// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {


  /// @brief  e+e- > tau+ tau-
  class ALEPH_2001_I555653 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(ALEPH_2001_I555653);

    /// @name Analysis methods
    /// @{

    /// Book histograms and initialise projections before the run
    void init() {

      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(ChargedFinalState(), "FS");
      declare(UnstableParticles(), "UFS");

      // book hists
      book(_h_e,   {-0.9, -0.7, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 0.7, 0.9 });
      book(_h_mu,  {-0.9, -0.7, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 0.7, 0.9 });
      book(_h_pi,  {-0.9, -0.7, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 0.7, 0.9 });
      book(_h_rho, {-0.9, -0.7, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 0.7, 0.9 });
      for (size_t ix=0; ix < _h_e->numBins(); ++ix) {
        const string suff = to_string(ix);
        book(_h_e->bin(ix+1),   "_h_e_"+suff,   20, -1.0, 1.0);
        book(_h_mu->bin(ix+1),  "_h_mu_"+suff,  20, -1.0, 1.0);
        book(_h_pi->bin(ix+1),  "_h_pi_"+suff,  20, -1.0, 1.0);
        book(_h_rho->bin(ix+1), "_h_rho_"+suff, 20, -1.0, 1.0);
      }
    }

    void findTau(const Particle & p, unsigned int & nprod, Particles& piP,
     		         Particles& pi0, Particles& ell, Particles& nu_ell, Particles& nu_tau) {
      for (const Particle& child : p.children()) {
        if (child.pid()==PID::ELECTRON || child.pid()==PID::MUON) {
          ++nprod;
          ell.push_back(child);
        }
        else if (child.pid()==PID::NU_EBAR || child.pid()==PID::NU_MUBAR) {
          ++nprod;
          nu_ell.push_back(child);
        }
        else if (child.pid()==PID::PIMINUS) {
          ++nprod;
          piP.push_back(child);
        }
        else if (child.pid()==PID::PI0) {
          ++nprod;
          pi0.push_back(child);
        }
        else if (child.pid()==PID::NU_TAU) {
          ++nprod;
          nu_tau.push_back(child);
        }
        else if (child.pid()==PID::GAMMA) {
          continue;
        }
        else if (child.children().empty() || child.pid()==221 || child.pid()==331) {
          ++nprod;
        }
        else {
          findTau(child,nprod,piP,pi0,ell,nu_ell,nu_tau);
        }
      }
    }

    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // require 2 chanrged particles to veto hadronic events
      if (apply<ChargedFinalState>(event, "FS").particles().size()!=2) vetoEvent;
      // Get beams and average beam momentum
      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
      Vector3 axis;
      if (beams.first.pid()>0) {
        axis = beams.first .momentum().p3().unit();
      }
      else {
        axis = beams.second.momentum().p3().unit();
      }
      // loop over tau leptons
      for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::pid==15)) {
        unsigned int nprod(0);
        Particles piP, pi0, ell, nu_ell, nu_tau;
        findTau(p,nprod,piP, pi0, ell, nu_ell, nu_tau);
        LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
        double cBeam = axis.dot(p.momentum().p3().unit());
        if (nprod==2 && nu_tau.size()==1 && piP.size()==1) {
          FourMomentum pPi = boost1.transform(piP[0].momentum());
          double cTheta = pPi.p3().unit().dot(p.momentum().p3().unit());
          _h_pi->fill(cBeam,cTheta);
        }
        else if (nprod==3 && nu_tau.size()==1 && ell.size()==1 && nu_ell.size()==1) {
          if(ell[0].pid()==PID::ELECTRON) {
            _h_e->fill(cBeam,2.*ell[0].momentum().t()/sqrtS());
          }
          else {
            _h_mu->fill(cBeam,2.*ell[0].momentum().t()/sqrtS());
          }
        }
        else if (nprod==3 && nu_tau.size()==1 && piP.size()==1&& pi0.size()==1) {
          FourMomentum pRho = boost1.transform(piP[0].momentum()+pi0[0].momentum());
          double cTheta = pRho.p3().unit().dot(p.momentum().p3().unit());
          _h_rho->fill(cBeam, cTheta);
        }
      }
    }

    pair<double,double> calcP(Histo1DPtr hist,unsigned int imode) {
      if (hist->numEntries()==0.) return make_pair(0.,0.);
      double sum1(0.),sum2(0.);
      for (const auto& bin : hist->bins()) {
        double Oi = bin.sumW();
        if (Oi==0.) continue;
        double ai(0.),bi(0.);
        // tau -> pi/rho nu
        if (imode==0) {
          ai = 0.5*(bin.xMax()-bin.xMin());
          bi = 0.5*ai*(bin.xMax()+bin.xMin());
        }
        // lepton mode
        else {
          ai = (-5*bin.xMin() + 3*pow(bin.xMin(),3) -   pow(bin.xMin(),4) + 5*bin.xMax() - 3*pow(bin.xMax(),3) +   pow(bin.xMax(),4))/3.;
          bi = (  -bin.xMin() + 3*pow(bin.xMin(),3) - 2*pow(bin.xMin(),4) +   bin.xMax() - 3*pow(bin.xMax(),3) + 2*pow(bin.xMax(),4))/3.;
        }
        double Ei = bin.errW();
        sum1 += sqr(bi/Ei);
        sum2 += bi/sqr(Ei)*(Oi-ai);
      }
      return make_pair(sum2/sum1,sqrt(1./sum1));
    }

    /// Normalise histograms etc., after the run
    void finalize() {
      Estimate1DPtr _h_P;
      book(_h_P,2,1,1);
      for (size_t ix=1; ix < _h_e->numBins()+1; ++ix) {
        normalize(_h_e->bin(ix));
        pair<double,double> P_e  = calcP(_h_e->bin(ix), 1);
        double s1 = P_e.first/sqr(P_e.second);
        double s2 = 1./sqr(P_e.second);

        normalize(_h_mu->bin(ix));
        pair<double,double> P_mu = calcP(_h_mu->bin(ix), 1);
        s1 += P_mu.first/sqr(P_mu.second);
        s2 += 1./sqr(P_mu.second);

        normalize(_h_pi->bin(ix));
        pair<double,double> P_pi = calcP(_h_pi->bin(ix), 0);
        s1 += P_pi.first/sqr(P_pi.second);
        s2 += 1./sqr(P_pi.second);

        normalize(_h_rho->bin(ix));
        pair<double,double> P_rho = calcP(_h_rho->bin(ix), 0);
        P_rho.first  /=0.46;
        P_rho.second /=0.46;
        s1 += P_rho.first/sqr(P_rho.second);
        s2 += 1./sqr(P_rho.second);
        // average
        _h_P->bin(ix).set(s1/s2, sqrt(1./s2));
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DGroupPtr _h_e, _h_mu, _h_pi, _h_rho;
    /// @}


  };


  RIVET_DECLARE_PLUGIN(ALEPH_2001_I555653);

}
