Trk::GaussianTrackDensity::TrackDensity Class Reference

Inheritance diagram for Trk::GaussianTrackDensity::TrackDensity:

Collaboration diagram for Trk::GaussianTrackDensity::TrackDensity:

Classes
struct	pred_entry_by_max
struct	pred_perigee

Public Member Functions
	TrackDensity (bool gaussStep)
virtual	~TrackDensity ()=default
virtual double	trackDensity (double z) const override final
	Evaluate the density function at the specified coordinate along the beamline.
virtual void	trackDensity (double z, double &density, double &firstDerivative, double &secondDerivative) const override final
	Evaluate the density and its first two derivatives at the specified coordinate.
double	globalMaximum () const
	Return position of global maximum for density function.
std::pair< double, double >	globalMaximumWithWidth () const
	Return position of global maximum with Gaussian width for density function.
void	addTrack (const Perigee &itrk, const double d0SignificanceCut, const double z0SignificanceCut)
	Add a track to the set being considered.

Private Types
using	trackMap
using	lowerMap

Private Member Functions
void	updateMaximum (double trialZ, double trialValue, double secondDerivative, double &maxZ, double &maxValue, double &maxSecondDerivative) const
double	stepSize (double y, double dy, double ddy) const

Private Attributes
bool	m_gaussStep
double	m_maxRange = 0
trackMap	m_trackMap
lowerMap	m_lowerMap

Detailed Description

Definition at line 114 of file GaussianTrackDensity.h.

Member Typedef Documentation

lowerMap

using Trk::GaussianTrackDensity::TrackDensity::lowerMap

private

Initial value:

 std::map<
            GaussianTrackDensity::TrackEntry, Perigee, pred_entry_by_max,
            SG::ArenaPoolSTLAllocator<
                std::pair<const GaussianTrackDensity::TrackEntry, Perigee>>>

Definition at line 189 of file GaussianTrackDensity.h.

trackMap

using Trk::GaussianTrackDensity::TrackDensity::trackMap

private

Initial value:

 
            std::map<Perigee, GaussianTrackDensity::TrackEntry, pred_perigee,
                     SG::ArenaPoolSTLAllocator<std::pair<
                         const Perigee, GaussianTrackDensity::TrackEntry>>>

Definition at line 184 of file GaussianTrackDensity.h.

Constructor & Destructor Documentation

TrackDensity()

Trk::GaussianTrackDensity::TrackDensity::TrackDensity ( bool gaussStep )

inlineexplicit

Definition at line 116 of file GaussianTrackDensity.h.

: m_gaussStep(gaussStep) {}

~TrackDensity()

virtual Trk::GaussianTrackDensity::TrackDensity::~TrackDensity ( )

virtualdefault

Member Function Documentation

addTrack()

void Trk::GaussianTrackDensity::TrackDensity::addTrack	(	const Perigee &	itrk,
		const double	d0SignificanceCut,
		const double	z0SignificanceCut )

Add a track to the set being considered.

Parameters

itrk	Track parameters.
d0SignificanceCut	Significance cut on d0.
z0SignificanceCut	Significance cut on z0.

Definition at line 222 of file GaussianTrackDensity.cxx.

  {
    if (m_trackMap.count(itrk) != 0) return;
    const double d0 = itrk.parameters()[Trk::d0];
    const double z0 = itrk.parameters()[Trk::z0];
    const AmgSymMatrix(5) & perigeeCov = *(itrk.covariance());
    const double cov_dd = perigeeCov(Trk::d0, Trk::d0);
    if ( cov_dd <= 0 ) return;
    if ( d0*d0/cov_dd > d0SignificanceCut ) return;
    const double cov_zz = perigeeCov(Trk::z0, Trk::z0);
    if (cov_zz <= 0 ) return;
    const double cov_dz = perigeeCov(Trk::d0, Trk::z0);
    const double covDeterminant = cov_dd*cov_zz - cov_dz*cov_dz;
    if ( covDeterminant <= 0 ) return;
    double constantTerm = -(d0*d0*cov_zz + z0*z0*cov_dd + 2*d0*z0*cov_dz) / (2*covDeterminant);
    const double linearTerm = (d0*cov_dz + z0*cov_dd) / covDeterminant ; // minus signs and factors of 2 cancel...
    const double quadraticTerm = -cov_dd / (2*covDeterminant);
    double discriminant = linearTerm*linearTerm - 4*quadraticTerm*(constantTerm + 2*z0SignificanceCut);
    if (discriminant < 0) return;
    discriminant = std::sqrt(discriminant);
    const double zMax = (-linearTerm - discriminant)/(2*quadraticTerm);
    const double zMin = (-linearTerm + discriminant)/(2*quadraticTerm);
    m_maxRange = std::max(m_maxRange, std::max(zMax-z0, z0-zMin));
    constantTerm -= std::log(2*M_PI*std::sqrt(covDeterminant));
    m_trackMap.emplace(std::piecewise_construct,
                       std::forward_as_tuple(itrk),
                       std::forward_as_tuple(constantTerm, linearTerm, quadraticTerm, zMin, zMax));
    m_lowerMap.emplace(std::piecewise_construct,
                       std::forward_as_tuple(constantTerm, linearTerm, quadraticTerm, zMin, zMax),
                       std::forward_as_tuple(itrk));
  }

globalMaximum()

double Trk::GaussianTrackDensity::TrackDensity::globalMaximum

(

)

const

Return position of global maximum for density function.

Parameters

msg	Message stream.

Definition at line 210 of file GaussianTrackDensity.cxx.

  {
    return GaussianTrackDensity::TrackDensity::globalMaximumWithWidth().first;
  }

globalMaximumWithWidth()

std::pair< double, double > Trk::GaussianTrackDensity::TrackDensity::globalMaximumWithWidth

(

)

const

Return position of global maximum with Gaussian width for density function.

Definition at line 160 of file GaussianTrackDensity.cxx.

  {
    // strategy:
    // the global maximum must be somewhere near a track...
    // since we can calculate the first and second derivatives, at each point we can determine
    // a) whether the function is curved up (minimum) or down (maximum)
    // b) the distance to nearest maximum, assuming either Newton (parabolic) or Gaussian local behavior
    //
    // For each track where the second derivative is negative, find step to nearest maximum
    // Take that step, and then do one final refinement
    // The largest density encountered in this procedure (after checking all tracks) is considered the maximum
    //
    double maximumPosition = 0.0;
    double maximumDensity = 0.0;
    double maxCurvature = 0. ;
    const std::pair<double,double> invalidResult(0.,std::numeric_limits<double>::quiet_NaN());
    if (m_trackMap.empty()) return invalidResult;
    for (const auto& entry : m_trackMap)
    {
      double trialZ = entry.first.parameters()[Trk::z0];
      double density   = 0.0;
      double slope     = 0.0;
      double curvature = 0.0;
      trackDensity( trialZ, density, slope, curvature );
      if ( curvature >= 0.0 || density <= 0.0 ) {
        continue;
      }
      updateMaximum( trialZ, density, curvature, maximumPosition, maximumDensity, maxCurvature);
      trialZ += stepSize( density, slope, curvature );
      trackDensity( trialZ, density, slope, curvature );
      if ( curvature >= 0.0 || density <= 0.0 ) {
        continue;
      }
      updateMaximum( trialZ, density, curvature, maximumPosition, maximumDensity, maxCurvature);
      trialZ += stepSize( density, slope, curvature );
      trackDensity( trialZ, density, slope, curvature );
      if ( curvature >= 0.0 || density <= 0.0) {
        continue;
      }
      updateMaximum( trialZ, density, curvature, maximumPosition, maximumDensity, maxCurvature);
    }
    if (maxCurvature == 0.) return invalidResult;
    return {maximumPosition,std::sqrt(-maximumDensity/maxCurvature)};
  }

stepSize()

double Trk::GaussianTrackDensity::TrackDensity::stepSize ( double y, double dy, double ddy ) const

inlineprivate

Definition at line 162 of file GaussianTrackDensity.h.

                                                                      {
        return (m_gaussStep ? (y * dy) / (dy * dy - y * ddy) : -dy / ddy);
        }

trackDensity() [1/2]

double Trk::GaussianTrackDensity::TrackDensity::trackDensity ( double z ) const

finaloverridevirtual

Evaluate the density function at the specified coordinate along the beamline.

Definition at line 130 of file GaussianTrackDensity.cxx.

  {
    double firstDeriv, secondDeriv = 0;  // unused in this case
    double density = 0;
    // use the existing trackDensity method to avoid duplication of logic
    trackDensity(z,density,firstDeriv,secondDeriv);
    return density;
  }

trackDensity() [2/2]

void Trk::GaussianTrackDensity::TrackDensity::trackDensity ( double z, double & density, double & firstDerivative, double & secondDerivative ) const

finaloverridevirtual

Evaluate the density and its first two derivatives at the specified coordinate.

Definition at line 145 of file GaussianTrackDensity.cxx.

  {
    TrackDensityEval densityResult(z);
    for (const auto & trackAndPerigeePair : m_lowerMap){
      densityResult.addTrack(trackAndPerigeePair.first);
    }
    density = densityResult.density();
    firstDerivative = densityResult.firstDerivative();
    secondDerivative = densityResult.secondDerivative();
  }

updateMaximum()

void Trk::GaussianTrackDensity::TrackDensity::updateMaximum ( double trialZ, double trialValue, double secondDerivative, double & maxZ, double & maxValue, double & maxSecondDerivative ) const

inlineprivate

Definition at line 151 of file GaussianTrackDensity.h.

                                                                     {
        if (trialValue > maxValue) {
          maxZ = trialZ;
          maxValue = trialValue;
          maxSecondDerivative = secondDerivative;
        }
        }

Member Data Documentation

m_gaussStep

bool Trk::GaussianTrackDensity::TrackDensity::m_gaussStep

private

Definition at line 165 of file GaussianTrackDensity.h.

m_lowerMap

lowerMap Trk::GaussianTrackDensity::TrackDensity::m_lowerMap

private

Definition at line 195 of file GaussianTrackDensity.h.

m_maxRange

double Trk::GaussianTrackDensity::TrackDensity::m_maxRange = 0

private

Definition at line 166 of file GaussianTrackDensity.h.

m_trackMap

trackMap Trk::GaussianTrackDensity::TrackDensity::m_trackMap

private

Definition at line 194 of file GaussianTrackDensity.h.

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The documentation for this class was generated from the following files:

• GaussianTrackDensity.h
• GaussianTrackDensity.cxx