quadTree.h

 
//**********************************************************************************************************
/*
 * quadTree.cpp
 *
 */
 
/*
 * Programmer:    R Ben Metcalf
 */
#ifndef QUAD_TREE_H_
#define QUAD_TREE_H_
 
//#include "utilities_slsim.h"
//#include "utilities.h"
#include "Tree.h"
#include "qTreeNB.h"
//#include "lens_halos.h"
 
//short const treeNBdim = 2;
 
 
template<typename PType>
class TreeQuadParticles {
public:
  TreeQuadParticles(
   PType *xpt
      ,IndexType Npoints
      ,float mass_fixed = -1
      ,float size_fixed = -1
      ,PosType my_inv_area = 0 
      ,int bucket = 5
      ,PosType theta_force = 0.1
      ,bool my_periodic_buffer = false
      ,PosType my_inv_screening_scale = 0
      ,PosType maximum_range = -1
      );
 
 ~TreeQuadParticles();
  
  void force2D(PosType const *ray,PosType *alpha,KappaType *kappa,KappaType *gamma
                       ,KappaType *phi) const;
 
  void force2D_recur(const PosType *ray,PosType *alpha,KappaType *kappa
                             ,KappaType *gamma,KappaType *phi);
  
  void neighbors(PosType ray[],PosType rmax,std::list<IndexType> &neighbors) const;
  //void neighbors(PosType ray[],PosType rmax,std::vector<PType *> &neighbors) const;
  
  void printParticlesInBranch(unsigned long number);
  
 void printBranchs(int level = -1);
  
protected:
  
 PType *xxp;
  bool MultiMass;
  double mass_fixed = 0.0;
  bool MultiRadius;
  double size_fixed = 0.0;
  double inv_area;
 
  IndexType Nparticles;
  //PosType sigma_background;
  int Nbucket;
  
  PosType force_theta;
  PosType max_range;
  
  std::unique_ptr<QTreeNB<PType> > tree;
  std::vector<IndexType> index;
  
  std::vector<PosType> workspace;
  
 //bool haloON;
 //LensHaloHndl *halos;
  
  PosType realray[2];
  int incell,incell2;
  
  bool periodic_buffer;
  PosType inv_screening_scale2;
  PosType original_xl;  // x-axis size of simulation used for peridic buffering.  Requrement that it top branch be square my make it differ from the size of top branch.
  PosType original_yl;  // x-axis size of simulation used for peridic buffering.
  
  //QTreeNB<PType> * BuildQTreeNB(PType *xp,IndexType Nparticles,IndexType *particles);
  void BuildQTreeNB(PType *xp,IndexType Nparticles);
  void _BuildQTreeNB(IndexType nparticles,IndexType *particles);
  
  inline short WhichQuad(PosType *x,QBranchNB &branch);
  
  //inline bool atLeaf();
  inline bool inbox(const PosType *ray,const PosType *p1,const PosType *p2){
    return (ray[0]>=p1[0])*(ray[0]<=p2[0])*(ray[1]>=p1[1])*(ray[1]<=p2[1]);
  }
  //int cutbox(PosType *ray,PosType *p1,PosType *p2,float rmax);
  
  void CalcMoments();
  void rotate_coordinates(PosType **coord);
  
  // Internal profiles for a Gaussian particle
  inline PosType alpha_h(PosType r2s2,PosType sigma) const{
    return (sigma > 0.0 ) ? ( exp(-0.5*r2s2) - 1.0 ) : -1.0;
  }
  inline PosType kappa_h(PosType r2s2,PosType sigma) const{
    return 0.5*r2s2*exp(-0.5*r2s2);
  }
  inline PosType gamma_h(PosType r2s2,PosType sigma) const{
    return (sigma > 0.0 ) ? (-2.0 + (2.0 + r2s2)*exp(-0.5*r2s2) ) : -2.0;
  }
  inline PosType phi_h(PosType r2s2,PosType sigma) const{
    //ERROR_MESSAGE();  // not yet written
    //exit(1);
    return 0;
  }
  
  
  /* cubic B-spline kernel for particle profile
   
   The lensing quantities are added to and a point mass is subtracted
   */
  inline void b_spline_profile(
                               PosType *xcm       // vector in Mpc connecting ray to center of particle
                               ,PosType r         // distance from center in Mpc
                               ,PosType Mass      // mass in solar masses
                               ,PosType size      // size scale in Mpc
                               ,PosType *alpha    // deflection angle times Sigma_crit
                               ,KappaType *kappa  // surface density
                               ,KappaType *gamma  // shear times Sigma_crit
                               ,KappaType *phi
                               ) const {
    
    PosType q = r/size;
    PosType M,sigma;
    if(q > 2){
      sigma = 0;
      M = 1;
    }else{
      PosType q2=q*q,q3=q2*q,q4=q2*q2,q5=q4*q;
      
      sigma = (8 - 12*q + 6*q2 - q3)/4;
      if(q > 1){
        sigma *= 10/size/size/7/PI;
        M = (-1 + 20*q2*(1 - q + 3*q2/8 - q3/20) )/7;
        *phi += Mass*(-1232. + 1200*q2 - 800.*q3 + 225.*q4 - 24*q5 + 120*log(2./q) )/840/PI;
      }else{
        sigma = 10*( sigma - 1 + 3*q - 3*q2 + q3)/size/size/7/PI;
        M = 10*q2*(1 - 3*q/4 + 3*q3/10)/7;
        
        *phi += Mass*( phiintconst + 10*(q2/2 - 3*q4/4 + 3*q5/50)/7
                      )/PI;
      }
    }
    
    PosType alpha_r,gt;  // deflection * Sig_crit / Mass
    alpha_r = (M-1)/PI/r;
    gt = alpha_r/r - sigma;
    
    alpha[0] -= Mass*alpha_r*xcm[0]/r;
    alpha[1] -= Mass*alpha_r*xcm[1]/r;
    gamma[0] -= gt*Mass*(xcm[0]*xcm[0]-xcm[1]*xcm[1])/r/r;
    gamma[1] -= gt*Mass*2*xcm[0]*xcm[1]/r/r;
    *kappa += Mass*sigma;
    *phi -= Mass*log(r)/PI;
  }
  
  /* Exponential kernel for particle profile
   
   The lensing quantities are added to and a point mass is subtracted
   */
  inline void exponential_profile(
                                  PosType *xcm
                                  ,PosType rcm2       // distance from center in Mpc
                                  ,PosType Mass
                                  ,PosType size    // size scale in Mpc
                                  ,PosType *alpha
                                  ,KappaType *kappa
                                  ,KappaType *gamma
                                  ,KappaType *phi
                                  ) const {
    
    
    PosType prefac = Mass/rcm2/PI;
    PosType arg1 = rcm2/(size*size);
    
    PosType tmp = (alpha_h(arg1,size) + 1.0)*prefac;
    alpha[0] += tmp*xcm[0];
    alpha[1] += tmp*xcm[1];
    
    
    *kappa += kappa_h(arg1,size)*prefac;
    
    tmp = (gamma_h(arg1,size) + 2.0)*prefac/rcm2;
    
    gamma[0] += 0.5*(xcm[0]*xcm[0]-xcm[1]*xcm[1])*tmp;
    gamma[1] += xcm[0]*xcm[1]*tmp;
    
    // TODO: makes sure the normalization of phi_h agrees with this
    //*phi += (phi_h(arg1,size) + 0.5*log(rcm2))*prefac*rcm2;
  }
  
 //QTreeNB<PType> * rotate_simulation(PType *xp,IndexType Nparticles,IndexType *particles
 //  ,PosType **coord,PosType theta,float *rsph,float *mass
 //  ,bool MultiRadius,bool MultiMass);
 //QTreeNB<PType> * rotate_project(PType *xp,IndexType Nparticles,IndexType *particles
 //  ,PosType **coord,PosType theta,float *rsph,float *mass
 //  ,bool MultiRadius,bool MultiMass);
  void cuttoffscale(QTreeNB<PType> * tree,PosType *theta);
 
  void walkTree_recur(QBranchNB *branch,PosType const *ray,PosType *alpha,KappaType *kappa,KappaType *gamma,KappaType *phi);
 
  void walkTree_iter(QBiterator<PType> &treeit, PosType const *ray,PosType *alpha,KappaType *kappa
                     ,KappaType *gamma,KappaType *phi) const;
  
  PosType phiintconst;
};
 
 
 
template<typename PType>
TreeQuadParticles<PType>::TreeQuadParticles(
                    PType *xpt
                   ,IndexType Npoints
                   ,float mass_fixed
                   ,float size_fixed
                   ,PosType my_inv_area 
                   ,int bucket
                   ,PosType theta_force
                   ,bool my_periodic_buffer  
                   ,PosType my_inv_screening_scale   
                   ,PosType maximum_range  
 
):
xxp(xpt)
,inv_area(my_inv_area)
,Nparticles(Npoints)
,Nbucket(bucket)
,force_theta(theta_force)
,max_range(maximum_range)
,periodic_buffer(my_periodic_buffer)
,inv_screening_scale2(my_inv_screening_scale*my_inv_screening_scale)
{
  index.resize(Npoints);
  IndexType ii;
  if(mass_fixed <= 0 ) MultiMass = true; else MultiMass = false;
  if(size_fixed <= 0 ) MultiRadius = true; else MultiRadius = false;
  
  for(ii=0;ii<Npoints;++ii) index[ii] = ii;
  
  if(Npoints > 0){
    BuildQTreeNB(xxp,Npoints);
    CalcMoments();
  }
  
  phiintconst = (120*log(2.) - 631.)/840 + 19./70;
  
  return;
}
 
template<typename PType>
TreeQuadParticles<PType>::~TreeQuadParticles()
{
  if(Nparticles == 0) return;
  return;
}
 
template<typename PType>
//QTreeNB<PType> * TreeQuadParticles<PType>::BuildQTreeNB(PType *xxp,IndexType Nparticles,IndexType *particles){
void TreeQuadParticles<PType>::BuildQTreeNB(PType *xxp,IndexType Nparticles){
  IndexType i;
  short j;
  PosType p1[2],p2[2];
  
  for(j=0;j<2;++j){
    p1[j]=xxp[0][j];
    p2[j]=xxp[0][j];
  }
  
  // Find borders that enclose all particles
  for(i=0;i<Nparticles;++i){
    for(j=0;j<2;++j){
      if(xxp[i][j] < p1[j] ) p1[j]=xxp[i][j];
      if(xxp[i][j] > p2[j] ) p2[j]=xxp[i][j];
    }
  }
  
  if(Nparticles == 1){
    p1[0]=-0.25;
    p1[1]=-0.25;
    p2[0]=0.25;
    p2[1]=0.25;
  }
  
  // store true dimensions of simulation
  PosType lengths[2] = {p2[0]-p1[0],p2[1]-p1[1]};
  original_xl = lengths[0];
  original_yl = lengths[1];
  
  if(lengths[0] == 0 || lengths[1] == 0){
    throw std::invalid_argument("particles in same place.");
  }
  
  // If region is not square, make it square.
  j = lengths[0] > lengths[1] ? 1 : 0;
  p2[j] = p1[j] + lengths[!j];
  
  /* Initialize tree root */
  //tree = new QTreeNB<PType>(xxp,particles,Nparticles,p1,p2);
  tree.reset( new QTreeNB<PType>(xxp,index.data(),Nparticles,p1,p2) );
 
  /* build the tree */
  workspace.resize(Nparticles);
  _BuildQTreeNB(Nparticles,index.data());
  workspace.clear();
  workspace.shrink_to_fit();
  
  /* visit every branch to find center of mass and cutoff scale */
  tree->moveTop();
  
  //return tree;
  return;
}
 
template<typename PType>
inline short TreeQuadParticles<PType>::WhichQuad(PosType *x,QBranchNB &branch){
  return (x[0] < branch.center[0]) + 2*(x[1] < branch.center[1]);
}
 
template<typename PType>
void TreeQuadParticles<PType>::_BuildQTreeNB(IndexType nparticles,IndexType *particles){
  
  QBranchNB *cbranch = tree->current; // pointer to current branch
  IndexType i,j,cut,cut2;
  
  cbranch->center[0] = (cbranch->boundary_p1[0] + cbranch->boundary_p2[0])/2;
  cbranch->center[1] = (cbranch->boundary_p1[1] + cbranch->boundary_p2[1])/2;
  cbranch->quad[0] = cbranch->quad[1]=cbranch->quad[2]=0;
  cbranch->mass = 0.0;
    
  double theta_range = 2*force_theta;
  if(max_range > 0){
    double boxsize = 1.732*(cbranch->boundary_p2[0] - cbranch->boundary_p1[0]);
    theta_range = boxsize / MAX(sqrt(cbranch->center[0]*cbranch->center[0]
           + cbranch->center[1]*cbranch->center[1] )
           - max_range, boxsize );
  }
    
  // leaf case
  if(cbranch->nparticles <= Nbucket
     || force_theta > theta_range
     ){
    PosType r;
    cbranch->Nbig_particles = 0;
    for(i=0;i<cbranch->nparticles;++i){
      r = xxp[particles[i]*MultiRadius].size();
      if(r < (cbranch->boundary_p2[0]-cbranch->boundary_p1[0])) ++cbranch->Nbig_particles;
    }
    if(cbranch->Nbig_particles){
      //cbranch->big_particles = new IndexType[cbranch->Nbig_particles];
      cbranch->big_particles.reset(new IndexType[cbranch->Nbig_particles]);
      
      for(i=0,j=0;i<cbranch->nparticles;++i){
        r = xxp[particles[i]*MultiRadius].size();
        if(r < (cbranch->boundary_p2[0]-cbranch->boundary_p1[0])) cbranch->big_particles[j++] = particles[i];
      }
    }else{
      cbranch->big_particles.reset(nullptr);
    }
    
    return;
  }
  
  // find particles too big to be in children
  
  //PosType *x = new PosType[cbranch->nparticles];
  PosType *x = workspace.data();
  
  cbranch->Nbig_particles=0;
  
  if(MultiRadius){
    // store the particles that are too large to be in a child at the end of the list of particles in cbranch
    for(i=0;i<cbranch->nparticles;++i){
      x[i] = xxp[particles[i]].size();
    }
    PosType maxsize = (cbranch->boundary_p2[0]-cbranch->boundary_p1[0])/2;
    
    // sort particles in size
    //quicksort(particles,x,cbranch->nparticles);
    Utilities::quickPartition(maxsize,&cut,particles,x,cbranch->nparticles);
    
    if(cut < cbranch->nparticles){
      if(tree->atTop()){
        cbranch->Nbig_particles = cut2 = cbranch->nparticles-cut;
      }else{
        Utilities::quickPartition(2*maxsize,&cut2,&particles[cut],&x[cut],cbranch->nparticles-cut);
        cbranch->Nbig_particles = cut2;
      }
      
      cbranch->big_particles.reset(new IndexType[cbranch->Nbig_particles]);
      for(i=cut;i<(cut+cut2);++i) cbranch->big_particles[i-cut] = particles[i];
    }
    
  }else{
    //x[0] = xxp[0].Size();
    x[0] = size_fixed;
    if(x[0] > (cbranch->boundary_p2[0]-cbranch->boundary_p1[0])/2
       && x[0] < (cbranch->boundary_p2[0]-cbranch->boundary_p1[0])){
      cbranch->Nbig_particles = cbranch->nparticles;
      //cbranch->big_particles = cbranch->particles;
      cbranch->big_particles.reset(new IndexType[cbranch->Nbig_particles]);
      for(i=0;i<cbranch->nparticles;++i) cbranch->big_particles[i] = cbranch->particles[particles[i]];
    }
  }
  
  assert( cbranch->nparticles >= cbranch->Nbig_particles );
  IndexType NpInChildren = cbranch->nparticles;// - cbranch->Nbig_particles;
  assert(NpInChildren >= 0);
  
  if(NpInChildren == 0){
    //delete[] x;
    return;
  }
  
  IndexType cutx,cuty;
  PosType xcut,ycut;
  
  QBranchNB *child0 = new QBranchNB(cbranch);
  QBranchNB *child1 = new QBranchNB(cbranch);
  QBranchNB *child2 = new QBranchNB(cbranch);
  QBranchNB *child3 = new QBranchNB(cbranch);
  
  tree->attachChildrenToCurrent(child0,child1,child2,child3);
  
  // initialize boundaries of children
  
  child0->boundary_p1[0]=cbranch->center[0];
  child0->boundary_p1[1]=cbranch->center[1];
  child0->boundary_p2[0]=cbranch->boundary_p2[0];
  child0->boundary_p2[1]=cbranch->boundary_p2[1];
  
  child1->boundary_p1[0]=cbranch->boundary_p1[0];
  child1->boundary_p1[1]=cbranch->center[1];
  child1->boundary_p2[0]=cbranch->center[0];
  child1->boundary_p2[1]=cbranch->boundary_p2[1];
  
  child2->boundary_p1[0]=cbranch->center[0];
  child2->boundary_p1[1]=cbranch->boundary_p1[1];
  child2->boundary_p2[0]=cbranch->boundary_p2[0];
  child2->boundary_p2[1]=cbranch->center[1];
  
  child3->boundary_p1[0]=cbranch->boundary_p1[0];
  child3->boundary_p1[1]=cbranch->boundary_p1[1];
  child3->boundary_p2[0]=cbranch->center[0];
  child3->boundary_p2[1]=cbranch->center[1];
  
  
  // **** makes sure force does not require nbucket at leaf
  
  xcut = cbranch->center[0];
  ycut = cbranch->center[1];
  
  // divide along y direction
  for(i=0;i<NpInChildren;++i) x[i] = tree->xxp[particles[i]][1];
  Utilities::quickPartition(ycut,&cuty,particles,x,NpInChildren);
  
  if(cuty > 0){
    // divide first group in the x direction
    for(i=0;i<cuty;++i) x[i] = tree->xxp[particles[i]][0];
    Utilities::quickPartition(xcut,&cutx,particles,x,cuty);
    
    child3->nparticles=cutx;
    assert(child3->nparticles >= 0);
    if(child3->nparticles > 0)
      child3->particles = particles;
    else child3->particles = NULL;
    
    child2->nparticles = cuty - cutx;
    assert(child2->nparticles >= 0);
    if(child2->nparticles > 0)
      child2->particles = &particles[cutx];
    else child2->particles = NULL;
    
  }else{
    child3->nparticles = 0;
    child3->particles = NULL;
    
    child2->nparticles = 0;
    child2->particles = NULL;
  }
  
  if(cuty < NpInChildren){
    // divide second group in the x direction
    for(i=cuty;i<NpInChildren;++i) x[i-cuty] = tree->xxp[particles[i]][0];
    Utilities::quickPartition(xcut,&cutx,&particles[cuty],x,NpInChildren-cuty);
    
    child1->nparticles=cutx;
    assert(child1->nparticles >= 0);
    if(child1->nparticles > 0)
      child1->particles = &particles[cuty];
    else child1->particles = NULL;
    
    child0->nparticles=NpInChildren - cuty - cutx;
    assert(child0->nparticles >= 0);
    if(child0->nparticles > 0)
      child0->particles = &particles[cuty + cutx];
    else child0->particles = NULL;
    
  }else{
    child1->nparticles = 0;
    child1->particles = NULL;
    
    child0->nparticles = 0;
    child0->particles = NULL;
  }
  
  //delete[] x;
  
  tree->moveToChild(0);
  _BuildQTreeNB(child0->nparticles,child0->particles);
  tree->moveUp();
  
  tree->moveToChild(1);
  _BuildQTreeNB(child1->nparticles,child1->particles);
  tree->moveUp();
  
  tree->moveToChild(2);
  _BuildQTreeNB(child2->nparticles,child2->particles);
  tree->moveUp();
  
  tree->moveToChild(3);
  _BuildQTreeNB(child3->nparticles,child3->particles);
  tree->moveUp();
  
  return;
}
 
// calculates moments of the mass and the cutoff scale for each box
template<typename PType>
void TreeQuadParticles<PType>::CalcMoments(){
  
  //*** make compatable
  IndexType i;
  PosType rcom,xcm[2],xcut;
  QBranchNB *cbranch;
  PosType tmp;
  double absmass; // absolute magnitude of mass
  
  tree->moveTop();
  do{
    cbranch=tree->current; /* pointer to current branch */
    
    cbranch->rmax = sqrt( pow(cbranch->boundary_p2[0]-cbranch->boundary_p1[0],2)
                         + pow(cbranch->boundary_p2[1]-cbranch->boundary_p1[1],2) );
    
    // calculate mass
    for(i=0,cbranch->mass=0,absmass=0;i<cbranch->nparticles;++i){
      cbranch->mass += xxp[cbranch->particles[i]*MultiMass].mass();
      absmass += fabs(xxp[cbranch->particles[i]*MultiMass].mass());
    }
    // calculate center of mass
    cbranch->center[0]=cbranch->center[1]=0;
    for(i=0;i<cbranch->nparticles;++i){
      tmp = fabs(xxp[cbranch->particles[i]*MultiMass].mass());
 
      //tmp = haloON ? halos[cbranch->particles[i]*MultiMass].mass : masses[cbranch->particles[i]*MultiMass];
      cbranch->center[0] += tmp*tree->xxp[cbranch->particles[i]][0]/absmass;
      cbranch->center[1] += tmp*tree->xxp[cbranch->particles[i]][1]/absmass;
    }
    // calculate quadropole moment of branch
    cbranch->quad[0]=cbranch->quad[1]=cbranch->quad[2]=0;
    for(i=0;i<cbranch->nparticles;++i){
      xcm[0]=tree->xxp[cbranch->particles[i]][0]-cbranch->center[0];
      xcm[1]=tree->xxp[cbranch->particles[i]][1]-cbranch->center[1];
      xcut = pow(xcm[0],2) + pow(xcm[1],2);
      tmp = xxp[cbranch->particles[i]*MultiMass].mass();
 
      cbranch->quad[0] += (xcut-2*xcm[0]*xcm[0])*tmp;
      cbranch->quad[1] += (xcut-2*xcm[1]*xcm[1])*tmp;
      cbranch->quad[2] += -2*xcm[0]*xcm[1]*tmp;
    }
    
    // largest distance from center of mass of cell
    for(i=0,rcom=0.0;i<2;++i) rcom += ( pow(cbranch->center[i]-cbranch->boundary_p1[i],2) > pow(cbranch->center[i]-cbranch->boundary_p2[i],2) ) ?
      pow(cbranch->center[i]-cbranch->boundary_p1[i],2) : pow(cbranch->center[i]-cbranch->boundary_p2[i],2);
    
    rcom=sqrt(rcom);
    
    if(force_theta > 0.0){
      cbranch->r2crit_angle = 1.15470*rcom/(force_theta);
      cbranch->r2crit_angle *= cbranch->r2crit_angle;
    }else  cbranch->r2crit_angle=1.0e100;
    
  }while(tree->WalkStep(true));
  
  return;
}
 
template<typename PType>
void TreeQuadParticles<PType>::rotate_coordinates(PosType **coord){
  IndexType i;
  short j;
  PosType tmp[3];
  
  /* rotate particle positions */
  for(i=0;i<tree->top->nparticles;++i){
    for(j=0;j<3;++j) tmp[j]=0.0;
    for(j=0;j<3;++j){
      tmp[0]+=coord[0][j]*xxp[i][j];
      tmp[1]+=coord[1][j]*xxp[i][j];
      tmp[2]+=coord[2][j]*xxp[i][j];
    }
    for(j=0;j<3;++j) xxp[i][j]=tmp[j];
  }
  return;
}
 
template<typename PType>
void TreeQuadParticles<PType>::force2D(const PosType *ray,PosType *alpha,KappaType *kappa,KappaType *gamma,KappaType *phi) const{
  
  alpha[0]=alpha[1]=gamma[0]=gamma[1]=gamma[2]=0.0;
  *kappa=*phi=0.0;
  
  if(Nparticles == 0) return;
  
  assert(tree);
  QBiterator<PType> it(tree);
  
  if(periodic_buffer){
    PosType tmp_ray[2];
    
    for(int i = -1;i<2;++i){
      for(int j = -1;j<2;++j){
        tmp_ray[0] = ray[0] + i*original_xl;
        tmp_ray[1] = ray[1] + j*original_yl;
        walkTree_iter(it,tmp_ray,alpha,kappa,gamma,phi);
      }
    }
  }else{
    walkTree_iter(it,ray,alpha,kappa,gamma,phi);
  }
  
  // Subtract off uniform mass sheet to compensate for the extra mass
  //  added to the universe in the halos.
  //alpha[0] -= ray[0]*sigma_background*(inv_screening_scale2 == 0);
  //alpha[1] -= ray[1]*sigma_background*(inv_screening_scale2 == 0);
  //*kappa -= sigma_background;
  
  return;
}
 
template<typename PType>
void TreeQuadParticles<PType>::neighbors(PosType ray[],PosType rmax,std::list<IndexType> &neighbors) const{
  QBiterator<PType> it(tree);
  neighbors.clear();
  
  PosType r2 = rmax*rmax;
  bool decend=true;
  it.movetop();
  do{
    int cut = Utilities::cutbox(ray,(*it)->boundary_p1,(*it)->boundary_p2,rmax);
    decend = true;
    
    if(cut == 0){      // box outside circle
      decend = false;
    }else if(cut == 1){  // whole box inside circle
      for(int i=0;i<(*it)->nparticles;++i) neighbors.push_back((*it)->particles[i]);
      decend = false;
    }else if((*it)->child0 == NULL){  // at leaf
      for(int i=0;i<(*it)->nparticles;++i){
        if( (tree->xxp[(*it)->particles[i]][0] - ray[0])*(tree->xxp[(*it)->particles[i]][0] - ray[0])
           + (tree->xxp[(*it)->particles[i]][1] - ray[1])*(tree->xxp[(*it)->particles[i]][1] - ray[1]) < r2) neighbors.push_back((*it)->particles[i]);
      }
      decend = false;
    }
  }while(it.TreeWalkStep(decend));
  
}
 
template<typename PType>
void TreeQuadParticles<PType>::walkTree_iter(
                             QBiterator<PType> &treeit,
                             const PosType *ray
                             ,PosType *alpha
                             ,KappaType *kappa
                             ,KappaType *gamma
                             ,KappaType *phi
                             ) const {
  
  PosType xcm[2],rcm2cell,rcm2,tmp,boxsize2;
  IndexType i;
  bool allowDescent=true;
  unsigned long count=0,tmp_index;
  PosType prefac;
  //bool notscreen = true;
  
  assert(tree);
  
  treeit.movetop();
  //tree->moveTop();
  do{
    ++count;
    allowDescent=false;
    
    /*
     if(inv_screening_scale2 != 0) notscreen = BoxIntersectCircle(ray,3*sqrt(1.0/inv_screening_scale2)
     ,(*treeit)->boundary_p1
     ,(*treeit)->boundary_p2);
     else notscreen = true;
     */
    //if(tree->current->nparticles > 0)
    if((*treeit)->nparticles > 0)
    {
      
      xcm[0]=(*treeit)->center[0]-ray[0];
      xcm[1]=(*treeit)->center[1]-ray[1];
      
      rcm2cell = xcm[0]*xcm[0] + xcm[1]*xcm[1];
      
      boxsize2 = ((*treeit)->boundary_p2[0]-(*treeit)->boundary_p1[0])*((*treeit)->boundary_p2[0]-(*treeit)->boundary_p1[0]);
      
      if( rcm2cell < ((*treeit)->rcrit_angle)*((*treeit)->rcrit_angle) || rcm2cell < 5.83*boxsize2)
      {
        
        // includes rcrit_particle constraint
        allowDescent=true;
        
        
        // Treat all particles in a leaf as a point particle
        if(treeit.atLeaf())
        {
          
          for(i = 0 ; i < (*treeit)->nparticles ; ++i)
          {
            
            xcm[0] = tree->xp[(*treeit)->particles[i]][0] - ray[0];
            xcm[1] = tree->xp[(*treeit)->particles[i]][1] - ray[1];
            
            rcm2 = xcm[0]*xcm[0] + xcm[1]*xcm[1];
            double screening = exp(-rcm2*inv_screening_scale2);
            if(rcm2 < 1e-20) rcm2 = 1e-20;
            
            //tmp_index = MultiMass*(*treeit)->particles[i];
            
            //if(haloON){ prefac = halos[tmp_index]->get_mass(); }
            //else{ prefac = masses[tmp_index]; }
            
            double mass;
            if(MultiMass) mass = xxp[(*treeit)->particles[i]].Mass();
            else mass = mass_fixed;
            
            prefac = mass/rcm2/PI*screening;
            tmp = -mass*( screening/rcm2/PI - inv_area);
            
            alpha[0] += tmp*xcm[0];
            alpha[1] += tmp*xcm[1];
            
            tmp = -2.0*prefac/rcm2;
            
            gamma[0] += 0.5*(xcm[0]*xcm[0]-xcm[1]*xcm[1])*tmp;
            gamma[1] += xcm[0]*xcm[1]*tmp;
            
            *kappa -= mass*inv_area;
            *phi += (prefac*log(rcm2) - mass*inv_area)*rcm2*0.5;
            
          } // end of for
        } // end of if(tree->atLeaf())
        
        
        // Find the particles that intersect with ray and add them individually.
        if(rcm2cell < 5.83*boxsize2)
        {
          
          for(i = 0 ; i < (*treeit)->Nbig_particles ; ++i)
          {
            
            tmp_index = (*treeit)->big_particles[i];
            
            xcm[0] = tree->xp[tmp_index][0] - ray[0];
            xcm[1] = tree->xp[tmp_index][1] - ray[1];
            
            rcm2 = xcm[0]*xcm[0] + xcm[1]*xcm[1];
           
            if(rcm2 < 1e-20) rcm2 = 1e-20;
 
            //PosType size = sizes[tmp_index*MultiRadius];
            PosType size = xxp[tmp_index*MultiRadius].size();
 
            // intersecting, subtract the point particle
            if(rcm2 < 4*size*size)
              {
                b_spline_profile(xcm,sqrt(rcm2),xxp[MultiMass*tmp_index].Mass(),size,alpha,kappa,gamma,phi);
              }
            
          }
        }
        
      }
      else
      { // use whole cell
        
        allowDescent=false;
        
        // monopole
        double screening = exp(-rcm2cell*inv_screening_scale2);
        //double tmp = -1.0*(*treeit)->mass/rcm2cell/PI*screening;
        double tmp = (*treeit)->mass*( inv_area - screening/rcm2cell/PI );
 
        alpha[0] += tmp*xcm[0];
        alpha[1] += tmp*xcm[1];
        
        {      //  taken out to speed up
          tmp=-2.0*(*treeit)->mass/PI/rcm2cell/rcm2cell*screening;
          gamma[0] += 0.5*(xcm[0]*xcm[0]-xcm[1]*xcm[1])*tmp;
          gamma[1] += xcm[0]*xcm[1]*tmp;
          
          *phi += 0.5*(*treeit)->mass*log( rcm2cell )/PI*screening;
          *phi -= 0.5*( (*treeit)->quad[0]*xcm[0]*xcm[0] + (*treeit)->quad[1]*xcm[1]*xcm[1] + 2*(*treeit)->quad[2]*xcm[0]*xcm[1] )/(PI*rcm2cell*rcm2cell)*screening;
        }
        
        // quadrapole contribution
        //   the kappa and gamma are not calculated to this order
        alpha[0] -= ((*treeit)->quad[0]*xcm[0] + (*treeit)->quad[2]*xcm[1])
        /(rcm2cell*rcm2cell)/PI*screening;
        alpha[1] -= ((*treeit)->quad[1]*xcm[1] + (*treeit)->quad[2]*xcm[0])
        /(rcm2cell*rcm2cell)/PI*screening;
        
        tmp = 4*((*treeit)->quad[0]*xcm[0]*xcm[0] + (*treeit)->quad[1]*xcm[1]*xcm[1]
                 + 2*(*treeit)->quad[2]*xcm[0]*xcm[1])/(rcm2cell*rcm2cell*rcm2cell)/PI*screening;
        
        alpha[0] += tmp*xcm[0];
        alpha[1] += tmp*xcm[1];
        
        *kappa -= (*treeit)->mass * inv_area;
        *phi -= 0.5*(*treeit)->mass*inv_area;
      }
    }
  }while(treeit.TreeWalkStep(allowDescent));
  
  
  // Subtract off uniform mass sheet to compensate for the extra mass
  //  added to the universe in the halos.
  //alpha[0] -= ray[0]*sigma_background*(inv_screening_scale2 == 0.0);
  //alpha[1] -= ray[1]*sigma_background*(inv_screening_scale2 == 0.0);
  //{      //  taken out to speed up
  //  *kappa -= sigma_background;
  //  // *phi -= sigma_background * sigma_background ;
  //}
  
  return;
}
 
 
template<typename PType>
void TreeQuadParticles<PType>::force2D_recur(const PosType *ray,PosType *alpha,KappaType *kappa,KappaType *gamma,KappaType *phi){
  
  
  alpha[0]=alpha[1]=gamma[0]=gamma[1]=gamma[2]=0.0;
  *kappa=*phi=0.0;
  
  if(Nparticles == 0) return;
  assert(tree);
  
  //walkTree_recur(tree->top,ray,&alpha[0],kappa,&gamma[0],phi);
  
  if(periodic_buffer){
    PosType tmp_ray[2],tmp_c[2];
    
    // for points outside of primary zone shift to primary zone
    //if(inbox(ray,tree->top->boundary_p1,tree->top->boundary_p2)){
    tmp_c[0] = ray[0];
    tmp_c[1] = ray[1];
    /*}else{
     int di[2];
     PosType center[2] = { (tree->top->boundary_p1[0] + tree->top->boundary_p2[0])/2 ,
     (tree->top->boundary_p1[1] + tree->top->boundary_p2[1])/2 };
     
     di[0] = (int)( 2*(ray[0] - center[0])/lx );
     di[1] = (int)( 2*(ray[1] - center[1])/ly );
     
     di[0] = (di[0] > 0) ? (di[0] + 1)/2 : (di[0] - 1)/2;
     di[1] = (di[1] > 0) ? (di[1] + 1)/2 : (di[1] - 1)/2;
     
     tmp_c[0] = ray[0] - lx * di[0];
     tmp_c[1] = ray[1] - ly * di[1];
     
     assert(inbox(tmp_c,tree->top->boundary_p1,tree->top->boundary_p2));
     }*/
    
    for(int i = -1;i<2;++i){
      for(int j = -1;j<2;++j){
        tmp_ray[0] = tmp_c[0] + i*original_xl;
        tmp_ray[1] = tmp_c[1] + j*original_yl;
        walkTree_recur(tree->top,tmp_ray,alpha,kappa,gamma,phi);
      }
    }
  }else{
    walkTree_recur(tree->top,ray,alpha,kappa,gamma,phi);
  }
  
  // Subtract off uniform mass sheet to compensate for the extra mass
  //  added to the universe in the halos.
  //alpha[0] -= ray[0]*sigma_background*(inv_screening_scale2 == 0);
  //alpha[1] -= ray[1]*sigma_background*(inv_screening_scale2 == 0);
  
  //*kappa -= sigma_background;
  
  return;
}
 
 
template<typename PType>
void TreeQuadParticles<PType>::walkTree_recur(QBranchNB *branch,PosType const *ray,PosType *alpha,KappaType *kappa,KappaType *gamma, KappaType *phi){
  
  PosType xcm[2],rcm2cell,rcm2,tmp,boxsize2;
  IndexType i;
  std::size_t tmp_index;
  PosType prefac;
  /*bool notscreen = true;
   
   if(inv_screening_scale2 != 0) notscreen = BoxIntersectCircle(ray,3*sqrt(1.0/inv_screening_scale2), branch->boundary_p1, branch->boundary_p2);
   */
  if(branch->nparticles > 0)
  {
    xcm[0]=branch->center[0]-ray[0];
    xcm[1]=branch->center[1]-ray[1];
    
    rcm2cell = xcm[0]*xcm[0] + xcm[1]*xcm[1];
    
    boxsize2 = (branch->boundary_p2[0]-branch->boundary_p1[0])*(branch->boundary_p2[0]-branch->boundary_p1[0]);
    
    if( rcm2cell < branch->r2crit_angle || rcm2cell < 5.83*boxsize2)
    {
      
      // Treat all particles in a leaf as a point particle
      if(tree->atLeaf(branch))
      {
        
        for(i = 0 ; i < branch->nparticles ; ++i){
          
          xcm[0] = tree->xxp[branch->particles[i]][0] - ray[0];
          xcm[1] = tree->xxp[branch->particles[i]][1] - ray[1];
          
          rcm2 = xcm[0]*xcm[0] + xcm[1]*xcm[1];
          double screening = exp(-rcm2*inv_screening_scale2);
          if(rcm2 < 1e-20) rcm2 = 1e-20;
          
          tmp_index = MultiMass*branch->particles[i];
          
          //if(haloON ) { prefac = halos[tmp_index]->get_mass(); }
          //else{ prefac = masses[tmp_index]; }
          double mass = xxp[tmp_index].mass();
          prefac = mass*screening/rcm2/PI;
          //prefac /= rcm2*PI/screening;
          
          
          alpha[0] += (inv_area*mass - prefac)*xcm[0];
          alpha[1] += (inv_area*mass - prefac)*xcm[1];
          
          {
            tmp = -2.0*prefac/rcm2;
            
            gamma[0] += 0.5*(xcm[0]*xcm[0]-xcm[1]*xcm[1])*tmp;
            gamma[1] += xcm[0]*xcm[1]*tmp;
            
            *kappa -= mass*inv_area;
            *phi += prefac*rcm2*0.5*log(rcm2) - mass*inv_area*rcm2/2;
          }
        }
      }
      
      // Find the particles that intersect with ray and add them individually.
      if(rcm2cell < 5.83*boxsize2)
      {
        
        for(i = 0 ; i < branch->Nbig_particles ; ++i)
        {
          
          tmp_index = branch->big_particles[i];
          
          xcm[0] = tree->xxp[tmp_index][0] - ray[0];
          xcm[1] = tree->xxp[tmp_index][1] - ray[1];
          rcm2 = xcm[0]*xcm[0] + xcm[1]*xcm[1];
          
            if(rcm2 < 1e-20) rcm2 = 1e-20;
            
            PosType size = xxp[tmp_index*MultiRadius].size();
            
            // intersecting, subtract the point particle
            if(rcm2 < 4*size*size)
            {
              
              b_spline_profile(xcm,sqrt(rcm2),xxp[MultiMass*tmp_index].mass(),size,alpha,kappa,gamma,phi);
              
            }
          
        }
      }
      
      if(branch->child0 != NULL)
        walkTree_recur(branch->child0,&ray[0],&alpha[0],kappa,&gamma[0],&phi[0]);
      if(branch->child1 != NULL)
        walkTree_recur(branch->child1,&ray[0],&alpha[0],kappa,&gamma[0],&phi[0]);
      if(branch->child2 != NULL)
        walkTree_recur(branch->child2,&ray[0],&alpha[0],kappa,&gamma[0],&phi[0]);
      if(branch->child3 != NULL)
        walkTree_recur(branch->child3,&ray[0],&alpha[0],kappa,&gamma[0],&phi[0]);
      
    }
    else
    { // use whole cell
      
      double screening = exp(-rcm2cell*inv_screening_scale2);
      double tmp = branch->mass*inv_area - branch->mass/rcm2cell/PI*screening;
      
      alpha[0] += tmp*xcm[0];
      alpha[1] += tmp*xcm[1];
      
      {      //  taken out to speed up
        tmp=-2.0*branch->mass/PI/rcm2cell/rcm2cell*screening;
        gamma[0] += 0.5*(xcm[0]*xcm[0]-xcm[1]*xcm[1])*tmp;
        gamma[1] += xcm[0]*xcm[1]*tmp;
        
        *phi += 0.5*tree->current->mass*log( rcm2cell )/PI*screening;
        *phi -= 0.5*( tree->current->quad[0]*xcm[0]*xcm[0] + tree->current->quad[1]*xcm[1]*xcm[1] + 2*tree->current->quad[2]*xcm[0]*xcm[1] )/(PI*rcm2cell*rcm2cell)*screening;
      }
      
      // quadrapole contribution
      //   the kappa and gamma are not calculated to this order
      alpha[0] -= (branch->quad[0]*xcm[0] + branch->quad[2]*xcm[1])
      /(rcm2cell*rcm2cell)/PI*screening;
      alpha[1] -= (branch->quad[1]*xcm[1] + branch->quad[2]*xcm[0])
      /(rcm2cell*rcm2cell)/PI*screening;
      
      tmp = 4*(branch->quad[0]*xcm[0]*xcm[0] + branch->quad[1]*xcm[1]*xcm[1]
               + 2*branch->quad[2]*xcm[0]*xcm[1])/(rcm2cell*rcm2cell*rcm2cell)/PI*screening;
      
      alpha[0] += tmp*xcm[0];
      alpha[1] += tmp*xcm[1];
      
      *kappa -= inv_area * branch->mass;
      *phi -= 0.5*branch->mass*rcm2cell*inv_area;
      
      return;
    }
    
  }
  return;
}
 
template<typename PType>
void TreeQuadParticles<PType>::printParticlesInBranch(unsigned long number){
  unsigned long i;
  
  tree->moveTop();
  do{
    if(tree->current->number == number){
      std::cout << tree->current->nparticles << std::endl;
      for(i=0;i<tree->current->nparticles;++i){
        std::cout << xxp[tree->current->particles[i]][0] << "  "
        << xxp[tree->current->particles[i]][1] << std::endl;
      }
      return;
    }
  }while(tree->WalkStep(true));
  
  return;
}
template<typename PType>
void TreeQuadParticles<PType>::printBranchs(int level){
  
  bool decend = true;
  tree->moveTop();
  do{
    std::cout << tree->current->boundary_p1[0] << "  " << tree->current->boundary_p1[1] << "   "
    << tree->current->boundary_p2[0] << "  " << tree->current->boundary_p2[1] << std::endl;
    if(tree->current->level == level) decend = false;
    else decend = true;
  }while(tree->WalkStep(decend));
  
  return;
};
 
#endif /* QUAD_TREE_H_ */