EventShape.cc

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#include "DPGAnalysis/SiStripTools/interface/EventShape.h"
#include <DataFormats/TrackReco/interface/Track.h>
#include <TVector3.h>
#include <vector>
#include <TMatrixDSym.h>
#include <TMatrixDSymEigen.h>
#include <TVectorD.h>

using namespace edm;
using namespace reco;
using namespace std;
using reco::TrackCollection;

EventShape::EventShape(reco::TrackCollection& tracks) : eigenvalues(3) {
  for (reco::TrackCollection::const_iterator itTrack = tracks.begin(); itTrack < tracks.end(); ++itTrack) {
    p.push_back(TVector3(itTrack->px(), itTrack->py(), itTrack->pz()));
  }

  // first fill the momentum tensor
  TMatrixDSym MomentumTensor(3);
  for (std::vector<TVector3>::const_iterator momentum = p.begin(); momentum < p.end(); ++momentum) {
    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j <= i; j++) {
        MomentumTensor[i][j] += momentum[i] * momentum[j];
      }
  }
  MomentumTensor *= 1 / (MomentumTensor[0][0] + MomentumTensor[1][1] + MomentumTensor[2][2]);
  // find the eigen values
  TMatrixDSymEigen eigen(MomentumTensor);
  TVectorD eigenvals = eigen.GetEigenValues();
  eigenvalues[0] = eigenvals[0];
  eigenvalues[1] = eigenvals[1];
  eigenvalues[2] = eigenvals[2];
  sort(eigenvalues.begin(), eigenvalues.end());
}

math::XYZTLorentzVectorF EventShape::thrust() const {
  math::XYZTLorentzVectorF output = math::XYZTLorentzVectorF(0, 0, 0, 0);
  TVector3 qtbo;
  TVector3 zero(0., 0., 0.);
  float vnew = 0.;
  uint32_t Np = p.size();

  // for more than 2 tracks
  if (Np > 2) {
    float vmax = 0.;
    TVector3 vn, vm, vc, vl;
    for (unsigned int i = 0; i < Np - 1; i++)
      for (unsigned int j = i + 1; j < Np; j++) {
        vc = p[i].Cross(p[j]);
        vl = zero;
        for (unsigned int k = 0; k < Np; k++)
          if ((k != i) && (k != j)) {
            if (p[k].Dot(vc) >= 0.)
              vl = vl + p[k];
            else
              vl = vl - p[k];
          }
        // make all four sign-combinations for i,j
        vn = vl + p[j] + p[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl + p[j] - p[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl - p[j] + p[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl - p[j] - p[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
      }
    // sum momenta of all particles and iterate
    for (int iter = 1; iter <= 4; iter++) {
      qtbo = zero;
      for (unsigned int i = 0; i < Np; i++)
        if (vm.Dot(p[i]) >= 0.)
          qtbo = qtbo + p[i];
        else
          qtbo = qtbo - p[i];
      vnew = qtbo.Mag2();
      if (vnew == vmax)
        break;
      vmax = vnew;
      vm = qtbo;
    }
  }  // of if Np > 2
  else if (Np == 2)
    if (p[0].Dot(p[1]) >= 0.)
      qtbo = p[0] + p[1];
    else
      qtbo = p[0] - p[1];
  else if (Np == 1)
    qtbo = p[0];
  else {
    qtbo = zero;
    return output;
  }
  // normalize thrust -division by total momentum-
  float vsum = 0.;
  for (unsigned int i = 0; i < Np; i++)
    vsum = vsum + p[i].Mag();
  vnew = qtbo.Mag();
  float v = vnew / vsum;
  float x = qtbo.X() / vnew;
  float y = qtbo.Y() / vnew;
  float z = qtbo.Z() / vnew;
  output.SetPxPyPzE(x, y, z, v);
  return output;
}

math::XYZTLorentzVectorF EventShape::thrust(const reco::TrackCollection& tracks) {
  std::vector<TVector3> pp;
  uint32_t Np = tracks.size();
  math::XYZTLorentzVectorF output = math::XYZTLorentzVectorF(0, 0, 0, 0);
  for (reco::TrackCollection::const_iterator itTrack = tracks.begin(); itTrack < tracks.end(); ++itTrack) {
    pp.push_back(TVector3(itTrack->px(), itTrack->py(), itTrack->pz()));
  }
  TVector3 qtbo;
  TVector3 zero(0., 0., 0.);
  float vnew = 0.;

  // for more than 2 tracks
  if (Np > 2) {
    float vmax = 0.;
    TVector3 vn, vm, vc, vl;
    for (unsigned int i = 0; i < Np - 1; i++)
      for (unsigned int j = i + 1; j < Np; j++) {
        vc = pp[i].Cross(pp[j]);
        vl = zero;
        for (unsigned int k = 0; k < Np; k++)
          if ((k != i) && (k != j)) {
            if (pp[k].Dot(vc) >= 0.)
              vl = vl + pp[k];
            else
              vl = vl - pp[k];
          }
        // make all four sign-combinations for i,j
        vn = vl + pp[j] + pp[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl + pp[j] - pp[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl - pp[j] + pp[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
        vn = vl - pp[j] - pp[i];
        vnew = vn.Mag2();
        if (vnew > vmax) {
          vmax = vnew;
          vm = vn;
        }
      }
    // sum momenta of all particles and iterate
    for (int iter = 1; iter <= 4; iter++) {
      qtbo = zero;
      for (unsigned int i = 0; i < Np; i++)
        if (vm.Dot(pp[i]) >= 0.)
          qtbo = qtbo + pp[i];
        else
          qtbo = qtbo - pp[i];
      vnew = qtbo.Mag2();
      if (vnew == vmax)
        break;
      vmax = vnew;
      vm = qtbo;
    }
  }  // of if Np > 2
  else if (Np == 2)
    if (pp[0].Dot(pp[1]) >= 0.)
      qtbo = pp[0] + pp[1];
    else
      qtbo = pp[0] - pp[1];
  else if (Np == 1)
    qtbo = pp[0];
  else {
    qtbo = zero;
    return output;
  }
  // normalize thrust -division by total momentum-
  float vsum = 0.;
  for (unsigned int i = 0; i < Np; i++)
    vsum = vsum + pp[i].Mag();
  vnew = qtbo.Mag();
  float v = vnew / vsum;
  float x = qtbo.X() / vnew;
  float y = qtbo.Y() / vnew;
  float z = qtbo.Z() / vnew;
  output.SetPxPyPzE(x, y, z, v);
  return output;
}

float EventShape::sphericity(const reco::TrackCollection& tracks) {
  // a critical check
  if (tracks.empty())
    return 0;

  // first fill the momentum tensor
  TMatrixDSym MomentumTensor(3);
  for (reco::TrackCollection::const_iterator itTrack = tracks.begin(); itTrack < tracks.end(); ++itTrack) {
    std::vector<double> momentum(3);
    momentum[0] = itTrack->px();
    momentum[1] = itTrack->py();
    momentum[2] = itTrack->pz();
    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j <= i; j++) {
        MomentumTensor[i][j] += momentum[i] * momentum[j];
      }
  }
  MomentumTensor *= 1 / (MomentumTensor[0][0] + MomentumTensor[1][1] + MomentumTensor[2][2]);
  // find the eigen values
  TMatrixDSymEigen eigen(MomentumTensor);
  TVectorD eigenvals = eigen.GetEigenValues();
  vector<float> eigenvaluess(3);
  eigenvaluess[0] = eigenvals[0];
  eigenvaluess[1] = eigenvals[1];
  eigenvaluess[2] = eigenvals[2];
  sort(eigenvaluess.begin(), eigenvaluess.end());
  // compute spericity
  float sph = (1.5 * (1 - eigenvaluess[2]));
  return sph;
}

float EventShape::aplanarity(const reco::TrackCollection& tracks) {
  // a critical check
  if (tracks.empty())
    return 0;
  // first fill the momentum tensor
  TMatrixDSym MomentumTensor(3);
  for (reco::TrackCollection::const_iterator itTrack = tracks.begin(); itTrack < tracks.end(); ++itTrack) {
    std::vector<double> momentum(3);
    momentum[0] = itTrack->px();
    momentum[1] = itTrack->py();
    momentum[2] = itTrack->pz();
    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j <= i; j++) {
        MomentumTensor[i][j] += momentum[i] * momentum[j];
      }
  }
  MomentumTensor *= 1 / (MomentumTensor[0][0] + MomentumTensor[1][1] + MomentumTensor[2][2]);
  // find the eigen values
  TMatrixDSymEigen eigen(MomentumTensor);
  TVectorD eigenvals = eigen.GetEigenValues();
  vector<float> eigenvaluess(3);
  eigenvaluess[0] = eigenvals[0];
  eigenvaluess[1] = eigenvals[1];
  eigenvaluess[2] = eigenvals[2];
  sort(eigenvaluess.begin(), eigenvaluess.end());
  // compute aplanarity
  return (1.5 * eigenvaluess[0]);
}

float EventShape::planarity(const reco::TrackCollection& tracks) {
  // First a critical check
  if (tracks.empty())
    return 0;
  // first fill the momentum tensor
  TMatrixDSym MomentumTensor(3);
  for (reco::TrackCollection::const_iterator itTrack = tracks.begin(); itTrack < tracks.end(); ++itTrack) {
    std::vector<double> momentum(3);
    momentum[0] = itTrack->px();
    momentum[1] = itTrack->py();
    momentum[2] = itTrack->pz();
    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j <= i; j++) {
        MomentumTensor[i][j] += momentum[i] * momentum[j];
      }
  }
  MomentumTensor *= 1 / (MomentumTensor[0][0] + MomentumTensor[1][1] + MomentumTensor[2][2]);
  // find the eigen values
  TMatrixDSymEigen eigen(MomentumTensor);
  TVectorD eigenvals = eigen.GetEigenValues();
  vector<float> eigenvaluess(3);
  eigenvaluess[0] = eigenvals[0];
  eigenvaluess[1] = eigenvals[1];
  eigenvaluess[2] = eigenvals[2];
  sort(eigenvaluess.begin(), eigenvaluess.end());
  // compute planarity
  return (eigenvaluess[0] / eigenvaluess[1]);
}

float EventShape::sphericity() const {
  // compute sphericity
  return (1.5 * (1 - eigenvalues[2]));
}

float EventShape::aplanarity() const {
  // compute aplanarity
  return (1.5 * eigenvalues[0]);
}

float EventShape::planarity() const {
  // compute planarity
  return (eigenvalues[0] / eigenvalues[1]);
}