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	diff --git a/include/HEJ/EventReweighter.hh b/include/HEJ/EventReweighter.hh
	index eccc9cf..87a0279 100644
	--- a/include/HEJ/EventReweighter.hh
	+++ b/include/HEJ/EventReweighter.hh
	@@ -1,197 +1,197 @@
	/** \file
	* \brief Declares the EventReweighter class
	*
	* EventReweighter is the main class used within HEJ 2. It reweights the
	* resummation events.
	*
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#pragma once

	#include <array>
	#include <memory>
	#include <vector>

	#include "HEJ/Config.hh"
	#include "HEJ/event_types.hh"
	#include "HEJ/MatrixElement.hh"
	#include "HEJ/Parameters.hh"
	#include "HEJ/PDF.hh"
	#include "HEJ/PDG_codes.hh"
	-#include "HEJ/RNG.hh"
	#include "HEJ/ScaleFunction.hh"
	#include "HEJ/StatusCode.hh"

	namespace LHEF {
	class HEPRUP;
	}

	namespace HEJ {
	class Event;
	+ class RNG;

	//! Beam parameters
	/**
	* Currently, only symmetric beams are supported,
	* so there is a single beam energy.
	*/
	struct Beam{
	double E; /*< Beam energy /
	std::array<ParticleID, 2> type; /*< Beam particles /
	};

	//! Main class for reweighting events in HEJ.
	class EventReweighter{
	using EventType = event_type::EventType;

	public:
	EventReweighter(
	Beam beam, /*< Beam Energy /
	int pdf_id, /*< PDF ID /
	ScaleGenerator scale_gen, /*< Scale settings /
	EventReweighterConfig conf, /*< Configuration parameters /
	std::shared_ptr<RNG> ran /*< Random number generator /
	);

	EventReweighter(
	LHEF::HEPRUP const & heprup, /*< LHEF event header /
	ScaleGenerator scale_gen, /*< Scale settings /
	EventReweighterConfig conf, /*< Configuration parameters /
	std::shared_ptr<RNG> ran /*< Random number generator /
	);

	//! Get the used pdf
	PDF const & pdf() const;

	//! Get event treatment
	EventTreatment treatment(EventType type) const;

	//! Generate resummation events for a given fixed-order event
	/**
	* @param ev Fixed-order event corresponding
	* to the resummation events
	* @param num_events Number of trial resummation configurations.
	* @returns A vector of resummation events.
	*
	* The result vector depends on the type of the input event and the
	* treatment of different types as specified in the constructor:
	*
	* \ref reweight The result vector contains between
	* 0 and num_events resummation events.
	*
	* \ref keep If the input event passes the resummation jet cuts
	* the result vector contains one event. Otherwise it is empty.
	*
	* \ref discard The result vector is empty
	*/
	std::vector<Event> reweight(
	Event const & ev,
	int num_events
	);

	//! Gives all StatusCodes of the last reweight()
	/**
	* Each StatusCode corresponds to one tried generation. Only good
	* StatusCodes generated an event.
	*/
	std::vector<StatusCode> const & status() const {
	return status_;
	}

	private:
	template<typename... T>
	PDF const & pdf(T&& ...);

	/** \internal
	* \brief main generation/reweighting function:
	* generate phase space points and divide out Born factors
	*/
	std::vector<Event> gen_res_events(
	Event const & ev, size_t num_events
	);
	std::vector<Event> rescale(
	Event const & Born_ev, std::vector<Event> events
	) const;

	/** \internal
	* \brief Do the Jets pass the resummation Cuts?
	*
	* @param ev Event in Question
	* @returns 0 or 1 depending on if ev passes Jet Cuts
	*/
	bool jets_pass_resummation_cuts(Event const & ev) const;

	/** \internal
	* \brief pdf_factors Function
	*
	* @param ev Event in Question
	* @returns EventFactor due to PDFs
	*
	* Calculates the Central value and the variation due
	* to the PDF choice made.
	*/
	Weights pdf_factors(Event const & ev) const;

	/** \internal
	* \brief matrix_elements Function
	*
	* @param ev Event in question
	* @returns EventFactor due to MatrixElements
	*
	* Calculates the Central value and the variation due
	* to the Matrix Element.
	*/
	Weights matrix_elements(Event const & ev) const;

	/** \internal
	* \brief Scale-dependent part of fixed-order matrix element
	*
	* @param ev Event in question
	* @returns EventFactor scale variation due to FO-ME.
	*
	* This is only called to compute the scale variation for events where
	* we don't do resummation (e.g. non-FKL).
	* Since at tree level the scale dependence is just due to alpha_s,
	* it is enough to return the alpha_s(mur) factors in the matrix element.
	* The rest drops out in the ratio of (output event ME)/(input event ME),
	* so we never have to compute it.
	*/
	Weights fixed_order_scale_ME(Event const & ev) const;

	/** \internal
	* \brief Computes the tree level matrix element
	*
	* @param ev Event in Question
	* @returns HEJ approximation to Tree level Matrix Element
	*
	* This computes the HEJ approximation to the tree level FO
	* Matrix element which is used within the LO weighting process.
	*/
	double tree_matrix_element(Event const & ev) const;

	//! \internal General parameters
	EventReweighterConfig param_;

	//! \internal Beam energy
	double E_beam_;

	//! \internal PDF
	PDF pdf_;

	//! \internal Object to calculate the square of the matrix element
	MatrixElement MEt2_;
	//! \internal Object to calculate event renormalisation and factorisation scales
	ScaleGenerator scale_gen_;
	//! \internal random number generator
	std::shared_ptr<RNG> ran_;
	//! \internal StatusCode of each attempt
	std::vector<StatusCode> status_;
	};

	template<typename... T>
	PDF const & EventReweighter::pdf(T&&... t){
	return pdf_ = PDF{std::forward<T>(t)...};
	}

	} // namespace HEJ
	diff --git a/include/HEJ/JetSplitter.hh b/include/HEJ/JetSplitter.hh
	index 5ea9517..38dbafc 100644
	--- a/include/HEJ/JetSplitter.hh
	+++ b/include/HEJ/JetSplitter.hh
	@@ -1,78 +1,72 @@
	/**
	* \file
	* \brief Declaration of the JetSplitter class
	*
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#pragma once

	#include <memory>
	-#include <utility>
	#include <vector>

	#include "fastjet/JetDefinition.hh"

	-#include "HEJ/RNG.hh"
	-
	namespace fastjet {
	class PseudoJet;
	}

	namespace HEJ {
	+ class RNG;
	+
	//! Class to split jets into their constituents
	class JetSplitter {
	public:
	struct SplitResult {
	std::vector<fastjet::PseudoJet> constituents;
	double weight;
	};

	//! Constructor
	/**
	* @param jet_def Jet definition
	* @param min_pt Minimum jet transverse momentum
	* @param ran Random number generator
	*/
	JetSplitter(
	fastjet::JetDefinition jet_def, double min_pt,
	std::shared_ptr<RNG> ran
	- ):
	- R_{jet_def.R()},
	- min_jet_pt_{min_pt},
	- jet_def_{jet_def},
	- ran_{std::move(ran)}
	- {}
	+ );

	//! Split a get into constituents
	/**
	* @param j2split Jet to be split
	* @param ncons Number of constituents
	* @returns The constituent momenta
	* together with the associated weight
	*/
	SplitResult split(fastjet::PseudoJet const & j2split, int ncons) const;

	//! Maximum distance of constituents to jet axis
	static constexpr double R_factor = 5./3.;

	private:
	//! \internal split jet into two partons
	SplitResult Split2(fastjet::PseudoJet const & j2split) const;

	/** \internal
	* @brief sample y-phi distance to jet pt axis for a jet splitting into two
	* partons
	*
	* @param wt Multiplied by the weight of the sampling point
	* @returns The distance in units of the jet radius
	*/
	double sample_distance_2p(double & wt) const;

	double R_;
	double min_jet_pt_;
	fastjet::JetDefinition jet_def_;
	std::shared_ptr<RNG> ran_;
	};
	} // namespace HEJ
	diff --git a/include/HEJ/PhaseSpacePoint.hh b/include/HEJ/PhaseSpacePoint.hh
	index f930af8..9c36cc3 100644
	--- a/include/HEJ/PhaseSpacePoint.hh
	+++ b/include/HEJ/PhaseSpacePoint.hh
	@@ -1,197 +1,197 @@
	/** \file
	* \brief Contains the PhaseSpacePoint Class
	*
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#pragma once

	#include <array>
	#include <memory>
	#include <unordered_map>
	#include <vector>

	#include "HEJ/Config.hh"
	#include "HEJ/Particle.hh"
	-#include "HEJ/RNG.hh"
	#include "HEJ/StatusCode.hh"

	namespace HEJ{
	class Event;
	+ class RNG;

	//! A point in resummation phase space
	class PhaseSpacePoint{
	public:
	//! No default PhaseSpacePoint Constructor
	PhaseSpacePoint() = delete;

	//! PhaseSpacePoint Constructor
	/**
	* @param ev Clustered Jet Event
	* @param conf Configuration parameters
	* @param ran Random number generator
	*/
	PhaseSpacePoint(
	Event const & ev,
	PhaseSpacePointConfig conf,
	std::shared_ptr<RNG> ran
	);

	//! Get phase space point weight
	double weight() const{
	return weight_;
	}

	//! Access incoming particles
	std::array<Particle, 2> const & incoming() const{
	return incoming_;
	}

	//! Access outgoing particles
	std::vector<Particle> const & outgoing() const{
	return outgoing_;
	}

	//! Particle decays
	/**
	* The key in the returned map corresponds to the index in the
	* vector returned by outgoing()
	*/
	std::unordered_map<size_t, std::vector<Particle>> const & decays() const{
	return decays_;
	}

	//! Status code of generation
	StatusCode status() const{
	return status_;
	}

	static constexpr int ng_max = 1000; //!< maximum number of extra gluons

	private:
	//! /internal returns the clustered jets sorted in rapidity
	std::vector<fastjet::PseudoJet> cluster_jets(
	std::vector<fastjet::PseudoJet> const & partons
	) const;
	bool pass_resummation_cuts(
	std::vector<fastjet::PseudoJet> const & jets
	) const;
	bool pass_extremal_cuts(
	fastjet::PseudoJet const & ext_parton,
	fastjet::PseudoJet const & jet
	) const;
	int sample_ng(std::vector<fastjet::PseudoJet> const & Born_jets);
	int sample_ng_jets(int ng, std::vector<fastjet::PseudoJet> const & Born_jets);
	double probability_in_jet(
	std::vector<fastjet::PseudoJet> const & Born_jets
	) const;
	std::vector<fastjet::PseudoJet> gen_non_jet(
	int ng_non_jet,
	double ptmin, double ptmax
	);
	void rescale_qqx_rapidities(
	std::vector<fastjet::PseudoJet> & out_partons,
	std::vector<fastjet::PseudoJet> const & jets,
	const double ymin1, const double ymax2,
	const int qqxbackjet
	);
	void rescale_rapidities(
	std::vector<fastjet::PseudoJet> & partons,
	double ymin, double ymax
	);
	std::vector<fastjet::PseudoJet> reshuffle(
	std::vector<fastjet::PseudoJet> const & Born_jets,
	fastjet::PseudoJet const & q
	);
	/** \interal final jet test
	* - number of jets must match Born kinematics
	* - no partons designated as nonjet may end up inside jets
	* - all other outgoing partons must end up inside jets
	* - the extremal (in rapidity) partons must be inside the extremal jets
	* - rapidities must be the same (by construction)
	*/
	bool jets_ok(
	std::vector<fastjet::PseudoJet> const & Born_jets,
	std::vector<fastjet::PseudoJet> const & partons
	) const;
	void reconstruct_incoming(std::array<Particle, 2> const & Born_incoming);
	double phase_space_normalisation(
	int num_Born_jets,
	int num_res_partons
	) const;
	/** \interal Distribute gluon in jet
	* @param jets jets to distribute gluon in
	* @param ng_jets number of gluons
	* @param qqxbackjet position of first (backwards) qqx jet
	*
	* relies on JetSplitter
	*/
	std::vector<fastjet::PseudoJet> split(
	std::vector<fastjet::PseudoJet> const & jets,
	int ng_jets, size_t qqxbackjet
	);
	std::vector<int> distribute_jet_partons(
	int ng_jets, std::vector<fastjet::PseudoJet> const & jets
	);
	std::vector<fastjet::PseudoJet> split(
	std::vector<fastjet::PseudoJet> const & jets,
	std::vector<int> const & np_in_jet,
	size_t qqxbackjet
	);
	bool split_preserved_jets(
	std::vector<fastjet::PseudoJet> const & jets,
	std::vector<fastjet::PseudoJet> const & jet_partons
	) const;
	template<class Particle>
	Particle const & most_backward_FKL(
	std::vector<Particle> const & partons
	) const;
	template<class Particle>
	Particle const & most_forward_FKL(
	std::vector<Particle> const & partons
	) const;
	template<class Particle>
	Particle & most_backward_FKL(std::vector<Particle> & partons) const;
	template<class Particle>
	Particle & most_forward_FKL(std::vector<Particle> & partons) const;
	bool extremal_ok(
	std::vector<fastjet::PseudoJet> const & partons
	) const;
	/** \internal
	* Assigns PDG IDs to outgoing partons, i.e. labels them as quarks
	*
	* \note This function assumes outgoing_ to be pure partonic when called,
	* i.e. A/W/Z/h bosons should _not be set_ at this stage
	*/
	void label_quarks(Event const & event);
	/** \internal
	* This function will label the qqx pair in a qqx event back to their
	* original types from the input event.
	*/
	void label_qqx(Event const & event);
	void copy_AWZH_boson_from(Event const & event);

	bool momentum_conserved() const;

	bool contains_idx(
	fastjet::PseudoJet const & jet, fastjet::PseudoJet const & parton
	) const;

	bool unob_, unof_, qqxb_, qqxf_, qqxmid_;

	double weight_;

	PhaseSpacePointConfig param_;

	std::array<Particle, 2> incoming_;
	std::vector<Particle> outgoing_;
	//! \internal Particle decays in the format {outgoing index, decay products}
	std::unordered_map<size_t, std::vector<Particle>> decays_;

	std::shared_ptr<RNG> ran_;

	StatusCode status_;
	};

	} // namespace HEJ
	diff --git a/src/EventReweighter.cc b/src/EventReweighter.cc
	index 082e8d4..c27d033 100644
	--- a/src/EventReweighter.cc
	+++ b/src/EventReweighter.cc
	@@ -1,283 +1,284 @@
	/**
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#include "HEJ/EventReweighter.hh"

	#include <algorithm>
	#include <assert.h>
	#include <limits>
	#include <math.h>
	#include <stddef.h>
	#include <string>
	#include <unordered_map>
	#include <utility>

	#include "fastjet/ClusterSequence.hh"

	#include "LHEF/LHEF.h"

	#include "HEJ/Event.hh"
	#include "HEJ/exceptions.hh"
	#include "HEJ/Particle.hh"
	#include "HEJ/PDG_codes.hh"
	#include "HEJ/PhaseSpacePoint.hh"
	+#include "HEJ/RNG.hh"

	namespace HEJ{
	- using EventType = event_type::EventType;
	-
	namespace {

	static_assert(
	std::numeric_limits<double>::has_quiet_NaN,
	"no quiet NaN for double"
	);
	constexpr double NaN = std::numeric_limits<double>::quiet_NaN();

	Event::EventData to_EventData(PhaseSpacePoint const & psp){
	Event::EventData result;
	result.incoming=psp.incoming();
	assert(result.incoming.size() == 2);
	result.outgoing=psp.outgoing();
	// 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);
	result.decays = psp.decays();
	result.parameters.central = {NaN, NaN, psp.weight()};
	return result;
	}

	} // namespace anonymous

	EventReweighter::EventReweighter(
	LHEF::HEPRUP const & heprup,
	ScaleGenerator scale_gen,
	EventReweighterConfig conf,
	std::shared_ptr<RNG> ran
	):
	EventReweighter{
	HEJ::Beam{
	heprup.EBMUP.first,
	{{
	static_cast<HEJ::ParticleID>(heprup.IDBMUP.first),
	static_cast<HEJ::ParticleID>(heprup.IDBMUP.second)
	}}
	},
	heprup.PDFSUP.first,
	std::move(scale_gen),
	std::move(conf),
	std::move(ran)
	}
	{
	if(heprup.EBMUP.second != E_beam_){
	throw std::invalid_argument(
	"asymmetric beam: " + std::to_string(E_beam_)
	+ " ---> <--- " + std::to_string(heprup.EBMUP.second)
	);
	};
	if(heprup.PDFSUP.second != pdf_.id()){
	throw std::invalid_argument(
	"conflicting PDF ids: " + std::to_string(pdf_.id())
	+ " vs. " + std::to_string(heprup.PDFSUP.second)
	);
	}
	}

	EventReweighter::EventReweighter(
	Beam beam,
	int pdf_id,
	ScaleGenerator scale_gen,
	EventReweighterConfig conf,
	std::shared_ptr<RNG> ran
	):
	param_{std::move(conf)},
	E_beam_{beam.E},
	pdf_{pdf_id, beam.type.front(), beam.type.back()},
	MEt2_{
	[this](double mu){ return pdf_.Halphas(mu); },
	param_.ME_config
	},
	scale_gen_{std::move(scale_gen)},
	ran_{std::move(ran)}
	- {}
	+ {
	+ assert(ran_);
	+ }

	PDF const & EventReweighter::pdf() const{
	return pdf_;
	}

	std::vector<Event> EventReweighter::reweight(
	Event const & input_ev, int num_events
	){
	auto res_events{ gen_res_events(input_ev, num_events) };
	if(res_events.empty()) return {};
	for(auto & event: res_events) event = scale_gen_(std::move(event));
	return rescale(input_ev, std::move(res_events));
	}

	EventTreatment EventReweighter::treatment(EventType type) const {
	return param_.treat.at(type);
	}

	std::vector<Event> EventReweighter::gen_res_events(
	Event const & ev,
	size_t phase_space_points
	){
	assert(ev.variations().empty());
	status_.clear();

	switch(treatment(ev.type())){
	case EventTreatment::discard: {
	status_.emplace_back(StatusCode::discard);
	return {};
	}
	case EventTreatment::keep:
	if(! jets_pass_resummation_cuts(ev)) {
	status_.emplace_back(StatusCode::failed_resummation_cuts);
	return {};
	}
	else {
	status_.emplace_back(StatusCode::good);
	return {ev};
	}
	default:;
	}
	const double Born_shat = shat(ev);

	std::vector<Event> resummation_events;
	status_.reserve(phase_space_points);
	for(size_t psp_number = 0; psp_number < phase_space_points; ++psp_number){
	PhaseSpacePoint psp{ev, param_.psp_config, ran_};
	status_.emplace_back(psp.status());
	assert(psp.status() != StatusCode::unspecified);
	if(psp.status() != StatusCode::good) continue;
	assert(psp.weight() != 0.);
	if(psp.incoming()[0].E() > E_beam_ \|\| psp.incoming()[1].E() > E_beam_) {
	status_.back() = StatusCode::too_much_energy;
	continue;
	}

	resummation_events.emplace_back(
	to_EventData( std::move(psp) ).cluster(
	param_.jet_param().def, param_.jet_param().min_pt
	)
	);
	auto & new_event = resummation_events.back();
	assert( new_event.valid_hej_state(
	param_.psp_config.max_ext_soft_pt_fraction,
	param_.psp_config.min_extparton_pt ) );
	if( new_event.type() != ev.type() )
	throw std::logic_error{"Resummation Event does not match Born event"};
	new_event.generate_colours(*ran_);
	assert(new_event.variations().empty());
	new_event.central().mur = ev.central().mur;
	new_event.central().muf = ev.central().muf;
	const double resum_shat = shat(new_event);
	new_event.central().weight = ev.central().weightBorn_shat*Born_shat/
	(phase_space_pointsresum_shatresum_shat);
	}
	return resummation_events;
	}

	std::vector<Event> EventReweighter::rescale(
	Event const & Born_ev,
	std::vector<Event> events
	) const{
	const double Born_pdf = pdf_factors(Born_ev).central;
	const double Born_ME = tree_matrix_element(Born_ev);

	for(auto & cur_event: events){
	const auto pdf = pdf_factors(cur_event);
	assert(pdf.variations.size() == cur_event.variations().size());
	const auto ME = matrix_elements(cur_event);
	assert(ME.variations.size() == cur_event.variations().size());
	cur_event.parameters() = pdfME/(Born_pdf*Born_ME);
	}
	return events;
	}

	bool EventReweighter::jets_pass_resummation_cuts(
	Event const & ev
	) const{
	const auto out_as_PseudoJet = to_PseudoJet(filter_partons(ev.outgoing()));
	fastjet::ClusterSequence cs{out_as_PseudoJet, param_.jet_param().def};
	return cs.inclusive_jets(param_.jet_param().min_pt).size() == ev.jets().size();
	}

	Weights EventReweighter::pdf_factors(Event const & ev) const{
	auto const & a = ev.incoming().front();
	auto const & b = ev.incoming().back();
	const double xa = a.p.e()/E_beam_;
	const double xb = b.p.e()/E_beam_;

	Weights result;
	std::unordered_map<double, double> known_pdf;
	result.central =
	pdf_.pdfpt(0,xa,ev.central().muf,a.type)*
	pdf_.pdfpt(1,xb,ev.central().muf,b.type);
	known_pdf.emplace(ev.central().muf, result.central);

	result.variations.reserve(ev.variations().size());
	for(auto const & ev_param: ev.variations()){
	const double muf = ev_param.muf;
	auto cur_pdf = known_pdf.find(muf);
	if(cur_pdf == known_pdf.end()){
	cur_pdf = known_pdf.emplace(
	muf,
	pdf_.pdfpt(0,xa,muf,a.type)*pdf_.pdfpt(1,xb,muf,b.type)
	).first;
	}
	result.variations.emplace_back(cur_pdf->second);
	}
	assert(result.variations.size() == ev.variations().size());
	return result;
	}

	Weights
	EventReweighter::matrix_elements(Event const & ev) const{
	assert(param_.treat.count(ev.type()) > 0);
	if(param_.treat.find(ev.type())->second == EventTreatment::keep){
	return fixed_order_scale_ME(ev);
	}

	return MEt2_(ev);
	}

	double EventReweighter::tree_matrix_element(Event const & ev) const{
	assert(ev.variations().empty());
	assert(param_.treat.count(ev.type()) > 0);
	if(param_.treat.find(ev.type())->second == EventTreatment::keep){
	return fixed_order_scale_ME(ev).central;
	}
	return MEt2_.tree(ev).central;
	}

	Weights
	EventReweighter::fixed_order_scale_ME(Event const & ev) const{
	int alpha_s_power = 0;
	for(auto const & part: ev.outgoing()){
	if(is_parton(part))
	++alpha_s_power;
	else if(part.type == pid::Higgs) {
	alpha_s_power += 2;
	}
	// nothing to do for other uncoloured particles
	}

	Weights result;
	result.central = pow(pdf_.Halphas(ev.central().mur), alpha_s_power);
	for(auto const & var: ev.variations()){
	result.variations.emplace_back(
	pow(pdf_.Halphas(var.mur), alpha_s_power)
	);
	}
	return result;
	}

	} // namespace HEJ
	diff --git a/src/JetSplitter.cc b/src/JetSplitter.cc
	index e43a4f1..bf85e2f 100644
	--- a/src/JetSplitter.cc
	+++ b/src/JetSplitter.cc
	@@ -1,178 +1,191 @@
	/**
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#include "HEJ/JetSplitter.hh"

	#include <array>
	#include <assert.h>
	#include <numeric>
	+#include <utility>

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

	#include "HEJ/Constants.hh"
	#include "HEJ/exceptions.hh"
	+#include "HEJ/RNG.hh"

	namespace HEJ {
	namespace{
	constexpr double ccut=HEJ::CMINPT; // min parton pt

	template<class Iterator>
	bool same_pt_and_rapidity(
	Iterator begin, Iterator end,
	fastjet::PseudoJet const & jet
	){
	constexpr double ep = 1e-2;
	const fastjet::PseudoJet reconstructed_jet = std::accumulate(
	begin, end, fastjet::PseudoJet{}
	);
	return
	(std::abs(reconstructed_jet.pt() - jet.pt()) < ep)
	&& (std::abs(reconstructed_jet.rapidity() - jet.rapidity()) < ep)
	;
	}

	bool all_in_one_jet(
	std::vector<fastjet::PseudoJet> const & partons,
	fastjet::JetDefinition jet_def, double min_jet_pt
	){
	fastjet::ClusterSequence ev(partons, jet_def);
	const std::vector<fastjet::PseudoJet> testjet = ev.inclusive_jets(min_jet_pt);
	return testjet.size() == 1u
	&& testjet[0].constituents().size() == partons.size();
	}
	}
	+ JetSplitter::JetSplitter(
	+ fastjet::JetDefinition jet_def, double min_pt,
	+ std::shared_ptr<RNG> ran
	+ ):
	+ R_{jet_def.R()},
	+ min_jet_pt_{min_pt},
	+ jet_def_{jet_def},
	+ ran_{std::move(ran)}
	+ {
	+ assert(ran_);
	+ }

	using SplitResult = JetSplitter::SplitResult;

	SplitResult JetSplitter::split(
	fastjet::PseudoJet const & j2split, int ncons
	) const{
	if(ncons <= 0) {
	throw std::invalid_argument{
	"number of requested jet constituents less than 1"
	};
	}
	double swt = 1.;

	std::vector<fastjet::PseudoJet> jcons;
	if(ncons == 1){
	jcons.emplace_back(j2split);
	jcons.back().set_user_index(0);
	return {jcons, swt};
	}
	if(ncons == 2){
	return Split2(j2split);
	}
	const double R_max = R_factor*R_;
	assert(R_max < M_PI);

	double pt_remaining = j2split.pt();
	const double phi_jet = j2split.phi();
	const double y_jet = j2split.rapidity();
	for(int i = 0; i < ncons - 1; ++i){
	/**
	* Generate rapidity and azimuthal angle with a distance
	* R = sqrt(delta_y^2 + delta_phi^2) < R_max
	* from the jet centre
	*/
	const double R = R_max*ran_->flat();
	const double theta = 2M_PIran_->flat();
	const double delta_phi = R*cos(theta);
	const double delta_y = R*sin(theta);

	/**
	* Generate pt such that the total contribution of all partons
	* along the jet pt axis does not exceed the jet pt
	*/
	const double pt_max = pt_remaining/cos(delta_phi);
	assert(pt_max > 0);
	if(pt_max < ccut) return {}; // no pt remaining for this parton
	const double pt = (pt_max - ccut)*ran_->flat() + ccut;
	pt_remaining -= pt*cos(delta_phi);

	jcons.emplace_back(
	ptcos(phi_jet + delta_phi), ptsin(phi_jet + delta_phi),
	ptsinh(y_jet + delta_y), ptcosh(y_jet + delta_y)
	);
	jcons.back().set_user_index(i);
	swt = 2M_PIRR_maxpt(pt_max - ccut);
	}

	const fastjet::PseudoJet p_total = std::accumulate(
	jcons.begin(), jcons.end(), fastjet::PseudoJet{}
	);

	// Calculate the pt of the last parton
	const double last_px = j2split.px() - p_total.px();
	const double last_py = j2split.py() - p_total.py();
	const double last_pt = sqrt(last_pxlast_px + last_pylast_py);
	if(last_pt < ccut) return {};

	// Calculate the rapidity of the last parton using the requirement that the
	// new jet must have the same rapidity as the LO jet.
	const double exp_2y_jet = (j2split.e() + j2split.pz())/(j2split.e() - j2split.pz());
	const double bb = (p_total.e()+p_total.pz()) - exp_2y_jet*(p_total.e()-p_total.pz());
	const double lasty = log((-bb+sqrt(bbbb+4.exp_2y_jetlast_ptlast_pt))/(2.*last_pt));

	jcons.emplace_back(
	last_px, last_py, last_ptsinh(lasty), last_ptcosh(lasty)
	);
	jcons.back().set_user_index(ncons-1);
	assert(same_pt_and_rapidity(begin(jcons), end(jcons), j2split));

	// Test that the last parton is not too far away from the jet centre.
	if (jcons.back().delta_R(j2split) > R_max) return {};

	if(! all_in_one_jet(jcons, jet_def_, min_jet_pt_)) return {};

	return {jcons, swt};
	}

	double JetSplitter::sample_distance_2p(double & wt) const{
	static constexpr double x_small = 0.1;
	static constexpr double p_small = 0.4;

	const double pR = ran_->flat();
	if(pR < p_small){
	wt *= x_small/p_small;
	return x_small/p_small*pR;
	}
	wt *= (1-x_small)/(1-p_small);
	return (1-x_small)/(1-p_small)*(pR-p_small) + x_small;
	}

	SplitResult JetSplitter::Split2(fastjet::PseudoJet const & j2split) const{
	static constexpr size_t ncons = 2;
	std::vector<fastjet::PseudoJet> jcons(ncons);
	std::array<double, ncons> R, phi, y, pt;
	double wt = 1;

	const double theta = 2M_PIran_->flat(); // angle in y-phi plane
	// empiric observation: we are always within the jet radius
	R[0] = sample_distance_2p(wt)*R_;
	R[1] = -sample_distance_2p(wt)*R_;
	for(size_t i = 0; i <= 1; ++i){
	phi[i] = j2split.phi() + R[i]*cos(theta);
	y[i] = j2split.rapidity() + R[i]*sin(theta);
	}
	for(size_t i = 0; i <= 1; ++i){
	pt[i] = (j2split.py() - tan(phi[1-i])*j2split.px())/
	(sin(phi[i]) - tan(phi[1-i])*cos(phi[i]));
	if(pt[i] < ccut) return {};
	jcons[i].reset_PtYPhiM(pt[i], y[i], phi[i]);
	jcons[i].set_user_index(i);
	}
	assert(same_pt_and_rapidity(begin(jcons), end(jcons), j2split));

	if(! all_in_one_jet(jcons, jet_def_, min_jet_pt_)) return {};
	wt = 2M_PIpt[0]R[0]R_R_;
	// from transformation of delta(R[1] - ...) to delta(pt[0] - ...)
	const double dphi0 = phi[0] - j2split.phi();
	const double ptJ = j2split.pt();
	const double jacobian = cos(theta)pt[1]pt[1]/(ptJ*sin(dphi0));
	return {jcons, jacobian*wt};
	}
	}
	diff --git a/src/PhaseSpacePoint.cc b/src/PhaseSpacePoint.cc
	index 8a956d1..aef2b4e 100644
	--- a/src/PhaseSpacePoint.cc
	+++ b/src/PhaseSpacePoint.cc
	@@ -1,810 +1,811 @@
	/**
	* \authors The HEJ collaboration (see AUTHORS for details)
	* \date 2019
	* \copyright GPLv2 or later
	*/
	#include "HEJ/PhaseSpacePoint.hh"

	#include <algorithm>
	#include <assert.h>
	#include <numeric>
	#include <random>

	#include "fastjet/ClusterSequence.hh"

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

	// user indices for partons with extremal rapidity
	constexpr int qqxmid1_idx = -9;
	constexpr int qqxmid2_idx = -8;
	constexpr int qqxb_idx = -7;
	constexpr int qqxf_idx = -6;
	constexpr int unob_idx = -5;
	constexpr int unof_idx = -4;
	constexpr int backward_FKL_idx = -3;
	constexpr int forward_FKL_idx = -2;
	}

	namespace {
	double estimate_ng_mean(std::vector<fastjet::PseudoJet> const & Born_jets){
	const double delta_y =
	Born_jets.back().rapidity() - Born_jets.front().rapidity();
	assert(delta_y > 0);
	// Formula derived from fit in arXiv:1805.04446 (see Fig. 2)
	return 0.975052*delta_y;
	}
	}

	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();
	}

	int PhaseSpacePoint::sample_ng(std::vector<fastjet::PseudoJet> const & Born_jets){
	const double ng_mean = estimate_ng_mean(Born_jets);
	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::copy_AWZH_boson_from(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{}
	);
	outgoing_.insert(insertion_point, *AWZH_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);
	decays_.emplace(new_idx, decay_it->second);
	}

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

	namespace {

	auto get_first_anyquark_emission(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 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_first_anyquark_emission(ev);
	return get_back_quark_jet(ev, firstquark);
	}

	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;
	}
	}

	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_first_anyquark_emission(event);

	// 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_.max_ext_soft_pt_fraction;
	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 WEmit = std::find_if(
	begin(ev.outgoing()), end(ev.outgoing()),
	[](Particle const & s){ return abs(s.type) == pid::Wp; }
	);

	if (WEmit != 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;
	}
	} 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, std::shared_ptr<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)},
	ran_{std::move(ran)},
	status_{unspecified}
	{
	+ assert(ran_);
	weight_ = 1;
	const auto & Born_jets = ev.jets();
	const int ng = sample_ng(Born_jets);
	weight_ /= std::tgamma(ng + 1);
	const int ng_jets = sample_ng_jets(ng, Born_jets);
	std::vector<fastjet::PseudoJet> out_partons = gen_non_jet(
	ng - ng_jets, CMINPT, param_.jet_param.min_pt
	);

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

	const auto qperp = std::accumulate(
	begin(out_partons), end(out_partons),
	fastjet::PseudoJet{}
	);
	const auto jets = reshuffle(Born_jets, qperp);
	if(weight_ == 0.) {
	status_ = failed_reshuffle;
	return;
	}
	if(! pass_resummation_cuts(jets)){
	status_ = failed_resummation_cuts;
	weight_ = 0.;
	return;
	}
	std::vector<fastjet::PseudoJet> jet_partons = split(jets, ng_jets, qqxbackjet);
	if(weight_ == 0.) {
	status_ = StatusCode::failed_split;
	return;
	}
	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 & p: out_partons){
	outgoing_.emplace_back(Particle{pid::gluon, std::move(p), {}});
	}
	assert(!outgoing_.empty());

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

	copy_AWZH_boson_from(ev);

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

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

	std::vector<fastjet::PseudoJet> partons(count);
	for(size_t i = 0; i < (size_t) count; ++i){
	const double r1 = ran_->flat();
	const double pt = ptmin + ptpartan(r1temp1);
	const double temp2 = 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 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(
	std::vector<fastjet::PseudoJet> const & Born_jets
	) const{
	assert(std::is_sorted(begin(Born_jets), end(Born_jets), rapidity_less{}));
	assert(Born_jets.size() >= 2);

	const double dy =
	Born_jets.back().rapidity() - Born_jets.front().rapidity();
	const double R = param_.jet_param.def.R();
	const int njets = Born_jets.size();
	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(
	int ng, std::vector<fastjet::PseudoJet> const & Born_jets
	){
	const double p_J = probability_in_jet(Born_jets);
	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::vector<fastjet::PseudoJet> PhaseSpacePoint::reshuffle(
	std::vector<fastjet::PseudoJet> const & Born_jets,
	fastjet::PseudoJet const & q
	){
	if(q == fastjet::PseudoJet{0, 0, 0, 0}) return Born_jets;
	const auto jets = resummation_jet_momenta(Born_jets, q);
	if(jets.empty()){
	weight_ = 0;
	return {};
	}

	// additional Jacobian to ensure Born integration over delta gives 1
	weight_ *= resummation_jet_weight(Born_jets, q);
	return jets;
	}

	std::vector<int> PhaseSpacePoint::distribute_jet_partons(
	int ng_jets, std::vector<fastjet::PseudoJet> const & jets
	){
	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() == backward_FKL_idx;
	}
	) != 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() == forward_FKL_idx;
	}
	) != 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 anonymous
	#endif

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

	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_.max_ext_soft_pt_fraction;
	}

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

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

	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]);
	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(backward_FKL_idx);
	}
	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_)?unob_idx:qqxb_idx);
	}

	else if (i == most_forward_FKL_idx){
	extremal = std::max_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(forward_FKL_idx);
	}
	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_)?unof_idx:qqxf_idx);
	}
	else if((qqxmid_ && i == qqxbackjet)){
	extremal = std::max_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(qqxmid1_idx);
	}
	else if((qqxmid_ && i == qqxbackjet+1)){
	extremal = std::min_element(
	first_new_parton, end(jet_partons), rapidity_less{}
	);
	extremal->set_user_index(qqxmid2_idx);
	}
	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() != unob_idx) return false;
	if(unof_ && partons.back().user_index() != unof_idx) return false;
	if(qqxb_ && partons.front().user_index() != qqxb_idx) return false;
	if(qqxf_ && partons.back().user_index() != qqxf_idx) return false;
	return
	most_backward_FKL(partons).user_index() == backward_FKL_idx
	&& most_forward_FKL(partons).user_index() == forward_FKL_idx;
	}

	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_.max_ext_soft_pt_fraction;
	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(size_t i = 0; i < jets.size(); ++i){
	assert(jets[i].has_constituents());
	for(auto && parton: jets[i].constituents()){
	if(is_nonjet_parton(parton)) return false;
	}
	in_jet += jets[i].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;
	for(size_t i = 0; i < jets.size(); ++i){
	assert(nearby_ep(jets[i].rapidity(), Born_jets[i].rapidity(), 1e-2));
	}
	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());
	}

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

	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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