EventShapeVariables Class Reference

Class for the calculation of several event shape variables. More...

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

Public Member Functions
double	aplanarity (double=2.) const
double	C (double=2.) const
double	circularity (const unsigned int &numberOfSteps=1000) const
double	D (double=2.) const
	EventShapeVariables (const edm::View< reco::Candidate > &inputVectors)
	constructor from reco::Candidates More...
	EventShapeVariables (const std::vector< math::XYZVector > &inputVectors)
	constructor from XYZ coordinates More...
	EventShapeVariables (const std::vector< math::RhoEtaPhiVector > &inputVectors)
	constructor from rho eta phi coordinates More...
	EventShapeVariables (const std::vector< math::RThetaPhiVector > &inputVectors)
	constructor from r theta phi coordinates More...
double	isotropy (const unsigned int &numberOfSteps=1000) const
double	sphericity (double=2.) const
	~EventShapeVariables ()
	default destructor More...

Private Member Functions
TVectorD	compEigenValues (double=2.) const
TMatrixDSym	compMomentumTensor (double=2.) const
	helper function to fill the 3 dimensional momentum tensor from the inputVecotrs where needed More...

Private Attributes
std::vector< math::XYZVector >	inputVectors_
	cashing of input vectors More...

Detailed Description

Class for the calculation of several event shape variables.

Class for the calculation of several event shape variables. Isotropy, sphericity, aplanarity and circularity are supported. The class supports vectors of 3d vectors and edm::Views of reco::Candidates as input. The 3d vectors can be given in cartesian, cylindrical or polar coordinates. It exploits the ROOT::TMatrixDSym for the calculation of the sphericity and aplanarity.

See http://cepa.fnal.gov/psm/simulation/mcgen/lund/pythia_manual/pythia6.3/pythia6301/node213.html for an explanation of sphericity, aplanarity and the quantities C and D.

Author: Sebastian Naumann-Emme, University of Hamburg Roger Wolf, University of Hamburg Christian Veelken, UC Davis

Definition at line 32 of file EventShapeVariables.h.

Constructor & Destructor Documentation

EventShapeVariables::EventShapeVariables ( const edm::View< reco::Candidate > &  inputVectors )

explicit

constructor from reco::Candidates

Definition at line 6 of file EventShapeVariables.cc.

References edm::View< T >::begin(), edm::View< T >::end(), inputVectors_, and edm::View< T >::size().

{
  //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 )

explicit

constructor from XYZ coordinates

Definition at line 16 of file EventShapeVariables.cc.

  : inputVectors_(inputVectors)
{}

EventShapeVariables::EventShapeVariables ( const std::vector< math::RhoEtaPhiVector > &  inputVectors )

explicit

constructor from rho eta phi coordinates

Definition at line 21 of file EventShapeVariables.cc.

References 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 )

explicit

constructor from r theta phi coordinates

Definition at line 30 of file EventShapeVariables.cc.

References 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()));
  }
}

EventShapeVariables::~EventShapeVariables ( )

inline

default destructor

Definition at line 44 of file EventShapeVariables.h.

{};

Member Function Documentation

double EventShapeVariables::aplanarity

(

double

r = 2.

)

const

1.5*q1 where 0<=q1<=q2<=q3 are the eigenvalues of the momemtum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return values are 0.5 for spherical and 0 for plane and linear events

1.5*q1 where 0<=q1<=q2<=q3 are the eigenvalues of the momentum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return values are 0.5 for spherical and 0 for plane and linear events

Definition at line 153 of file EventShapeVariables.cc.

References compEigenValues().

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  TVectorD eigenValues = compEigenValues(r);
  return 1.5*eigenValues(2);
}

double EventShapeVariables::C

(

double

r = 2.

)

const

3.*(q1*q2+q1*q3+q2*q3) where 0<=q1<=q2<=q3 are the eigenvalues of the momemtum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return value is between 0 and 1 and measures the 3-jet structure of the event (C vanishes for a "perfect" 2-jet event)

3.*(q1*q2+q1*q3+q2*q3) where 0<=q1<=q2<=q3 are the eigenvalues of the momentum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return value is between 0 and 1 and measures the 3-jet structure of the event (C vanishes for a "perfect" 2-jet event)

Definition at line 163 of file EventShapeVariables.cc.

References compEigenValues().

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  TVectorD eigenValues = compEigenValues(r);
  return 3.*(eigenValues(0)*eigenValues(1) + eigenValues(0)*eigenValues(2) + eigenValues(1)*eigenValues(2));
}

double EventShapeVariables::circularity

(

const unsigned int &

numberOfSteps = 1000

)

const

the return value is 1 for spherical and 0 linear events in r-phi. This function needs the number of steps to determine how fine the granularity of the algorithm in phi should be

Definition at line 62 of file EventShapeVariables.cc.

References Abs(), SiPixelRawToDigiRegional_cfi::deltaPhi, i, inputVectors_, j, phi, Pi, tmp, x, and y.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  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;
}

TVectorD EventShapeVariables::compEigenValues ( double  r = 2. ) const

private

helper function to fill the 3 dimensional vector of eigen-values; the largest (smallest) eigen-value is stored at index position 0 (2)

Definition at line 124 of file EventShapeVariables.cc.

References compMomentumTensor().

Referenced by aplanarity(), C(), D(), and sphericity().

{
  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;
}

TMatrixDSym EventShapeVariables::compMomentumTensor ( double  r = 2. ) const

private

helper function to fill the 3 dimensional momentum tensor from the inputVecotrs where needed

helper function to fill the 3 dimensional momentum tensor from the inputVectors where needed

Definition at line 85 of file EventShapeVariables.cc.

References i, inputVectors_, and p2.

Referenced by compEigenValues().

{
  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;
}

double EventShapeVariables::D

(

double

r = 2.

)

const

27.*(q1*q2*q3) where 0<=q1<=q2<=q3 are the eigenvalues of the momemtum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return value is between 0 and 1 and measures the 4-jet structure of the event (D vanishes for a planar event)

Definition at line 173 of file EventShapeVariables.cc.

References compEigenValues().

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  TVectorD eigenValues = compEigenValues(r);
  return 27.*eigenValues(0)*eigenValues(1)*eigenValues(2);
}

double EventShapeVariables::isotropy

(

const unsigned int &

numberOfSteps = 1000

)

const

the return value is 1 for spherical events and 0 for events linear in r-phi. This function needs the number of steps to determine how fine the granularity of the algorithm in phi should be

Definition at line 42 of file EventShapeVariables.cc.

References Abs(), SiPixelRawToDigiRegional_cfi::deltaPhi, i, inputVectors_, j, phi, Pi, x, and y.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  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::sphericity

(

double

r = 2.

)

const

1.5*(q1+q2) where 0<=q1<=q2<=q3 are the eigenvalues of the momemtum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return values are 1 for spherical, 3/4 for plane and 0 for linear events

1.5*(q1+q2) where 0<=q1<=q2<=q3 are the eigenvalues of the momentum tensor sum{p_j[a]*p_j[b]}/sum{p_j**2} normalized to 1. Return values are 1 for spherical, 3/4 for plane and 0 for linear events

Definition at line 144 of file EventShapeVariables.cc.

References compEigenValues().

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

{
  TVectorD eigenValues = compEigenValues(r);
  return 1.5*(eigenValues(1) + eigenValues(2));
}

Member Data Documentation

std::vector<math::XYZVector> EventShapeVariables::inputVectors_

private

cashing of input vectors

Definition at line 79 of file EventShapeVariables.h.

Referenced by circularity(), compMomentumTensor(), EventShapeVariables(), and isotropy().