ROOT::Math::Impl Namespace Reference

Functions
template<typename Scalar >
Scalar	Eta_FromRhoZ (Scalar rho, Scalar z)
	Calculate eta given rho and zeta. More...
template<typename Scalar >
Scalar	Eta_FromTheta (Scalar theta, Scalar r)
	Implementation of eta from -log(tan(theta/2)). More...

Function Documentation

template<typename Scalar >

Scalar ROOT::Math::Impl::Eta_FromRhoZ ( Scalar  rho, Scalar  z  )

inline

Calculate eta given rho and zeta.

This formula is faster than the standard calculation (below) from log(tan(theta/2) but one has to be careful when rho is much smaller than z (large eta values) Formula is eta = log( zs + sqrt(zs^2 + 1) ) where zs = z/rho

For large value of z_scaled (tan(theta) ) one can appoximate the sqrt via a Taylor expansion We do the approximation of the sqrt if the numerical error is of the same order of second term of the sqrt.expansion: eps > 1/zs^4 => zs > 1/(eps^0.25)

When rho == 0 we use etaMax (see definition in etaMax.h)

Definition at line 50 of file eta.h.

Referenced by ROOT::Math::Cartesian3D< Double32_t >::Eta(), ROOT::Math::Cylindrical3D< T >::Eta(), ROOT::Math::PxPyPzE4D< Double32_t >::Eta(), and ROOT::Math::PxPyPzM4D< ScalarType >::Eta().

template<typename Scalar >

Scalar ROOT::Math::Impl::Eta_FromTheta ( Scalar  theta, Scalar  r  )

inline

Implementation of eta from -log(tan(theta/2)).

This is convenient when theta is already known (for example in a polar coorindate system)

Definition at line 84 of file eta.h.

Referenced by ROOT::Math::Polar3D< T >::Eta().