PhaseSpacePoint.cc
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PhaseSpacePoint.cc
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	/**
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019-2020
	* \copyright GPLv2 or later
	*/
	#include "HEJ/PhaseSpacePoint.hh"

	#include <algorithm>
	#include <cassert>
	#include <cmath>
	#include <cstdlib>
	#include <functional>
	#include <iterator>
	#include <limits>
	#include <numeric>
	#include <random>
	#include <tuple>
	#include <utility>

	#include "CLHEP/Vector/LorentzVector.h"

	#include "fastjet/ClusterSequence.hh"
	#include "fastjet/JetDefinition.hh"

	#include "HEJ/Constants.hh"
	#include "HEJ/Event.hh"
	#include "HEJ/JetSplitter.hh"
	#include "HEJ/PDG_codes.hh"
	#include "HEJ/RNG.hh"
	#include "HEJ/event_types.hh"
	#include "HEJ/kinematics.hh"
	#include "HEJ/resummation_jet.hh"
	#include "HEJ/utility.hh"

	namespace HEJ {
	namespace {
	constexpr int MAX_JET_USER_IDX = PhaseSpacePoint::NG_MAX;

	bool is_nonjet_parton(fastjet::PseudoJet const & parton){
	assert(parton.user_index() != -1);
	return parton.user_index() > MAX_JET_USER_IDX;
	}

	bool is_jet_parton(fastjet::PseudoJet const & parton){
	assert(parton.user_index() != -1);
	return parton.user_index() <= MAX_JET_USER_IDX;
	}

	namespace user_idx {
	//! user indices for partons with extremal rapidity
	enum ID: int {
	qqxmid1 = -9,
	qqxmid2 = -8,
	qqxb = -7,
	qqxf = -6,
	unob = -5,
	unof = -4,
	backward_fkl = -3,
	forward_fkl = -2,
	};
	} // namespace user_idx
	using UID = user_idx::ID;

	double phase_space_normalisation(
	int num_Born_jets, int num_out_partons
	){
	return std::pow(16.*std::pow(M_PI,3), num_Born_jets - num_out_partons);
	}

	} // namespace

	Event::EventData to_EventData(PhaseSpacePoint psp){
	Event::EventData result;
	result.incoming = std::move(psp).incoming_; // NOLINT(bugprone-use-after-move)
	result.outgoing = std::move(psp).outgoing_; // NOLINT(bugprone-use-after-move)
	// technically Event::EventData doesn't have to be sorted,
	// but PhaseSpacePoint should be anyway
	assert(
	std::is_sorted(
	begin(result.outgoing), end(result.outgoing),
	rapidity_less{}
	)
	);
	assert(result.outgoing.size() >= 2);
	static_assert(
	std::numeric_limits<double>::has_quiet_NaN,
	"no quiet NaN for double"
	);
	constexpr double nan = std::numeric_limits<double>::quiet_NaN();
	result.decays = std::move(psp).decays_; // NOLINT(bugprone-use-after-move)
	result.parameters.central = {nan, nan, psp.weight()}; // NOLINT(bugprone-use-after-move)
	return result;
	}

	std::vector<fastjet::PseudoJet> PhaseSpacePoint::cluster_jets(
	std::vector<fastjet::PseudoJet> const & partons
	) const{
	fastjet::ClusterSequence cs(partons, param_.jet_param.def);
	return sorted_by_rapidity(cs.inclusive_jets(param_.jet_param.min_pt));
	}

	bool PhaseSpacePoint::pass_resummation_cuts(
	std::vector<fastjet::PseudoJet> const & jets
	) const{
	return cluster_jets(jets).size() == jets.size();
	}

	namespace {
	// find iterators to central qqbar emission
	auto get_central_qqbar(Event const & ev) {
	// find born quarks (ignore extremal partons)
	auto const firstquark = std::find_if(
	std::next(ev.begin_partons()), std::prev(ev.end_partons(), 2),
	[](Particle const & s){ return (is_anyquark(s)); }
	);
	// assert that it is a q-q_bar pair.
	assert(std::distance(firstquark, ev.end_partons()) != 2);
	assert(
	( is_quark(firstquark) && is_antiquark(std::next(firstquark)) )
	\|\| ( is_antiquark(firstquark) && is_quark(std::next(firstquark)) )
	);
	return std::make_pair(firstquark, std::next(firstquark));
	}

	//! returns index of most backward q-qbar jet
	template<class Iterator>
	int get_back_quark_jet(Event const & ev, Iterator firstquark){
	// find jets at FO corresponding to the quarks
	// technically this isn't necessary for LO
	std::vector<int> const born_indices{ ev.particle_jet_indices() };
	const auto firstquark_idx = std::distance(ev.begin_partons(), firstquark);
	int const firstjet_idx = born_indices[firstquark_idx];
	assert(firstjet_idx>0);
	assert( born_indices[firstquark_idx+1] == firstjet_idx+1 );

	return firstjet_idx;
	}

	//! returns index of most backward q-qbar jet
	int getBackQuarkJet(Event const & ev){
	const auto firstquark = get_central_qqbar(ev).first;
	return get_back_quark_jet(ev, firstquark);
	}
	}

	double PhaseSpacePoint::estimate_emission_rapidity_range(
	Event const & ev
	) const {
	assert(std::is_sorted(begin(ev.jets()), end(ev.jets()), rapidity_less{}));

	double delta_y =
	most_forward_FKL(ev.jets()).rapidity()
	- most_backward_FKL(ev.jets()).rapidity();
	// neglect tiny probability for emission between central qqbar pair
	if(ev.type() == event_type::central_qqx) {
	const int qjet = getBackQuarkJet(ev);
	delta_y -= ev.jets()[qjet+1].rapidity() - ev.jets()[qjet].rapidity();
	}
	assert(delta_y >= 0);
	return delta_y;
	}

	double PhaseSpacePoint::estimate_ng_mean(Event const & ev) const {
	// Formula derived from fit in arXiv:1805.04446 (see Fig. 2)
	constexpr double GLUONS_PER_RAPIDITY = 0.975052;
	return GLUONS_PER_RAPIDITY*estimate_emission_rapidity_range(ev);
	}

	int PhaseSpacePoint::sample_ng(Event const & event, RNG & ran){
	const double ng_mean = estimate_ng_mean(event);
	std::poisson_distribution<int> dist(ng_mean);
	const int ng = dist(ran);
	assert(ng >= 0);
	assert(ng < NG_MAX);
	weight_ = std::tgamma(ng + 1)std::exp(ng_mean)*std::pow(ng_mean, -ng);
	return ng;
	}

	void PhaseSpacePoint::boost_AWZH_boson_from(fastjet::PseudoJet boostedbosonm, Event const & event){
	auto const & from = event.outgoing();

	const auto AWZH_boson = std::find_if(
	begin(from), end(from),
	[](Particle const & p){ return is_AWZH_boson(p); }
	);
	if(AWZH_boson == end(from)) return;
	auto insertion_point = std::lower_bound(
	begin(outgoing_), end(outgoing_), *AWZH_boson, rapidity_less{}
	);
	// copy awzh particle
	auto bAWZH_boson = *AWZH_boson;
	bAWZH_boson.p=boostedbosonm;
	outgoing_.insert(insertion_point, bAWZH_boson);

	// copy decay products
	const int idx = std::distance(begin(from), AWZH_boson);
	assert(idx >= 0);
	const auto decay_it = event.decays().find(idx);
	if(decay_it != end(event.decays())){
	const int new_idx = std::distance(begin(outgoing_), insertion_point);
	assert(new_idx >= 0);
	assert(outgoing_[new_idx].type == AWZH_boson->type);
	// change the momenta of the decay products.
	// boost to rest frame of input boson, then from rest frame of shuffled boson
	auto decayparticles=decay_it->second;
	auto boost1=CLHEP::HepLorentzVector((AWZH_boson).px(),(AWZH_boson).py(),
	(AWZH_boson).pz(),(AWZH_boson).E());
	auto boost2=CLHEP::HepLorentzVector(boostedbosonm.px(),boostedbosonm.py(),
	boostedbosonm.pz(),boostedbosonm.E());

	auto vec1=CLHEP::HepLorentzVector(decayparticles[0].p.px(),decayparticles[0].p.py(),
	decayparticles[0].p.pz(),decayparticles[0].p.E());
	auto vec2=CLHEP::HepLorentzVector(decayparticles[1].p.px(),decayparticles[1].p.py(),
	decayparticles[1].p.pz(),decayparticles[1].p.E());

	auto rvec1=vec1.boost(boost1.findBoostToCM());
	auto rvec2=vec2.boost(boost1.findBoostToCM());

	auto bvec1=vec1.boost(-boost2.findBoostToCM());
	auto bvec2=vec2.boost(-boost2.findBoostToCM());

	decayparticles[0].p=fastjet::PseudoJet(bvec1.px(),bvec1.py(),bvec1.pz(),bvec1.e());
	decayparticles[1].p=fastjet::PseudoJet(bvec2.px(),bvec2.py(),bvec2.pz(),bvec2.e());
	decays_.emplace(new_idx, decayparticles);
	}

	assert(std::is_sorted(begin(outgoing_), end(outgoing_), rapidity_less{}));
	}

	namespace {

	template<class ConstIterator, class Iterator>
	void label_extremal_qqx(
	ConstIterator born_begin, ConstIterator born_end,
	Iterator first_out
	){
	// find born quarks
	const auto firstquark = std::find_if(
	born_begin, born_end-1,
	[](Particle const & s){ return (is_anyquark(s)); }
	);
	assert(firstquark != born_end-1);
	const auto secondquark = std::find_if(
	firstquark+1, born_end,
	[](Particle const & s){ return (is_anyquark(s)); }
	);
	assert(secondquark != born_end);
	assert( ( is_quark(firstquark) && is_antiquark(secondquark) )
	\|\| ( is_antiquark(firstquark) && is_quark(secondquark) ));
	assert(first_out->type == ParticleID::gluon);
	assert((first_out+1)->type == ParticleID::gluon);

	// copy type from born
	first_out->type = firstquark->type;
	(first_out+1)->type = secondquark->type;
	}
	} // namespace

	void PhaseSpacePoint::label_qqx(Event const & event){
	assert(std::is_sorted(begin(outgoing_), end(outgoing_), rapidity_less{}));
	assert(filter_partons(outgoing_).size() == outgoing_.size());
	if(qqxb_){
	label_extremal_qqx( event.outgoing().cbegin(), event.outgoing().cend(),
	outgoing_.begin()
	);
	return;
	}
	if(qqxf_){ // same as qqxb with reversed order
	label_extremal_qqx( event.outgoing().crbegin(), event.outgoing().crend(),
	outgoing_.rbegin()
	);
	return;
	}
	// central qqx
	const auto firstquark = get_central_qqbar(event).first;

	// find jets at FO corresponding to the quarks
	// technically this isn't necessary for LO
	const auto firstjet_idx = get_back_quark_jet(event, firstquark);

	// find corresponding jets after resummation
	fastjet::ClusterSequence cs{to_PseudoJet(outgoing_), param_.jet_param.def};
	auto const jets = fastjet::sorted_by_rapidity(
	cs.inclusive_jets( param_.jet_param.min_pt ));
	std::vector<int> const resum_indices{ cs.particle_jet_indices({jets}) };

	// assert that jets didn't move
	assert(nearby_ep( ( event.jets().cbegin()+firstjet_idx )->rapidity(),
	jets[ firstjet_idx ].rapidity(), 1e-2) );
	assert(nearby_ep( ( event.jets().cbegin()+firstjet_idx+1 )->rapidity(),
	jets[ firstjet_idx+1 ].rapidity(), 1e-2) );

	// find last partons in first (central) jet
	size_t idx_out = 0;
	for(size_t i=resum_indices.size()-2; i>0; --i)
	if(resum_indices[i] == firstjet_idx){
	idx_out = i;
	break;
	}
	assert(idx_out != 0);

	// check that there is sufficient pt in jets from the quarks
	const double minpartonjetpt = 1. - param_.soft_pt_regulator;
	if (outgoing_[idx_out].p.pt()<minpartonjetpt*( event.jets().cbegin()+firstjet_idx )->pt()){
	weight_=0.;
	status_ = StatusCode::wrong_jets;
	return;
	}

	if (outgoing_[idx_out+1].p.pt()<minpartonjetpt*( event.jets().cbegin()+firstjet_idx+1 )->pt()){
	weight_=0.;
	status_ = StatusCode::wrong_jets;
	return;
	}
	// check that no additional emission between jets
	// such configurations are possible if we have an gluon gets generated
	// inside the rapidities of the qqx chain, but clusted to a
	// differnet/outside jet. Changing this is non trivial
	if(resum_indices[idx_out+1] != resum_indices[idx_out]+1){
	weight_=0.;
	status_ = StatusCode::gluon_in_qqx;
	return;
	}
	outgoing_[idx_out].type = firstquark->type;
	outgoing_[idx_out+1].type = std::next(firstquark)->type;
	}

	void PhaseSpacePoint::label_quarks(Event const & ev){
	const auto WZEmit = std::find_if(
	begin(ev.outgoing()), end(ev.outgoing()),
	[](Particle const & s){ return (std::abs(s.type) == pid::Wp \|\| s.type == pid::Z_photon_mix); }
	);

	if (WZEmit != end(ev.outgoing())){
	if(!qqxb_) {
	const size_t backward_FKL_idx = unob_?1:0;
	const auto backward_FKL = std::next(ev.begin_partons(), backward_FKL_idx);
	outgoing_[backward_FKL_idx].type = backward_FKL->type;
	}
	if(!qqxf_) {
	const size_t forward_FKL_idx = unof_?1:0;
	const auto forward_FKL = std::prev(ev.end_partons(), 1+forward_FKL_idx);
	outgoing_.rbegin()[unof_].type = forward_FKL->type; // NOLINT
	}
	} else {
	most_backward_FKL(outgoing_).type = ev.incoming().front().type;
	most_forward_FKL(outgoing_).type = ev.incoming().back().type;
	}

	if(qqxmid_\|\|qqxb_\|\|qqxf_){
	label_qqx(ev);
	}
	}

	PhaseSpacePoint::PhaseSpacePoint(
	Event const & ev, PhaseSpacePointConfig conf, RNG & ran
	):
	unob_{ev.type() == event_type::unob},
	unof_{ev.type() == event_type::unof},
	qqxb_{ev.type() == event_type::qqxexb},
	qqxf_{ev.type() == event_type::qqxexf},
	qqxmid_{ev.type() == event_type::qqxmid},
	param_{std::move(conf)},
	status_{unspecified}
	{
	// legacy code: override new variable with old
	if(param_.max_ext_soft_pt_fraction){
	param_.soft_pt_regulator = *param_.max_ext_soft_pt_fraction;
	param_.max_ext_soft_pt_fraction = {};
	}

	weight_ = 1;
	auto const & Born_jets = ev.jets();
	const int ng = sample_ng(ev, ran);
	weight_ /= std::tgamma(ng + 1);
	const int ng_jets = sample_ng_jets(ev, ng, ran);
	std::vector<fastjet::PseudoJet> out_partons = gen_non_jet(
	ng - ng_jets, CMINPT, param_.jet_param.min_pt, ran
	);

	int qqxbackjet(-1);
	if(qqxmid_){
	qqxbackjet = getBackQuarkJet(ev);
	}

	// reshuffle soft momenta
	const auto qperp = std::accumulate(
	begin(out_partons), end(out_partons),
	fastjet::PseudoJet{}
	);

	std::vector<fastjet::PseudoJet> jets;
	optional<fastjet::PseudoJet> boson;
	std::tie(jets, boson) = reshuffle(ev, qperp);
	if(weight_ == 0.) {
	status_ = failed_reshuffle;
	return;
	}
	if(! pass_resummation_cuts(jets)){
	status_ = failed_resummation_cuts;
	weight_ = 0.;
	return;
	}

	// split jets in multiple partons
	std::vector<fastjet::PseudoJet> jet_partons = split(
	jets, ng_jets, qqxbackjet, ran
	);
	if(weight_ == 0.) {
	status_ = StatusCode::failed_split;
	return;
	}

	// rescale rapidity interval
	if(qqxmid_){
	rescale_qqx_rapidities(
	out_partons, jets,
	most_backward_FKL(jet_partons).rapidity(),
	most_forward_FKL(jet_partons).rapidity(),
	qqxbackjet
	);
	}
	else{
	rescale_rapidities(
	out_partons,
	most_backward_FKL(jet_partons).rapidity(),
	most_forward_FKL(jet_partons).rapidity()
	);
	}
	if(! cluster_jets(out_partons).empty()){
	weight_ = 0.;
	status_ = StatusCode::empty_jets;
	return;
	}
	std::sort(begin(out_partons), end(out_partons), rapidity_less{});
	assert(
	std::is_sorted(begin(jet_partons), end(jet_partons), rapidity_less{})
	);
	const auto first_jet_parton = out_partons.insert(
	end(out_partons), begin(jet_partons), end(jet_partons)
	);
	std::inplace_merge(
	begin(out_partons), first_jet_parton, end(out_partons), rapidity_less{}
	);

	if(! jets_ok(Born_jets, out_partons)){
	weight_ = 0.;
	status_ = StatusCode::wrong_jets;
	return;
	}

	weight_ *= phase_space_normalisation(Born_jets.size(), out_partons.size());

	outgoing_.reserve(out_partons.size() + 1); // one slot for possible A, W, Z, H
	for( auto it = std::make_move_iterator(out_partons.begin());
	it != std::make_move_iterator(out_partons.end());
	++it
	){
	outgoing_.emplace_back( Particle{pid::gluon, *it, {}});
	}
	assert(!outgoing_.empty());

	label_quarks(ev);
	if(weight_ == 0.) {
	//! @TODO optimise s.t. this is not possible
	// status is handled internally
	return;
	}

	// reattach boson & decays
	if(boson){
	boost_AWZH_boson_from(*boson,ev);
	}

	reconstruct_incoming(ev.incoming());
	status_ = StatusCode::good;
	}

	std::vector<fastjet::PseudoJet> PhaseSpacePoint::gen_non_jet(
	int const ng_non_jet, double const ptmin, double const ptmax, RNG & ran
	){
	// heuristic parameters for pt sampling
	const double ptpar = 1.3 + ng_non_jet/5.;
	const double temp1 = std::atan((ptmax - ptmin)/ptpar);

	std::vector<fastjet::PseudoJet> partons(ng_non_jet);
	for(int i = 0; i < ng_non_jet; ++i){
	const double r1 = ran.flat();
	const double pt = ptmin + ptparstd::tan(r1temp1);
	const double temp2 = std::cos(r1*temp1);
	const double phi = 2M_PIran.flat();
	weight_ = 2.0M_PIptptpartemp1/(temp2temp2);
	// we don't know the allowed rapidity span yet,
	// set a random value to be rescaled later on
	const double y = ran.flat();
	partons[i].reset_PtYPhiM(pt, y, phi);
	// Set user index higher than any jet-parton index
	// in order to assert that these are not inside jets
	partons[i].set_user_index(i + 1 + NG_MAX);

	assert(ptmin-1e-5 <= partons[i].pt() && partons[i].pt() <= ptmax+1e-5);
	}
	assert(std::all_of(partons.cbegin(), partons.cend(), is_nonjet_parton));
	return sorted_by_rapidity(partons);
	}

	void PhaseSpacePoint::rescale_qqx_rapidities(
	std::vector<fastjet::PseudoJet> & out_partons,
	std::vector<fastjet::PseudoJet> const & jets,
	const double ymin1, const double ymax2,
	const int qqxbackjet
	){
	const double ymax1 = jets[qqxbackjet].rapidity();
	const double ymin2 = jets[qqxbackjet+1].rapidity();
	constexpr double ep = 1e-7;
	const double tot_y = ymax1 - ymin1 + ymax2 - ymin2;

	std::vector<std::reference_wrapper<fastjet::PseudoJet>> refpart(
	out_partons.begin(), out_partons.end());

	double ratio = (ymax1 - ymin1)/tot_y;

	const auto gap{ std::find_if(refpart.begin(), refpart.end(),
	[ratio](fastjet::PseudoJet const & p){
	return (p.rapidity()>=ratio);} ) };

	double ymin = ymin1;
	double ymax = ymax1;
	double dy = ymax - ymin - 2*ep;
	double offset = 0.;
	for(auto it_part=refpart.begin(); it_part<refpart.end(); ++it_part){
	if(it_part == gap){
	ymin = ymin2;
	ymax = ymax2;
	dy = ymax - ymin - 2*ep;
	offset = ratio;
	ratio = 1-ratio;
	}
	fastjet::PseudoJet & part = *it_part;
	assert(offset <= part.rapidity() && part.rapidity() < ratio+offset);
	const double y = ymin + ep + dy*((part.rapidity()-offset)/ratio);
	part.reset_momentum_PtYPhiM(part.pt(), y, part.phi());
	weight_ = tot_y-4.ep;
	assert(ymin <= part.rapidity() && part.rapidity() <= ymax);
	}
	assert(is_sorted(begin(out_partons), end(out_partons), rapidity_less{}));
	}

	void PhaseSpacePoint::rescale_rapidities(
	std::vector<fastjet::PseudoJet> & partons,
	double ymin, double ymax
	){
	constexpr double ep = 1e-7;
	for(auto & parton: partons){
	assert(0 <= parton.rapidity() && parton.rapidity() <= 1);
	const double dy = ymax - ymin - 2*ep;
	const double y = ymin + ep + dy*parton.rapidity();
	parton.reset_momentum_PtYPhiM(parton.pt(), y, parton.phi());
	weight_ *= dy;
	assert(ymin <= parton.rapidity() && parton.rapidity() <= ymax);
	}
	}

	namespace {
	template<typename T, typename... Rest>
	auto min(T const & a, T const & b, Rest&&... r) {
	using std::min;
	return min(a, min(b, std::forward<Rest>(r)...));
	}
	}

	double PhaseSpacePoint::probability_in_jet(Event const & ev) const{
	const double dy = estimate_emission_rapidity_range(ev);
	const double R = param_.jet_param.def.R();
	// jets into which we predominantly emit
	const int njets = ev.jets().size() - unof_ - unob_ - qqxb_ - qqxf_;
	assert(njets >= 2);
	const double p_J_y_large = (njets-1)RR/(2.*dy);
	const double p_J_y0 = njets*R/M_PI;
	return min(p_J_y_large, p_J_y0, 1.);
	}

	int PhaseSpacePoint::sample_ng_jets(Event const & event, int ng, RNG & ran){
	const double p_J = probability_in_jet(event);
	std::binomial_distribution<> bin_dist(ng, p_J);
	const int ng_J = bin_dist(ran);
	weight_ = std::pow(p_J, -ng_J)std::pow(1 - p_J, ng_J - ng);
	return ng_J;
	}

	std::pair< std::vector<fastjet::PseudoJet>,
	optional<fastjet::PseudoJet> >
	PhaseSpacePoint::reshuffle(
	Event const & ev,
	fastjet::PseudoJet const & q
	){
	// Create a copy of the outgoing momenta not containing decay products
	std::vector<fastjet::PseudoJet const *> born_momenta;
	born_momenta.reserve(ev.jets().size());
	std::transform(ev.jets().cbegin(), ev.jets().cend(),
	back_inserter(born_momenta),
	[](fastjet::PseudoJet const & t) { return &t; });

	// check if there is one (or more) bosons in the event.
	const auto AWZH_boson = std::find_if(
	begin(ev.outgoing()), end(ev.outgoing()),
	[](Particle const & p){ return is_AWZH_boson(p); }
	);

	optional<fastjet::PseudoJet> boson;
	if(AWZH_boson != end(ev.outgoing())){
	boson = AWZH_boson->p;
	}

	// reshuffle all momenta
	if(q == fastjet::PseudoJet{0, 0, 0, 0}) return {ev.jets(), boson};
	// add boson to reshuffling
	if(boson) {
	born_momenta.push_back(&*boson);
	}
	auto shuffle_momenta = resummation_jet_momenta(born_momenta, q);
	if(shuffle_momenta.empty()){
	weight_ = 0;
	return {};
	}
	// additional Jacobian to ensure Born integration over delta gives 1
	weight_ *= resummation_jet_weight(born_momenta, q);

	// take out boson again
	optional<fastjet::PseudoJet> shuffle_boson;
	if(boson){
	shuffle_boson = std::move(shuffle_momenta.back());
	shuffle_momenta.pop_back();
	}

	return {shuffle_momenta, shuffle_boson};
	}

	std::vector<int> PhaseSpacePoint::distribute_jet_partons(
	int ng_jets, std::vector<fastjet::PseudoJet> const & jets, RNG & ran
	){
	size_t first_valid_jet = 0;
	size_t num_valid_jets = jets.size();
	const double R_eff = 5./3.*param_.jet_param.def.R();
	// if there is an unordered jet too far away from the FKL jets
	// then extra gluon constituents of the unordered jet would
	// violate the FKL rapidity ordering
	if((unob_\|\|qqxb_) && jets[0].delta_R(jets[1]) > R_eff){
	++first_valid_jet;
	--num_valid_jets;
	}
	else if((unof_\|\|qqxf_) && jets[jets.size()-1].delta_R(jets[jets.size()-2]) > R_eff){
	--num_valid_jets;
	}
	std::vector<int> np(jets.size(), 1);
	for(int i = 0; i < ng_jets; ++i){
	++np[first_valid_jet + ran.flat() * num_valid_jets];
	}
	weight_ *= std::pow(num_valid_jets, ng_jets);
	return np;
	}

	#ifndef NDEBUG
	namespace {
	bool tagged_FKL_backward(
	std::vector<fastjet::PseudoJet> const & jet_partons
	){
	return std::find_if(
	begin(jet_partons), end(jet_partons),
	[](fastjet::PseudoJet const & p){
	return p.user_index() == UID::backward_fkl;
	}
	) != end(jet_partons);
	}

	bool tagged_FKL_forward(
	std::vector<fastjet::PseudoJet> const & jet_partons
	){
	// the most forward FKL parton is most likely near the end of jet_partons;
	// start search from there
	return std::find_if(
	jet_partons.rbegin(), jet_partons.rend(),
	[](fastjet::PseudoJet const & p){
	return p.user_index() == UID::forward_fkl;
	}
	) != jet_partons.rend();
	}

	bool tagged_FKL_extremal(
	std::vector<fastjet::PseudoJet> const & jet_partons
	){
	return tagged_FKL_backward(jet_partons) && tagged_FKL_forward(jet_partons);
	}

	} // namespace
	#endif

	std::vector<fastjet::PseudoJet> PhaseSpacePoint::split(
	std::vector<fastjet::PseudoJet> const & jets,
	int ng_jets, size_t qqxbackjet, RNG & ran
	){
	return split(
	jets, distribute_jet_partons(ng_jets, jets, ran), qqxbackjet, ran);
	}

	bool PhaseSpacePoint::pass_extremal_cuts(
	fastjet::PseudoJet const & ext_parton,
	fastjet::PseudoJet const & jet
	) const{
	if(ext_parton.pt() < param_.min_extparton_pt) return false;
	return (ext_parton - jet).pt()/jet.pt() < param_.soft_pt_regulator;
	}

	std::vector<fastjet::PseudoJet> PhaseSpacePoint::split(
	std::vector<fastjet::PseudoJet> const & jets,
	std::vector<int> const & np,
	size_t qqxbackjet,
	RNG & ran
	){
	assert(! jets.empty());
	assert(jets.size() == np.size());
	assert(pass_resummation_cuts(jets));

	const size_t most_backward_FKL_idx = 0 + unob_ + qqxb_; // NOLINT
	const size_t most_forward_FKL_idx = jets.size() - 1 - unof_ - qqxf_; // NOLINT
	auto const & jet = param_.jet_param;
	const JetSplitter jet_splitter{jet.def, jet.min_pt};

	std::vector<fastjet::PseudoJet> jet_partons;
	// randomly distribute jet gluons among jets
	for(size_t i = 0; i < jets.size(); ++i){
	auto split_res = jet_splitter.split(jets[i], np[i], ran);
	weight_ *= split_res.weight;
	if(weight_ == 0) return {};
	assert(
	std::all_of(
	begin(split_res.constituents), end(split_res.constituents),
	is_jet_parton
	)
	);
	const auto first_new_parton = jet_partons.insert(
	end(jet_partons),
	begin(split_res.constituents), end(split_res.constituents)
	);
	// mark uno and extremal FKL emissions here so we can check
	// their position once all emissions are generated
	// also mark qqxmid partons, and apply appropriate pt cut.
	auto extremal = end(jet_partons);
	if (i == most_backward_FKL_idx){ //FKL backward emission
	extremal = std::min_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(UID::backward_fkl);
	}
	else if(((unob_ \|\| qqxb_) && i == 0)){
	// unordered/qqxb
	extremal = std::min_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index((unob_)?UID::unob:UID::qqxb);
	}

	else if (i == most_forward_FKL_idx){
	extremal = std::max_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(UID::forward_fkl);
	}
	else if(((unof_ \|\| qqxf_) && i == jets.size() - 1)){
	// unordered/qqxf
	extremal = std::max_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index((unof_)?UID::unof:UID::qqxf);
	}
	else if((qqxmid_ && i == qqxbackjet)){
	extremal = std::max_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(UID::qqxmid1);
	}
	else if((qqxmid_ && i == qqxbackjet+1)){
	extremal = std::min_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(UID::qqxmid2);
	}
	if(
	extremal != end(jet_partons)
	&& !pass_extremal_cuts(*extremal, jets[i])
	){
	weight_ = 0;
	return {};
	}
	}
	assert(tagged_FKL_extremal(jet_partons));
	std::sort(begin(jet_partons), end(jet_partons), rapidity_less{});
	if(
	!extremal_ok(jet_partons)
	\|\| !split_preserved_jets(jets, jet_partons)
	){
	weight_ = 0.;
	return {};
	}
	return jet_partons;
	}

	bool PhaseSpacePoint::extremal_ok(
	std::vector<fastjet::PseudoJet> const & partons
	) const{
	assert(std::is_sorted(begin(partons), end(partons), rapidity_less{}));
	if(unob_ && partons.front().user_index() != UID::unob) return false;
	if(unof_ && partons.back().user_index() != UID::unof) return false;
	if(qqxb_ && partons.front().user_index() != UID::qqxb) return false;
	if(qqxf_ && partons.back().user_index() != UID::qqxf) return false;
	return
	most_backward_FKL(partons).user_index() == UID::backward_fkl
	&& most_forward_FKL(partons).user_index() == UID::forward_fkl;
	}

	bool PhaseSpacePoint::split_preserved_jets(
	std::vector<fastjet::PseudoJet> const & jets,
	std::vector<fastjet::PseudoJet> const & jet_partons
	) const{
	assert(std::is_sorted(begin(jets), end(jets), rapidity_less{}));

	const auto split_jets = cluster_jets(jet_partons);
	// this can happen if two overlapping jets
	// are both split into more than one parton
	if(split_jets.size() != jets.size()) return false;
	for(size_t i = 0; i < split_jets.size(); ++i){
	// this can happen if there are two overlapping jets
	// and a parton is assigned to the "wrong" jet
	if(!nearby_ep(jets[i].rapidity(), split_jets[i].rapidity(), 1e-2)){
	return false;
	}
	}
	return true;
	}

	template<class Particle>
	Particle const & PhaseSpacePoint::most_backward_FKL(
	std::vector<Particle> const & partons
	) const{
	return partons[0 + unob_ + qqxb_];
	}

	template<class Particle>
	Particle const & PhaseSpacePoint::most_forward_FKL(
	std::vector<Particle> const & partons
	) const{
	const size_t idx = partons.size() - 1 - unof_ - qqxf_;
	assert(idx < partons.size());
	return partons[idx];
	}

	template<class Particle>
	Particle & PhaseSpacePoint::most_backward_FKL(
	std::vector<Particle> & partons
	) const{
	return partons[0 + unob_ + qqxb_];
	}

	template<class Particle>
	Particle & PhaseSpacePoint::most_forward_FKL(
	std::vector<Particle> & partons
	) const{
	const size_t idx = partons.size() - 1 - unof_ - qqxf_;
	assert(idx < partons.size());
	return partons[idx];
	}

	bool PhaseSpacePoint::contains_idx(
	fastjet::PseudoJet const & jet, fastjet::PseudoJet const & parton
	) const {
	auto const & constituents = jet.constituents();
	const int idx = parton.user_index();
	const bool injet = std::find_if(
	begin(constituents), end(constituents),
	[idx](fastjet::PseudoJet const & con){return con.user_index() == idx;}
	) != end(constituents);
	const double minpartonjetpt = 1. - param_.soft_pt_regulator;
	return ((parton.pt()>minpartonjetpt*jet.pt())&&injet);
	}

	bool PhaseSpacePoint::jets_ok(
	std::vector<fastjet::PseudoJet> const & Born_jets,
	std::vector<fastjet::PseudoJet> const & partons
	) const{
	fastjet::ClusterSequence cs(partons, param_.jet_param.def);
	const auto jets = sorted_by_rapidity(cs.inclusive_jets(param_.jet_param.min_pt));
	if(jets.size() != Born_jets.size()) return false;
	int in_jet = 0;
	for(auto const & jet : jets){
	assert(jet.has_constituents());
	for(auto && parton: jet.constituents()){
	if(is_nonjet_parton(parton)) return false;
	}
	in_jet += jet.constituents().size();
	}
	const int expect_in_jet = std::count_if(
	partons.cbegin(), partons.cend(), is_jet_parton
	);
	if(in_jet != expect_in_jet) return false;
	// note that PseudoJet::contains does not work here
	if(! (
	contains_idx(most_backward_FKL(jets), most_backward_FKL(partons))
	&& contains_idx(most_forward_FKL(jets), most_forward_FKL(partons))
	)) return false;
	if(unob_ && !contains_idx(jets.front(), partons.front())) return false;
	if(qqxb_ && !contains_idx(jets.front(), partons.front())) return false;
	if(unof_ && !contains_idx(jets.back(), partons.back())) return false;
	if(qqxf_ && !contains_idx(jets.back(), partons.back())) return false;
	#ifndef NDEBUG
	for(size_t i = 0; i < jets.size(); ++i){
	assert(nearby_ep(jets[i].rapidity(), Born_jets[i].rapidity(), 1e-2));
	}
	#endif
	return true;
	}

	void PhaseSpacePoint::reconstruct_incoming(
	std::array<Particle, 2> const & Born_incoming
	){
	std::tie(incoming_[0].p, incoming_[1].p) = incoming_momenta(outgoing_);
	for(size_t i = 0; i < incoming_.size(); ++i){
	incoming_[i].type = Born_incoming[i].type;
	}
	assert(momentum_conserved());
	}

	bool PhaseSpacePoint::momentum_conserved() const{
	fastjet::PseudoJet diff;
	for(auto const & in: incoming()) diff += in.p;
	const double norm = diff.E();
	for(auto const & out: outgoing()) diff -= out.p;
	return nearby(diff, fastjet::PseudoJet{}, norm);
	}

	} //namespace HEJ

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