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	C ()
double	circularity (const unsigned int &numberOfSteps=1000) const
double	D ()
	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...
const std::vector< double > &	getEigenValues ()
const std::vector< double > &	getEigenValuesNoNorm ()
const TMatrixD &	getEigenVectors ()
double	getFWmoment (unsigned l)
const std::vector< double > &	getFWmoments ()
double	isotropy (const unsigned int &numberOfSteps=1000) const
void	set_r (double r)
	set exponent for computation of momentum tensor and related products More...
void	setFWmax (unsigned m)
	set number of Fox-Wolfram moments to compute More...
double	sphericity ()
	~EventShapeVariables ()
	default destructor More...

Private Member Functions
void	compTensorsAndVectors ()
void	computeFWmoments ()

Private Attributes
std::vector< double >	eigenValues_
std::vector< double >	eigenValuesNoNorm_
TVectorD	eigenValuesNoNormTmp_
TVectorD	eigenValuesTmp_
TMatrixD	eigenVectors_
std::vector< double >	fwmom_
bool	fwmom_computed_
unsigned	fwmom_maxl_
	Owen ; save computed Fox-Wolfram moments. More...
std::vector< math::XYZVector >	inputVectors_
	caching of input vectors More...
double	r_
	caching of output More...
bool	tensors_computed_

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 https://arxiv.org/pdf/hep-ph/0603175v2.pdf#page=524 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 inputVectors_, set_r(), setFWmax(), and edm::View< T >::size().

                                                                                   : eigenVectors_(3,3)
{
  inputVectors_.reserve( inputVectors.size() );
  for (const auto& vec : inputVectors){
    inputVectors_.push_back(math::XYZVector(vec.px(), vec.py(), vec.pz()));
  }
  //default values
  set_r(2.);
  setFWmax(10);
}

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

explicit

constructor from XYZ coordinates

Definition at line 19 of file EventShapeVariables.cc.

References set_r(), and setFWmax().

                                                                                     : inputVectors_(inputVectors), eigenVectors_(3,3)
{
  //default values
  set_r(2.);
  setFWmax(10);
}

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

explicit

constructor from rho eta phi coordinates

Definition at line 27 of file EventShapeVariables.cc.

References inputVectors_, set_r(), and setFWmax().

                                                                                           : eigenVectors_(3,3)
{
  inputVectors_.reserve( inputVectors.size() );
  for (const auto& vec : inputVectors){
    inputVectors_.push_back(math::XYZVector(vec.x(), vec.y(), vec.z()));
  }
  //default values
  set_r(2.);
  setFWmax(10);
}

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

explicit

constructor from r theta phi coordinates

Definition at line 39 of file EventShapeVariables.cc.

References inputVectors_, set_r(), and setFWmax().

                                                                                           : eigenVectors_(3,3)
{
  inputVectors_.reserve( inputVectors.size() );
  for (const auto& vec : inputVectors){
    inputVectors_.push_back(math::XYZVector(vec.x(), vec.y(), vec.z()));
  }
  //default values
  set_r(2.);
  setFWmax(10);
}

EventShapeVariables::~EventShapeVariables ( )

inline

default destructor

Definition at line 44 of file EventShapeVariables.h.

References aplanarity(), C(), circularity(), D(), isotropy(), funct::m, alignCSCRings::r, set_r(), setFWmax(), and sphericity().

{};

Member Function Documentation

double EventShapeVariables::aplanarity

(

)

1.5*q2 where q0>=q1>=q2>=0 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 177 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

{
  if(!tensors_computed_) compTensorsAndVectors();
  return 1.5*eigenValues_[2];
}

double EventShapeVariables::C

(

)

3.*(q0*q1+q0*q2+q1*q2) where q0>=q1>=q2>=0 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 187 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

{
  if(!tensors_computed_) compTensorsAndVectors();
  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 76 of file EventShapeVariables.cc.

References Abs(), jets_cff::area, hiPixelPairStep_cff::deltaPhi, mps_fire::i, inputVectors_, phi, Pi, and tmp.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

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

void EventShapeVariables::compTensorsAndVectors ( )

private

helper function to fill the 3 dimensional momentum tensor from the inputVectors where needed also fill the 3 dimensional vectors of eigen-values and eigen-vectors; the largest (smallest) eigen-value is stored at index position 0 (2)

Definition at line 114 of file EventShapeVariables.cc.

References eigenValues_, eigenValuesNoNorm_, eigenValuesNoNormTmp_, eigenValuesTmp_, eigenVectors_, inputVectors_, p2, r_, and tensors_computed_.

Referenced by aplanarity(), C(), D(), getEigenValues(), getEigenValuesNoNorm(), getEigenVectors(), and sphericity().

{
  if(tensors_computed_) return;

  if ( inputVectors_.size() < 2 ){
    tensors_computed_ = true;
    return;
  }

  TMatrixDSym momentumTensor(3);
  momentumTensor.Zero();

  // fill momentumTensor from inputVectors
  double norm = 0.;
  for (const auto& vec: inputVectors_){
    double p2 = vec.Dot(vec);
    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*vec.x()*vec.x();
    momentumTensor(0,1) += pRminus2*vec.x()*vec.y();
    momentumTensor(0,2) += pRminus2*vec.x()*vec.z();
    momentumTensor(1,0) += pRminus2*vec.y()*vec.x();
    momentumTensor(1,1) += pRminus2*vec.y()*vec.y();
    momentumTensor(1,2) += pRminus2*vec.y()*vec.z();
    momentumTensor(2,0) += pRminus2*vec.z()*vec.x();
    momentumTensor(2,1) += pRminus2*vec.z()*vec.y();
    momentumTensor(2,2) += pRminus2*vec.z()*vec.z();
  }

  if( momentumTensor.IsSymmetric() && ( momentumTensor.NonZeros() != 0 ) ){
    momentumTensor.EigenVectors(eigenValuesNoNormTmp_);
  }
  eigenValuesNoNorm_[0] = eigenValuesNoNormTmp_(0);
  eigenValuesNoNorm_[1] = eigenValuesNoNormTmp_(1);
  eigenValuesNoNorm_[2] = eigenValuesNoNormTmp_(2);

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

  // now get eigens
  if( momentumTensor.IsSymmetric() && ( momentumTensor.NonZeros() != 0 ) ){
    eigenVectors_ = momentumTensor.EigenVectors(eigenValuesTmp_);
  }
  eigenValues_[0] = eigenValuesTmp_(0);
  eigenValues_[1] = eigenValuesTmp_(1);
  eigenValues_[2] = eigenValuesTmp_(2);

  tensors_computed_ = true;  
}

void EventShapeVariables::computeFWmoments ( )

private

reduce computation by exploiting symmetry: all off-diagonal elements appear twice in the sum

compute higher legendre polynomials recursively need to keep track of two previous values

initial cases

store new value

Definition at line 230 of file EventShapeVariables.cc.

References fwmom_, fwmom_computed_, fwmom_maxl_, mps_fire::i, inputVectors_, and gen::n.

Referenced by getEigenVectors(), getFWmoment(), and getFWmoments().

                                           {
  if(fwmom_computed_) return;

  double esum_total(0.) ;
  for ( unsigned int i = 0 ; i < inputVectors_.size() ; i ++ ) {
     esum_total += inputVectors_[i].R() ;
  } // i
  double esum_total_sq = esum_total * esum_total ;

  for ( unsigned int i = 0 ; i < inputVectors_.size() ; i ++ ) {

     double p_i = inputVectors_[i].R() ;
     if ( p_i <= 0 ) continue ;

     for ( unsigned int j = 0 ; j <= i ; j ++ ) {

        double p_j = inputVectors_[j].R() ;
        if ( p_j <= 0 ) continue ;

        int symmetry_factor = 2;
        if( j == i ) symmetry_factor = 1;
        double p_ij = p_i * p_j;
        double cosTheta = inputVectors_[i].Dot( inputVectors_[j] ) / (p_ij) ;
        double pi_pj_over_etot2 = p_ij / esum_total_sq ;

        double Pn1 = 0;
        double Pn2 = 0;
        for ( unsigned n = 0; n < fwmom_maxl_; n ++ ) {
            if ( n == 0 ) {
                Pn2 = pi_pj_over_etot2;
                fwmom_[0] += Pn2*symmetry_factor;
            }
            else if ( n == 1 ) {
                Pn1 = pi_pj_over_etot2 * cosTheta;
                fwmom_[1] += Pn1*symmetry_factor;
            }
            else {
                double Pn = ((2*n-1)*cosTheta*Pn1 - (n-1)*Pn2)/n;
                fwmom_[n] += Pn*symmetry_factor;
                Pn2 = Pn1;
                Pn1 = Pn;
            }
        }

     } // j
  } // i

  fwmom_computed_ = true;

} // computeFWmoments

double EventShapeVariables::D

(

)

27.*(q0*q1*q2) where q0>=q1>=q2>=0 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 4-jet structure of the event (D vanishes for a planar event)

27.*(q0*q1*q2) where q0>=q1>=q2>=0 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 197 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

{
  if(!tensors_computed_) compTensorsAndVectors();
  return 27.*eigenValues_[0]*eigenValues_[1]*eigenValues_[2];
}

const std::vector<double>& EventShapeVariables::getEigenValues ( )

inline

Definition at line 78 of file EventShapeVariables.h.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

{ if(!tensors_computed_) compTensorsAndVectors(); return eigenValues_; }

const std::vector<double>& EventShapeVariables::getEigenValuesNoNorm ( )

inline

Definition at line 79 of file EventShapeVariables.h.

References compTensorsAndVectors(), eigenValuesNoNorm_, and tensors_computed_.

{ if(!tensors_computed_) compTensorsAndVectors(); return eigenValuesNoNorm_; }

const TMatrixD& EventShapeVariables::getEigenVectors ( )

inline

Definition at line 80 of file EventShapeVariables.h.

References compTensorsAndVectors(), computeFWmoments(), eigenVectors_, getFWmoment(), getFWmoments(), checklumidiff::l, and tensors_computed_.

{ if(!tensors_computed_) compTensorsAndVectors(); return eigenVectors_; }

double EventShapeVariables::getFWmoment

(

unsigned

l

)

Definition at line 214 of file EventShapeVariables.cc.

References computeFWmoments(), fwmom_, fwmom_computed_, fwmom_maxl_, and checklumidiff::l.

Referenced by getEigenVectors().

                                                    {

  if ( l > fwmom_maxl_ ) return 0. ;

  if ( !fwmom_computed_ ) computeFWmoments() ;

  return fwmom_[l] ;

} // getFWmoment

const std::vector< double > & EventShapeVariables::getFWmoments

(

)

Definition at line 224 of file EventShapeVariables.cc.

References computeFWmoments(), fwmom_, and fwmom_computed_.

Referenced by getEigenVectors().

                                                           {
  if ( !fwmom_computed_ ) computeFWmoments() ;

  return fwmom_;
}

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 54 of file EventShapeVariables.cc.

References Abs(), hiPixelPairStep_cff::deltaPhi, mps_fire::i, inputVectors_, phi, and Pi.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

{
  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;
    double cosphi = TMath::Cos(phi);
    double sinphi = TMath::Sin(phi);
    for(const auto& vec : inputVectors_){
      // sum over inner product of unit vectors and momenta
      sum+=TMath::Abs(cosphi*vec.x()+sinphi*vec.y());
    }
    if( eOut<0. || sum<eOut ) eOut=sum;
    if( eIn <0. || sum>eIn  ) eIn =sum;
  }
  return (eIn-eOut)/eIn;
}

void EventShapeVariables::set_r

(

double

r

)

set exponent for computation of momentum tensor and related products

invalidate previous cached computations

Definition at line 101 of file EventShapeVariables.cc.

References eigenValues_, eigenValuesNoNorm_, alignCSCRings::r, r_, and tensors_computed_.

Referenced by EventShapeVariables(), and ~EventShapeVariables().

{
  r_ = r;
  tensors_computed_ = false;
  eigenValues_ = std::vector<double>(3,0);
  eigenValuesNoNorm_ = std::vector<double>(3,0);
}

void EventShapeVariables::setFWmax

(

unsigned

m

)

set number of Fox-Wolfram moments to compute

Definition at line 207 of file EventShapeVariables.cc.

References fwmom_, fwmom_computed_, fwmom_maxl_, and funct::m.

Referenced by EventShapeVariables(), and ~EventShapeVariables().

{
  fwmom_maxl_ = m;
  fwmom_computed_ = false;
  fwmom_ = std::vector<double>(fwmom_maxl_,0.);
}

double EventShapeVariables::sphericity

(

)

1.5*(q1+q2) where q0>=q1>=q2>=0 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 168 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel(), and ~EventShapeVariables().

{
  if(!tensors_computed_) compTensorsAndVectors();
  return 1.5*(eigenValues_[1] + eigenValues_[2]);
}

Member Data Documentation

std::vector<double> EventShapeVariables::eigenValues_

private

Definition at line 101 of file EventShapeVariables.h.

Referenced by aplanarity(), C(), compTensorsAndVectors(), D(), getEigenValues(), set_r(), and sphericity().

std::vector<double> EventShapeVariables::eigenValuesNoNorm_

private

Definition at line 101 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors(), getEigenValuesNoNorm(), and set_r().

TVectorD EventShapeVariables::eigenValuesNoNormTmp_

private

Definition at line 100 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors().

TVectorD EventShapeVariables::eigenValuesTmp_

private

Definition at line 100 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors().

TMatrixD EventShapeVariables::eigenVectors_

private

Definition at line 99 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors(), and getEigenVectors().

std::vector<double> EventShapeVariables::fwmom_

private

Definition at line 105 of file EventShapeVariables.h.

Referenced by computeFWmoments(), getFWmoment(), getFWmoments(), and setFWmax().

bool EventShapeVariables::fwmom_computed_

private

Definition at line 106 of file EventShapeVariables.h.

Referenced by computeFWmoments(), getFWmoment(), getFWmoments(), and setFWmax().

unsigned EventShapeVariables::fwmom_maxl_

private

Owen ; save computed Fox-Wolfram moments.

Definition at line 104 of file EventShapeVariables.h.

Referenced by computeFWmoments(), getFWmoment(), and setFWmax().

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

private

caching of input vectors

Definition at line 94 of file EventShapeVariables.h.

Referenced by circularity(), compTensorsAndVectors(), computeFWmoments(), EventShapeVariables(), and isotropy().

double EventShapeVariables::r_

private

caching of output

Definition at line 97 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors(), and set_r().

bool EventShapeVariables::tensors_computed_

private

Definition at line 98 of file EventShapeVariables.h.

Referenced by aplanarity(), C(), compTensorsAndVectors(), D(), getEigenValues(), getEigenValuesNoNorm(), getEigenVectors(), set_r(), and sphericity().