OUT0  );
    out10 =_mm_load_pd (OUT0+2);
    out01 =_mm_load_pd (OUT1  );
    out11 =_mm_load_pd (OUT1+2);
    //#pragma unroll
    for(int i2=0;i2<8;i2+=2){
      m00 =_mm_load1_pd (M_   );
      m10 =_mm_load1_pd (M_+ 2);
      m01 =_mm_load1_pd (M_+16);
      m11 =_mm_load1_pd (M_+18);

      in00 =_mm_load_pd (IN0_  );
      in10 =_mm_load_pd (IN0_+2);
      in01 =_mm_load_pd (IN1_  );
      in11 =_mm_load_pd (IN1_+2);

      out00 = _mm_add_pd   (out00, _mm_mul_pd(m00 , in00 ));
      out00 = _mm_add_pd   (out00, _mm_mul_pd(m01 , in10 ));
      out01 = _mm_add_pd   (out01, _mm_mul_pd(m00 , in01 ));
      out01 = _mm_add_pd   (out01, _mm_mul_pd(m01 , in11 ));
      out10 = _mm_add_pd   (out10, _mm_mul_pd(m10 , in00 ));
      out10 = _mm_add_pd   (out10, _mm_mul_pd(m11 , in10 ));
      out11 = _mm_add_pd   (out11, _mm_mul_pd(m10 , in01 ));
      out11 = _mm_add_pd   (out11, _mm_mul_pd(m11 , in11 ));


      m00 =_mm_load1_pd (M_+   1);
      m10 =_mm_load1_pd (M_+ 2+1);
      m01 =_mm_load1_pd (M_+16+1);
      m11 =_mm_load1_pd (M_+18+1);
      in00 =_mm_shuffle_pd (in00,in00,_MM_SHUFFLE2(0,1));
      in01 =_mm_shuffle_pd (in01,in01,_MM_SHUFFLE2(0,1));
      in10 =_mm_shuffle_pd (in10,in10,_MM_SHUFFLE2(0,1));
      in11 =_mm_shuffle_pd (in11,in11,_MM_SHUFFLE2(0,1));
      out00 = _mm_addsub_pd(out00, _mm_mul_pd(m00, in00));
      out00 = _mm_addsub_pd(out00, _mm_mul_pd(m01, in10));
      out01 = _mm_addsub_pd(out01, _mm_mul_pd(m00, in01));
      out01 = _mm_addsub_pd(out01, _mm_mul_pd(m01, in11));
      out10 = _mm_addsub_pd(out10, _mm_mul_pd(m10, in00));
      out10 = _mm_addsub_pd(out10, _mm_mul_pd(m11, in10));
      out11 = _mm_addsub_pd(out11, _mm_mul_pd(m10, in01));
      out11 = _mm_addsub_pd(out11, _mm_mul_pd(m11, in11));

      M_+=32; // Jump to (column+2).
      IN0_+=4;
      IN1_+=4;
    }
    _mm_store_pd (OUT0  ,out00);
    _mm_store_pd (OUT0+2,out10);
    _mm_store_pd (OUT1  ,out01);
    _mm_store_pd (OUT1+2,out11);
    M_+=4-64*2; // Jump back to first column (row+2).
    OUT0+=4;
    OUT1+=4;
  }
#endif
}
#endif

#if defined(__SSE3__)
template<>
inline void matmult_8x8x2<float>(float*& M_, float*& IN0, float*& IN1, float*& OUT0, float*& OUT1){
#if defined __SSE3__ // SSE code.
  __m128 out00,out01,out10,out11;
  __m128 out20,out21,out30,out31;
  float* in0__ = IN0;
  float* in1__ = IN1;

  out00 = _mm_load_ps(OUT0);
  out01 = _mm_load_ps(OUT1);
  out10 = _mm_load_ps(OUT0+4);
  out11 = _mm_load_ps(OUT1+4);
  out20 = _mm_load_ps(OUT0+8);
  out21 = _mm_load_ps(OUT1+8);
  out30 = _mm_load_ps(OUT0+12);
  out31 = _mm_load_ps(OUT1+12);
  for(int i2=0;i2<8;i2+=2){
    __m128 m00;
    __m128 ot00;
    __m128 mt0,mtt0;
    __m128 in00,in00_r,in01,in01_r;



    in00 = _mm_castpd_ps(_mm_load_pd1((const double*)in0__));
    in00_r = _mm_shuffle_ps(in00,in00,_MM_SHUFFLE(2,3,0,1));
    in01 = _mm_castpd_ps(_mm_load_pd1((const double*)in1__));
    in01_r = _mm_shuffle_ps(in01,in01,_MM_SHUFFLE(2,3,0,1));

    m00 = _mm_load_ps(M_);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out00= _mm_add_ps   (out00,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out00= _mm_addsub_ps(out00,_mm_mul_ps(mtt0,in00_r));

    out01 = _mm_add_ps   (out01,_mm_mul_ps( mt0,in01  ));
    out01 = _mm_addsub_ps(out01,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+4);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out10= _mm_add_ps   (out10,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out10= _mm_addsub_ps(out10,_mm_mul_ps(mtt0,in00_r));

    out11 = _mm_add_ps   (out11,_mm_mul_ps( mt0,in01  ));
    out11 = _mm_addsub_ps(out11,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+8);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out20= _mm_add_ps   (out20,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out20= _mm_addsub_ps(out20,_mm_mul_ps(mtt0,in00_r));

    out21 = _mm_add_ps   (out21,_mm_mul_ps( mt0,in01  ));
    out21 = _mm_addsub_ps(out21,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+12);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out30= _mm_add_ps   (out30,_mm_mul_ps( mt0,  in00));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out30= _mm_addsub_ps(out30,_mm_mul_ps(mtt0,in00_r));

    out31 = _mm_add_ps   (out31,_mm_mul_ps( mt0,in01  ));
    out31 = _mm_addsub_ps(out31,_mm_mul_ps(mtt0,in01_r));



    in00 = _mm_castpd_ps(_mm_load_pd1((const double*) (in0__+2)));
    in00_r = _mm_shuffle_ps(in00,in00,_MM_SHUFFLE(2,3,0,1));
    in01 = _mm_castpd_ps(_mm_load_pd1((const double*) (in1__+2)));
    in01_r = _mm_shuffle_ps(in01,in01,_MM_SHUFFLE(2,3,0,1));

    m00 = _mm_load_ps(M_+16);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out00= _mm_add_ps   (out00,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out00= _mm_addsub_ps(out00,_mm_mul_ps(mtt0,in00_r));

    out01 = _mm_add_ps   (out01,_mm_mul_ps( mt0,in01  ));
    out01 = _mm_addsub_ps(out01,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+20);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out10= _mm_add_ps   (out10,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out10= _mm_addsub_ps(out10,_mm_mul_ps(mtt0,in00_r));

    out11 = _mm_add_ps   (out11,_mm_mul_ps( mt0,in01 ));
    out11 = _mm_addsub_ps(out11,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+24);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out20= _mm_add_ps   (out20,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out20= _mm_addsub_ps(out20,_mm_mul_ps(mtt0,in00_r));

    out21 = _mm_add_ps   (out21,_mm_mul_ps( mt0,in01  ));
    out21 = _mm_addsub_ps(out21,_mm_mul_ps(mtt0,in01_r));

    m00 = _mm_load_ps(M_+28);

    mt0  = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(2,2,0,0));
    out30= _mm_add_ps   (out30,_mm_mul_ps( mt0,in00  ));
    mtt0 = _mm_shuffle_ps(m00,m00,_MM_SHUFFLE(3,3,1,1));
    out30= _mm_addsub_ps(out30,_mm_mul_ps(mtt0,in00_r));

    out31 = _mm_add_ps   (out31,_mm_mul_ps( mt0,in01  ));
    out31 = _mm_addsub_ps(out31,_mm_mul_ps(mtt0,in01_r));

    M_ += 32;
    in0__ += 4;
    in1__ += 4;
  }
  _mm_store_ps(OUT0,out00);
  _mm_store_ps(OUT1,out01);
  _mm_store_ps(OUT0+4,out10);
  _mm_store_ps(OUT1+4,out11);
  _mm_store_ps(OUT0+8,out20);
  _mm_store_ps(OUT1+8,out21);
  _mm_store_ps(OUT0+12,out30);
  _mm_store_ps(OUT1+12,out31);
#endif
}
#endif

template <class Real_t>
void VListHadamard(size_t dof, size_t M_dim, size_t ker_dim0, size_t ker_dim1, Vector<size_t>& interac_dsp,
    Vector<size_t>& interac_vec, Vector<Real_t*>& precomp_mat, Vector<Real_t>& fft_in, Vector<Real_t>& fft_out){

  size_t chld_cnt=1UL<<COORD_DIM;
  size_t fftsize_in =M_dim*ker_dim0*chld_cnt*2;
  size_t fftsize_out=M_dim*ker_dim1*chld_cnt*2;
  Real_t* zero_vec0=mem::aligned_new<Real_t>(fftsize_in );
  Real_t* zero_vec1=mem::aligned_new<Real_t>(fftsize_out);
  size_t n_out=fft_out.Dim()/fftsize_out;

  // Set buff_out to zero.
  #pragma omp parallel for
  for(size_t k=0;k<n_out;k++){
    Vector<Real_t> dnward_check_fft(fftsize_out, &fft_out[k*fftsize_out], false);
    dnward_check_fft.SetZero();
  }

  // Build list of interaction pairs (in, out vectors).
  size_t mat_cnt=precomp_mat.Dim();
  size_t blk1_cnt=interac_dsp.Dim()/mat_cnt;
  const size_t V_BLK_SIZE=V_BLK_CACHE*64/sizeof(Real_t);
  Real_t** IN_ =mem::aligned_new<Real_t*>(2*V_BLK_SIZE*blk1_cnt*mat_cnt);
  Real_t** OUT_=mem::aligned_new<Real_t*>(2*V_BLK_SIZE*blk1_cnt*mat_cnt);
  #pragma omp parallel for
  for(size_t interac_blk1=0; interac_blk1<blk1_cnt*mat_cnt; interac_blk1++){
    size_t interac_dsp0 = (interac_blk1==0?0:interac_dsp[interac_blk1-1]);
    size_t interac_dsp1 =                    interac_dsp[interac_blk1  ] ;
    size_t interac_cnt  = interac_dsp1-interac_dsp0;
    for(size_t j=0;j<interac_cnt;j++){
      IN_ [2*V_BLK_SIZE*interac_blk1 +j]=&fft_in [interac_vec[(interac_dsp0+j)*2+0]];
      OUT_[2*V_BLK_SIZE*interac_blk1 +j]=&fft_out[interac_vec[(interac_dsp0+j)*2+1]];
    }
    IN_ [2*V_BLK_SIZE*interac_blk1 +interac_cnt]=zero_vec0;
    OUT_[2*V_BLK_SIZE*interac_blk1 +interac_cnt]=zero_vec1;
  }

  int omp_p=omp_get_max_threads();
  #pragma omp parallel for
  for(int pid=0; pid<omp_p; pid++){
    size_t a=( pid   *M_dim)/omp_p;
    size_t b=((pid+1)*M_dim)/omp_p;

    for(int in_dim=0;in_dim<ker_dim0;in_dim++)
    for(int ot_dim=0;ot_dim<ker_dim1;ot_dim++)
    for(size_t     blk1=0;     blk1<blk1_cnt;    blk1++)
    for(size_t        k=a;        k<       b;       k++)
    for(size_t mat_indx=0; mat_indx< mat_cnt;mat_indx++){
      size_t interac_blk1 = blk1*mat_cnt+mat_indx;
      size_t interac_dsp0 = (interac_blk1==0?0:interac_dsp[interac_blk1-1]);
      size_t interac_dsp1 =                    interac_dsp[interac_blk1  ] ;
      size_t interac_cnt  = interac_dsp1-interac_dsp0;

      Real_t** IN = IN_ + 2*V_BLK_SIZE*interac_blk1;
      Real_t** OUT= OUT_+ 2*V_BLK_SIZE*interac_blk1;

      Real_t* M = precomp_mat[mat_indx] + k*chld_cnt*chld_cnt*2 + (ot_dim+in_dim*ker_dim1)*M_dim*128;
      {
        for(size_t j=0;j<interac_cnt;j+=2){
          Real_t* M_   = M;
          Real_t* IN0  = IN [j+0] + (in_dim*M_dim+k)*chld_cnt*2;
          Real_t* IN1  = IN [j+1] + (in_dim*M_dim+k)*chld_cnt*2;
          Real_t* OUT0 = OUT[j+0] + (ot_dim*M_dim+k)*chld_cnt*2;
          Real_t* OUT1 = OUT[j+1] + (ot_dim*M_dim+k)*chld_cnt*2;

#ifdef __SSE__
          if (j+2 < interac_cnt) { // Prefetch
            _mm_prefetch(((char *)(IN[j+2] + (in_dim*M_dim+k)*chld_cnt*2)), _MM_HINT_T0);
            _mm_prefetch(((char *)(IN[j+2] + (in_dim*M_dim+k)*chld_cnt*2) + 64), _MM_HINT_T0);
            _mm_prefetch(((char *)(IN[j+3] + (in_dim*M_dim+k)*chld_cnt*2)), _MM_HINT_T0);
            _mm_prefetch(((char *)(IN[j+3] + (in_dim*M_dim+k)*chld_cnt*2) + 64), _MM_HINT_T0);

            _mm_prefetch(((char *)(OUT[j+2] + (ot_dim*M_dim+k)*chld_cnt*2)), _MM_HINT_T0);
            _mm_prefetch(((char *)(OUT[j+2] + (ot_dim*M_dim+k)*chld_cnt*2) + 64), _MM_HINT_T0);
            _mm_prefetch(((char *)(OUT[j+3] + (ot_dim*M_dim+k)*chld_cnt*2)), _MM_HINT_T0);
            _mm_prefetch(((char *)(OUT[j+3] + (ot_dim*M_dim+k)*chld_cnt*2) + 64), _MM_HINT_T0);
          }
#endif

          matmult_8x8x2(M_, IN0, IN1, OUT0, OUT1);
        }
      }
    }
  }

  // Compute flops.
  {
    Profile::Add_FLOP(8*8*8*(interac_vec.Dim()/2)*M_dim*ker_dim0*ker_dim1*dof);
  }

  // Free memory
  mem::aligned_delete<Real_t*>(IN_ );
  mem::aligned_delete<Real_t*>(OUT_);
  mem::aligned_delete<Real_t>(zero_vec0);
  mem::aligned_delete<Real_t>(zero_vec1);
}

template <class FMMNode>
void FMM_Pts<FMMNode>::V_ListSetup(SetupData<Real_t>&  setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  if(level==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=aux_kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=V1_Type;

    setup_data. input_data=&buff[0];
    setup_data.output_data=&buff[1];
    Vector<FMMNode_t*>& nodes_in =n_list[2];
    Vector<FMMNode_t*>& nodes_out=n_list[3];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level-1 || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level-1 || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }
  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++)  input_vector.push_back(&((FMMData*)((FMMNode*)((FMMNode*)nodes_in [i])->Child(0))->FMMData())->upward_equiv);
  for(size_t i=0;i<nodes_out.size();i++) output_vector.push_back(&((FMMData*)((FMMNode*)((FMMNode*)nodes_out[i])->Child(0))->FMMData())->dnward_equiv);

  /////////////////////////////////////////////////////////////////////////////

  size_t n_in =nodes_in .size();
  size_t n_out=nodes_out.size();

  // Setup precomputed data.
  SetupPrecomp(setup_data,device);

  // Build interac_data
  Profile::Tic("Interac-Data",&this->comm,true,25);
  Matrix<char>& interac_data=setup_data.interac_data;
  if(n_out>0 && n_in >0){ // Build precomp_data, interac_data

    size_t precomp_offset=0;
    Mat_Type& interac_type=setup_data.interac_type[0];
    size_t mat_cnt=this->interac_list.ListCount(interac_type);
    Matrix<size_t> precomp_data_offset;
    std::vector<size_t> interac_mat;
    { // Load precomp_data for interac_type.
      Matrix<char>& precomp_data=*setup_data.precomp_data;
      char* indx_ptr=precomp_data[0]+precomp_offset;
      size_t total_size=((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
      size_t mat_cnt_  =((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
      size_t max_depth =((size_t*)indx_ptr)[0]; indx_ptr+=sizeof(size_t);
      precomp_data_offset.ReInit(mat_cnt_,1+(2+2)*max_depth, (size_t*)indx_ptr, false);
      precomp_offset+=total_size;
      for(size_t mat_id=0;mat_id<mat_cnt;mat_id++){
        Matrix<Real_t>& M0 = this->mat->Mat(level, interac_type, mat_id);
        assert(M0.Dim(0)>0 && M0.Dim(1)>0); UNUSED(M0);
        interac_mat.push_back(precomp_data_offset[mat_id][0]);
      }
    }

    size_t dof;
    size_t m=MultipoleOrder();
    size_t ker_dim0=setup_data.kernel->ker_dim[0];
    size_t ker_dim1=setup_data.kernel->ker_dim[1];
    size_t fftsize;
    {
      size_t n1=m*2;
      size_t n2=n1*n1;
      size_t n3_=n2*(n1/2+1);
      size_t chld_cnt=1UL<<COORD_DIM;
      fftsize=2*n3_*chld_cnt;
      dof=1;
    }

    int omp_p=omp_get_max_threads();
    size_t buff_size=DEVICE_BUFFER_SIZE*1024l*1024l;
    size_t n_blk0=2*fftsize*dof*(ker_dim0*n_in +ker_dim1*n_out)*sizeof(Real_t)/buff_size;
    if(n_blk0==0) n_blk0=1;

    std::vector<std::vector<size_t> >  fft_vec(n_blk0);
    std::vector<std::vector<size_t> > ifft_vec(n_blk0);
    std::vector<std::vector<size_t> > interac_vec(n_blk0);
    std::vector<std::vector<size_t> > interac_dsp(n_blk0);
    {
      Matrix<Real_t>&  input_data=*setup_data. input_data;
      Matrix<Real_t>& output_data=*setup_data.output_data;
      std::vector<std::vector<FMMNode*> > nodes_blk_in (n_blk0);
      std::vector<std::vector<FMMNode*> > nodes_blk_out(n_blk0);

      for(size_t i=0;i<n_in;i++) ((FMMNode*)nodes_in[i])->node_id=i;
      for(size_t blk0=0;blk0<n_blk0;blk0++){
        size_t blk0_start=(n_out* blk0   )/n_blk0;
        size_t blk0_end  =(n_out*(blk0+1))/n_blk0;

        std::vector<FMMNode*>& nodes_in_ =nodes_blk_in [blk0];
        std::vector<FMMNode*>& nodes_out_=nodes_blk_out[blk0];
        { // Build node list for blk0.
          std::set<void*> nodes_in;
          for(size_t i=blk0_start;i<blk0_end;i++){
            nodes_out_.push_back((FMMNode*)nodes_out[i]);
            std::vector<FMMNode*>& lst=((FMMNode*)nodes_out[i])->interac_list[interac_type];
            for(size_t k=0;k<mat_cnt;k++) if(lst[k]!=NULL) nodes_in.insert(lst[k]);
          }
          for(std::set<void*>::iterator node=nodes_in.begin(); node != nodes_in.end(); node++){
            nodes_in_.push_back((FMMNode*)*node);
          }

          size_t  input_dim=nodes_in_ .size()*ker_dim0*dof*fftsize;
          size_t output_dim=nodes_out_.size()*ker_dim1*dof*fftsize;
          size_t buffer_dim=(ker_dim0+ker_dim1)*dof*fftsize*omp_p;
          if(buff_size<(input_dim + output_dim + buffer_dim)*sizeof(Real_t))
            buff_size=(input_dim + output_dim + buffer_dim)*sizeof(Real_t);
        }

        { // Set fft vectors.
          for(size_t i=0;i<nodes_in_ .size();i++) fft_vec[blk0].push_back((size_t)(& input_vector[nodes_in_[i]->node_id][0][0]- input_data[0]));
          for(size_t i=0;i<nodes_out_.size();i++)ifft_vec[blk0].push_back((size_t)(&output_vector[blk0_start   +     i ][0][0]-output_data[0]));
        }
      }

      for(size_t blk0=0;blk0<n_blk0;blk0++){ // Hadamard interactions.
        std::vector<FMMNode*>& nodes_in_ =nodes_blk_in [blk0];
        std::vector<FMMNode*>& nodes_out_=nodes_blk_out[blk0];
        for(size_t i=0;i<nodes_in_.size();i++) nodes_in_[i]->node_id=i;
        { // Next blocking level.
          size_t n_blk1=nodes_out_.size()*(2)*sizeof(Real_t)/(64*V_BLK_CACHE);
          if(n_blk1==0) n_blk1=1;

          size_t interac_dsp_=0;
          for(size_t blk1=0;blk1<n_blk1;blk1++){
            size_t blk1_start=(nodes_out_.size()* blk1   )/n_blk1;
            size_t blk1_end  =(nodes_out_.size()*(blk1+1))/n_blk1;
            for(size_t k=0;k<mat_cnt;k++){
              for(size_t i=blk1_start;i<blk1_end;i++){
                std::vector<FMMNode*>& lst=((FMMNode*)nodes_out_[i])->interac_list[interac_type];
                if(lst[k]!=NULL){
                  interac_vec[blk0].push_back(lst[k]->node_id*fftsize*ker_dim0*dof);
                  interac_vec[blk0].push_back(    i          *fftsize*ker_dim1*dof);
                  interac_dsp_++;
                }
              }
              interac_dsp[blk0].push_back(interac_dsp_);
            }
          }
        }
      }
    }

    { // Set interac_data.
      size_t data_size=sizeof(size_t)*6; // buff_size, m, dof, ker_dim0, ker_dim1, n_blk0
      for(size_t blk0=0;blk0<n_blk0;blk0++){
        data_size+=sizeof(size_t)+    fft_vec[blk0].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+   ifft_vec[blk0].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+interac_vec[blk0].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+interac_dsp[blk0].size()*sizeof(size_t);
      }
      data_size+=sizeof(size_t)+interac_mat.size()*sizeof(size_t);
      if(data_size>interac_data.Dim(0)*interac_data.Dim(1))
        interac_data.Resize(1,data_size);
      char* data_ptr=&interac_data[0][0];

      ((size_t*)data_ptr)[0]=buff_size; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=        m; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=      dof; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]= ker_dim0; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]= ker_dim1; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=   n_blk0; data_ptr+=sizeof(size_t);

      ((size_t*)data_ptr)[0]= interac_mat.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &interac_mat[0], interac_mat.size()*sizeof(size_t));
      data_ptr+=interac_mat.size()*sizeof(size_t);

      for(size_t blk0=0;blk0<n_blk0;blk0++){
        ((size_t*)data_ptr)[0]= fft_vec[blk0].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, & fft_vec[blk0][0],  fft_vec[blk0].size()*sizeof(size_t));
        data_ptr+= fft_vec[blk0].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=ifft_vec[blk0].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &ifft_vec[blk0][0], ifft_vec[blk0].size()*sizeof(size_t));
        data_ptr+=ifft_vec[blk0].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=interac_vec[blk0].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &interac_vec[blk0][0], interac_vec[blk0].size()*sizeof(size_t));
        data_ptr+=interac_vec[blk0].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=interac_dsp[blk0].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &interac_dsp[blk0][0], interac_dsp[blk0].size()*sizeof(size_t));
        data_ptr+=interac_dsp[blk0].size()*sizeof(size_t);
      }
    }
  }
  Profile::Toc();

  Profile::Tic("Host2Device",&this->comm,false,25);
  if(device){ // Host2Device
    setup_data.interac_data. AllocDevice(true);
  }
  Profile::Toc();
}

template <class FMMNode>
void FMM_Pts<FMMNode>::V_List     (SetupData<Real_t>&  setup_data, bool device){
  assert(!device); //Can not run on accelerator yet.

  int np;
  MPI_Comm_size(comm,&np);
  if(setup_data.interac_data.Dim(0)==0 || setup_data.interac_data.Dim(1)==0){
    if(np>1) Profile::Tic("Host2Device",&this->comm,false,25);
    if(np>1) Profile::Toc();
    return;
  }

  Profile::Tic("Host2Device",&this->comm,false,25);
  int level=setup_data.level;
  size_t buff_size=*((size_t*)&setup_data.interac_data[0][0]);
  typename Matrix<Real_t>::Device         M_d;
  typename Vector<char>::Device          buff;
  typename Matrix<char>::Device  precomp_data;
  typename Matrix<char>::Device  interac_data;
  typename Matrix<Real_t>::Device  input_data;
  typename Matrix<Real_t>::Device output_data;
  Matrix<Real_t>& M = this->mat->Mat(level, DC2DE_Type, 0);

  if(device){
    if(this->dev_buffer.Dim()<buff_size) this->dev_buffer.Resize(buff_size);
    M_d         =                       M. AllocDevice(false);
    buff        =       this-> dev_buffer. AllocDevice(false);
    precomp_data= setup_data.precomp_data->AllocDevice(false);
    interac_data= setup_data.interac_data. AllocDevice(false);
    input_data  = setup_data.  input_data->AllocDevice(false);
    output_data = setup_data. output_data->AllocDevice(false);
  }else{
    if(this->cpu_buffer.Dim()<buff_size) this->cpu_buffer.Resize(buff_size);
    M_d         =                       M;
    buff        =       this-> cpu_buffer;
    precomp_data=*setup_data.precomp_data;
    interac_data= setup_data.interac_data;
    input_data  =*setup_data.  input_data;
    output_data =*setup_data. output_data;
  }
  Profile::Toc();

  { // Offloaded computation.

    // Set interac_data.
    size_t m, dof, ker_dim0, ker_dim1, n_blk0;
    std::vector<Vector<size_t> >  fft_vec;
    std::vector<Vector<size_t> > ifft_vec;
    std::vector<Vector<size_t> > interac_vec;
    std::vector<Vector<size_t> > interac_dsp;
    Vector<Real_t*> precomp_mat;
    { // Set interac_data.
      char* data_ptr=&interac_data[0][0];

      buff_size=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      m        =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      dof      =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      ker_dim0 =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      ker_dim1 =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      n_blk0   =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);

      fft_vec .resize(n_blk0);
      ifft_vec.resize(n_blk0);
      interac_vec.resize(n_blk0);
      interac_dsp.resize(n_blk0);

      Vector<size_t> interac_mat;
      interac_mat.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+interac_mat.Dim()*sizeof(size_t);
      precomp_mat.Resize(interac_mat.Dim());
      for(size_t i=0;i<interac_mat.Dim();i++){
        precomp_mat[i]=(Real_t*)(precomp_data[0]+interac_mat[i]);
      }

      for(size_t blk0=0;blk0<n_blk0;blk0++){
        fft_vec[blk0].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+fft_vec[blk0].Dim()*sizeof(size_t);

        ifft_vec[blk0].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+ifft_vec[blk0].Dim()*sizeof(size_t);

        interac_vec[blk0].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+interac_vec[blk0].Dim()*sizeof(size_t);

        interac_dsp[blk0].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+interac_dsp[blk0].Dim()*sizeof(size_t);
      }
    }

    int omp_p=omp_get_max_threads();
    size_t M_dim, fftsize;
    {
      size_t n1=m*2;
      size_t n2=n1*n1;
      size_t n3_=n2*(n1/2+1);
      size_t chld_cnt=1UL<<COORD_DIM;
      fftsize=2*n3_*chld_cnt;
      M_dim=n3_;
    }

    for(size_t blk0=0;blk0<n_blk0;blk0++){ // interactions
      size_t n_in = fft_vec[blk0].Dim();
      size_t n_out=ifft_vec[blk0].Dim();

      size_t  input_dim=n_in *ker_dim0*dof*fftsize;
      size_t output_dim=n_out*ker_dim1*dof*fftsize;
      size_t buffer_dim=(ker_dim0+ker_dim1)*dof*fftsize*omp_p;

      Vector<Real_t> fft_in ( input_dim, (Real_t*)&buff[         0                           ],false);
      Vector<Real_t> fft_out(output_dim, (Real_t*)&buff[ input_dim            *sizeof(Real_t)],false);
      Vector<Real_t>  buffer(buffer_dim, (Real_t*)&buff[(input_dim+output_dim)*sizeof(Real_t)],false);

      { //  FFT
        if(np==1) Profile::Tic("FFT",&comm,false,100);
        Vector<Real_t>  input_data_( input_data.dim[0]* input_data.dim[1],  input_data[0], false);
        FFT_UpEquiv(dof, m, ker_dim0,  fft_vec[blk0],  input_data_, fft_in, buffer);
        if(np==1) Profile::Toc();
      }
      { // Hadamard
#ifdef PVFMM_HAVE_PAPI
#ifdef __VERBOSE__
        std::cout << "Starting counters new\n";
        if (PAPI_start(EventSet) != PAPI_OK) std::cout << "handle_error3" << std::endl;
#endif
#endif
        if(np==1) Profile::Tic("HadamardProduct",&comm,false,100);
        VListHadamard<Real_t>(dof, M_dim, ker_dim0, ker_dim1, interac_dsp[blk0], interac_vec[blk0], precomp_mat, fft_in, fft_out);
        if(np==1) Profile::Toc();
#ifdef PVFMM_HAVE_PAPI
#ifdef __VERBOSE__
        if (PAPI_stop(EventSet, values) != PAPI_OK) std::cout << "handle_error4" << std::endl;
        std::cout << "Stopping counters\n";
#endif
#endif
      }
      { // IFFT
        if(np==1) Profile::Tic("IFFT",&comm,false,100);
        Matrix<Real_t> M(M_d.dim[0],M_d.dim[1],M_d[0],false);
        Vector<Real_t> output_data_(output_data.dim[0]*output_data.dim[1], output_data[0], false);
        FFT_Check2Equiv(dof, m, ker_dim1, ifft_vec[blk0], fft_out, output_data_, buffer, M);
        if(np==1) Profile::Toc();
      }
    }
  }
}



template <class FMMNode>
void FMM_Pts<FMMNode>::Down2DownSetup(SetupData<Real_t>& setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=aux_kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=D2D_Type;

    setup_data. input_data=&buff[1];
    setup_data.output_data=&buff[1];
    Vector<FMMNode_t*>& nodes_in =n_list[1];
    Vector<FMMNode_t*>& nodes_out=n_list[1];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level  ) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++)  input_vector.push_back(&((FMMData*)((FMMNode*)nodes_in [i])->FMMData())->dnward_equiv);
  for(size_t i=0;i<nodes_out.size();i++) output_vector.push_back(&((FMMData*)((FMMNode*)nodes_out[i])->FMMData())->dnward_equiv);

  SetupInterac(setup_data,device);
}

template <class FMMNode>
void FMM_Pts<FMMNode>::Down2Down     (SetupData<Real_t>& setup_data, bool device){
  //Add Down2Down contribution.
  EvalList(setup_data, device);
}





template <class FMMNode>
void FMM_Pts<FMMNode>::SetupInteracPts(SetupData<Real_t>& setup_data, bool shift_src, bool shift_trg, Matrix<Real_t>* M, bool device){
  int level=setup_data.level;
  std::vector<Mat_Type>& interac_type_lst=setup_data.interac_type;

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  Matrix<Real_t>& output_data=*setup_data.output_data;
  Matrix<Real_t>&  input_data=*setup_data. input_data;
  Matrix<Real_t>&  coord_data=*setup_data. coord_data;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector;

  size_t n_in =nodes_in .size();
  size_t n_out=nodes_out.size();
  //setup_data.precomp_data=NULL;

  // Build interac_data
  Profile::Tic("Interac-Data",&this->comm,true,25);
  Matrix<char>& interac_data=setup_data.interac_data;
  if(n_out>0 && n_in >0){
    size_t ker_dim0=setup_data.kernel->ker_dim[0];
    size_t ker_dim1=setup_data.kernel->ker_dim[1];
    size_t dof=1;
    for(size_t i=0;i<n_in ;i++) ((FMMNode*)nodes_in [i])->node_id=i;

    std::vector<size_t> trg_interac_cnt(n_out,0);
    std::vector<size_t> trg_coord(n_out);
    std::vector<size_t> trg_value(n_out);
    std::vector<size_t> trg_cnt(n_out);
    std::vector<Real_t> scaling(n_out*(ker_dim0+ker_dim1),0);
    { // Set trg data
      Mat_Type& interac_type=interac_type_lst[0];
      for(size_t i=0;i<n_out;i++){
        if(!((FMMNode*)nodes_out[i])->IsGhost() && (level==-1 || ((FMMNode*)nodes_out[i])->Depth()==level)){
          trg_cnt  [i]=output_vector[i*2+0]->Dim()/COORD_DIM;
          trg_coord[i]=(size_t)(&output_vector[i*2+0][0][0]- coord_data[0]);
          trg_value[i]=(size_t)(&output_vector[i*2+1][0][0]-output_data[0]);

          Real_t* s=&scaling[i*(ker_dim0+ker_dim1)];
          for(size_t j=0;j<ker_dim1;j++){
            if(!this->Homogen()) s[j]=1.0;
            else if(interac_type==S2U_Type) s[         j]=pow(0.5, setup_data.kernel->trg_scal[j]*((FMMNode*)nodes_out[i])->Depth());
            else if(interac_type==  X_Type) s[         j]=pow(0.5, setup_data.kernel->trg_scal[j]*((FMMNode*)nodes_out[i])->Depth());
          }
          for(size_t j=0;j<ker_dim0;j++){
            if(!this->Homogen()) s[ker_dim1+j]=1.0;
            else if(interac_type==S2U_Type) s[ker_dim1+j]=pow(0.5, setup_data.kernel->src_scal[j]*((FMMNode*)nodes_out[i])->Depth());
            else if(interac_type==  X_Type) s[ker_dim1+j]=pow(0.5, setup_data.kernel->src_scal[j]*((FMMNode*)nodes_out[i])->Depth());
          }
        }
      }
    }

    std::vector<std::vector<size_t> > src_cnt(n_out);
    std::vector<std::vector<size_t> > src_coord(n_out);
    std::vector<std::vector<size_t> > src_value(n_out);
    std::vector<std::vector<Real_t> > shift_coord(n_out);
    for(size_t type_indx=0; type_indx<interac_type_lst.size(); type_indx++){
      Mat_Type& interac_type=interac_type_lst[type_indx];
      size_t mat_cnt=this->interac_list.ListCount(interac_type);

      for(size_t i=0;i<n_out;i++){ // For each target node.
        if(!((FMMNode*)nodes_out[i])->IsGhost() && (level==-1 || ((FMMNode*)nodes_out[i])->Depth()==level)){
          std::vector<FMMNode*>& lst=((FMMNode*)nodes_out[i])->interac_list[interac_type];
          for(size_t mat_indx=0;mat_indx<mat_cnt;mat_indx++) if(lst[mat_indx]!=NULL){ // For each direction.
            size_t j=lst[mat_indx]->node_id;
            if(input_vector[j*4+0]->Dim()>0 || input_vector[j*4+2]->Dim()>0){
              trg_interac_cnt[i]++;
              { // Determine shift for periodic boundary condition
                Real_t* sc=lst[mat_indx]->Coord();
                Real_t* tc=((FMMNode*)nodes_out[i])->Coord();
                int* rel_coord=this->interac_list.RelativeCoord(interac_type, mat_indx);
                shift_coord[i].push_back((tc[0]>sc[0] && rel_coord[0]>0? 1.0:
                                         (tc[0]<sc[0] && rel_coord[0]<0?-1.0:0.0)) +
                                         (shift_src?sc[0]:0) - (shift_trg?tc[0]:0) );
                shift_coord[i].push_back((tc[1]>sc[1] && rel_coord[1]>0? 1.0:
                                         (tc[1]<sc[1] && rel_coord[1]<0?-1.0:0.0)) +
                                         (shift_src?sc[1]:0) - (shift_trg?tc[1]:0) );
                shift_coord[i].push_back((tc[2]>sc[2] && rel_coord[2]>0? 1.0:
                                         (tc[2]<sc[2] && rel_coord[2]<0?-1.0:0.0)) +
                                         (shift_src?sc[2]:0) - (shift_trg?tc[2]:0) );
              }

              { // Set src data
                if(input_vector[j*4+0]!=NULL){
                  src_cnt  [i].push_back(input_vector[j*4+0]->Dim()/COORD_DIM);
                  src_coord[i].push_back((size_t)(& input_vector[j*4+0][0][0]- coord_data[0]));
                  src_value[i].push_back((size_t)(& input_vector[j*4+1][0][0]- input_data[0]));
                }else{
                  src_cnt  [i].push_back(0);
                  src_coord[i].push_back(0);
                  src_value[i].push_back(0);
                }
                if(input_vector[j*4+2]!=NULL){
                  src_cnt  [i].push_back(input_vector[j*4+2]->Dim()/COORD_DIM);
                  src_coord[i].push_back((size_t)(& input_vector[j*4+2][0][0]- coord_data[0]));
                  src_value[i].push_back((size_t)(& input_vector[j*4+3][0][0]- input_data[0]));
                }else{
                  src_cnt  [i].push_back(0);
                  src_coord[i].push_back(0);
                  src_value[i].push_back(0);
                }
              }
            }
          }
        }
      }
    }

    { // Set interac_data.
      size_t data_size=sizeof(size_t)*4;
      data_size+=sizeof(size_t)+trg_interac_cnt.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+trg_coord.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+trg_value.size()*sizeof(size_t);
      data_size+=sizeof(size_t)+trg_cnt  .size()*sizeof(size_t);
      data_size+=sizeof(size_t)+scaling  .size()*sizeof(Real_t);
      data_size+=sizeof(size_t)*2+(M!=NULL?M->Dim(0)*M->Dim(1)*sizeof(Real_t):0);
      for(size_t i=0;i<n_out;i++){
        data_size+=sizeof(size_t)+src_cnt  [i].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+src_coord[i].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+src_value[i].size()*sizeof(size_t);
        data_size+=sizeof(size_t)+shift_coord[i].size()*sizeof(Real_t);
      }
      if(data_size>interac_data.Dim(0)*interac_data.Dim(1))
        interac_data.Resize(1,data_size);
      char* data_ptr=&interac_data[0][0];

      ((size_t*)data_ptr)[0]=data_size; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]= ker_dim0; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]= ker_dim1; data_ptr+=sizeof(size_t);
      ((size_t*)data_ptr)[0]=      dof; data_ptr+=sizeof(size_t);

      ((size_t*)data_ptr)[0]=trg_interac_cnt.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &trg_interac_cnt[0], trg_interac_cnt.size()*sizeof(size_t));
      data_ptr+=trg_interac_cnt.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=trg_coord.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &trg_coord[0], trg_coord.size()*sizeof(size_t));
      data_ptr+=trg_coord.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=trg_value.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &trg_value[0], trg_value.size()*sizeof(size_t));
      data_ptr+=trg_value.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=trg_cnt.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &trg_cnt[0], trg_cnt.size()*sizeof(size_t));
      data_ptr+=trg_cnt.size()*sizeof(size_t);

      ((size_t*)data_ptr)[0]=scaling.size(); data_ptr+=sizeof(size_t);
      mem::memcopy(data_ptr, &scaling[0], scaling.size()*sizeof(Real_t));
      data_ptr+=scaling.size()*sizeof(Real_t);

      if(M!=NULL){
        ((size_t*)data_ptr)[0]=M->Dim(0); data_ptr+=sizeof(size_t);
        ((size_t*)data_ptr)[0]=M->Dim(1); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, M[0][0], M->Dim(0)*M->Dim(1)*sizeof(Real_t));
        data_ptr+=M->Dim(0)*M->Dim(1)*sizeof(Real_t);
      }else{
        ((size_t*)data_ptr)[0]=0; data_ptr+=sizeof(size_t);
        ((size_t*)data_ptr)[0]=0; data_ptr+=sizeof(size_t);
      }

      for(size_t i=0;i<n_out;i++){
        ((size_t*)data_ptr)[0]=src_cnt[i].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &src_cnt[i][0], src_cnt[i].size()*sizeof(size_t));
        data_ptr+=src_cnt[i].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=src_coord[i].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &src_coord[i][0], src_coord[i].size()*sizeof(size_t));
        data_ptr+=src_coord[i].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=src_value[i].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &src_value[i][0], src_value[i].size()*sizeof(size_t));
        data_ptr+=src_value[i].size()*sizeof(size_t);

        ((size_t*)data_ptr)[0]=shift_coord[i].size(); data_ptr+=sizeof(size_t);
        mem::memcopy(data_ptr, &shift_coord[i][0], shift_coord[i].size()*sizeof(Real_t));
        data_ptr+=shift_coord[i].size()*sizeof(Real_t);
      }
    }

    size_t buff_size=DEVICE_BUFFER_SIZE*1024l*1024l;
    if(this->dev_buffer.Dim()<buff_size) this->dev_buffer.Resize(buff_size);
    if(this->cpu_buffer.Dim()<buff_size) this->cpu_buffer.Resize(buff_size);
  }
  Profile::Toc();

  Profile::Tic("Host2Device",&this->comm,false,25);
  if(device){ // Host2Device
    setup_data.interac_data .AllocDevice(true);
  }
  Profile::Toc();
}

template <class FMMNode>
template <int SYNC>
void FMM_Pts<FMMNode>::EvalListPts(SetupData<Real_t>& setup_data, bool device){
  if(setup_data.interac_data.Dim(0)==0 || setup_data.interac_data.Dim(1)==0){
    Profile::Tic("Host2Device",&this->comm,false,25);
    Profile::Toc();
    Profile::Tic("DeviceComp",&this->comm,false,20);
    Profile::Toc();
    return;
  }

  bool have_gpu=false;
#if defined(PVFMM_HAVE_CUDA)
  have_gpu=true;
#endif

  Profile::Tic("Host2Device",&this->comm,false,25);
  typename Vector<char>::Device          buff;
  //typename Matrix<char>::Device  precomp_data;
  typename Matrix<char>::Device  interac_data;
  typename Matrix<Real_t>::Device  coord_data;
  typename Matrix<Real_t>::Device  input_data;
  typename Matrix<Real_t>::Device output_data;
  if(device && !have_gpu){
    buff        =       this-> dev_buffer. AllocDevice(false);
    interac_data= setup_data.interac_data. AllocDevice(false);
    //if(setup_data.precomp_data!=NULL) precomp_data= setup_data.precomp_data->AllocDevice(false);
    if(setup_data.  coord_data!=NULL) coord_data  = setup_data.  coord_data->AllocDevice(false);
    if(setup_data.  input_data!=NULL) input_data  = setup_data.  input_data->AllocDevice(false);
    if(setup_data. output_data!=NULL) output_data = setup_data. output_data->AllocDevice(false);
  }else{
    buff        =       this-> cpu_buffer;
    interac_data= setup_data.interac_data;
    //if(setup_data.precomp_data!=NULL) precomp_data=*setup_data.precomp_data;
    if(setup_data.  coord_data!=NULL) coord_data  =*setup_data.  coord_data;
    if(setup_data.  input_data!=NULL) input_data  =*setup_data.  input_data;
    if(setup_data. output_data!=NULL) output_data =*setup_data. output_data;
  }
  Profile::Toc();

  size_t ptr_single_layer_kernel=(size_t)setup_data.kernel->ker_poten;
  size_t ptr_double_layer_kernel=(size_t)setup_data.kernel->dbl_layer_poten;

  Profile::Tic("DeviceComp",&this->comm,false,20);
  int lock_idx=-1;
  int wait_lock_idx=-1;
  if(device) wait_lock_idx=MIC_Lock::curr_lock();
  if(device) lock_idx=MIC_Lock::get_lock();
  #ifdef __INTEL_OFFLOAD
  if(device) ptr_single_layer_kernel=setup_data.kernel->dev_ker_poten;
  if(device) ptr_double_layer_kernel=setup_data.kernel->dev_dbl_layer_poten;
  #pragma offload if(device) target(mic:0) signal(&MIC_Lock::lock_vec[device?lock_idx:0])
  #endif
  { // Offloaded computation.

    // Set interac_data.
    size_t data_size;
    size_t ker_dim0;
    size_t ker_dim1;
    size_t dof, n_out;
    Vector<size_t> trg_interac_cnt;
    Vector<size_t> trg_coord;
    Vector<size_t> trg_value;
    Vector<size_t> trg_cnt;
    Vector<Real_t> scaling;
    Matrix<Real_t> M;
    Vector< Vector<size_t> > src_cnt;
    Vector< Vector<size_t> > src_coord;
    Vector< Vector<size_t> > src_value;
    Vector< Vector<Real_t> > shift_coord;
    { // Set interac_data.
      char* data_ptr=&interac_data[0][0];

      data_size=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      ker_dim0=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      ker_dim1=((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);
      dof     =((size_t*)data_ptr)[0]; data_ptr+=sizeof(size_t);

      trg_interac_cnt.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+trg_interac_cnt.Dim()*sizeof(size_t);
      n_out=trg_interac_cnt.Dim();

      trg_coord.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+trg_coord.Dim()*sizeof(size_t);

      trg_value.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+trg_value.Dim()*sizeof(size_t);

      trg_cnt.ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+trg_cnt.Dim()*sizeof(size_t);

      scaling.ReInit(((size_t*)data_ptr)[0],(Real_t*)(data_ptr+sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)+scaling.Dim()*sizeof(Real_t);

      M.ReInit(((size_t*)data_ptr)[0],((size_t*)data_ptr)[1],(Real_t*)(data_ptr+2*sizeof(size_t)),false);
      data_ptr+=sizeof(size_t)*2+M.Dim(0)*M.Dim(1)*sizeof(Real_t);

      src_cnt.Resize(n_out);
      src_coord.Resize(n_out);
      src_value.Resize(n_out);
      shift_coord.Resize(n_out);
      for(size_t i=0;i<n_out;i++){
        src_cnt[i].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+src_cnt[i].Dim()*sizeof(size_t);

        src_coord[i].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+src_coord[i].Dim()*sizeof(size_t);

        src_value[i].ReInit(((size_t*)data_ptr)[0],(size_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+src_value[i].Dim()*sizeof(size_t);

        shift_coord[i].ReInit(((size_t*)data_ptr)[0],(Real_t*)(data_ptr+sizeof(size_t)),false);
        data_ptr+=sizeof(size_t)+shift_coord[i].Dim()*sizeof(Real_t);
      }
    }

    if(device) MIC_Lock::wait_lock(wait_lock_idx);

    //Compute interaction from point sources.
    { // interactions
      typename Kernel<Real_t>::Ker_t single_layer_kernel=(typename Kernel<Real_t>::Ker_t)ptr_single_layer_kernel;
      typename Kernel<Real_t>::Ker_t double_layer_kernel=(typename Kernel<Real_t>::Ker_t)ptr_double_layer_kernel;

      int omp_p=omp_get_max_threads();
      Vector<Real_t*> thread_buff(omp_p);
      size_t thread_buff_size=buff.dim/sizeof(Real_t)/omp_p;
      for(int i=0;i<omp_p;i++) thread_buff[i]=(Real_t*)&buff[i*thread_buff_size*sizeof(Real_t)];

      #pragma omp parallel for schedule(dynamic)
      for(size_t i=0;i<n_out;i++)
      if(trg_interac_cnt[i]>0 && trg_cnt[i]>0){
        int thread_id=omp_get_thread_num();
        Real_t* s_coord=thread_buff[thread_id];
        Real_t* t_value=output_data[0]+trg_value[i];
        if(M.Dim(0)>0 && M.Dim(1)>0){
          s_coord+=dof*M.Dim(0);
          t_value=thread_buff[thread_id];
          for(size_t j=0;j<dof*M.Dim(0);j++) t_value[j]=0;
        }

        size_t interac_cnt=0;
        for(size_t j=0;j<trg_interac_cnt[i];j++){
          if(ptr_single_layer_kernel!=(size_t)NULL){// Single layer kernel
            Real_t* src_coord_=coord_data[0]+src_coord[i][2*j+0];
            assert(thread_buff_size>=dof*M.Dim(0)+dof*M.Dim(1)+src_cnt[i][2*j+0]*COORD_DIM);
            for(size_t k1=0;k1<src_cnt[i][2*j+0];k1++){ // Compute shifted source coordinates.
              for(size_t k0=0;k0<COORD_DIM;k0++){
                s_coord[k1*COORD_DIM+k0]=src_coord_[k1*COORD_DIM+k0]+shift_coord[i][j*COORD_DIM+k0];
              }
            }

            single_layer_kernel(                s_coord   , src_cnt[i][2*j+0], input_data[0]+src_value[i][2*j+0], dof,
                                coord_data[0]+trg_coord[i], trg_cnt[i]       , t_value, NULL);
            interac_cnt+=src_cnt[i][2*j+0]*trg_cnt[i];
          }else if(src_cnt[i][2*j+0]!=0 && trg_cnt[i]!=0){
            assert(ptr_single_layer_kernel); // Single-layer kernel not implemented
          }
          if(ptr_double_layer_kernel!=(size_t)NULL){// Double layer kernel
            Real_t* src_coord_=coord_data[0]+src_coord[i][2*j+1];
            assert(thread_buff_size>=dof*M.Dim(0)+dof*M.Dim(1)+src_cnt[i][2*j+1]*COORD_DIM);
            for(size_t k1=0;k1<src_cnt[i][2*j+1];k1++){ // Compute shifted source coordinates.
              for(size_t k0=0;k0<COORD_DIM;k0++){
                s_coord[k1*COORD_DIM+k0]=src_coord_[k1*COORD_DIM+k0]+shift_coord[i][j*COORD_DIM+k0];
              }
            }

            double_layer_kernel(                s_coord   , src_cnt[i][2*j+1], input_data[0]+src_value[i][2*j+1], dof,
                                coord_data[0]+trg_coord[i], trg_cnt[i]       , t_value, NULL);
            interac_cnt+=src_cnt[i][2*j+1]*trg_cnt[i];
          }else if(src_cnt[i][2*j+1]!=0 && trg_cnt[i]!=0){
            assert(ptr_double_layer_kernel); // Double-layer kernel not implemented
          }
        }
        if(M.Dim(0)>0 && M.Dim(1)>0 && interac_cnt>0){
          assert(trg_cnt[i]*ker_dim1==M.Dim(0));
          assert(trg_cnt[i]*ker_dim0==M.Dim(1));

          {// Scaling (ker_dim1)
            Real_t* s=&scaling[i*(ker_dim0+ker_dim1)];
            for(size_t j=0;j<dof*M.Dim(0);j+=ker_dim1){
              for(size_t k=0;k<ker_dim1;k++){
                t_value[j+k]*=s[k];
              }
            }
          }

          Matrix<Real_t>  in_vec(dof, M.Dim(0),             t_value, false);
          Matrix<Real_t> tmp_vec(dof, M.Dim(1),dof*M.Dim(0)+t_value, false);
          Matrix<Real_t>::GEMM(tmp_vec, in_vec, M, 0.0);

          Matrix<Real_t> out_vec(dof, M.Dim(1), output_data[0]+trg_value[i], false);
          {// Scaling (ker_dim0)
            Real_t* s=&scaling[i*(ker_dim0+ker_dim1)+ker_dim1];
            for(size_t j=0;j<dof*M.Dim(1);j+=ker_dim0){
              for(size_t k=0;k<ker_dim0;k++){
                out_vec[0][j+k]+=tmp_vec[0][j+k]*s[k];
              }
            }
          }

        }
      }
    }

    if(device) MIC_Lock::release_lock(lock_idx);
  }

  #ifdef __INTEL_OFFLOAD
  if(SYNC){
    #pragma offload if(device) target(mic:0)
    {if(device) MIC_Lock::wait_lock(lock_idx);}
  }
  #endif

  Profile::Toc();
}



template <class FMMNode>
void FMM_Pts<FMMNode>::X_ListSetup(SetupData<Real_t>&  setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=aux_kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=X_Type;

    setup_data. input_data=&buff[4];
    setup_data.output_data=&buff[1];
    setup_data. coord_data=&buff[6];
    Vector<FMMNode_t*>& nodes_in =n_list[4];
    Vector<FMMNode_t*>& nodes_out=n_list[1];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level-1 || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level   || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++){
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_value);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_value);
  }
  for(size_t i=0;i<nodes_out.size();i++){
    output_vector.push_back(&dnwd_check_surf[((FMMNode*)nodes_out[i])->Depth()]);
    output_vector.push_back(&((FMMData*)((FMMNode*)nodes_out[i])->FMMData())->dnward_equiv);
  }

  //Downward check to downward equivalent matrix.
  Matrix<Real_t>& M_dc2de = this->mat->Mat(level, DC2DE_Type, 0);
  this->SetupInteracPts(setup_data, false, true, &M_dc2de,device);
  { // Resize device buffer
    size_t n=setup_data.output_data->Dim(0)*setup_data.output_data->Dim(1)*sizeof(Real_t);
    if(this->dev_buffer.Dim()<n) this->dev_buffer.Resize(n);
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::X_List     (SetupData<Real_t>&  setup_data, bool device){
  //Add X_List contribution.
  this->EvalListPts(setup_data, device);
}



template <class FMMNode>
void FMM_Pts<FMMNode>::W_ListSetup(SetupData<Real_t>&  setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=W_Type;

    setup_data. input_data=&buff[0];
    setup_data.output_data=&buff[5];
    setup_data. coord_data=&buff[6];
    Vector<FMMNode_t*>& nodes_in =n_list[0];
    Vector<FMMNode_t*>& nodes_out=n_list[5];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level+1 || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level   || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++){
    input_vector .push_back(&upwd_equiv_surf[((FMMNode*)nodes_in [i])->Depth()]);
    input_vector .push_back(&((FMMData*)((FMMNode*)nodes_in [i])->FMMData())->upward_equiv);
    input_vector .push_back(NULL);
    input_vector .push_back(NULL);
  }
  for(size_t i=0;i<nodes_out.size();i++){
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_coord);
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_value);
  }

  this->SetupInteracPts(setup_data, true, false, NULL, device);
  { // Resize device buffer
    size_t n=setup_data.output_data->Dim(0)*setup_data.output_data->Dim(1)*sizeof(Real_t);
    if(this->dev_buffer.Dim()<n) this->dev_buffer.Resize(n);
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::W_List     (SetupData<Real_t>&  setup_data, bool device){
  //Add W_List contribution.
  this->EvalListPts(setup_data, device);
}



template <class FMMNode>
void FMM_Pts<FMMNode>::U_ListSetup(SetupData<Real_t>& setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=kernel;
    setup_data.interac_type.resize(3);
    setup_data.interac_type[0]=U0_Type;
    setup_data.interac_type[1]=U1_Type;
    setup_data.interac_type[2]=U2_Type;

    setup_data. input_data=&buff[4];
    setup_data.output_data=&buff[5];
    setup_data. coord_data=&buff[6];
    Vector<FMMNode_t*>& nodes_in =n_list[4];
    Vector<FMMNode_t*>& nodes_out=n_list[5];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if((level-1<=nodes_in [i]->Depth() && nodes_in [i]->Depth()<=level+1) || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if((                                  nodes_out[i]->Depth()==level  ) || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++){
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->src_value);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_coord);
    input_vector .push_back(&((FMMNode*)nodes_in [i])->surf_value);
  }
  for(size_t i=0;i<nodes_out.size();i++){
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_coord);
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_value);
  }

  this->SetupInteracPts(setup_data, false, false, NULL, device);
  { // Resize device buffer
    size_t n=setup_data.output_data->Dim(0)*setup_data.output_data->Dim(1)*sizeof(Real_t);
    if(this->dev_buffer.Dim()<n) this->dev_buffer.Resize(n);
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::U_List     (SetupData<Real_t>&  setup_data, bool device){
  //Add U_List contribution.
  this->EvalListPts(setup_data, device);
}



template <class FMMNode>
void FMM_Pts<FMMNode>::Down2TargetSetup(SetupData<Real_t>&  setup_data, std::vector<Matrix<Real_t> >& buff, std::vector<Vector<FMMNode_t*> >& n_list, int level, bool device){
  if(this->MultipoleOrder()==0) return;
  { // Set setup_data
    setup_data.level=level;
    setup_data.kernel=kernel;
    setup_data.interac_type.resize(1);
    setup_data.interac_type[0]=D2T_Type;

    setup_data. input_data=&buff[1];
    setup_data.output_data=&buff[5];
    setup_data. coord_data=&buff[6];
    Vector<FMMNode_t*>& nodes_in =n_list[1];
    Vector<FMMNode_t*>& nodes_out=n_list[5];

    setup_data.nodes_in .clear();
    setup_data.nodes_out.clear();
    for(size_t i=0;i<nodes_in .Dim();i++) if(nodes_in [i]->Depth()==level   || level==-1) setup_data.nodes_in .push_back(nodes_in [i]);
    for(size_t i=0;i<nodes_out.Dim();i++) if(nodes_out[i]->Depth()==level   || level==-1) setup_data.nodes_out.push_back(nodes_out[i]);
  }

  std::vector<void*>& nodes_in =setup_data.nodes_in ;
  std::vector<void*>& nodes_out=setup_data.nodes_out;
  std::vector<Vector<Real_t>*>&  input_vector=setup_data. input_vector;  input_vector.clear();
  std::vector<Vector<Real_t>*>& output_vector=setup_data.output_vector; output_vector.clear();
  for(size_t i=0;i<nodes_in .size();i++){
    input_vector .push_back(&dnwd_equiv_surf[((FMMNode*)nodes_in [i])->Depth()]);
    input_vector .push_back(&((FMMData*)((FMMNode*)nodes_in [i])->FMMData())->dnward_equiv);
    input_vector .push_back(NULL);
    input_vector .push_back(NULL);
  }
  for(size_t i=0;i<nodes_out.size();i++){
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_coord);
    output_vector.push_back(&((FMMNode*)nodes_out[i])->trg_value);
  }

  this->SetupInteracPts(setup_data, true, false, NULL, device);
  { // Resize device buffer
    size_t n=setup_data.output_data->Dim(0)*setup_data.output_data->Dim(1)*sizeof(Real_t);
    if(this->dev_buffer.Dim()<n) this->dev_buffer.Resize(n);
  }
}

template <class FMMNode>
void FMM_Pts<FMMNode>::Down2Target(SetupData<Real_t>&  setup_data, bool device){
  //Add Down2Target contribution.
  this->EvalListPts(setup_data, device);
}


template <class FMMNode>
void FMM_Pts<FMMNode>::PostProcessing(std::vector<FMMNode_t*>& nodes){
}


template <class FMMNode>
void FMM_Pts<FMMNode>::CopyOutput(FMMNode** nodes, size_t n){
}

}//end namespace