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

namespace Rivet {


  /// @brief psi(2S) -> Xi- Xibar+
  class BESIII_2022_I2099144 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2022_I2099144);


    /// @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_cTheta,"TMP/cTheta",20,-1.,1.);
      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 lambda0 baryons
      const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
      Particle Xi,XiBar;
      bool matched(false);
      for (const Particle& p :  ufs.particles(Cuts::abspid==3312)) {
       	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;
      	      }
      	    }
            // found baryon and antibaryon
      	    if(matched) {
	      if(p.pid()>0) {
		Xi    = p;
		XiBar = p2;
	      }
	      else {
		Xi    = p2;
		XiBar = p;
	      }
       	      break;
       	    }
       	  }
       	}
      	if(matched) break;
      }
      if(!matched) vetoEvent;
      // find the lambda and antilambda
      Particle Lambda,LamBar;
      if ( Xi.children()[0].pid() ==3122 )
	Lambda = Xi.children()[0];
      else if ( Xi.children()[1].pid() ==3122 )
	Lambda = Xi.children()[1];
      else vetoEvent;
      if ( XiBar.children()[0].pid() ==-3122 )
	LamBar = XiBar.children()[0];
      else if ( XiBar.children()[1].pid() ==-3122 )
	LamBar = XiBar.children()[1];
      else vetoEvent;
      // boost to the Xi rest frame
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.momentum().betaVec());
      Vector3 e1z = Xi.momentum().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      FourMomentum pLambda = boost1.transform(Lambda.momentum());
      Vector3 axis1 = pLambda.p3().unit();
      double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
      // boost to the Xi bar
      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(XiBar.momentum().betaVec());
      FourMomentum pLamBar = boost2.transform(LamBar.momentum());
      Vector3 axis2 = pLamBar.p3().unit();
      double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
      double cosX = axis.dot(Xi.momentum().p3().unit());
      double sinX = sqrt(1.-sqr(cosX));
      double T1 = sqr(sinX)*n1x*n2x+sqr(cosX)*n1z*n2z;
      double T2 = -sinX*cosX*(n1x*n2z+n1z*n2x);
      double T3 = -sinX*cosX*n1y;
      double T4 = -sinX*cosX*n2y;
      double T5 = n1z*n2z-sqr(sinX)*n1y*n2y;
      _h_T1->fill(cosX,T1);
      _h_T2->fill(cosX,T2);
      _h_T3->fill(cosX,T3);
      _h_T4->fill(cosX,T4);
      _h_T5->fill(cosX,T5);
      _h_cTheta->fill(cosX);
      _wsum->fill();
    }

    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));
    }

    pair<double,double> calcAlpha(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 = 0.5*(bin.xMax()-bin.xMin());
        double bi = 0.5*ai*(bin.xMax()+bin.xMin());
        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_cTheta);
      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);
      // calculate alpha0
      pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cTheta);
      Estimate0DPtr _h_alpha0;
      book(_h_alpha0,2,1,1);
      _h_alpha0->set(alpha0.first, make_pair(alpha0.second.first,alpha0.second.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.) return;
      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_M = (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_P = (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,2,1,3);
      _h_alphaM->set(aM, make_pair(-aM_M , -aM_P ));

      Estimate0DPtr _h_alphaP;
      book(_h_alphaP,2,1,4);
      _h_alphaP->set(aP, make_pair(-aP_M , -aP_P));
      // 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,2,1,2);
      _h_sin->set(Delta, make_pair( -ds_P, -ds_M));
    }

    /// @}


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


  };


  RIVET_DECLARE_PLUGIN(BESIII_2022_I2099144);

}
