Vector is a Python 3.8+ library (Python 3.6 and 3.7 supported till v0.9.0
and v1.0.0
, respectively) for 2D, 3D, and Lorentz vectors, especially arrays of vectors, to solve common physics problems in a NumPy-like way.
Main features of Vector:
- Pure Python with NumPy as its only dependency. This makes it easier to install.
- Vectors may be represented in a variety of coordinate systems: Cartesian, cylindrical, pseudorapidity, and any combination of these with time or proper time for Lorentz vectors. In all, there are 12 coordinate systems: {x-y vs ρ-φ in the azimuthal plane} × {z vs θ vs η longitudinally} × {t vs τ temporally}.
- Uses names and conventions set by ROOT's TLorentzVector and Math::LorentzVector, as well as scikit-hep/math, uproot-methods TLorentzVector, henryiii/hepvector, and coffea.nanoevents.methods.vector.
- Implemented on a variety of backends:
- pure Python objects
- NumPy arrays of vectors (as a structured array subclass)
- Awkward Arrays of vectors
- potential for more: CuPy, TensorFlow, Torch, JAX...
- NumPy/Awkward backends also implemented in Numba for JIT-compiled calculations on vectors.
- Distinction between geometrical vectors, which have a minimum of attribute and method names, and vectors representing momentum, which have synonyms like
pt
=rho
,energy
=t
,mass
=tau
.
To install, use pip install vector
or your favorite way to install in an environment.
This overview is based on the documentation here.
import vector
import numpy as np
import awkward as ak # at least version 1.2.0
import numba as nb
The easiest way to create one or many vectors is with a helper function:
vector.obj
to make a pure Python vector object,vector.arr
to make a NumPy array of vectors (orarray
, lowercase, likenp.array
),vector.awk
to make an Awkward Array of vectors (orArray
, uppercase, likeak.Array
).vector.zip
to make an Awkward Array of vectors (similar toak.zip
)
# Cartesian 2D vector
vector.obj(x=3, y=4)
# same in polar coordinates
vector.obj(rho=5, phi=0.9273)
# use "isclose" unless they are exactly equal
vector.obj(x=3, y=4).isclose(vector.obj(rho=5, phi=0.9273))
# Cartesian 3D vector
vector.obj(x=3, y=4, z=-2)
# Cartesian 4D vector
vector.obj(x=3, y=4, z=-2, t=10)
# in rho-phi-eta-t cylindrical coordinates
vector.obj(rho=5, phi=0.9273, eta=-0.39, t=10)
# use momentum-synonyms to get a momentum vector
vector.obj(pt=5, phi=0.9273, eta=-0.39, E=10)
vector.obj(rho=5, phi=0.9273, eta=-0.39, t=10) == vector.obj(
pt=5, phi=0.9273, eta=-0.390035, E=10
)
# geometrical vectors have to use geometrical names ("tau", not "mass")
vector.obj(rho=5, phi=0.9273, eta=-0.39, t=10).tau
# momentum vectors can use momentum names (as well as geometrical ones)
vector.obj(pt=5, phi=0.9273, eta=-0.39, E=10).mass
# any combination of azimuthal, longitudinal, and temporal coordinates is allowed
vector.obj(pt=5, phi=0.9273, theta=1.9513, mass=8.4262)
vector.obj(x=3, y=4, z=-2, t=10).isclose(
vector.obj(pt=5, phi=0.9273, theta=1.9513, mass=8.4262)
)
# Test instance type for any level of granularity.
(
# is a vector or array of vectors
isinstance(vector.obj(x=1.1, y=2.2), vector.Vector),
# is 2D (not 3D or 4D)
isinstance(vector.obj(x=1.1, y=2.2), vector.Vector2D),
# is a vector object (not an array)
isinstance(vector.obj(x=1.1, y=2.2), vector.VectorObject),
# has momentum synonyms
isinstance(vector.obj(px=1.1, py=2.2), vector.Momentum),
# has transverse plane (2D, 3D, or 4D)
isinstance(vector.obj(x=1.1, y=2.2, z=3.3, t=4.4), vector.Planar),
# has all spatial coordinates (3D or 4D)
isinstance(vector.obj(x=1.1, y=2.2, z=3.3, t=4.4), vector.Spatial),
# has temporal coordinates (4D)
isinstance(vector.obj(x=1.1, y=2.2, z=3.3, t=4.4), vector.Lorentz),
# azimuthal coordinate type
isinstance(vector.obj(x=1.1, y=2.2, z=3.3, t=4.4).azimuthal, vector.AzimuthalXY),
# longitudinal coordinate type
isinstance(
vector.obj(x=1.1, y=2.2, z=3.3, t=4.4).longitudinal, vector.LongitudinalZ
),
# temporal coordinate type
isinstance(vector.obj(x=1.1, y=2.2, z=3.3, t=4.4).temporal, vector.TemporalT),
)
The allowed keyword arguments for 2D vectors are:
x
andy
for Cartesian azimuthal coordinates,px
andpy
for momentum,rho
andphi
for polar azimuthal coordinates,pt
andphi
for momentum.
For 3D vectors, you need the above and:
-
z
for the Cartesian longitudinal coordinate, -
pz
for momentum, -
theta
for the spherical polar angle (from$0$ to$\pi$ , inclusive), -
eta
for pseudorapidity, which is a kind of spherical polar angle.
For 4D vectors, you need the above and:
t
for the Cartesian temporal coordinate,E
orenergy
to get four-momentum,tau
for the "proper time" (temporal coordinate in the vector's rest coordinate system),M
ormass
to get four-momentum.
Since momentum vectors have momentum-synonyms in addition to the geometrical names, any momentum-synonym will make the whole vector a momentum vector.
If you want to bypass the dimension and coordinate system inference through keyword arguments (e.g. for static typing), you can use specialized constructors:
vector.VectorObject2D.from_xy(1.1, 2.2)
vector.MomentumObject3D.from_rhophiz(1.1, 2.2, 3.3)
vector.VectorObject4D.from_xyetatau(1.1, 2.2, 3.3, 4.4)
and so on, for all combinations of azimuthal, longitudinal, and temporal coordinates, geometric and momentum-flavored.
# NumPy-like arguments (literally passed through to NumPy)
vector.array(
[(1.1, 2.1), (1.2, 2.2), (1.3, 2.3), (1.4, 2.4), (1.5, 2.5)],
dtype=[("x", float), ("y", float)],
)
# Pandas-like arguments (dict from names to column arrays)
vector.array({"x": [1.1, 1.2, 1.3, 1.4, 1.5], "y": [2.1, 2.2, 2.3, 2.4, 2.5]})
# As with objects, the coordinate system and dimension is taken from the names of the fields.
vector.array(
{
"x": [1.1, 1.2, 1.3, 1.4, 1.5],
"y": [2.1, 2.2, 2.3, 2.4, 2.5],
"z": [3.1, 3.2, 3.3, 3.4, 3.5],
"t": [4.1, 4.2, 4.3, 4.4, 4.5],
}
)
vector.array(
{
"pt": [1.1, 1.2, 1.3, 1.4, 1.5],
"phi": [2.1, 2.2, 2.3, 2.4, 2.5],
"eta": [3.1, 3.2, 3.3, 3.4, 3.5],
"M": [4.1, 4.2, 4.3, 4.4, 4.5],
}
)
Existing NumPy arrays can be viewed as arrays of vectors, but it needs to be a structured array with recognized field names.
np.arange(0, 24, 0.1).view( # NumPy array
[
("x", float),
("y", float),
("z", float),
("t", float),
] # interpret groups of four values as named fields
).view(
vector.VectorNumpy4D
) # give it vector properties and methods
Since VectorNumpy2D
, VectorNumpy3D
, VectorNumpy4D
, and their momentum equivalents are NumPy array subclasses, all of the normal NumPy methods and functions work on them.
np.arange(0, 24, 0.1).view(
[("x", float), ("y", float), ("z", float), ("t", float)]
).view(vector.VectorNumpy4D).reshape(6, 5, 2)
All of the keyword arguments and rules that apply to vector.obj
construction apply to vector.arr
dtypes.
Geometrical names are used in the dtype, even if momentum-synonyms are used in construction.
vector.arr({"px": [1, 2, 3, 4], "py": [1.1, 2.2, 3.3, 4.4], "pz": [0.1, 0.2, 0.3, 0.4]})
Awkward Arrays are arrays with more complex data structures than NumPy allows, such as variable-length lists, nested records, missing and even heterogeneous data (multiple data types: use sparingly).
The vector.awk
function behaves exactly like the ak.Array constructor, except that it makes arrays of vectors.
vector.awk(
[
[{"x": 1, "y": 1.1, "z": 0.1}, {"x": 2, "y": 2.2, "z": 0.2}],
[],
[{"x": 3, "y": 3.3, "z": 0.3}],
[
{"x": 4, "y": 4.4, "z": 0.4},
{"x": 5, "y": 5.5, "z": 0.5},
{"x": 6, "y": 6.6, "z": 0.6},
],
]
)
If you want any records named "Vector2D
", "Vector3D
", "Vector4D
", "Momentum2D
", "Momentum3D
", or "Momentum4D
" to be interpreted as vectors, register the behaviors globally.
vector.register_awkward()
ak.Array(
[
[{"x": 1, "y": 1.1, "z": 0.1}, {"x": 2, "y": 2.2, "z": 0.2}],
[],
[{"x": 3, "y": 3.3, "z": 0.3}],
[
{"x": 4, "y": 4.4, "z": 0.4},
{"x": 5, "y": 5.5, "z": 0.5},
{"x": 6, "y": 6.6, "z": 0.6},
],
],
with_name="Vector3D",
)
All of the keyword arguments and rules that apply to vector.obj
construction apply to vector.awk
field names.
Any geometrical coordinate can be computed from vectors in any coordinate system; they'll be provided or computed as needed.
vector.obj(x=3, y=4).rho
vector.obj(rho=5, phi=0.9273).x
vector.obj(rho=5, phi=0.9273).y
vector.obj(x=1, y=2, z=3).theta
vector.obj(x=1, y=2, z=3).eta
Some properties are not coordinates, but derived from them.
vector.obj(x=1, y=2, z=3).costheta
vector.obj(x=1, y=2, z=3).mag # spatial magnitude
vector.obj(x=1, y=2, z=3).mag2 # spatial magnitude squared
These properties are provided because they can be computed faster or with more numerical stability in different coordinate systems. For instance, the magnitude ignores phi
in polar coordinates.
vector.obj(rho=3, phi=0.123456789, z=4).mag2
Momentum vectors have geometrical properties as well as their momentum-synonyms.
vector.obj(px=3, py=4).rho
vector.obj(px=3, py=4).pt
vector.obj(x=1, y=2, z=3, E=4).tau
vector.obj(x=1, y=2, z=3, E=4).mass
Here's the key thing: arrays of vectors return arrays of coordinates.
vector.arr(
{
"x": [1.0, 2.0, 3.0, 4.0, 5.0],
"y": [1.1, 2.2, 3.3, 4.4, 5.5],
"z": [0.1, 0.2, 0.3, 0.4, 0.5],
}
).theta
vector.awk(
[
[{"x": 1, "y": 1.1, "z": 0.1}, {"x": 2, "y": 2.2, "z": 0.2}],
[],
[{"x": 3, "y": 3.3, "z": 0.3}],
[{"x": 4, "y": 4.4, "z": 0.4}, {"x": 5, "y": 5.5, "z": 0.5}],
]
).theta
# Make a large, random NumPy array of 3D momentum vectors.
array = (
np.random.normal(0, 1, 150)
.view([(x, float) for x in ("x", "y", "z")])
.view(vector.MomentumNumpy3D)
.reshape(5, 5, 2)
)
# Get the transverse momentum of each one.
array.pt
# The array and its components have the same shape.
array.shape
array.pt.shape
# Make a large, random Awkward Array of 3D momentum vectors.
array = vector.awk(
[
[
{x: np.random.normal(0, 1) for x in ("px", "py", "pz")}
for inner in range(np.random.poisson(1.5))
]
for outer in range(50)
]
)
# Get the transverse momentum of each one, in the same nested structure.
array.pt
# The array and its components have the same list lengths (and can therefore be used together in subsequent calculations).
ak.num(array)
ak.num(array.pt)
Vector methods require arguments (in parentheses), which may be scalars or other vectors, depending on the calculation.
vector.obj(x=3, y=4).rotateZ(0.1)
vector.obj(rho=5, phi=0.4).rotateZ(0.1)
# Broadcasts a scalar rotation angle of 0.5 to all elements of the NumPy array.
print(
vector.arr({"rho": [1, 2, 3, 4, 5], "phi": [0.1, 0.2, 0.3, 0.4, 0.5]}).rotateZ(0.5)
)
# Matches each rotation angle to an element of the NumPy array.
print(
vector.arr({"rho": [1, 2, 3, 4, 5], "phi": [0.1, 0.2, 0.3, 0.4, 0.5]}).rotateZ(
np.array([0.1, 0.2, 0.3, 0.4, 0.5])
)
)
# Broadcasts a scalar rotation angle of 0.5 to all elements of the Awkward Array.
print(
vector.awk(
[[{"rho": 1, "phi": 0.1}, {"rho": 2, "phi": 0.2}], [], [{"rho": 3, "phi": 0.3}]]
).rotateZ(0.5)
)
# Broadcasts a rotation angle of 0.1 to both elements of the first list, 0.2 to the empty list, and 0.3 to the only element of the last list.
print(
vector.awk(
[[{"rho": 1, "phi": 0.1}, {"rho": 2, "phi": 0.2}], [], [{"rho": 3, "phi": 0.3}]]
).rotateZ([0.1, 0.2, 0.3])
)
# Matches each rotation angle to an element of the Awkward Array.
print(
vector.awk(
[[{"rho": 1, "phi": 0.1}, {"rho": 2, "phi": 0.2}], [], [{"rho": 3, "phi": 0.3}]]
).rotateZ([[0.1, 0.2], [], [0.3]])
)
Some methods are equivalent to binary operators.
vector.obj(x=3, y=4).scale(10)
vector.obj(x=3, y=4) * 10
10 * vector.obj(x=3, y=4)
vector.obj(rho=5, phi=0.5) * 10
Some methods involve more than one vector.
vector.obj(x=1, y=2).add(vector.obj(x=5, y=5))
vector.obj(x=1, y=2) + vector.obj(x=5, y=5)
vector.obj(x=1, y=2).dot(vector.obj(x=5, y=5))
vector.obj(x=1, y=2) @ vector.obj(x=5, y=5)
The vectors can use different coordinate systems. Conversions are necessary, but minimized for speed and numeric stability.
# both are Cartesian, dot product is exact
vector.obj(x=3, y=4) @ vector.obj(x=6, y=8)
# one is polar, dot product is approximate
vector.obj(rho=5, phi=0.9273) @ vector.obj(x=6, y=8)
# one is polar, dot product is approximate
vector.obj(x=3, y=4) @ vector.obj(rho=10, phi=0.9273)
# both are polar, a formula that depends on phi differences is used
vector.obj(rho=5, phi=0.9273) @ vector.obj(rho=10, phi=0.9273)
In Python, some "operators" are actually built-in functions, such as abs
.
abs(vector.obj(x=3, y=4))
Note that abs
returns
rho
for 2D vectorsmag
for 3D vectorstau
(mass
) for 4D vectors
Use the named properties when you want magnitude in a specific number of dimensions; use abs
when you want the magnitude for any number of dimensions.
The vectors can be from different backends. Normal rules for broadcasting Python numbers, NumPy arrays, and Awkward Arrays apply.
vector.arr({"x": [1, 2, 3, 4, 5], "y": [0.1, 0.2, 0.3, 0.4, 0.5]}) + vector.obj(
x=10, y=5
)
(
vector.awk(
[ # an Awkward Array of vectors
[{"x": 1, "y": 1.1}, {"x": 2, "y": 2.2}],
[],
[{"x": 3, "y": 3.3}],
[{"x": 4, "y": 4.4}, {"x": 5, "y": 5.5}],
]
)
+ vector.obj(x=10, y=5) # and a single vector object
)
(
vector.awk(
[ # an Awkward Array of vectors
[{"x": 1, "y": 1.1}, {"x": 2, "y": 2.2}],
[],
[{"x": 3, "y": 3.3}],
[{"x": 4, "y": 4.4}, {"x": 5, "y": 5.5}],
]
)
+ vector.arr(
{"x": [4, 3, 2, 1], "y": [0.1, 0.1, 0.1, 0.1]}
) # and a NumPy array of vectors
)
Some operations are defined for 2D or 3D vectors, but are usable on higher-dimensional vectors because the additional components can be ignored or are passed through unaffected.
# deltaphi is a planar operation (defined on the transverse plane)
vector.obj(rho=1, phi=0.5).deltaphi(vector.obj(rho=2, phi=0.3))
# but we can use it on 3D vectors
vector.obj(rho=1, phi=0.5, z=10).deltaphi(vector.obj(rho=2, phi=0.3, theta=1.4))
# and 4D vectors
vector.obj(rho=1, phi=0.5, z=10, t=100).deltaphi(
vector.obj(rho=2, phi=0.3, theta=1.4, tau=1000)
)
# and mixed dimensionality
vector.obj(rho=1, phi=0.5).deltaphi(vector.obj(rho=2, phi=0.3, theta=1.4, tau=1000))
This is especially useful for giving 4D vectors all the capabilities of 3D vectors.
vector.obj(x=1, y=2, z=3).rotateX(np.pi / 4)
vector.obj(x=1, y=2, z=3, tau=10).rotateX(np.pi / 4)
vector.obj(pt=1, phi=1.3, eta=2).deltaR(vector.obj(pt=2, phi=0.3, eta=1))
vector.obj(pt=1, phi=1.3, eta=2, mass=5).deltaR(
vector.obj(pt=2, phi=0.3, eta=1, mass=10)
)
The opposite—using low-dimensional vectors in operations defined for higher numbers of dimensions—is sometimes defined. In these cases, a zero longitudinal or temporal component has to be imputed.
vector.obj(x=1, y=2, z=3) - vector.obj(x=1, y=2)
vector.obj(x=1, y=2, z=0).is_parallel(vector.obj(x=1, y=2))
And finally, in some cases, the function excludes a higher-dimensional component, even if the input vectors had them.
It would be confusing if the 3D cross-product returned a fourth component.
vector.obj(x=0.1, y=0.2, z=0.3, t=10).cross(vector.obj(x=0.4, y=0.5, z=0.6, t=20))
The (current) list of properties and methods is:
Planar (2D, 3D, 4D):
-
x
(px
) -
y
(py
) -
rho
(pt
): two-dimensional magnitude -
rho2
(pt2
): two-dimensional magnitude squared phi
-
deltaphi(vector)
: difference inphi
(signed and rectified to$-\pi$ through$\pi$ ) rotateZ(angle)
-
transform2D(obj)
: theobj
must supply components throughobj["xx"]
,obj["xy"]
,obj["yx"]
,obj["yy"]
-
is_parallel(vector, tolerance=1e-5)
: only true if they're pointing in the same direction -
is_antiparallel(vector, tolerance=1e-5)
: only true if they're pointing in opposite directions is_perpendicular(vector, tolerance=1e-5)
Spatial (3D, 4D):
-
z
(pz
) theta
eta
costheta
cottheta
-
mag
(p
): three-dimensional magnitude, does not include temporal component -
mag2
(p2
): three-dimensional magnitude squared -
cross
: cross-product (strictly 3D) -
deltaangle(vector)
: difference in angle (always non-negative) -
deltaeta(vector)
: difference ineta
(signed) -
deltaR(vector)
:$\Delta R = \sqrt{\Delta\phi^2 + \Delta\eta^2}$ -
deltaR2(vector)
: the above, squared rotateX(angle)
rotateY(angle)
-
rotate_axis(axis, angle)
: the magnitude ofaxis
is ignored, but it must be at least 3D -
rotate_euler(phi, theta, psi, order="zxz")
: the arguments are in the same order as ROOT::Math::EulerAngles, andorder="zxz"
agrees with ROOT's choice of conventions rotate_nautical(yaw, pitch, roll)
-
rotate_quaternion(u, i, j, k)
: again, the conventions match ROOT::Math::Quaternion. -
transform3D(obj)
: theobj
must supply components throughobj["xx"]
,obj["xy"]
, etc. -
is_parallel(vector, tolerance=1e-5)
: only true if they're pointing in the same direction -
is_antiparallel(vector, tolerance=1e-5)
: only true if they're pointing in opposite directions is_perpendicular(vector, tolerance=1e-5)
Lorentz (4D only):
-
t
(E
,energy
): follows the ROOT::Math::LorentzVector behavior of treating spacelike vectors as negativet
and negativetau
and truncating wrong-direction timelike vectors -
t2
(E2
,energy2
) -
tau
(M
,mass
): see note above -
tau2
(M2
,mass2
) -
beta
: scalar(s) between$0$ (inclusive) and$1$ (exclusive, unless the vector components are infinite) -
deltaRapidityPhi
:$\Delta R_{\mbox{rapidity}} = \Delta\phi^2 + \Delta \mbox{rapidity}^2$ -
deltaRapidityPhi2
: the above, squared -
gamma
: scalar(s) between$1$ (inclusive) and$\infty$ -
rapidity
: scalar(s) between$0$ (inclusive) and$\infty$ -
boost_p4(four_vector)
: change coordinate system using another 4D vector as the difference -
boost_beta(three_vector)
: change coordinate system using a 3D beta vector (all components between$-1$ and$+1$ ) -
boost(vector)
: uses the dimension of the givenvector
to determine behavior -
boostX(beta=None, gamma=None)
: supplybeta
xorgamma
, but not both -
boostY(beta=None, gamma=None)
: supplybeta
xorgamma
, but not both -
boostZ(beta=None, gamma=None)
: supplybeta
xorgamma
, but not both -
transform4D(obj)
: theobj
must supply components throughobj["xx"]
,obj["xy"]
, etc. -
to_beta3()
: turns afour_vector
(forboost_p4
) into athree_vector
(forboost_beta3
) is_timelike(tolerance=0)
is_spacelike(tolerance=0)
-
is_lightlike(tolerance=1e-5)
: note the different tolerance
All numbers of dimensions:
unit()
: note the parenthesesdot(vector)
: can also use the@
operatoradd(vector)
: can also use the+
operatorsubtract(vector)
: can also use the-
operatorscale(factor)
: can also use the*
operatorequal(vector)
: can also use the==
operator, but considerisclose
insteadnot_equal(vector)
: can also use the!=
operator, but considerisclose
insteadisclose(vector, rtol=1e-5, atol=1e-8, equal_nan=False)
: works like np.isclose; arrays also have an allclose method
Numba is a just-in-time (JIT) compiler for a mathematically relevant subset of NumPy and Python. It allows you to write fast code without leaving the Python environment. The drawback of Numba is that it can only compile code blocks involving objects and functions that it recognizes.
The Vector library includes extensions to inform Numba about vector objects, vector NumPy arrays, and vector Awkward Arrays. At the time of writing, the implementation of vector NumPy arrays is incomplete due to numba/numba#6148.
For instance, consider the following function:
@nb.njit
def compute_mass(v1, v2):
return (v1 + v2).mass
compute_mass(vector.obj(px=1, py=2, pz=3, E=4), vector.obj(px=-1, py=-2, pz=-3, E=4))
When the two MomentumObject4D
objects are passed as arguments, Numba recognizes them and replaces the Python objects with low-level structs. When it compiles the function, it recognizes +
as the 4D add
function and recognizes .mass
as the tau
component of the result.
Although this demonstrates that Numba can manipulate vector objects, there is no performance advantage (and a likely disadvantage) to compiling a calculation on just a few vectors. The advantage comes when many vectors are involved, in arrays.
# This is still not a large number. You want millions.
array = vector.awk(
[
[
dict(
{x: np.random.normal(0, 1) for x in ("px", "py", "pz")},
E=np.random.normal(10, 1),
)
for inner in range(np.random.poisson(1.5))
]
for outer in range(50)
]
)
@nb.njit
def compute_masses(array):
out = np.empty(len(array), np.float64)
for i, event in enumerate(array):
total = vector.obj(px=0.0, py=0.0, pz=0.0, E=0.0)
for vec in event:
total = total + vec
out[i] = total.mass
return out
compute_masses(array)
- 13th September 2022 - Constructing HEP vectors and analyzing HEP data using Vector - PyHEP 2022 (virtual) 🎥
- 20th July 2022 - Analysis Grand Challenge / HEP Scientific Python Ecosystem - DANCE/CoDaS@Snowmass 2022 computational and data science software training
- 25th April 2022 - Foundation libraries (uproot, awkward, hist, mplhep) - IRIS-HEP AGC Tools 2022 Workshop 🎥
- 3rd November 2021 - Data handling: uproot, awkward & vector - IRIS-HEP AGC Tools 2021 Workshop 🎥
Undoubtedly, there are rough edges, but most of the functionality is there and Vector is ready for user-testing. It can only be improved by your feedback!
Thanks goes to these wonderful people (emoji key):
Jim Pivarski 🚧 💻 📖 |
Henry Schreiner 🚧 💻 📖 |
Eduardo Rodrigues 🚧 💻 📖 |
N!no 📖 |
Peter Fackeldey 📖 |
Luke Kreczko 💻 |
Nicholas Smith 🤔 |
Jonas Eschle 🤔 |
This project follows the all-contributors specification. Contributions of any kind welcome! See CONTRIBUTING.md for information on setting up a development environment.
This library was primarily developed by Jim Pivarski, Henry Schreiner, and Eduardo Rodrigues.
Support for this work was provided by the National Science Foundation cooperative agreement OAC-1836650 (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.