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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 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 https://mozilla.org/MPL/2.0/.
 
 #include "ActsExamples/Io/Root/detail/NuclearInteractionParametrisation.hpp"
 
 #include "Acts/Definitions/Common.hpp"
 
 #include <cmath>
 #include <iterator>
 #include <limits>
 
 #include <Eigen/Eigenvalues>
 #include <TMath.h>
 #include <TVectorF.h>
 #include <TVectorT.h>
 
 namespace ActsExamples::detail::NuclearInteractionParametrisation {
 
 namespace {
 
 /// @brief Evaluate the location in a standard normal distribution for a value
 /// from a probability distribution
 ///
 /// @param [in] histo The probability distribution
 /// @param [in] mom The abscissa value in @p histo
 ///
 /// @return The location in a standard normal distribution
 float gaussianValue(TH1F const* histo, const float mom) {
   // Get the cumulative probability distribution
 
   // DrawNormalized and GetCumulative return pointers to histograms where ROOT
   // transfers ownership to the caller.
   std::unique_ptr<TH1F> normalised(
       dynamic_cast<TH1F*>(histo->DrawNormalized()));
   std::unique_ptr<TH1F> cumulative(
       dynamic_cast<TH1F*>(normalised->GetCumulative()));
   assert(cumulative);
   assert(normalised);
   // Find the cumulative probability
   const float binContent = cumulative->GetBinContent(cumulative->FindBin(mom));
   // Transform the probability to an entry in a standard normal distribution
   const float value = TMath::ErfInverse(2. * binContent - 1.);
 
   return value;
 }
 
 /// @brief Evaluate the invariant mass of two four vectors
 ///
 /// @param [in] fourVector1 The one four vector
 /// @param [in] fourVector2 The other four vector
 ///
 /// @return The invariant mass
 float invariantMass(const Acts::Vector4& fourVector1,
                     const Acts::Vector4& fourVector2) {
   Acts::Vector4 sum = fourVector1 + fourVector2;
   const double energy = sum[Acts::eEnergy];
   double momentum = sum.template segment<3>(Acts::eMom0).norm();
   return std::sqrt(energy * energy - momentum * momentum);
 }
 
 }  // namespace
 
 std::pair<Vector, Matrix> calculateMeanAndCovariance(
     unsigned int multiplicity, const EventProperties& events) {
   // Calculate the mean
   Vector mean = Vector::Zero(multiplicity);
   for (const std::vector<float>& event : events) {
     for (unsigned int j = 0; j < multiplicity; j++) {
       mean[j] += event[j];
     }
   }
   mean /= events.size();
 
   // Calculate the covariance matrix
   Matrix covariance = Matrix::Zero(multiplicity, multiplicity);
   for (unsigned int i = 0; i < multiplicity; i++) {
     for (unsigned int j = 0; j < multiplicity; j++) {
       for (unsigned int k = 0; k < events.size(); k++) {
         covariance(i, j) += (events[k][i] - mean[i]) * (events[k][j] - mean[j]);
       }
     }
   }
   covariance /= events.size();
 
   return {mean, covariance};
 }
 
 EigenspaceComponents calculateEigenspace(const Vector& mean,
                                          const Matrix& covariance) {
   // Calculate eigenvalues and eigenvectors
   Eigen::EigenSolver<Matrix> es(covariance);
   Vector eigenvalues = es.eigenvalues().real();
   Matrix eigenvectors = es.eigenvectors().real();
   // Transform the mean vector into eigenspace
   Vector meanEigenspace = eigenvectors * mean;
 
   return {eigenvalues, eigenvectors, meanEigenspace};
 }
 
 Parametrisation buildMomentumParameters(const EventCollection& events,
                                         unsigned int multiplicity, bool soft,
                                         unsigned int nBins) {
   // Strip off data
   auto momenta = prepareMomenta(events, multiplicity, soft);
   if (momenta.empty()) {
     return Parametrisation();
   }
 
   // Build histos
   ProbabilityDistributions histos = buildMomPerMult(momenta, nBins);
 
   // Build normal distribution
   auto momentaGaussian = convertEventToGaussian(histos, momenta);
   auto meanAndCovariance =
       calculateMeanAndCovariance(multiplicity + 1, momentaGaussian);
   // Calculate the transformation into the eigenspace of the covariance matrix
   EigenspaceComponents eigenspaceElements =
       calculateEigenspace(meanAndCovariance.first, meanAndCovariance.second);
   // Calculate the cumulative distributions
   return {eigenspaceElements, histos};
 }
 
 EventProperties prepareMomenta(const EventCollection& events,
                                unsigned int multiplicity,
                                bool soft)  // TODO: build enum instead of bool
 {
   EventProperties result;
   // Loop over all events
   for (const EventFraction& event : events) {
     // Test the multiplicity and type of the event
     if (event.multiplicity == multiplicity && event.soft == soft) {
       const float initialMomentum = event.initialParticle.absoluteMomentum();
       float sum = 0.;
       std::vector<float> momenta;
       momenta.reserve(multiplicity + 1);
       // Fill the vector with the scaled momenta
       for (const ActsExamples::SimParticle& p : event.finalParticles) {
         sum += p.absoluteMomentum();
         momenta.push_back(p.absoluteMomentum() / initialMomentum);
       }
       // Add the scaled sum of momenta
       momenta.push_back(sum / initialMomentum);
       result.push_back(std::move(momenta));
     }
   }
   return result;
 }
 
 ProbabilityDistributions buildMomPerMult(const EventProperties& events,
                                          unsigned int nBins) {
   // Fast exit
   if (events.empty()) {
     return {};
   }
   const unsigned int multMax = events[0].size();
 
   // Find the range of each histogram
   std::vector<float> min(multMax, std::numeric_limits<float>::max());
   std::vector<float> max(multMax, 0);
   for (const std::vector<float>& event : events) {
     for (unsigned int i = 0; i < multMax; i++) {
       min[i] = std::min(event[i], min[i]);
       max[i] = std::max(event[i], max[i]);
     }
   }
 
   // Evaluate the range of the histograms
   // This is used to avoid entries in over-/underflow bins
   std::vector<float> diff(multMax);
   for (unsigned int i = 0; i < multMax; i++) {
     diff[i] = (max[i] - min[i]) * 0.1;
   }
 
   // Build the histograms
   ProbabilityDistributions histos(multMax);
   for (unsigned int i = 0; i < multMax; i++) {
     histos[i] = new TH1F("", "", nBins, min[i] - diff[i], max[i] + diff[i]);
   }
 
   // Fill the histograms
   for (const std::vector<float>& event : events) {
     for (unsigned int i = 0; i < multMax; i++) {
       histos[i]->Fill(event[i]);
     }
   }
   return histos;
 }
 
 EventProperties convertEventToGaussian(const ProbabilityDistributions& histos,
                                        const EventProperties& events) {
   // Fast exit
   if (events.empty()) {
     return {};
   }
   const unsigned int multMax = events[0].size();
 
   // Loop over the events
   EventProperties gaussianEvents;
   for (const std::vector<float>& event : events) {
     // Transform the properties in the events
     std::vector<float> gaussianEvent;
     for (unsigned int i = 0; i < multMax; i++) {
       gaussianEvent.push_back(gaussianValue(histos[i], event[i]));
     }
     // Store the transformed event
     gaussianEvents.push_back(gaussianEvent);
   }
   return gaussianEvents;
 }
 
 EventProperties prepareInvariantMasses(const EventCollection& events,
                                        unsigned int multiplicity, bool soft) {
   EventProperties result;
   // Loop over all events
   for (const EventFraction& event : events) {
     // Test the multiplicity and type of the event
     if (event.multiplicity == multiplicity && event.soft == soft) {
       const auto fourVectorBefore = event.interactingParticle.fourMomentum();
       std::vector<float> invariantMasses;
       invariantMasses.reserve(multiplicity);
       // Fill the vector with the invariant masses
       for (const ActsExamples::SimParticle& p : event.finalParticles) {
         const auto fourVector = p.fourMomentum();
         invariantMasses.push_back(invariantMass(fourVectorBefore, fourVector));
       }
       result.push_back(invariantMasses);
     }
   }
   return result;
 }
 
 Parametrisation buildInvariantMassParameters(const EventCollection& events,
                                              unsigned int multiplicity,
                                              bool soft, unsigned int nBins) {
   // Strip off data
   auto invariantMasses = prepareInvariantMasses(events, multiplicity, soft);
   if (invariantMasses.empty()) {
     return Parametrisation();
   }
 
   // Build histos
   ProbabilityDistributions histos = buildMomPerMult(invariantMasses, nBins);
 
   // Build normal distribution
   auto invariantMassesGaussian =
       convertEventToGaussian(histos, invariantMasses);
   auto meanAndCovariance =
       calculateMeanAndCovariance(multiplicity, invariantMassesGaussian);
   // Calculate the transformation into the eigenspace of the covariance matrix
   EigenspaceComponents eigenspaceElements =
       calculateEigenspace(meanAndCovariance.first, meanAndCovariance.second);
   // Calculate the cumulative distributions
   return {eigenspaceElements, histos};
 }
 
 std::unordered_map<int, std::unordered_map<int, float>>
 cumulativePDGprobability(const EventCollection& events) {
   std::unordered_map<int, std::unordered_map<int, float>> counter;
 
   // Count how many and which particles were created by which particle
   for (const EventFraction& event : events) {
     if (event.finalParticles.empty()) {
       continue;
     }
     if (!event.soft) {
       counter[event.initialParticle.pdg()][event.finalParticles[0].pdg()]++;
     }
     for (unsigned int i = 1; i < event.multiplicity; i++) {
       counter[event.finalParticles[i - 1].pdg()]
              [event.finalParticles[i].pdg()]++;
     }
   }
 
   // Build a cumulative distribution
   for (const auto& element : counter) {
     float sum = 0;
     auto prevIt = counter[element.first].begin();
     for (auto it1 = counter[element.first].begin();
          it1 != counter[element.first].end(); it1++) {
       float binEntry = 0;
       if (it1 == counter[element.first].begin()) {
         binEntry = it1->second;
         prevIt = it1;
       } else {
         binEntry = it1->second - prevIt->second;
         prevIt = it1;
       }
       // Add content to next bins
       for (auto it2 = std::next(it1, 1); it2 != counter[element.first].end();
            it2++) {
         it2->second += binEntry;
         sum = it2->second;
       }
     }
     // Normalise the entry
     for (auto it1 = counter[element.first].begin();
          it1 != counter[element.first].end(); it1++) {
       it1->second /= sum;
     }
   }
   return counter;
 }
 
 std::pair<CumulativeDistribution, CumulativeDistribution>
 cumulativeMultiplicityProbability(const EventCollection& events,
                                   unsigned int multiplicityMax) {
   // Find the range of both histogram
   unsigned int minSoft = std::numeric_limits<unsigned int>::max();
   unsigned int maxSoft = 0;
   unsigned int minHard = std::numeric_limits<unsigned int>::max();
   unsigned int maxHard = 0;
   for (const EventFraction& event : events) {
     if (event.soft) {
       minSoft = std::min(event.multiplicity, minSoft);
       maxSoft = std::max(event.multiplicity, maxSoft);
     } else {
       minHard = std::min(event.multiplicity, minHard);
       maxHard = std::max(event.multiplicity, maxHard);
     }
   }
 
   // Build and fill the histograms
   TH1F* softHisto =
       new TH1F("", "", std::min(maxSoft, multiplicityMax) + 1 - minSoft,
                minSoft, std::min(maxSoft, multiplicityMax) + 1);
   TH1F* hardHisto =
       new TH1F("", "", std::min(maxHard, multiplicityMax) + 1 - minHard,
                minHard, std::min(maxHard, multiplicityMax) + 1);
   for (const EventFraction& event : events) {
     if (event.multiplicity <= multiplicityMax) {
       if (event.soft) {
         softHisto->Fill(event.multiplicity);
       } else {
         hardHisto->Fill(event.multiplicity);
       }
     }
   }
 
   return {softHisto, hardHisto};
 }
 
 TVectorF softProbability(const EventCollection& events) {
   std::size_t countSoft = 0;
   // Count the soft events
   for (const EventFraction& event : events) {
     if (event.soft) {
       countSoft++;
     }
   }
 
   TVectorF result(1);
   result[0] = static_cast<float>(countSoft) / events.size();
   return result;
 }
 
 CumulativeDistribution cumulativeNuclearInteractionProbability(
     const EventCollection& events, unsigned int interactionProbabilityBins) {
   // Find the limits of the histogram
   float min = std::numeric_limits<float>::max();
   float max = 0.;
   for (const EventFraction& event : events) {
     min =
         std::min(static_cast<float>(event.interactingParticle.pathInL0()), min);
     max =
         std::max(static_cast<float>(event.interactingParticle.pathInL0()), max);
   }
 
   // Fill the histogram
   TH1F* histo = new TH1F("", "", interactionProbabilityBins, min, max);
   for (const EventFraction& event : events) {
     histo->Fill(event.interactingParticle.pathInL0());
   }
 
   // Build the distributions
   return histo;  // TODO: in this case the normalisation is not taking into
                  // account
 }
 
 }  // namespace ActsExamples::detail::NuclearInteractionParametrisation

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