/usr/include/root/Math/GenVector/eta.h is in libroot-math-genvector-dev 5.34.30-0ubuntu8.
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// Authors: W. Brown, M. Fischler, L. Moneta 2005
/**********************************************************************
* *
* Copyright (c) 2005 , FNAL MathLib Team *
* *
* *
**********************************************************************/
// Header source file for function calculating eta
//
// Created by: Lorenzo Moneta at 14 Jun 2007
#ifndef ROOT_Math_GenVector_eta
#define ROOT_Math_GenVector_eta 1
#ifndef ROOT_Math_GenVector_etaMax
#include "Math/GenVector/etaMax.h"
#endif
#include <limits>
#include <cmath>
namespace ROOT {
namespace Math {
namespace Impl {
/**
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)
*/
template<typename Scalar>
inline Scalar Eta_FromRhoZ(Scalar rho, Scalar z) {
if (rho > 0) {
// value to control Taylor expansion of sqrt
static const Scalar big_z_scaled =
std::pow(std::numeric_limits<Scalar>::epsilon(),static_cast<Scalar>(-.25));
Scalar z_scaled = z/rho;
if (std::fabs(z_scaled) < big_z_scaled) {
return std::log(z_scaled+std::sqrt(z_scaled*z_scaled+1.0));
} else {
// apply correction using first order Taylor expansion of sqrt
return z>0 ? std::log(2.0*z_scaled + 0.5/z_scaled) : -std::log(-2.0*z_scaled);
}
}
// case vector has rho = 0
else if (z==0) {
return 0;
}
else if (z>0) {
return z + etaMax<Scalar>();
}
else {
return z - etaMax<Scalar>();
}
}
/**
Implementation of eta from -log(tan(theta/2)).
This is convenient when theta is already known (for example in a polar coorindate system)
*/
template<typename Scalar>
inline Scalar Eta_FromTheta(Scalar theta, Scalar r) {
Scalar tanThetaOver2 = std::tan( theta/2.);
if (tanThetaOver2 == 0) {
return r + etaMax<Scalar>();
}
else if (tanThetaOver2 > std::numeric_limits<Scalar>::max()) {
return -r - etaMax<Scalar>();
}
else {
return -std::log(tanThetaOver2);
}
}
} // end namespace Impl
} // namespace Math
} // namespace ROOT
#endif /* ROOT_Math_GenVector_etaMax */
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