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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 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 0055 double lowerBound = 0; 0056 // The upper bound 0057 double upperBound = 0; 0058 }; 0059 0060 /// @brief The Config struct 0061 struct Config { 0062 Config(double d0Sig = 3.5, double z0Sig = 12.) 0063 : d0MaxSignificance(d0Sig), 0064 z0MaxSignificance(z0Sig), 0065 d0SignificanceCut(d0Sig * d0Sig), 0066 z0SignificanceCut(z0Sig * z0Sig) {} 0067 0068 // Assumed shape of density function: 0069 // Gaussian (true) or parabolic (false) 0070 bool isGaussianShaped = true; 0071 0072 // Maximum d0 impact parameter significance to use a track 0073 double d0MaxSignificance; 0074 // Maximum z0 impact parameter significance to use a track 0075 double z0MaxSignificance; 0076 // Corresponding cut values 0077 double d0SignificanceCut; 0078 double z0SignificanceCut; 0079 0080 // Function to extract parameters from InputTrack 0081 InputTrack::Extractor extractParameters; 0082 }; 0083 0084 /// @brief The State struct 0085 struct State { 0086 // Constructor with size track map 0087 State(unsigned int nTracks) { trackEntries.reserve(nTracks); } 0088 // Vector to cache track information 0089 std::vector<TrackEntry> trackEntries; 0090 }; 0091 0092 /// Constructor with config 0093 GaussianTrackDensity(const Config& cfg) : m_cfg(cfg) { 0094 if (!m_cfg.extractParameters.connected()) { 0095 throw std::invalid_argument( 0096 "GaussianTrackDensity: " 0097 "No parameter extractor provided."); 0098 } 0099 } 0100 0101 /// @brief Calculates z position of global maximum with Gaussian width 0102 /// for density function. 0103 /// Strategy: 0104 /// The global maximum must be somewhere near a track. 0105 /// Since we can calculate the first and second derivatives, at each point we 0106 /// can determine a) whether the function is curved up (minimum) or down 0107 /// (maximum) b) the distance to nearest maximum, assuming either Newton 0108 /// (parabolic) or Gaussian local behavior. 0109 /// For each track where the second derivative is negative, find step to 0110 /// nearest maximum, take that step and then do one final refinement. The 0111 /// largest density encountered in this procedure (after checking all tracks) 0112 /// is considered the maximum. 0113 /// 0114 /// @param state The track density state 0115 /// @param trackList All input tracks 0116 /// 0117 /// @return Pair of position of global maximum and Gaussian width 0118 Result<std::optional<std::pair<double, double>>> globalMaximumWithWidth( 0119 State& state, const std::vector<InputTrack>& trackList) const; 0120 0121 /// @brief Calculates the z position of the global maximum 0122 /// 0123 /// @param state The track density state 0124 /// @param trackList All input tracks 0125 /// 0126 /// @return z position of the global maximum 0127 Result<std::optional<double>> globalMaximum( 0128 State& state, const std::vector<InputTrack>& trackList) const; 0129 0130 private: 0131 /// The configuration 0132 Config m_cfg; 0133 0134 /// @brief Add a track to the set being considered 0135 /// 0136 /// @param state The track density state 0137 /// @param trackList All input tracks 0138 Result<void> addTracks(State& state, 0139 const std::vector<InputTrack>& trackList) const; 0140 0141 /// @brief Evaluate the density function and its two first 0142 /// derivatives at the specified coordinate along the beamline 0143 /// 0144 /// @param state The track density state 0145 /// @param z z-position along the beamline 0146 /// 0147 /// @return Track density, first and second derivatives 0148 std::tuple<double, double, double> trackDensityAndDerivatives(State& state, 0149 double z) const; 0150 0151 /// @brief Update the current maximum values 0152 /// 0153 /// @param newZ The new z value 0154 /// @param newValue The new value at z position 0155 /// @param newSecondDerivative The new second derivative 0156 /// @param maxZ Maximum z value, will be compared against @p newZ 0157 /// @param maxValue Maximum value 0158 /// @param maxSecondDerivative Maximum of the second derivative 0159 /// @return The max z position, the max value at z position, the max second 0160 /// derivative 0161 std::tuple<double, double, double> updateMaximum( 0162 double newZ, double newValue, double newSecondDerivative, double maxZ, 0163 double maxValue, double maxSecondDerivative) const; 0164 0165 /// @brief Calculates the step size 0166 /// 0167 /// @param y Position value 0168 /// @param dy First derivative 0169 /// @param ddy Second derivative 0170 /// 0171 /// @return The step size 0172 double stepSize(double y, double dy, double ddy) const; 0173 0174 // Helper class to evaluate and store track density at specific position 0175 class GaussianTrackDensityStore { 0176 public: 0177 // Initialise at the z coordinate at which the density is to be evaluated 0178 GaussianTrackDensityStore(double z_coordinate) : m_z(z_coordinate) {} 0179 0180 // Add the contribution of a single track to the density 0181 void addTrackToDensity(const TrackEntry& entry); 0182 0183 // Return density, first and second derivatives 0184 inline std::tuple<double, double, double> densityAndDerivatives() const { 0185 return {m_density, m_firstDerivative, m_secondDerivative}; 0186 } 0187 0188 private: 0189 // Store density and derivatives for z position m_z 0190 double m_z; 0191 double m_density{0}; 0192 double m_firstDerivative{0}; 0193 double m_secondDerivative{0}; 0194 }; 0195 }; 0196 0197 } // namespace Acts
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