EventShapeVariables.cc

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#include "PhysicsTools/CandUtils/interface/EventShapeVariables.h"

#include "TMath.h"

EventShapeVariables::EventShapeVariables(const edm::View<reco::Candidate>& inputVectors)
{
  //std::cout << "inputVectors.size = " << inputVectors.size() << std::endl;
  inputVectors_.reserve( inputVectors.size() );
  for ( edm::View<reco::Candidate>::const_iterator vec = inputVectors.begin(); vec != inputVectors.end(); ++vec){
    inputVectors_.push_back(math::XYZVector(vec->px(), vec->py(), vec->pz()));
  }
}

EventShapeVariables::EventShapeVariables(const std::vector<math::XYZVector>& inputVectors) 
  : inputVectors_(inputVectors)
{}

EventShapeVariables::EventShapeVariables(const std::vector<math::RhoEtaPhiVector>& inputVectors)
{
  inputVectors_.reserve( inputVectors.size() );
  for ( std::vector<math::RhoEtaPhiVector>::const_iterator vec = inputVectors.begin(); vec != inputVectors.end(); ++vec ){
    inputVectors_.push_back(math::XYZVector(vec->x(), vec->y(), vec->z()));
  }
}

EventShapeVariables::EventShapeVariables(const std::vector<math::RThetaPhiVector>& inputVectors)
{
  inputVectors_.reserve( inputVectors.size() );
  for(std::vector<math::RThetaPhiVector>::const_iterator vec = inputVectors.begin(); vec != inputVectors.end(); ++vec ){
    inputVectors_.push_back(math::XYZVector(vec->x(), vec->y(), vec->z()));
  }
}
  
double 
EventShapeVariables::isotropy(const unsigned int& numberOfSteps) const
{
  const double deltaPhi=2*TMath::Pi()/numberOfSteps;
  double phi = 0, eIn =-1., eOut=-1.;
  for(unsigned int i=0; i<numberOfSteps; ++i){
    phi+=deltaPhi;
    double sum=0;
    for(unsigned int j=0; j<inputVectors_.size(); ++j){
      // sum over inner product of unit vectors and momenta
      sum+=TMath::Abs(TMath::Cos(phi)*inputVectors_[j].x()+TMath::Sin(phi)*inputVectors_[j].y());
    }
    if( eOut<0. || sum<eOut ) eOut=sum;
    if( eIn <0. || sum>eIn  ) eIn =sum;
  }
  return (eIn-eOut)/eIn;
}

double 
EventShapeVariables::circularity(const unsigned int& numberOfSteps) const
{
  const double deltaPhi=2*TMath::Pi()/numberOfSteps;
  double circularity=-1, phi=0, area = 0;
  for(unsigned int i=0;i<inputVectors_.size();i++) {
    area+=TMath::Sqrt(inputVectors_[i].x()*inputVectors_[i].x()+inputVectors_[i].y()*inputVectors_[i].y());
  }
  for(unsigned int i=0; i<numberOfSteps; ++i){
    phi+=deltaPhi;
    double sum=0, tmp=0.;
    for(unsigned int j=0; j<inputVectors_.size(); ++j){
      sum+=TMath::Abs(TMath::Cos(phi)*inputVectors_[j].x()+TMath::Sin(phi)*inputVectors_[j].y());
    }
    tmp=TMath::Pi()/2*sum/area;
    if( circularity<0 || tmp<circularity ){
      circularity=tmp;
    }
  }
  return circularity;
}

TMatrixDSym 
EventShapeVariables::compMomentumTensor(double r) const
{
  TMatrixDSym momentumTensor(3);
  momentumTensor.Zero();

  if ( inputVectors_.size() < 2 ){
    return momentumTensor;
  }

  // fill momentumTensor from inputVectors
  double norm = 0.;
  for ( int i = 0; i < (int)inputVectors_.size(); ++i ){
    double p2 = inputVectors_[i].Dot(inputVectors_[i]);
    double pR = ( r == 2. ) ? p2 : TMath::Power(p2, 0.5*r);
    norm += pR;
    double pRminus2 = ( r == 2. ) ? 1. : TMath::Power(p2, 0.5*r - 1.);
    momentumTensor(0,0) += pRminus2*inputVectors_[i].x()*inputVectors_[i].x();
    momentumTensor(0,1) += pRminus2*inputVectors_[i].x()*inputVectors_[i].y();
    momentumTensor(0,2) += pRminus2*inputVectors_[i].x()*inputVectors_[i].z();
    momentumTensor(1,0) += pRminus2*inputVectors_[i].y()*inputVectors_[i].x();
    momentumTensor(1,1) += pRminus2*inputVectors_[i].y()*inputVectors_[i].y();
    momentumTensor(1,2) += pRminus2*inputVectors_[i].y()*inputVectors_[i].z();
    momentumTensor(2,0) += pRminus2*inputVectors_[i].z()*inputVectors_[i].x();
    momentumTensor(2,1) += pRminus2*inputVectors_[i].z()*inputVectors_[i].y();
    momentumTensor(2,2) += pRminus2*inputVectors_[i].z()*inputVectors_[i].z();
  }

  //std::cout << "momentumTensor:" << std::endl;
  //std::cout << momentumTensor(0,0) << " " << momentumTensor(0,1) << " " << momentumTensor(0,2) 
  //          << momentumTensor(1,0) << " " << momentumTensor(1,1) << " " << momentumTensor(1,2) 
  //          << momentumTensor(2,0) << " " << momentumTensor(2,1) << " " << momentumTensor(2,2) << std::endl;

  // return momentumTensor normalized to determinant 1
  return (1./norm)*momentumTensor;
}

TVectorD
EventShapeVariables::compEigenValues(double r) const
{
  TVectorD eigenValues(3);
  TMatrixDSym myTensor = compMomentumTensor(r);
  if( myTensor.IsSymmetric() ){
    if( myTensor.NonZeros() != 0 ) myTensor.EigenVectors(eigenValues);
  }

  // CV: TMatrixDSym::EigenVectors returns eigen-values and eigen-vectors
  //     ordered by descending eigen-values, so no need to do any sorting here...
  //std::cout << "eigenValues(0) = " << eigenValues(0) << ","
  //          << " eigenValues(1) = " << eigenValues(1) << ","
  //          << " eigenValues(2) = " << eigenValues(2) << std::endl;

  return eigenValues;
}

double 
EventShapeVariables::sphericity(double r) const
{
  TVectorD eigenValues = compEigenValues(r);
  return 1.5*(eigenValues(1) + eigenValues(2));
}

double 
EventShapeVariables::aplanarity(double r) const
{
  TVectorD eigenValues = compEigenValues(r);
  return 1.5*eigenValues(2);
}

double 
EventShapeVariables::C(double r) const
{
  TVectorD eigenValues = compEigenValues(r);
  return 3.*(eigenValues(0)*eigenValues(1) + eigenValues(0)*eigenValues(2) + eigenValues(1)*eigenValues(2));
}

double 
EventShapeVariables::D(double r) const
{
  TVectorD eigenValues = compEigenValues(r);
  return 27.*eigenValues(0)*eigenValues(1)*eigenValues(2);
}