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0001 // This file is part of the ACTS project. 0002 // 0003 // Copyright (C) 2016 CERN for the benefit of the ACTS project 0004 // 0005 // This Source Code Form is subject to the terms of the Mozilla Public 0006 // License, v. 2.0. If a copy of the MPL was not distributed with this 0007 // file, You can obtain one at https://mozilla.org/MPL/2.0/. 0008 0009 #pragma once 0010 0011 #include "Acts/EventData/TrackParameters.hpp" 0012 #include "Acts/Vertexing/TrackAtVertex.hpp" 0013 0014 #include <map> 0015 #include <set> 0016 0017 namespace Acts { 0018 0019 /// @class GaussianTrackDensity 0020 /// 0021 /// @brief Class to model tracks as 2D density functions based on 0022 /// their d0 and z0 perigee parameters (mean value) and covariance 0023 /// matrices (determining the width of the function) 0024 class GaussianTrackDensity { 0025 public: 0026 /// @brief Struct to store information for a single track 0027 struct TrackEntry { 0028 /// @brief Default constructor 0029 TrackEntry() = default; 0030 /// @brief Constructor initializing all members 0031 /// @param z_ Trial z position 0032 /// @param c0_ z-independent term in exponent 0033 /// @param c1_ Linear coefficient in exponent 0034 /// @param c2_ Quadratic coefficient in exponent 0035 /// @param lowerBound_ The lower bound 0036 /// @param upperBound_ The upper bound 0037 TrackEntry(double z_, double c0_, double c1_, double c2_, 0038 double lowerBound_, double upperBound_) 0039 : z(z_), 0040 c0(c0_), 0041 c1(c1_), 0042 c2(c2_), 0043 lowerBound(lowerBound_), 0044 upperBound(upperBound_) {} 0045 0046 /// Trial z position for the track 0047 double z = 0; 0048 // Cached information for a single track 0049 /// z-independent term in exponent 0050 double c0 = 0; 0051 /// linear coefficient in exponent 0052 double c1 = 0; 0053 /// quadratic coefficient in exponent 0054 double c2 = 0; 0055 /// The lower bound for track density evaluation 0056 double lowerBound = 0; 0057 /// The upper bound for track density evaluation 0058 double upperBound = 0; 0059 }; 0060 0061 /// @brief The Config struct 0062 struct Config { 0063 /// Constructor with significance parameters 0064 /// @param d0Sig Maximum d0 significance for track selection (default: 3.5) 0065 /// @param z0Sig Maximum z0 significance for track selection (default: 12.0) 0066 explicit Config(double d0Sig = 3.5, double z0Sig = 12.) 0067 : d0MaxSignificance(d0Sig), 0068 z0MaxSignificance(z0Sig), 0069 d0SignificanceCut(d0Sig * d0Sig), 0070 z0SignificanceCut(z0Sig * z0Sig) {} 0071 0072 /// Assumed shape of density function: Gaussian (true) or parabolic (false) 0073 bool isGaussianShaped = true; 0074 0075 /// Maximum d0 impact parameter significance to use a track 0076 double d0MaxSignificance; 0077 /// Maximum z0 impact parameter significance to use a track 0078 double z0MaxSignificance; 0079 /// Corresponding cut values for d0 significance 0080 double d0SignificanceCut; 0081 /// Corresponding cut values for z0 significance 0082 double z0SignificanceCut; 0083 0084 /// Function to extract parameters from InputTrack 0085 InputTrack::Extractor extractParameters; 0086 }; 0087 0088 /// @brief The State struct 0089 struct State { 0090 /// Constructor with expected number of tracks 0091 /// @param nTracks Expected number of tracks (used to reserve memory) 0092 explicit State(unsigned int nTracks) { trackEntries.reserve(nTracks); } 0093 /// Vector to cache track information for density calculation 0094 std::vector<TrackEntry> trackEntries; 0095 }; 0096 0097 /// Constructor with config 0098 /// @param cfg The configuration parameters 0099 explicit GaussianTrackDensity(const Config& cfg) : m_cfg(cfg) { 0100 if (!m_cfg.extractParameters.connected()) { 0101 throw std::invalid_argument( 0102 "GaussianTrackDensity: " 0103 "No parameter extractor provided."); 0104 } 0105 } 0106 0107 /// @brief Calculates z position of global maximum with Gaussian width 0108 /// for density function. 0109 /// Strategy: 0110 /// The global maximum must be somewhere near a track. 0111 /// Since we can calculate the first and second derivatives, at each point we 0112 /// can determine a) whether the function is curved up (minimum) or down 0113 /// (maximum) b) the distance to nearest maximum, assuming either Newton 0114 /// (parabolic) or Gaussian local behavior. 0115 /// For each track where the second derivative is negative, find step to 0116 /// nearest maximum, take that step and then do one final refinement. The 0117 /// largest density encountered in this procedure (after checking all tracks) 0118 /// is considered the maximum. 0119 /// 0120 /// @param state The track density state 0121 /// @param trackList All input tracks 0122 /// 0123 /// @return Pair of position of global maximum and Gaussian width 0124 Result<std::optional<std::pair<double, double>>> globalMaximumWithWidth( 0125 State& state, const std::vector<InputTrack>& trackList) const; 0126 0127 /// @brief Calculates the z position of the global maximum 0128 /// 0129 /// @param state The track density state 0130 /// @param trackList All input tracks 0131 /// 0132 /// @return z position of the global maximum 0133 Result<std::optional<double>> globalMaximum( 0134 State& state, const std::vector<InputTrack>& trackList) const; 0135 0136 private: 0137 /// The configuration 0138 Config m_cfg; 0139 0140 /// @brief Add a track to the set being considered 0141 /// 0142 /// @param state The track density state 0143 /// @param trackList All input tracks 0144 Result<void> addTracks(State& state, 0145 const std::vector<InputTrack>& trackList) const; 0146 0147 /// @brief Evaluate the density function and its two first 0148 /// derivatives at the specified coordinate along the beamline 0149 /// 0150 /// @param state The track density state 0151 /// @param z z-position along the beamline 0152 /// 0153 /// @return Track density, first and second derivatives 0154 std::tuple<double, double, double> trackDensityAndDerivatives(State& state, 0155 double z) const; 0156 0157 /// @brief Update the current maximum values 0158 /// 0159 /// @param newZ The new z value 0160 /// @param newValue The new value at z position 0161 /// @param newSecondDerivative The new second derivative 0162 /// @param maxZ Maximum z value, will be compared against @p newZ 0163 /// @param maxValue Maximum value 0164 /// @param maxSecondDerivative Maximum of the second derivative 0165 /// @return The max z position, the max value at z position, the max second 0166 /// derivative 0167 std::tuple<double, double, double> updateMaximum( 0168 double newZ, double newValue, double newSecondDerivative, double maxZ, 0169 double maxValue, double maxSecondDerivative) const; 0170 0171 /// @brief Calculates the step size 0172 /// 0173 /// @param y Position value 0174 /// @param dy First derivative 0175 /// @param ddy Second derivative 0176 /// 0177 /// @return The step size 0178 double stepSize(double y, double dy, double ddy) const; 0179 0180 // Helper class to evaluate and store track density at specific position 0181 class GaussianTrackDensityStore { 0182 public: 0183 // Initialise at the z coordinate at which the density is to be evaluated 0184 explicit GaussianTrackDensityStore(double z_coordinate) 0185 : m_z(z_coordinate) {} 0186 0187 // Add the contribution of a single track to the density 0188 void addTrackToDensity(const TrackEntry& entry); 0189 0190 // Return density, first and second derivatives 0191 inline std::tuple<double, double, double> densityAndDerivatives() const { 0192 return {m_density, m_firstDerivative, m_secondDerivative}; 0193 } 0194 0195 private: 0196 // Store density and derivatives for z position m_z 0197 double m_z; 0198 double m_density{0}; 0199 double m_firstDerivative{0}; 0200 double m_secondDerivative{0}; 0201 }; 0202 }; 0203 0204 } // namespace Acts
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