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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/Vertexing/TrackAtVertex.hpp" 0012 0013 #include <map> 0014 #include <set> 0015 0016 namespace Acts { 0017 0018 /// @class GaussianTrackDensity 0019 /// 0020 /// @brief Class to model tracks as 2D density functions based on 0021 /// their d0 and z0 perigee parameters (mean value) and covariance 0022 /// matrices (determining the width of the function) 0023 class GaussianTrackDensity { 0024 public: 0025 /// @brief Struct to store information for a single track 0026 struct TrackEntry { 0027 /// @brief Default constructor 0028 TrackEntry() = default; 0029 /// @brief Constructor initializing all members 0030 /// @param z_ Trial z position 0031 /// @param c0_ z-independent term in exponent 0032 /// @param c1_ Linear coefficient in exponent 0033 /// @param c2_ Quadratic coefficient in exponent 0034 /// @param lowerBound_ The lower bound 0035 /// @param upperBound_ The upper bound 0036 TrackEntry(double z_, double c0_, double c1_, double c2_, 0037 double lowerBound_, double upperBound_) 0038 : z(z_), 0039 c0(c0_), 0040 c1(c1_), 0041 c2(c2_), 0042 lowerBound(lowerBound_), 0043 upperBound(upperBound_) {} 0044 0045 /// Trial z position for the track 0046 double z = 0; 0047 // Cached information for a single track 0048 /// z-independent term in exponent 0049 double c0 = 0; 0050 /// linear coefficient in exponent 0051 double c1 = 0; 0052 /// quadratic coefficient in exponent 0053 double c2 = 0; 0054 /// The lower bound for track density evaluation 0055 double lowerBound = 0; 0056 /// The upper bound for track density evaluation 0057 double upperBound = 0; 0058 }; 0059 0060 /// @brief The Config struct 0061 struct Config { 0062 /// Constructor with significance parameters 0063 /// @param d0Sig Maximum d0 significance for track selection (default: 3.5) 0064 /// @param z0Sig Maximum z0 significance for track selection (default: 12.0) 0065 explicit Config(double d0Sig = 3.5, double z0Sig = 12.) 0066 : d0MaxSignificance(d0Sig), 0067 z0MaxSignificance(z0Sig), 0068 d0SignificanceCut(d0Sig * d0Sig), 0069 z0SignificanceCut(z0Sig * z0Sig) {} 0070 0071 /// Assumed shape of density function: Gaussian (true) or parabolic (false) 0072 bool isGaussianShaped = true; 0073 0074 /// Maximum d0 impact parameter significance to use a track 0075 double d0MaxSignificance; 0076 /// Maximum z0 impact parameter significance to use a track 0077 double z0MaxSignificance; 0078 /// Corresponding cut values for d0 significance 0079 double d0SignificanceCut; 0080 /// Corresponding cut values for z0 significance 0081 double z0SignificanceCut; 0082 0083 /// Function to extract parameters from InputTrack 0084 InputTrack::Extractor extractParameters; 0085 }; 0086 0087 /// @brief The State struct 0088 struct State { 0089 /// Constructor with expected number of tracks 0090 /// @param nTracks Expected number of tracks (used to reserve memory) 0091 explicit State(unsigned int nTracks) { trackEntries.reserve(nTracks); } 0092 /// Vector to cache track information for density calculation 0093 std::vector<TrackEntry> trackEntries; 0094 }; 0095 0096 /// Constructor with config 0097 /// @param cfg The configuration parameters 0098 explicit GaussianTrackDensity(const Config& cfg) : m_cfg(cfg) { 0099 if (!m_cfg.extractParameters.connected()) { 0100 throw std::invalid_argument( 0101 "GaussianTrackDensity: " 0102 "No parameter extractor provided."); 0103 } 0104 } 0105 0106 /// @brief Calculates z position of global maximum with Gaussian width 0107 /// for density function. 0108 /// Strategy: 0109 /// The global maximum must be somewhere near a track. 0110 /// Since we can calculate the first and second derivatives, at each point we 0111 /// can determine a) whether the function is curved up (minimum) or down 0112 /// (maximum) b) the distance to nearest maximum, assuming either Newton 0113 /// (parabolic) or Gaussian local behavior. 0114 /// For each track where the second derivative is negative, find step to 0115 /// nearest maximum, take that step and then do one final refinement. The 0116 /// largest density encountered in this procedure (after checking all tracks) 0117 /// is considered the maximum. 0118 /// 0119 /// @param state The track density state 0120 /// @param trackList All input tracks 0121 /// 0122 /// @return Pair of position of global maximum and Gaussian width 0123 Result<std::optional<std::pair<double, double>>> globalMaximumWithWidth( 0124 State& state, const std::vector<InputTrack>& trackList) const; 0125 0126 /// @brief Calculates the z position of the global maximum 0127 /// 0128 /// @param state The track density state 0129 /// @param trackList All input tracks 0130 /// 0131 /// @return z position of the global maximum 0132 Result<std::optional<double>> globalMaximum( 0133 State& state, const std::vector<InputTrack>& trackList) const; 0134 0135 private: 0136 /// The configuration 0137 Config m_cfg; 0138 0139 /// @brief Add a track to the set being considered 0140 /// 0141 /// @param state The track density state 0142 /// @param trackList All input tracks 0143 Result<void> addTracks(State& state, 0144 const std::vector<InputTrack>& trackList) const; 0145 0146 /// @brief Evaluate the density function and its two first 0147 /// derivatives at the specified coordinate along the beamline 0148 /// 0149 /// @param state The track density state 0150 /// @param z z-position along the beamline 0151 /// 0152 /// @return Track density, first and second derivatives 0153 std::tuple<double, double, double> trackDensityAndDerivatives(State& state, 0154 double z) const; 0155 0156 /// @brief Update the current maximum values 0157 /// 0158 /// @param newZ The new z value 0159 /// @param newValue The new value at z position 0160 /// @param newSecondDerivative The new second derivative 0161 /// @param maxZ Maximum z value, will be compared against @p newZ 0162 /// @param maxValue Maximum value 0163 /// @param maxSecondDerivative Maximum of the second derivative 0164 /// @return The max z position, the max value at z position, the max second 0165 /// derivative 0166 std::tuple<double, double, double> updateMaximum( 0167 double newZ, double newValue, double newSecondDerivative, double maxZ, 0168 double maxValue, double maxSecondDerivative) const; 0169 0170 /// @brief Calculates the step size 0171 /// 0172 /// @param y Position value 0173 /// @param dy First derivative 0174 /// @param ddy Second derivative 0175 /// 0176 /// @return The step size 0177 double stepSize(double y, double dy, double ddy) const; 0178 0179 // Helper class to evaluate and store track density at specific position 0180 class GaussianTrackDensityStore { 0181 public: 0182 // Initialise at the z coordinate at which the density is to be evaluated 0183 explicit GaussianTrackDensityStore(double z_coordinate) 0184 : m_z(z_coordinate) {} 0185 0186 // Add the contribution of a single track to the density 0187 void addTrackToDensity(const TrackEntry& entry); 0188 0189 // Return density, first and second derivatives 0190 inline std::tuple<double, double, double> densityAndDerivatives() const { 0191 return {m_density, m_firstDerivative, m_secondDerivative}; 0192 } 0193 0194 private: 0195 // Store density and derivatives for z position m_z 0196 double m_z; 0197 double m_density{0}; 0198 double m_firstDerivative{0}; 0199 double m_secondDerivative{0}; 0200 }; 0201 }; 0202 0203 } // namespace Acts
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