Kinematics tools

Event_selection_framework

Kinematic tools are defined in Common/Kinematics package. SCT kinematics classes are based on Eigen3 library. ROOT implementation of vectors and matrices is abandoned intentionally as too slow.

Main definitions

Main set of aliases for basic kinematic entities in namespace sct is located in KineTypedefs.h. These aliases are to be used at maximum extent in the Aurora framework.

Entity	Alias	Source
1D vector	Vector1D	Eigen::Matrix<ftype, 1, S>
Three-vector	ThreeVector	sct::kine::ThreeVector<>
Lorentz-vector	FourVector	sct::kine::FourVector<>
Matrix	template<size_t D1, size_t D2> Matrix	Eigen::Matrix<ftype, D1, D2>
Square Matrix	template<size_t S> SquareMatrix	Eigen::Matrix<ftype, S, S>
3x3 matrix	ThreeMatrix	SquareMatrix<3>
4x4 matrix	FourMatrix	SquareMatrix<4>

Several APIs are described in detail below.

sct::kine::ThreeVector

ThreeVector.h (contributors: D. Yakovlev, V. Vorobyev)

The ThreeVector class is a template class inherits from Eigen::Matrix<ftype, 1, 3>

template <typename ftype = double>
class ThreeVector : public Eigen::Matrix<ftype, 1, 3>

ThreeVector can be initialized with Cartesian or polar coordinates:

ThreeVector v1(x, y, z);
ThreeVector v2 = ThreeVector::fromRPhiCosth(r, phi, costh)

ThreeVecotor API compared with ROOT TVector3 API

Operation	ThreeVector API	TVector3 API
x component	x(), px()	X(), Px()
y component	y(), py()	Y(), Py()
z component	z(), pz()	Z(), Pz()
Transverse momentum	pt()	Pt(), Perp()
Norm	norm()	Mag()
Squared norm	norm2(), squaredNorm()	Mag2()
Rotation around x axis	RotateX(double)	RotateX (Double_t)
Rotation around y axis	RotateY(double)	RotateY (Double_t)
Rotation around z axis	RotateZ(double)	RotateZ (Double_t)

The angle between two vectors can be obtained with

template <typename ftype> 
inline ftype angle(const ThreeVector<ftype>& v1, const ThreeVector<ftype> v2)

sct::kine::FourVector

FourVector.h (contributors: D. Yakovlev, V. Vorobyev)

--V.S.Vorobev (talk) 21:53, 25 April 2020 (+07)