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

namespace Rivet {


  /// @brief J/Psi, psi(2S) -> Sigma+ Sigmabar-
  class BESIII_2020_I1791570 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2020_I1791570);


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

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

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

      // Book histograms
      book(_h_T1, "/TMP/T1",20,-1.,1.);
      book(_h_T2, "/TMP/T2",20,-1.,1.);
      book(_h_T3, "/TMP/T3",20,-1.,1.);
      book(_h_T4, "/TMP/T4",20,-1.,1.);
      book(_h_T5, "/TMP/T5",20,-1.,1.);

      book(_h_cThetaL,"/TMP/cThetaL",20,-1.,1.);
      if(isCompatibleWithSqrtS(3.1*GeV,1e-2))
        book(_h_mu,1,1,1);
      else if(isCompatibleWithSqrtS(3.686*GeV,1e-2))
        book(_h_mu,1,1,2);
      else
        throw Error("Unexpected sqrtS ! Only 3.1 and 3.686 GeV atr supported");
      book(_wsum,"/TMP/wsum");
    }

    void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
      for( const Particle &child : p.children()) {
        if(child.children().empty()) {
          nRes[child.pid()]-=1;
          --ncount;
        }
        else
          findChildren(child,nRes,ncount);
      }
    }

    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // get the axis, direction of incoming electron
      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();
      // types of final state particles
      const FinalState& fs = apply<FinalState>(event, "FS");
      map<long,int> nCount;
      int ntotal(0);
      for (const Particle& p :  fs.particles()) {
        nCount[p.pid()] += 1;
        ++ntotal;
      }
      // loop over Sigma+ baryons
      const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
      Particle Sigma,SigBar;
      bool matched(false);
      for (const Particle& p :  ufs.particles(Cuts::abspid==3222)) {
        if(p.children().empty()) continue;
        map<long,int> nRes=nCount;
        int ncount = ntotal;
        findChildren(p,nRes,ncount);
        matched=false;
        // check for antiparticle
        for (const Particle& p2 :  ufs.particles(Cuts::pid==-p.pid())) {
          if(p2.children().empty()) continue;
          map<long,int> nRes2=nRes;
          int ncount2 = ncount;
          findChildren(p2,nRes2,ncount2);
          if(ncount2==0) {
            matched = true;
            for(auto const & val : nRes2) {
              if(val.second!=0) {
                matched = false;
                break;
              }
            }
            // fond baryon and antibaryon
            if(matched) {
              if(p.pid()>0) {
                Sigma = p;
                SigBar = p2;
              }
              else {
                Sigma = p2;
                SigBar = p;
              }
              break;
            }
          }
        }
        if(matched) break;
      }
      if(!matched) vetoEvent;
      // find proton
      Particle proton;
      matched = false;
      for (const Particle & p : Sigma.children()) {
        if(p.pid()==2212) {
          matched=true;
          proton=p;
        }
        else if(p.pid()!=111) {
          matched = false;
          break;
        }
      }
      if(!matched) vetoEvent;
      // find antiproton
      Particle pbar;
      matched = false;
      for (const Particle & p : SigBar.children()) {
        if(p.pid()==-2212) {
          matched=true;
          pbar=p;
        }
        else if(p.pid()!=111) {
          matched = false;
          break;
        }
      }
      if(!matched) vetoEvent;
      // boost to the Sigma rest frame
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.momentum().betaVec());
      Vector3 e1z = Sigma.momentum().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
      double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
      // boost to the Sigma bar
      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.momentum().betaVec());
      Vector3 axis2 = boost2.transform(pbar.momentum()).p3().unit();
      double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
      double cosL = axis.dot(Sigma.momentum().p3().unit());
      double sinL = sqrt(1.-sqr(cosL));
      double T1 = sqr(sinL)*n1x*n2x+sqr(cosL)*n1z*n2z;
      double T2 = -sinL*cosL*(n1x*n2z+n1z*n2x);
      double T3 = -sinL*cosL*n1y;
      double T4 = -sinL*cosL*n2y;
      double T5 = n1z*n2z-sqr(sinL)*n1y*n2y;
      double mu = -(n1y-n2y);
      _h_T1->fill(cosL,T1);
      _h_T2->fill(cosL,T2);
      _h_T3->fill(cosL,T3);
      _h_T4->fill(cosL,T4);
      _h_T5->fill(cosL,T5);
      _h_mu->fill(cosL,mu);
      _wsum->fill();
      _h_cThetaL->fill(cosL);
    }


    pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) {
      if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
      double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
      double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
      double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
      for (const auto& bin : hist->bins() ) {
        double Oi = bin.sumW();
        if(Oi==0.) continue;
        double a =  d*(bin.xMax() - bin.xMin());
        double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
        double Ei = bin.errW();
        sum1 +=   a*Oi/sqr(Ei);
        sum2 +=   b*Oi/sqr(Ei);
        sum3 += sqr(a)/sqr(Ei);
        sum4 += sqr(b)/sqr(Ei);
        sum5 +=    a*b/sqr(Ei);
      }
      // calculate alpha
      double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
      // and error
      double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
      double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
      double aa =  sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);
      double dis = sqr(bb)-4.*aa*cc;
      if(dis>0.) {
        dis = sqrt(dis);
        return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
      }
      else {
        return make_pair(alpha,make_pair(0.,0.));
      }
    }

    pair<double,double> calcCoeff(unsigned int imode,Histo1DPtr hist) {
      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.);
        if(imode==0) {
          bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.;
        }
        else if(imode>=2 && imode<=4) {
          bi = ( pow(bin.xMin(),3)*( -5. + 3.*sqr(bin.xMin()))  +
                 pow(bin.xMax(),3)*(  5. - 3.*sqr(bin.xMax())))/15.;
        }
        else
          assert(false);
        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() {
      normalize(_h_cThetaL);
      scale(_h_T1, 1./ *_wsum);
      scale(_h_T2, 1./ *_wsum);
      scale(_h_T3, 1./ *_wsum);
      scale(_h_T4, 1./ *_wsum);
      scale(_h_T5, 1./ *_wsum);
      scale(_h_mu, 2./ *_wsum);
      // histos for J/psi or psi(2s)
      int ih = isCompatibleWithSqrtS(3.1*GeV,1e-2) ? 1 : 2;
      // calculate alpha0
      pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cThetaL);
      Estimate0DPtr _h_alpha0;
      book(_h_alpha0,4,1,ih);
      _h_alpha0->set(alpha0.first, alpha0.second);
      double s2 = -1. + sqr(alpha0.first);
      double s3 = 3 + alpha0.first;
      double s1 = sqr(s3);
      // alpha- and alpha+ from proton data
      pair<double,double> c_T2 = calcCoeff(2,_h_T2);
      pair<double,double> c_T3 = calcCoeff(3,_h_T3);
      pair<double,double> c_T4 = calcCoeff(4,_h_T4);
      double s4 = sqr(c_T2.first);
      double s5 = sqr(c_T3.first);
      double s6 = sqr(c_T4.first);
      double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
      if(disc>=0.) {
        disc = sqrt(disc);
        double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
        double aP = c_T4.first/c_T3.first*aM;
        double aM_P = (2*(alpha0.first*c_T4.first*alpha0.second.first + c_T4.second*s2)*(disc + 2*s1*s5*s6)
                       - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
                                        (disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
                                               + 9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first -  s2*s3*c_T4.first*c_T3.second
                                                    - s2*s3*c_T3.first*c_T4.second)* s4
                                               + 8*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))
                                        /(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
          (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
        double aM_M = (2*(alpha0.first*c_T4.first*alpha0.second.second + c_T4.second*s2)*(disc + 2*s1*s5*s6)
                       - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
                                        (disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
                                               + 9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second -  s2*s3*c_T4.first*c_T3.second
                                                    - s2*s3*c_T3.first*c_T4.second)* s4
                                               + 8*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))
                                        /(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
          (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
        double aP_M = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/   (s2*s6)))*
                       (-2*c_T3.second -  (2*alpha0.first*c_T3.first*alpha0.second.first)/s2 +  (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)
                                                                                                             + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
                                                                                                                      +  9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first -  s2*s3*c_T4.first*c_T3.second
                                                                                                                            -  s2*s3*c_T3.first*c_T4.second)* s4 +
                                                                                                                      8*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))/
                                                                                                             (4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) -  9*s2*s3*c_T3.first*c_T4.first*s4)))/
                        (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
        double aP_P = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/   (s2*s6)))*
                       (-2*c_T3.second -  (2*alpha0.first*c_T3.first*alpha0.second.second)/s2 +  (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)
                                                                                                              + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
                                                                                                                       +  9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second -  s2*s3*c_T4.first*c_T3.second
                                                                                                                             -  s2*s3*c_T3.first*c_T4.second)* s4 +
                                                                                                                       8*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))/
                                                                                                              (4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) -  9*s2*s3*c_T3.first*c_T4.first*s4)))/
                        (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
        Estimate0DPtr _h_alphaM;
        book(_h_alphaM,2,1,1);
        _h_alphaM->set(aM, make_pair(-aM_M , -aM_P ));
        Estimate0DPtr _h_alphaP;
        book(_h_alphaP,2,1,2);
        _h_alphaP->set(aP, make_pair(-aP_M , -aP_P  ));
        Estimate0DPtr _h_alphabar;
        book(_h_alphabar,2,1,3);
        _h_alphabar->set(0.5*(aM-aP),
                                make_pair(0.5*sqrt(sqr(aM_M)+sqr(aP_P)) ,
                                          0.5*sqrt(sqr(aM_P)+sqr(aP_M))));
        // now for Delta
        double sDelta = (-2.*(3. + alpha0.first)*c_T3.first)/(aM*sqrt(1 - sqr(alpha0.first)));
        double cDelta = (-3*(3 + alpha0.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alpha0.first)));

        double Delta = asin(sDelta);
        if(cDelta<0.) Delta = M_PI-Delta;
        double ds_P = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +  c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.first + 3*alpha0.first*alpha0.second.first) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
                                      -  (-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
          (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/   (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
        double ds_M = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +  c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.second + 3*alpha0.first*alpha0.second.second) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
                                      -  (-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
          (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/   (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
        ds_P /= sqrt(1.-sqr(sDelta));
        ds_M /= sqrt(1.-sqr(sDelta));
        Estimate0DPtr _h_sin;
        book(_h_sin,3,1,ih);
        _h_sin->set(Delta/M_PI*180., make_pair( -ds_P/M_PI*180., -ds_M/M_PI*180. ));
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_T1,_h_T2,_h_T3,_h_T4,_h_T5;
    Histo1DPtr _h_cThetaL;
    Histo1DPtr _h_mu;
    CounterPtr _wsum;
    /// @}

  };


  RIVET_DECLARE_PLUGIN(BESIII_2020_I1791570);

}
