Vector: arrays of 2D, 3D, and Lorentz vectors




Installation
You can install Vector with pip and conda.
pip install vector
Introduction
Vector is a Python library for 2D and 3D spatial vectors, as well as 4D space-time vectors. It is especially intended for performing geometric calculations on arrays of vectors, rather than one vector at a time in a Python for loop.
Vector is part of the Scikit-HEP project, High Energy Physics (HEP) tools in Python.
Coordinate systems
Vectors may be expressed in any of these coordinate systems:
- the azimuthal plane may be Cartesian
x
y
or polar rho
($\rho$) phi
($\phi$)
- the longitudinal axis may be Cartesian
z
, polar theta
($\theta$), or pseudorapidity eta
($\eta$)
- the temporal component for space-time vectors may be Cartesian
t
or proper time tau
($\tau$)
in any combination. (That is, 4D vectors have 2×3×2 = 12 distinct coordinate systems.)
Backends
Vectors may be included in any of these data types:
Each of these "backends" provides the same suite of properties and methods, through a common "compute" library.
Geometric versus momentum
Finally, vectors come in two flavors:
- geometric: only one name for each property or method
- momentum: same property or method can be accessed with several synonyms, such as
pt
($p_T$, transverse momentum) for the azimuthal magnitude rho
($\rho$) and energy
and mass
for the Cartesian time t
and proper time tau
($\tau$).
Familiar conventions
Names and coordinate conventions were chosen to align with ROOT's TLorentzVector and Math::LorentzVector, as well as scikit-hep/math, uproot-methods TLorentzVector, henryiii/hepvector, and coffea.nanoevents.methods.vector.
Getting help
Contributing to Vector
If you want to contribute to Vector, pull requests are welcome!
Please install the latest version of the main
branch from source or a fork:
git clone https://github.com/scikit-hep/vector.git
cd vector
pip install -e .
Refer to CONTRIBUTING.md for more.
Citing Vector
To cite Vector, please use 
@article{Chopra2025,
doi = {10.21105/joss.07791},
url = {https://doi.org/10.21105/joss.07791},
year = {2025}, publisher = {The Open Journal},
volume = {10},
number = {109},
pages = {7791},
author = {Saransh Chopra and Henry Schreiner and Eduardo Rodrigues and Jonas Eschle and Jim Pivarski},
title = {Vector: JIT-compilable mathematical manipulations of ragged Lorentz vectors},
journal = {Journal of Open Source Software}
}
Documentation
Tutorials
Vector constructors
Vector functions
More ways to learn
Contributors
Thanks goes to these wonderful people (emoji key):
This project follows the
all-contributors
specification. Contributions of any kind welcome! See
CONTRIBUTING.md for information on setting up a
development environment.
Acknowledgements
This library was primarily developed by Saransh Chopra, Henry Schreiner, Jim Pivarski, Eduardo Rodrigues, and Jonas Eschle.
Support for this work was provided by the National Science Foundation cooperative agreement OAC-1836650 and PHY-2323298 (IRIS-HEP) and OAC-1450377 (DIANA/HEP). Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.