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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/Definitions/Algebra.hpp" 0012 #include "Acts/Definitions/TrackParametrization.hpp" 0013 #include "Acts/Definitions/Units.hpp" 0014 #include "Acts/Geometry/GeometryContext.hpp" 0015 #include "Acts/Surfaces/Surface.hpp" 0016 #include "Acts/Utilities/Zip.hpp" 0017 0018 #include <array> 0019 #include <optional> 0020 #include <stdexcept> 0021 0022 namespace Acts { 0023 0024 /// Estimate the full track parameters from three space points 0025 /// 0026 /// This method is based on the conformal map transformation. It estimates the 0027 /// full free track parameters, i.e. (x, y, z, t, dx, dy, dz, q/p) at the bottom 0028 /// space point. The bottom space is assumed to be the first element in the 0029 /// range defined by the iterators. The magnetic field (which might be along any 0030 /// direction) is also necessary for the momentum estimation. 0031 /// 0032 /// This is a purely spatial estimation, i.e. the time parameter will be set to 0033 /// 0. 0034 /// 0035 /// It resembles the method used in ATLAS for the track parameters estimated 0036 /// from seed, i.e. the function InDet::SiTrackMaker_xk::getAtaPlane here: 0037 /// https://acode-browser.usatlas.bnl.gov/lxr/source/athena/InnerDetector/InDetRecTools/SiTrackMakerTool_xk/src/SiTrackMaker_xk.cxx 0038 /// 0039 /// @tparam spacepoint_iterator_t The type of space point iterator 0040 /// 0041 /// @param sp0 is the bottom space point 0042 /// @param sp1 is the middle space point 0043 /// @param sp2 is the top space point 0044 /// @param bField is the magnetic field vector 0045 /// 0046 /// @return the free parameters 0047 FreeVector estimateTrackParamsFromSeed(const Vector3& sp0, const Vector3& sp1, 0048 const Vector3& sp2, 0049 const Vector3& bField); 0050 0051 /// Estimate the full track parameters from three space points 0052 /// 0053 /// This method is based on the conformal map transformation. It estimates the 0054 /// full free track parameters, i.e. (x, y, z, t, dx, dy, dz, q/p) at the bottom 0055 /// space point. The bottom space is assumed to be the first element in the 0056 /// range defined by the iterators. The magnetic field (which might be along any 0057 /// direction) is also necessary for the momentum estimation. 0058 /// 0059 /// It resembles the method used in ATLAS for the track parameters estimated 0060 /// from seed, i.e. the function InDet::SiTrackMaker_xk::getAtaPlane here: 0061 /// https://acode-browser.usatlas.bnl.gov/lxr/source/athena/InnerDetector/InDetRecTools/SiTrackMakerTool_xk/src/SiTrackMaker_xk.cxx 0062 /// 0063 /// @tparam spacepoint_iterator_t The type of space point iterator 0064 /// 0065 /// @param spRange is the range of space points 0066 /// @param bField is the magnetic field vector 0067 /// 0068 /// @return the free parameters 0069 template <std::ranges::range spacepoint_range_t> 0070 FreeVector estimateTrackParamsFromSeed(spacepoint_range_t spRange, 0071 const Vector3& bField) { 0072 // Check the number of provided space points 0073 if (spRange.size() != 3) { 0074 throw std::invalid_argument( 0075 "There should be exactly three space points provided."); 0076 } 0077 0078 // The global positions of the bottom, middle and space points 0079 std::array<Vector3, 3> spPositions = {Vector3::Zero(), Vector3::Zero(), 0080 Vector3::Zero()}; 0081 std::array<std::optional<double>, 3> spTimes = {std::nullopt, std::nullopt, 0082 std::nullopt}; 0083 // The first, second and third space point are assumed to be bottom, middle 0084 // and top space point, respectively 0085 for (auto [sp, spPosition, spTime] : 0086 Acts::zip(spRange, spPositions, spTimes)) { 0087 if (sp == nullptr) { 0088 throw std::invalid_argument("Empty space point found."); 0089 } 0090 spPosition = Vector3(sp->x(), sp->y(), sp->z()); 0091 spTime = sp->t(); 0092 } 0093 0094 FreeVector params = estimateTrackParamsFromSeed( 0095 spPositions[0], spPositions[1], spPositions[2], bField); 0096 params[eFreeTime] = spTimes[0].value_or(0); 0097 return params; 0098 } 0099 0100 /// Estimate the full track parameters from three space points 0101 /// 0102 /// This method is based on the conformal map transformation. It estimates the 0103 /// full bound track parameters, i.e. (loc0, loc1, phi, theta, q/p, t) at the 0104 /// bottom space point. The bottom space is assumed to be the first element 0105 /// in the range defined by the iterators. It must lie on the surface provided 0106 /// for the representation of the bound track parameters. The magnetic field 0107 /// (which might be along any direction) is also necessary for the momentum 0108 /// estimation. 0109 /// 0110 /// It resembles the method used in ATLAS for the track parameters estimated 0111 /// from seed, i.e. the function InDet::SiTrackMaker_xk::getAtaPlane here: 0112 /// https://acode-browser.usatlas.bnl.gov/lxr/source/athena/InnerDetector/InDetRecTools/SiTrackMakerTool_xk/src/SiTrackMaker_xk.cxx 0113 /// 0114 /// @tparam spacepoint_iterator_t The type of space point iterator 0115 /// 0116 /// @param gctx is the geometry context 0117 /// @param spRange is the range of space points 0118 /// @param surface is the surface of the bottom space point. The estimated bound 0119 /// track parameters will be represented also at this surface 0120 /// @param bField is the magnetic field vector 0121 /// 0122 /// @return bound parameters 0123 template <std::ranges::range spacepoint_range_t> 0124 Result<BoundVector> estimateTrackParamsFromSeed(const GeometryContext& gctx, 0125 spacepoint_range_t spRange, 0126 const Surface& surface, 0127 const Vector3& bField) { 0128 FreeVector freeParams = estimateTrackParamsFromSeed(spRange, bField); 0129 0130 const auto* sp0 = *spRange.begin(); 0131 Vector3 origin = Vector3(sp0->x(), sp0->y(), sp0->z()); 0132 Vector3 direction = freeParams.segment<3>(eFreeDir0); 0133 0134 BoundVector params = BoundVector::Zero(); 0135 params[eBoundPhi] = VectorHelpers::phi(direction); 0136 params[eBoundTheta] = VectorHelpers::theta(direction); 0137 params[eBoundQOverP] = freeParams[eFreeQOverP]; 0138 0139 // Transform the bottom space point to local coordinates of the provided 0140 // surface 0141 auto lpResult = surface.globalToLocal(gctx, origin, direction); 0142 if (!lpResult.ok()) { 0143 return Result<BoundVector>::failure(lpResult.error()); 0144 } 0145 Vector2 bottomLocalPos = lpResult.value(); 0146 // The estimated loc0 and loc1 0147 params[eBoundLoc0] = bottomLocalPos.x(); 0148 params[eBoundLoc1] = bottomLocalPos.y(); 0149 params[eBoundTime] = sp0->t().value_or(0); 0150 0151 return Result<BoundVector>::success(params); 0152 } 0153 0154 /// Configuration for the estimation of the covariance matrix of the track 0155 /// parameters with `estimateTrackParamCovariance`. 0156 struct EstimateTrackParamCovarianceConfig { 0157 /// The initial sigmas for the track parameters 0158 BoundVector initialSigmas = {1. * UnitConstants::mm, 0159 1. * UnitConstants::mm, 0160 1. * UnitConstants::degree, 0161 1. * UnitConstants::degree, 0162 1. * UnitConstants::e / UnitConstants::GeV, 0163 1. * UnitConstants::ns}; 0164 0165 /// The initial relative uncertainty of the q/pt 0166 double initialSigmaPtRel = 0.1; 0167 0168 /// The inflation factors for the variances of the track parameters 0169 BoundVector initialVarInflation = {1., 1., 1., 1., 1., 1.}; 0170 /// The inflation factor for time uncertainty if the time parameter was not 0171 /// estimated 0172 double noTimeVarInflation = 100.; 0173 }; 0174 0175 /// Estimate the covariance matrix of the given track parameters based on the 0176 /// provided configuration. The assumption is that we can model the uncertainty 0177 /// of the track parameters as a diagonal matrix with the provided initial 0178 /// sigmas. The inflation factors are used to inflate the initial variances 0179 /// based on the provided configuration. The uncertainty of q/p is estimated 0180 /// based on the relative uncertainty of the q/pt and the theta uncertainty. 0181 /// 0182 /// @param config is the configuration for the estimation 0183 /// @param params is the track parameters 0184 /// @param hasTime is true if the track parameters have time 0185 /// 0186 /// @return the covariance matrix of the track parameters 0187 BoundMatrix estimateTrackParamCovariance( 0188 const EstimateTrackParamCovarianceConfig& config, const BoundVector& params, 0189 bool hasTime); 0190 0191 } // namespace Acts
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