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 // This file is part of the Acts project.
 //
 // Copyright (C) 2021 CERN for the benefit of the Acts project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/TrackFitting/detail/GsfUtils.hpp"
 
 #include <algorithm>
 #include <array>
 #include <cassert>
 #include <cmath>
 #include <cstddef>
 #include <fstream>
 #include <mutex>
 #include <random>
 #include <stdexcept>
 #include <string>
 #include <tuple>
 
 #include <boost/container/static_vector.hpp>
 
 namespace Acts {
 
 namespace detail {
 
 struct GaussianComponent {
   ActsScalar weight = 0.0;
   ActsScalar mean = 0.0;
   ActsScalar var = 0.0;
 };
 
 /// Transform a gaussian component to a space where all values are defined from
 /// [-inf, inf]
 inline void transformComponent(const GaussianComponent &cmp,
                                double &transformed_weight,
                                double &transformed_mean,
                                double &transformed_var) {
   const auto &[weight, mean, var] = cmp;
 
   transformed_weight = std::log(weight) - std::log(1 - weight);
   transformed_mean = std::log(mean) - std::log(1 - mean);
   transformed_var = std::log(var);
 }
 
 /// Transform a gaussian component back from the [-inf, inf]-space to the usual
 /// space
 inline auto inverseTransformComponent(double transformed_weight,
                                       double transformed_mean,
                                       double transformed_var) {
   GaussianComponent cmp;
   cmp.weight = 1. / (1 + std::exp(-transformed_weight));
   cmp.mean = 1. / (1 + std::exp(-transformed_mean));
   cmp.var = std::exp(transformed_var);
 
   return cmp;
 }
 
 }  // namespace detail
 
 /// This class approximates the Bethe-Heitler with only one component. This is
 /// mainly inside @ref AtlasBetheHeitlerApprox, but can also be used as the
 /// only component approximation (then probably for debugging)
 struct BetheHeitlerApproxSingleCmp {
   /// Returns the number of components the returned mixture will have
   constexpr auto numComponents() const { return 1; }
 
   /// Checks if an input is valid for the parameterization. The threshold for
   /// x/x0 is 0.002 and orientates on the values used in ATLAS
   constexpr bool validXOverX0(ActsScalar x) const {
     return x < 0.002;
     ;
   }
 
   /// Returns array with length 1 containing a 1-component-representation of the
   /// Bethe-Heitler-Distribution
   ///
   /// @param x pathlength in terms of the radiation length
   static auto mixture(const ActsScalar x) {
     std::array<detail::GaussianComponent, 1> ret{};
 
     ret[0].weight = 1.0;
 
     const double c = x / std::log(2);
     ret[0].mean = std::pow(2, -c);
     ret[0].var = std::pow(3, -c) - std::pow(4, -c);
 
     return ret;
   }
 };
 
 /// This class approximates the Bethe-Heitler distribution as a gaussian
 /// mixture. To enable an approximation for continuous input variables, the
 /// weights, means and variances are internally parametrized as a Nth order
 /// polynomial.
 /// @todo This class is rather inflexible: It forces two data representations,
 /// making it a bit awkward to add a single parameterization. It would be good
 /// to generalize this at some point.
 template <int NComponents, int PolyDegree>
 class AtlasBetheHeitlerApprox {
   static_assert(NComponents > 0);
   static_assert(PolyDegree > 0);
 
  public:
   struct PolyData {
     std::array<ActsScalar, PolyDegree + 1> weightCoeffs;
     std::array<ActsScalar, PolyDegree + 1> meanCoeffs;
     std::array<ActsScalar, PolyDegree + 1> varCoeffs;
   };
 
   using Data = std::array<PolyData, NComponents>;
 
  private:
   Data m_lowData;
   Data m_highData;
   bool m_lowTransform;
   bool m_highTransform;
 
   constexpr static double m_noChangeLimit = 0.0001;
   constexpr static double m_singleGaussianLimit = 0.002;
   double m_lowLimit = 0.10;
   double m_highLimit = 0.20;
 
  public:
   /// Construct the Bethe-Heitler approximation description with two
   /// parameterizations, one for lower ranges, one for higher ranges.
   /// Is it assumed that the lower limit of the high-x/x0 data is equal
   /// to the upper limit of the low-x/x0 data.
   ///
   /// @param lowData data for the lower x/x0 range
   /// @param highData data for the higher x/x0 range
   /// @param lowTransform whether the low data need to be transformed
   /// @param highTransform whether the high data need to be transformed
   /// @param lowLimit the upper limit for the low data
   /// @param highLimit the upper limit for the high data
   constexpr AtlasBetheHeitlerApprox(const Data &lowData, const Data &highData,
                                     bool lowTransform, bool highTransform,
                                     double lowLimit = 0.1,
                                     double highLimit = 0.2)
       : m_lowData(lowData),
         m_highData(highData),
         m_lowTransform(lowTransform),
         m_highTransform(highTransform),
         m_lowLimit(lowLimit),
         m_highLimit(highLimit) {}
 
   /// Returns the number of components the returned mixture will have
   constexpr auto numComponents() const { return NComponents; }
 
   /// Checks if an input is valid for the parameterization
   ///
   /// @param x pathlength in terms of the radiation length
   constexpr bool validXOverX0(ActsScalar x) const { return x < m_highLimit; }
 
   /// Generates the mixture from the polynomials and reweights them, so
   /// that the sum of all weights is 1
   ///
   /// @param x pathlength in terms of the radiation length
   auto mixture(ActsScalar x) const {
     using Array =
         boost::container::static_vector<detail::GaussianComponent, NComponents>;
     // Build a polynom
     auto poly = [](ActsScalar xx,
                    const std::array<ActsScalar, PolyDegree + 1> &coeffs) {
       ActsScalar sum{0.};
       for (const auto c : coeffs) {
         sum = xx * sum + c;
       }
       assert((std::isfinite(sum) && "polynom result not finite"));
       return sum;
     };
 
     // Lambda which builds the components
     auto make_mixture = [&](const Data &data, double xx, bool transform) {
       // Value initialization should garanuee that all is initialized to zero
       Array ret(NComponents);
       ActsScalar weight_sum = 0;
       for (int i = 0; i < NComponents; ++i) {
         // These transformations must be applied to the data according to ATHENA
         // (TrkGaussianSumFilter/src/GsfCombinedMaterialEffects.cxx:79)
         if (transform) {
           ret[i] = detail::inverseTransformComponent(
               poly(xx, data[i].weightCoeffs), poly(xx, data[i].meanCoeffs),
               poly(xx, data[i].varCoeffs));
         } else {
           ret[i].weight = poly(xx, data[i].weightCoeffs);
           ret[i].mean = poly(xx, data[i].meanCoeffs);
           ret[i].var = poly(xx, data[i].varCoeffs);
         }
 
         weight_sum += ret[i].weight;
       }
 
       for (int i = 0; i < NComponents; ++i) {
         ret[i].weight /= weight_sum;
       }
 
       return ret;
     };
 
     // Return no change
     if (x < m_noChangeLimit) {
       Array ret(1);
 
       ret[0].weight = 1.0;
       ret[0].mean = 1.0;  // p_initial = p_final
       ret[0].var = 0.0;
 
       return ret;
     }
     // Return single gaussian approximation
     if (x < m_singleGaussianLimit) {
       Array ret(1);
       ret[0] = BetheHeitlerApproxSingleCmp::mixture(x)[0];
       return ret;
     }
     // Return a component representation for lower x0
     if (x < m_lowLimit) {
       return make_mixture(m_lowData, x, m_lowTransform);
     }
     // Return a component representation for higher x0
     // Cap the x because beyond the parameterization goes wild
     const auto high_x = std::min(m_highLimit, x);
     return make_mixture(m_highData, high_x, m_highTransform);
   }
 
   /// Loads a parameterization from a file according to the Atlas file
   /// description
   ///
   /// @param low_parameters_path Path to the foo.par file that stores
   /// the parameterization for low x/x0
   /// @param high_parameters_path Path to the foo.par file that stores
   /// the parameterization for high x/x0
   /// @param lowLimit the upper limit for the low x/x0-data
   /// @param highLimit the upper limit for the high x/x0-data
   static auto loadFromFiles(const std::string &low_parameters_path,
                             const std::string &high_parameters_path,
                             double lowLimit = 0.1, double highLimit = 0.2) {
     auto read_file = [](const std::string &filepath) {
       std::ifstream file(filepath);
 
       if (!file) {
         throw std::invalid_argument("Could not open '" + filepath + "'");
       }
 
       std::size_t n_cmps = 0, degree = 0;
       bool transform_code = false;
 
       file >> n_cmps >> degree >> transform_code;
 
       if (NComponents != n_cmps) {
         throw std::invalid_argument("Wrong number of components in '" +
                                     filepath + "'");
       }
 
       if (PolyDegree != degree) {
         throw std::invalid_argument("Wrong polynom order in '" + filepath +
                                     "'");
       }
 
       Data data;
 
       for (auto &cmp : data) {
         for (auto &coeff : cmp.weightCoeffs) {
           file >> coeff;
         }
         for (auto &coeff : cmp.meanCoeffs) {
           file >> coeff;
         }
         for (auto &coeff : cmp.varCoeffs) {
           file >> coeff;
         }
       }
 
       return std::make_tuple(data, transform_code);
     };
 
     const auto [lowData, lowTransform] = read_file(low_parameters_path);
     const auto [highData, highTransform] = read_file(high_parameters_path);
 
     return AtlasBetheHeitlerApprox(lowData, highData, lowTransform,
                                    highTransform, lowLimit, highLimit);
   }
 };
 
 /// Creates a @ref AtlasBetheHeitlerApprox object based on an ATLAS
 /// configuration, that are stored as static data in the source code.
 /// This may not be an optimal configuration, but should allow to run
 /// the GSF without the need to load files
 AtlasBetheHeitlerApprox<6, 5> makeDefaultBetheHeitlerApprox();
 
 }  // namespace Acts

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