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() [1/4]

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() [2/4]

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

explicit

constructor from XYZ coordinates

Definition at line 17 of file EventShapeVariables.cc.

References set_r(), and setFWmax().

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

EventShapeVariables() [3/4]

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

explicit

constructor from rho eta phi coordinates

Definition at line 25 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() [4/4]

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

explicit

constructor from r theta phi coordinates

Definition at line 36 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::~EventShapeVariables ( )

inline

default destructor

Definition at line 43 of file EventShapeVariables.h.

{};

Member Function Documentation

aplanarity()

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 166 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

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

C()

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 175 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

                              {
  if (!tensors_computed_)
    compTensorsAndVectors();
  return 3. *
         (eigenValues_[0] * eigenValues_[1] + eigenValues_[0] * eigenValues_[2] + eigenValues_[1] * eigenValues_[2]);
}

circularity()

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 71 of file EventShapeVariables.cc.

References custom_jme_cff::area, SiPixelRawToDigiRegional_cfi::deltaPhi, mps_fire::i, inputVectors_, photonAnalyzer_cfi::numberOfSteps, phi, Pi, and createJobs::tmp.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

                                                                               {
  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;
}

compTensorsAndVectors()

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 105 of file EventShapeVariables.cc.

References eigenValues_, eigenValuesNoNorm_, eigenValuesNoNormTmp_, eigenValuesTmp_, eigenVectors_, inputVectors_, SiStripOfflineCRack_cfg::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;
}

computeFWmoments()

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 218 of file EventShapeVariables.cc.

References fwmom_, fwmom_computed_, fwmom_maxl_, mps_fire::i, inputVectors_, dqmiolumiharvest::j, and dqmiodumpmetadata::n.

Referenced by 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

D()

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 185 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

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

getEigenValues()

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

inline

Definition at line 77 of file EventShapeVariables.h.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

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

getEigenValuesNoNorm()

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

inline

Definition at line 82 of file EventShapeVariables.h.

References compTensorsAndVectors(), eigenValuesNoNorm_, and tensors_computed_.

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

getEigenVectors()

const TMatrixD& EventShapeVariables::getEigenVectors ( )

inline

Definition at line 87 of file EventShapeVariables.h.

References compTensorsAndVectors(), eigenVectors_, and tensors_computed_.

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

getFWmoment()

double EventShapeVariables::getFWmoment

(

unsigned

l

)

Definition at line 200 of file EventShapeVariables.cc.

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

                                                  {
  if (l > fwmom_maxl_)
    return 0.;

  if (!fwmom_computed_)
    computeFWmoments();

  return fwmom_[l];

}  // getFWmoment

getFWmoments()

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

(

)

Definition at line 211 of file EventShapeVariables.cc.

References computeFWmoments(), fwmom_, and fwmom_computed_.

                                                           {
  if (!fwmom_computed_)
    computeFWmoments();

  return fwmom_;
}

isotropy()

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 49 of file EventShapeVariables.cc.

References SiPixelRawToDigiRegional_cfi::deltaPhi, mps_fire::i, inputVectors_, photonAnalyzer_cfi::numberOfSteps, phi, and Pi.

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;
    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;
}

set_r()

void EventShapeVariables::set_r

(

double

r

)

set exponent for computation of momentum tensor and related products

invalidate previous cached computations

Definition at line 94 of file EventShapeVariables.cc.

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

Referenced by EventShapeVariables().

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

setFWmax()

void EventShapeVariables::setFWmax

(

unsigned

m

)

set number of Fox-Wolfram moments to compute

Definition at line 194 of file EventShapeVariables.cc.

References fwmom_, fwmom_computed_, fwmom_maxl_, and visualization-live-secondInstance_cfg::m.

Referenced by EventShapeVariables().

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

sphericity()

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 158 of file EventShapeVariables.cc.

References compTensorsAndVectors(), eigenValues_, and tensors_computed_.

Referenced by TtFullHadSignalSel::TtFullHadSignalSel().

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

Member Data Documentation

eigenValues_

std::vector<double> EventShapeVariables::eigenValues_

private

Definition at line 112 of file EventShapeVariables.h.

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

eigenValuesNoNorm_

std::vector<double> EventShapeVariables::eigenValuesNoNorm_

private

Definition at line 112 of file EventShapeVariables.h.

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

eigenValuesNoNormTmp_

TVectorD EventShapeVariables::eigenValuesNoNormTmp_

private

Definition at line 111 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors().

eigenValuesTmp_

TVectorD EventShapeVariables::eigenValuesTmp_

private

Definition at line 111 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors().

eigenVectors_

TMatrixD EventShapeVariables::eigenVectors_

private

Definition at line 110 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors(), and getEigenVectors().

fwmom_

std::vector<double> EventShapeVariables::fwmom_

private

Definition at line 116 of file EventShapeVariables.h.

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

fwmom_computed_

bool EventShapeVariables::fwmom_computed_

private

Definition at line 117 of file EventShapeVariables.h.

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

fwmom_maxl_

unsigned EventShapeVariables::fwmom_maxl_

private

Owen ; save computed Fox-Wolfram moments.

Definition at line 115 of file EventShapeVariables.h.

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

inputVectors_

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

private

caching of input vectors

Definition at line 105 of file EventShapeVariables.h.

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

r_

double EventShapeVariables::r_

private

caching of output

Definition at line 108 of file EventShapeVariables.h.

Referenced by compTensorsAndVectors(), and set_r().

tensors_computed_

bool EventShapeVariables::tensors_computed_

private

Definition at line 109 of file EventShapeVariables.h.

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