#include <ParticleState.h>

Public Types
typedef int	Charge
	electric charge type More...

typedef math::XYZTLorentzVector	LorentzVector
	Lorentz vector. More...

typedef math::XYZPoint	Point
	point in the space More...

typedef math::PtEtaPhiMLorentzVector	PolarLorentzVector
	Lorentz vector. More...

typedef math::XYZVector	Vector
	point in the space More...

Public Member Functions
Vector	boostToCM () const

int	charge () const
	electric charge More...

double	energy () const
	energy More...

double	et () const
	transverse energy More...

double	et2 () const
	transverse energy squared (use this for cuts)! More...

double	eta () const
	momentum pseudorapidity More...

bool	longLived () const
	is long lived? More...

double	mass () const
	mass More...

bool	massConstraint () const
	do mass constraint? More...

double	massSqr () const
	mass squared More...

Vector	momentum () const
	spatial momentum vector More...

double	mt () const
	transverse mass More...

double	mtSqr () const
	transverse mass squared More...

double	p () const
	magnitude of momentum vector More...

const LorentzVector &	p4 () const
	four-momentum Lorentz vector More...

	ParticleState ()
	default constructor More...

	ParticleState (Charge q, const GlobalVector &p3, float iEnergy, float imass, const Point &vertex=Point(0, 0, 0), int pdgId=0, int status=0, bool integerCharge=true)

	ParticleState (Charge q, const LorentzVector &p4, const Point &vertex=Point(0, 0, 0), int pdgId=0, int status=0, bool integerCharge=true)
	constructor from values More...

	ParticleState (Charge q, const PolarLorentzVector &p4, const Point &vertex=Point(0, 0, 0), int pdgId=0, int status=0, bool integerCharge=true)
	constructor from values More...

	ParticleState (Charge q, const PtEtaPhiMass &p4, const Point &vertex=Point(0, 0, 0), int pdgId=0, int status=0, bool integerCharge=true)
	constructor from values More...

int	pdgId () const
	PDG identifier. More...

double	phi () const
	momentum azimuthal angle More...

const PolarLorentzVector &	polarP4 () const
	four-momentum Lorentz vector More...

double	pt () const
	transverse momentum More...

double	px () const
	x coordinate of momentum vector More...

double	py () const
	y coordinate of momentum vector More...

double	pz () const
	z coordinate of momentum vector More...

double	rapidity () const
	repidity More...

void	setCartesian ()
	set internal cache More...

void	setCharge (Charge q)
	set electric charge More...

void	setLongLived ()
	set long lived flag More...

void	setMass (double m)
	set particle mass More...

void	setMassConstraint ()
	set mass constraint flag More...

void	setP4 (const LorentzVector &p4)
	set 4-momentum More...

void	setP4 (const PolarLorentzVector &p4)
	set 4-momentum More...

void	setPdgId (int pdgId)

void	setPz (double pz)

void	setStatus (int status)
	set status word More...

void	setThreeCharge (Charge qx3)
	set electric charge More...

void	setVertex (const Point &vertex)
	set vertex More...

int	status () const
	status word More...

double	theta () const
	momentum polar angle More...

int	threeCharge () const
	electric charge More...

const Point &	vertex () const
	vertex position More...

double	vx () const
	x coordinate of vertex position More...

double	vy () const
	y coordinate of vertex position More...

double	vz () const
	z coordinate of vertex position More...

double	y () const
	repidity More...

Private Attributes
LorentzVector	p4Cartesian_
	internal cache for p4 More...

PolarLorentzVector	p4Polar_
	four-momentum Lorentz vector More...

int	pdgId_
	PDG identifier. More...

Charge	qx3_
	electric charge More...

int	status_
	status word More...

Point	vertex_
	vertex position More...

Static Private Attributes
static const unsigned int	longLivedTag = 65536

static const unsigned int	massConstraintTag = 131072

Detailed Description

Base class describing a generic reconstructed particle its main subclass is Candidate

Author: Luca Lista, INFN

Definition at line 22 of file ParticleState.h.

Member Typedef Documentation

◆ Charge

typedef int reco::ParticleState::Charge

electric charge type

Definition at line 25 of file ParticleState.h.

◆ LorentzVector

typedef math::XYZTLorentzVector reco::ParticleState::LorentzVector

Lorentz vector.

Definition at line 27 of file ParticleState.h.

◆ Point

typedef math::XYZPoint reco::ParticleState::Point

point in the space

Definition at line 31 of file ParticleState.h.

◆ PolarLorentzVector

typedef math::PtEtaPhiMLorentzVector reco::ParticleState::PolarLorentzVector

Lorentz vector.

Definition at line 29 of file ParticleState.h.

◆ Vector

typedef math::XYZVector reco::ParticleState::Vector

point in the space

Definition at line 33 of file ParticleState.h.

Constructor & Destructor Documentation

◆ ParticleState() [1/5]

reco::ParticleState::ParticleState ( )

inline

default constructor

Definition at line 35 of file ParticleState.h.

35 : vertex_(0, 0, 0), qx3_(0), pdgId_(0), status_(0) {}

◆ ParticleState() [2/5]

reco::ParticleState::ParticleState	(	Charge	q,
		const PtEtaPhiMass &	p4,
		const Point &	vertex = `Point(0, 0, 0)`,
		int	pdgId = `0`,
		int	status = `0`,
		bool	integerCharge = `true`
	)

inline

constructor from values

Definition at line 38 of file ParticleState.h.

         : vertex_(vertex),
           p4Polar_(p4.pt(), p4.eta(), p4.phi(), p4.mass()),
           p4Cartesian_(p4Polar_),
           qx3_(integerCharge ? q * 3 : q),
           pdgId_(pdgId),
           status_(status) {}

◆ ParticleState() [3/5]

reco::ParticleState::ParticleState	(	Charge	q,
		const LorentzVector &	p4,
		const Point &	vertex = `Point(0, 0, 0)`,
		int	pdgId = `0`,
		int	status = `0`,
		bool	integerCharge = `true`
	)

inline

constructor from values

Definition at line 52 of file ParticleState.h.

         : vertex_(vertex),
           p4Polar_(p4),
           p4Cartesian_(p4),
           qx3_(integerCharge ? q * 3 : q),
           pdgId_(pdgId),
           status_(status) {}

◆ ParticleState() [4/5]

reco::ParticleState::ParticleState	(	Charge	q,
		const PolarLorentzVector &	p4,
		const Point &	vertex = `Point(0, 0, 0)`,
		int	pdgId = `0`,
		int	status = `0`,
		bool	integerCharge = `true`
	)

inline

constructor from values

Definition at line 66 of file ParticleState.h.

         : vertex_(vertex),
           p4Polar_(p4),
           p4Cartesian_(p4),
           qx3_(integerCharge ? q * 3 : q),
           pdgId_(pdgId),
           status_(status) {}

◆ ParticleState() [5/5]

reco::ParticleState::ParticleState	(	Charge	q,
		const GlobalVector &	p3,
		float	iEnergy,
		float	imass,
		const Point &	vertex = `Point(0, 0, 0)`,
		int	pdgId = `0`,
		int	status = `0`,
		bool	integerCharge = `true`
	)

inline

Definition at line 79 of file ParticleState.h.

         : vertex_(vertex),
           p4Polar_(p3.perp(), p3.eta(), p3.phi(), imass),
           p4Cartesian_(p3.x(), p3.y(), p3.z(), iEnergy),
           qx3_(integerCharge ? q * 3 : q),
           pdgId_(pdgId),
           status_(status) {}

Member Function Documentation

◆ boostToCM()

Vector reco::ParticleState::boostToCM ( ) const

inline

boost vector to boost a Lorentz vector to the particle center of mass system

Definition at line 113 of file ParticleState.h.

113 { return p4Cartesian_.BoostToCM(); }

References p4Cartesian_.

Referenced by reco::Particle::boostToCM(), and reco::LeafCandidate::boostToCM().

◆ charge()

int reco::ParticleState::charge ( ) const

inline

electric charge

Definition at line 98 of file ParticleState.h.

98 { return qx3_ / 3; }

References qx3_.

Referenced by reco::Particle::charge(), and reco::LeafCandidate::charge().

◆ energy()

double reco::ParticleState::energy ( ) const

inline

energy

Definition at line 117 of file ParticleState.h.

117 { return p4Cartesian_.E(); }

References p4Cartesian_.

Referenced by reco::Particle::energy(), reco::LeafCandidate::energy(), and Jet.Jet::rawEnergy().

◆ et()

double reco::ParticleState::et ( ) const

inline

transverse energy

Definition at line 119 of file ParticleState.h.

119 { return (pt() <= 0) ? 0 : p4Cartesian_.Et(); }

References p4Cartesian_, and pt().

Referenced by reco::Particle::et(), and reco::LeafCandidate::et().

◆ et2()

double reco::ParticleState::et2 ( ) const

inline

transverse energy squared (use this for cuts)!

Definition at line 121 of file ParticleState.h.

121 { return (pt() <= 0) ? 0 : p4Cartesian_.Et2(); }

References p4Cartesian_, and pt().

Referenced by reco::Particle::et2(), and reco::LeafCandidate::et2().

◆ eta()

double reco::ParticleState::eta ( ) const

inline

momentum pseudorapidity

Definition at line 143 of file ParticleState.h.

143 { return p4Polar_.eta(); }

References p4Polar_.

Referenced by Particle.Particle::__str__(), reco::Particle::eta(), reco::LeafCandidate::eta(), Jet.Jet::jetID(), and Jet.Jet::puJetId().

◆ longLived()

bool reco::ParticleState::longLived ( ) const

inline

is long lived?

Definition at line 188 of file ParticleState.h.

188 { return status_ & longLivedTag; }

References longLivedTag, and status_.

Referenced by reco::Particle::longLived(), and reco::LeafCandidate::longLived().

◆ mass()

double reco::ParticleState::mass ( ) const

inline

mass

Definition at line 123 of file ParticleState.h.

123 { return p4Polar_.mass(); }

References p4Polar_.

Referenced by Particle.Particle::__str__(), DiObject.DiMuon::__str__(), reco::Particle::mass(), reco::LeafCandidate::mass(), and massSqr().

◆ massConstraint()

bool reco::ParticleState::massConstraint ( ) const

inline

do mass constraint?

Definition at line 192 of file ParticleState.h.

192 { return status_ & massConstraintTag; }

References massConstraintTag, and status_.

Referenced by reco::Particle::massConstraint(), and reco::LeafCandidate::massConstraint().

◆ massSqr()

double reco::ParticleState::massSqr ( ) const

inline

mass squared

Definition at line 125 of file ParticleState.h.

125 { return mass() * mass(); }

References mass().

◆ momentum()

Vector reco::ParticleState::momentum ( ) const

inline

spatial momentum vector

Definition at line 110 of file ParticleState.h.

110 { return p4Cartesian_.Vect(); }

References p4Cartesian_.

Referenced by reco::Particle::momentum(), and reco::LeafCandidate::momentum().

◆ mt()

double reco::ParticleState::mt ( ) const

inline

transverse mass

Definition at line 127 of file ParticleState.h.

127 { return p4Polar_.Mt(); }

References p4Polar_.

Referenced by reco::Particle::mt(), and reco::LeafCandidate::mt().

◆ mtSqr()

double reco::ParticleState::mtSqr ( ) const

inline

transverse mass squared

Definition at line 129 of file ParticleState.h.

129 { return p4Polar_.Mt2(); }

References p4Polar_.

Referenced by reco::Particle::mtSqr(), and reco::LeafCandidate::mtSqr().

◆ p()

double reco::ParticleState::p ( ) const

inline

magnitude of momentum vector

Definition at line 115 of file ParticleState.h.

115 { return p4Cartesian_.P(); }

References p4Cartesian_.

Referenced by reco::Particle::p(), reco::LeafCandidate::p(), and Electron.Electron::ptErr().

◆ p4()

const LorentzVector& reco::ParticleState::p4 ( ) const

inline

four-momentum Lorentz vector

Definition at line 106 of file ParticleState.h.

106 { return p4Cartesian_; }

References p4Cartesian_.

Referenced by Tau.Tau::dxy_approx(), Tau.Tau::dz(), reco::Particle::p4(), reco::LeafCandidate::p4(), Lepton.Lepton::p4WithFSR(), and setP4().

◆ pdgId()

int reco::ParticleState::pdgId ( ) const

inline

PDG identifier.

Definition at line 178 of file ParticleState.h.

178 { return pdgId_; }

References pdgId_.

Referenced by Particle.Particle::__str__(), reco::Particle::pdgId(), reco::LeafCandidate::pdgId(), and setPdgId().

◆ phi()

double reco::ParticleState::phi ( ) const

inline

momentum azimuthal angle

Definition at line 139 of file ParticleState.h.

139 { return p4Polar_.phi(); }

References p4Polar_.

Referenced by Particle.Particle::__str__(), reco::Particle::phi(), reco::LeafCandidate::phi(), and ntupleDataFormat.Track::phiPull().

◆ polarP4()

const PolarLorentzVector& reco::ParticleState::polarP4 ( ) const

inline

four-momentum Lorentz vector

Definition at line 108 of file ParticleState.h.

108 { return p4Polar_; }

References p4Polar_.

Referenced by reco::Particle::polarP4(), and reco::LeafCandidate::polarP4().

◆ pt()

double reco::ParticleState::pt ( ) const

inline

transverse momentum

Definition at line 137 of file ParticleState.h.

137 { return p4Polar_.pt(); }

References p4Polar_.

Referenced by Particle.Particle::__str__(), DiObject.DiMuon::__str__(), Photon.Photon::calScaledIsoValueExp(), Photon.Photon::calScaledIsoValueLin(), Photon.Photon::calScaledIsoValueQuadr(), et(), et2(), Electron.Electron::mvaIDLoose(), Electron.Electron::mvaIDRun2(), Electron.Electron::mvaIDTight(), reco::Particle::pt(), reco::LeafCandidate::pt(), Electron.Electron::ptErr(), ntupleDataFormat.Track::ptPull(), Lepton.Lepton::relIso(), Lepton.Lepton::relIsoFromEA(), Lepton.Lepton::relIsoR(), and Jet.Jet::setCorrP4().

◆ px()

double reco::ParticleState::px ( ) const

inline

x coordinate of momentum vector

Definition at line 131 of file ParticleState.h.

131 { return p4Cartesian_.Px(); }

References p4Cartesian_.

Referenced by reco::Particle::px(), and reco::LeafCandidate::px().

◆ py()

double reco::ParticleState::py ( ) const

inline

y coordinate of momentum vector

Definition at line 133 of file ParticleState.h.

133 { return p4Cartesian_.Py(); }

References p4Cartesian_.

Referenced by reco::Particle::py(), and reco::LeafCandidate::py().

◆ pz()

double reco::ParticleState::pz ( ) const

inline

z coordinate of momentum vector

Definition at line 135 of file ParticleState.h.

135 { return p4Cartesian_.Pz(); }

References p4Cartesian_.

Referenced by reco::Particle::pz(), reco::LeafCandidate::pz(), and setPz().

◆ rapidity()

double reco::ParticleState::rapidity ( ) const

inline

repidity

Definition at line 145 of file ParticleState.h.

145 { return p4Polar_.Rapidity(); }

References p4Polar_.

Referenced by reco::Particle::rapidity(), reco::LeafCandidate::rapidity(), and y().

◆ setCartesian()

void reco::ParticleState::setCartesian ( )

inline

set internal cache

Definition at line 95 of file ParticleState.h.

95 { p4Cartesian_ = p4Polar_; }

References p4Cartesian_, and p4Polar_.

Referenced by setMass().

◆ setCharge()

void reco::ParticleState::setCharge ( Charge q )

inline

set electric charge

Definition at line 100 of file ParticleState.h.

100 { qx3_ = q * 3; }

References data-class-funcs::q, and qx3_.

Referenced by reco::Particle::setCharge(), and reco::LeafCandidate::setCharge().

◆ setLongLived()

void reco::ParticleState::setLongLived ( )

inline

set long lived flag

Definition at line 186 of file ParticleState.h.

186 { status_ |= longLivedTag; }

References longLivedTag, and status_.

Referenced by reco::Particle::setLongLived(), and reco::LeafCandidate::setLongLived().

◆ setMass()

void reco::ParticleState::setMass ( double m )

inline

set particle mass

Definition at line 159 of file ParticleState.h.

                            {
       p4Polar_.SetM(m);
       setCartesian();
     }

References visualization-live-secondInstance_cfg::m, p4Polar_, and setCartesian().

Referenced by reco::Particle::setMass(), and reco::LeafCandidate::setMass().

◆ setMassConstraint()

void reco::ParticleState::setMassConstraint ( )

inline

set mass constraint flag

Definition at line 190 of file ParticleState.h.

190 { status_ |= massConstraintTag; }

References massConstraintTag, and status_.

Referenced by reco::Particle::setMassConstraint(), and reco::LeafCandidate::setMassConstraint().

◆ setP4() [1/2]

void reco::ParticleState::setP4 ( const LorentzVector & p4 )

inline

set 4-momentum

Definition at line 149 of file ParticleState.h.

                                         {
       p4Cartesian_ = p4;
       p4Polar_ = p4;
     }

References p4(), p4Cartesian_, and p4Polar_.

Referenced by Jet.Jet::setCorrP4(), reco::Particle::setP4(), and reco::LeafCandidate::setP4().

◆ setP4() [2/2]

void reco::ParticleState::setP4 ( const PolarLorentzVector & p4 )

inline

set 4-momentum

Definition at line 154 of file ParticleState.h.

                                              {
       p4Polar_ = p4;
       p4Cartesian_ = p4;
     }

References p4(), p4Cartesian_, and p4Polar_.

Referenced by Jet.Jet::setCorrP4().

◆ setPdgId()

void reco::ParticleState::setPdgId ( int pdgId )

inline

Definition at line 180 of file ParticleState.h.

180 { pdgId_ = pdgId; }

References pdgId(), and pdgId_.

Referenced by reco::Particle::setPdgId(), and reco::LeafCandidate::setPdgId().

◆ setPz()

void reco::ParticleState::setPz ( double pz )

inline

Definition at line 163 of file ParticleState.h.

                           {
       p4Cartesian_.SetPz(pz);
       p4Polar_ = p4Cartesian_;
     }

References p4Cartesian_, p4Polar_, and pz().

Referenced by reco::Particle::setPz(), and reco::LeafCandidate::setPz().

◆ setStatus()

void reco::ParticleState::setStatus ( int status )

inline

set status word

Definition at line 184 of file ParticleState.h.

184 { status_ = status; }

References status(), and status_.

Referenced by reco::Particle::setStatus(), and reco::LeafCandidate::setStatus().

◆ setThreeCharge()

void reco::ParticleState::setThreeCharge ( Charge qx3 )

inline

set electric charge

Definition at line 104 of file ParticleState.h.

104 { qx3_ = qx3; }

References qx3_.

Referenced by reco::Particle::setThreeCharge(), and reco::LeafCandidate::setThreeCharge().

◆ setVertex()

void reco::ParticleState::setVertex ( const Point & vertex )

inline

set vertex

Definition at line 176 of file ParticleState.h.

176 { vertex_ = vertex; }

References vertex(), and vertex_.

Referenced by reco::Particle::setVertex(), and reco::LeafCandidate::setVertex().

◆ status()

int reco::ParticleState::status ( ) const

inline

status word

Definition at line 182 of file ParticleState.h.

182 { return status_; }

References status_.

Referenced by setStatus(), reco::Particle::status(), and reco::LeafCandidate::status().

◆ theta()

double reco::ParticleState::theta ( ) const

inline

momentum polar angle

Definition at line 141 of file ParticleState.h.

141 { return p4Cartesian_.Theta(); }

References p4Cartesian_.

Referenced by reco::Particle::theta(), reco::LeafCandidate::theta(), and Tau.Tau::zImpact().

◆ threeCharge()

int reco::ParticleState::threeCharge ( ) const

inline

electric charge

Definition at line 102 of file ParticleState.h.

102 { return qx3_; }

References qx3_.

Referenced by reco::Particle::threeCharge(), and reco::LeafCandidate::threeCharge().

◆ vertex()

const Point& reco::ParticleState::vertex ( ) const

inline

vertex position

Definition at line 168 of file ParticleState.h.

168 { return vertex_; }

References vertex_.

Referenced by Tau.Tau::dxy(), setVertex(), reco::Particle::vertex(), and reco::LeafCandidate::vertex().

◆ vx()

double reco::ParticleState::vx ( ) const

inline

x coordinate of vertex position

Definition at line 170 of file ParticleState.h.

170 { return vertex_.X(); }

References vertex_.

Referenced by reco::Particle::vx(), and reco::LeafCandidate::vx().

◆ vy()

double reco::ParticleState::vy ( ) const

inline

y coordinate of vertex position

Definition at line 172 of file ParticleState.h.

172 { return vertex_.Y(); }

References vertex_.

Referenced by reco::Particle::vy(), and reco::LeafCandidate::vy().

◆ vz()

double reco::ParticleState::vz ( ) const

inline

z coordinate of vertex position

Definition at line 174 of file ParticleState.h.

174 { return vertex_.Z(); }

References vertex_.

Referenced by reco::Particle::vz(), and reco::LeafCandidate::vz().

◆ y()

double reco::ParticleState::y ( ) const

inline

repidity

Definition at line 147 of file ParticleState.h.

147 { return rapidity(); }

References rapidity().

Referenced by svgfig.Ellipse::__repr__(), geometryXMLparser.Alignable::pos(), ntupleDataFormat._HitObject::r(), and ntupleDataFormat._HitObject::r3D().

Member Data Documentation

◆ longLivedTag

const unsigned int reco::ParticleState::longLivedTag = 65536

staticprivate

Definition at line 195 of file ParticleState.h.

Referenced by longLived(), and setLongLived().

◆ massConstraintTag

const unsigned int reco::ParticleState::massConstraintTag = 131072

staticprivate

Definition at line 196 of file ParticleState.h.

Referenced by massConstraint(), and setMassConstraint().

◆ p4Cartesian_

LorentzVector reco::ParticleState::p4Cartesian_

private

internal cache for p4

Definition at line 205 of file ParticleState.h.

Referenced by boostToCM(), energy(), et(), et2(), momentum(), p(), p4(), px(), py(), pz(), setCartesian(), setP4(), setPz(), and theta().

◆ p4Polar_

PolarLorentzVector reco::ParticleState::p4Polar_

private

four-momentum Lorentz vector

Definition at line 203 of file ParticleState.h.

Referenced by eta(), mass(), mt(), mtSqr(), phi(), polarP4(), pt(), rapidity(), setCartesian(), setMass(), setP4(), and setPz().

◆ pdgId_

int reco::ParticleState::pdgId_

private

PDG identifier.

Definition at line 211 of file ParticleState.h.

Referenced by pdgId(), and setPdgId().

◆ qx3_

Charge reco::ParticleState::qx3_

private

electric charge

Definition at line 208 of file ParticleState.h.

Referenced by charge(), setCharge(), setThreeCharge(), and threeCharge().

◆ status_

int reco::ParticleState::status_

private

status word

Definition at line 213 of file ParticleState.h.

Referenced by longLived(), massConstraint(), setLongLived(), setMassConstraint(), setStatus(), and status().

◆ vertex_

Point reco::ParticleState::vertex_

private

vertex position

Definition at line 200 of file ParticleState.h.

Referenced by setVertex(), vertex(), vx(), vy(), and vz().

Public Types

Public Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ Charge

◆ LorentzVector

◆ Point

◆ PolarLorentzVector

◆ Vector

Constructor & Destructor Documentation

◆ ParticleState() [1/5]

◆ ParticleState() [2/5]

◆ ParticleState() [3/5]

◆ ParticleState() [4/5]

◆ ParticleState() [5/5]

Member Function Documentation

◆ boostToCM()

◆ charge()

◆ energy()

◆ et()

◆ et2()

◆ eta()

◆ longLived()

◆ mass()

◆ massConstraint()

◆ massSqr()

◆ momentum()

◆ mt()

◆ mtSqr()

◆ p()

◆ p4()

◆ pdgId()

◆ phi()

◆ polarP4()

◆ pt()

◆ px()

◆ py()

◆ pz()

◆ rapidity()

◆ setCartesian()

◆ setCharge()

◆ setLongLived()

◆ setMass()

◆ setMassConstraint()

◆ setP4() [1/2]

◆ setP4() [2/2]

◆ setPdgId()

◆ setPz()

◆ setStatus()

◆ setThreeCharge()

◆ setVertex()

◆ status()

◆ theta()

◆ threeCharge()

◆ vertex()

◆ vx()

◆ vy()

◆ vz()

◆ y()

Member Data Documentation

◆ longLivedTag

◆ massConstraintTag

◆ p4Cartesian_

◆ p4Polar_

◆ pdgId_

◆ qx3_

◆ status_

◆ vertex_