VtxTrackFinder.cpp

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#include "VtxTrackFinder.h"
#include <cmath>
#include <iostream>
#include <algorithm>
#include <Eigen/LU>
#include <Eigen/Core>


using namespace std;
using namespace Eigen;

/*
bool SimpleHit3D_LessThan(SimpleHit3D i, SimpleHit3D j)
{
  return (i.index<j.index);
}

bool SimpleTrack3D_Equality(SimpleTrack3D i, SimpleTrack3D j)
{
  if(i.hits.size()!=j.hits.size())
    return false;
  for(unsigned int ihit = 0; ihit < i.hits.size(); ihit++)
    if(i.hits[ihit].index!=j.hits[ihit].index)
      return false;
    return true;
}

bool is_lessthan(vector<SimpleHit3D> i, vector<SimpleHit3D> j, unsigned int ihit)
{
  if(i[ihit].index<j[ihit].index){//if any index for i is < j then it is less than
    return true;
  }
  else if(i[ihit].index==j[ihit].index){//if equal
    if(ihit < i.size()-1)//and not at the end of the vector
      return is_lessthan(i,j,ihit+1);//look at the next index
      else return false;//otherwise at end of vector being equal so return false
  }
  else return false;//if index is not < or == then it must be > so return false
}

bool SimpleTrack3D_LessThan(SimpleTrack3D i , SimpleTrack3D j)
{//wrapper for recursive is_lessthan

if(i.hits.size()!=j.hits.size()){//if the hits aren't the same size
    if(i.hits.size()<j.hits.size())//and if no. of hits in i < no. of hits in j
      return true; //consider i < j
      else return false; // otherwise i > j
}
return is_lessthan(i.hits,j.hits,0);//i.size should == j.size so we should be able to compare them index by index

}
*/

VtxTrackFinder::VtxTrackFinder(vector<float>& detrad, unsigned int n_phi, unsigned int n_d, unsigned int n_k, unsigned int n_dzdl, unsigned int n_z0, HelixResolution& min_resolution, HelixResolution& max_resolution, HelixRange& range) : HelixHough(n_phi, n_d, n_k, n_dzdl, n_z0, min_resolution, max_resolution, range), using_vertex(false), vertex_sigma_xy(0.002), vertex_sigma_z(0.005), chi2_cut(3.)
{
  for(unsigned int i=0;i<detrad.size();++i)
  {
    detector_radii.push_back(detrad[i]);
  }
}


void VtxTrackFinder::findTracks(vector<SimpleHit3D>& hits, vector<SimpleTrack3D>& tracks)
{
  vector<double> chi2_hits;
  SimpleTrack3D temp_track;
  temp_track.hits.resize(4, hits[0]);
  for(unsigned int i1=0;i1<hits.size();++i1)
  {
    temp_track.hits[0] = hits[i1];
    for(unsigned int i2=(i1+1);i2<hits.size();++i2)
    {
      if( (hits[i2].layer == hits[i1].layer)){continue;}
      temp_track.hits[1] = hits[i2];
      for(unsigned int i3=(i2+1);i3<hits.size();++i3)
      {
        if((hits[i3].layer == hits[i2].layer) || (hits[i3].layer == hits[i1].layer)){continue;}
        temp_track.hits[2] = hits[i3];
        for(unsigned int i4=(i3+1);i4<hits.size();++i4)
        {
          if( (hits[i4].layer == hits[i3].layer) || (hits[i4].layer == hits[i2].layer) || (hits[i4].layer == hits[i1].layer)){continue;}
          temp_track.hits[3] = hits[i4];
          
          vector<unsigned int> tempcomb;
          tempcomb.assign(4,0);
          tempcomb[0] = temp_track.hits[0].index;
          tempcomb[1] = temp_track.hits[1].index;
          tempcomb[2] = temp_track.hits[2].index;
          tempcomb[3] = temp_track.hits[3].index;
          sort(tempcomb.begin(), tempcomb.end());
          set<vector<unsigned int> >::iterator it = combos.find(tempcomb);
          if(it != combos.end()){continue;}
          combos.insert(tempcomb);
          double chi2 = fitTrack(temp_track, chi2_hits);
          if(chi2 > chi2_cut){continue;}
          tracks.push_back(temp_track);
        }
      }
    }
  }
}


void VtxTrackFinder::finalize(vector<SimpleTrack3D>& input, vector<SimpleTrack3D>& output)
{
  unsigned int nt = input.size();
  for(unsigned int i=0;i<nt;++i)
  {
    output.push_back(input[i]);
  }
}


double VtxTrackFinder::fitTrack(SimpleTrack3D& track, vector<double>& chi2_hit)
{
  if(using_vertex == true)
  {
    track.hits.push_back(SimpleHit3D(0.,0., 0.,0., 0.,0., 0, 0));
  }
  
  chi2_hit.clear();
  chi2_hit.resize(track.hits.size(), 0.);
  
  MatrixXf y = MatrixXf::Zero(track.hits.size(), 1);
  for(unsigned int i=0;i<track.hits.size();i++)
  {
    y(i, 0) = ( pow(track.hits[i].x,2) + pow(track.hits[i].y,2) );
    if((using_vertex==true ) && (i == (track.hits.size() - 1))){y(i, 0) /= vertex_sigma_xy;}
    else{y(i, 0) /= layer_xy_resolution[track.hits[i].layer];}
  }
  
  MatrixXf X = MatrixXf::Zero(track.hits.size(), 3);
  for(unsigned int i=0;i<track.hits.size();i++)
  {
    X(i, 0) = track.hits[i].x;
    X(i, 1) = track.hits[i].y;
    X(i, 2) = -1.;
    if((using_vertex==true ) && (i == (track.hits.size() - 1)))
    {
      X(i, 0) /= vertex_sigma_xy;
      X(i, 1) /= vertex_sigma_xy;
      X(i, 2) /= vertex_sigma_xy;
    }
    else
    {
      X(i, 0) /= layer_xy_resolution[track.hits[i].layer];
      X(i, 1) /= layer_xy_resolution[track.hits[i].layer];
      X(i, 2) /= layer_xy_resolution[track.hits[i].layer];
    }
  }
  
  MatrixXf Xt = X.transpose();
  
  MatrixXf prod = Xt*X;
  MatrixXf inv = prod.fullPivLu().inverse();
  
  MatrixXf beta = inv*Xt*y;
  
  float cx = beta(0,0)*0.5;
  float cy = beta(1,0)*0.5;
  float r = sqrt(cx*cx + cy*cy - beta(2,0));
  
  float phi = atan2(cy, cx);
  float d = sqrt(cx*cx + cy*cy) - r;
  float k = 1./r;
  
  MatrixXf diff = y - (X*beta);
  MatrixXf chi2 = (diff.transpose())*diff;
  
  float dx = d*cos(phi);
  float dy = d*sin(phi);
  
  MatrixXf y2 = MatrixXf::Zero(track.hits.size(), 1);
  for(unsigned int i=0;i<track.hits.size();i++)
  {
    y2(i,0) = track.hits[i].z;
    if((using_vertex==true ) && (i == (track.hits.size() - 1))){y2(i, 0) /= vertex_sigma_z;}
    else{y2(i, 0) /= layer_z_resolution[track.hits[i].layer];}
  }
  
  MatrixXf X2 = MatrixXf::Zero(track.hits.size(), 2);
  for(unsigned int i=0;i<track.hits.size();i++)
  {
    float D = sqrt( pow(dx - track.hits[i].x, 2) + pow(dy - track.hits[i].y,2));
    float s = 0.0;
    
    if(0.5*k*D > 0.1)
    {
      float v = 0.5*k*D;
      if(v >= 0.999999){v = 0.999999;}
      s = 2.*asin(v)/k;
    }
    else
    {
      float temp1 = k*D*0.5;temp1*=temp1;
      float temp2 = D*0.5;
      s += 2.*temp2;
      temp2*=temp1;
      s += temp2/3.;
      temp2*=temp1;
      s += (3./20.)*temp2;
      temp2*=temp1;
      s += (5./56.)*temp2;
    }
    
    X2(i,0) = s;  
    X2(i,1) = 1.0;
    
    if((using_vertex==true ) && (i == (track.hits.size() - 1)))
    {
      X2(i, 0) /= vertex_sigma_z;
      X2(i, 1) /= vertex_sigma_z;
    }
    else
    {
      X2(i, 0) /= layer_z_resolution[track.hits[i].layer];
      X2(i, 1) /= layer_z_resolution[track.hits[i].layer];
    }
  }
  
  MatrixXf Xt2 = X2.transpose();
  MatrixXf prod2 = Xt2*X2;
  MatrixXf inv2 = prod2.fullPivLu().inverse();
  MatrixXf beta2 = inv2*Xt2*y2;
  
  MatrixXf diff2 = y2 - (X2*beta2);
  MatrixXf chi2_z = (diff2.transpose())*diff2;
  
  float z0 = beta2(1,0);
  float dzdl = beta2(0,0)/sqrt(1. + beta2(0,0)*beta2(0,0));
  
  track.phi = phi;
  track.d = d;
  track.kappa = k;
  track.dzdl = dzdl;
  track.z0 = z0;
  
  if(track.kappa!=0.)
  {
    r=1./track.kappa;
  }
  else
  {
    r=1.0e10;
  }
  
  cx = (track.d+r)*cos(track.phi);
  cy = (track.d+r)*sin(track.phi);
  
  float chi2_tot = 0.;
  for(unsigned int h=0;h<track.hits.size();h++)
  {
    float dx1 = track.hits[h].x - cx;
    float dy1 = track.hits[h].y - cy;
    
    float dx2 = track.hits[h].x + cx;
    float dy2 = track.hits[h].y + cy;
    
    float xydiff1 = sqrt(dx1*dx1 + dy1*dy1) - r;
    float xydiff2 = sqrt(dx2*dx2 + dy2*dy2) - r;
    float xydiff = xydiff2;
    if(fabs(xydiff1) < fabs(xydiff2)){ xydiff = xydiff1; }
    
    float ls_xy = layer_xy_resolution[track.hits[h].layer];
    if((using_vertex == true) && (h == (track.hits.size() - 1)))
    {
      ls_xy = vertex_sigma_xy;
    }
    
    chi2_hit[h] = 0.;
    chi2_hit[h] += xydiff*xydiff/(ls_xy*ls_xy);
    chi2_hit[h] += diff2(h,0)*diff2(h,0);
    
    chi2_tot += chi2_hit[h];
  }
  
  unsigned int deg_of_freedom = 2*track.hits.size() - 5;
  
  if(using_vertex == true)
  {
    track.hits.pop_back();
    chi2_hit.pop_back();
  }
    
  return (chi2_tot)/((double)(deg_of_freedom));
}