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# Copyright (c) 2019-2025, Saransh Chopra, Henry Schreiner, Eduardo Rodrigues, Jonas Eschle, and Jim Pivarski.
#
# Distributed under the 3-clause BSD license, see accompanying file LICENSE
# or https://github.com/scikit-hep/vector for details.
from __future__ import annotations
import pytest
import vector
sympy = pytest.importorskip("sympy")
pytestmark = pytest.mark.sympy
x, y = sympy.symbols("x y")
rho, phi = sympy.symbols("rho phi")
z, eta, theta = sympy.symbols("z eta theta")
t, tau = sympy.symbols("t tau")
px, py = sympy.symbols("px py")
pt = sympy.symbols("pt")
pz = sympy.symbols("pz")
M, m, mass, E, e, energy = sympy.symbols("M m mass E e energy")
def test_construction():
# generic
# 2D coords
for vec_cls in (vector.VectorSympy2D, vector.VectorSympy3D, vector.VectorSympy4D):
coords = {"x": x, "y": y}
if vec_cls in (vector.VectorSympy3D, vector.VectorSympy4D):
coords["z"] = z
if vec_cls == vector.VectorSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.x == x
assert vec.y == y
assert vec.phi == sympy.atan2(y, x)
assert vec.rho == sympy.sqrt(x**2 + y**2)
assert isinstance(vec.azimuthal, vector.backends.sympy.AzimuthalSympyXY)
assert vec.azimuthal.elements == (x, y)
coords = {"rho": rho, "phi": phi}
if vec_cls in (vector.VectorSympy3D, vector.VectorSympy4D):
coords["z"] = z
if vec_cls == vector.VectorSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.x == rho * sympy.cos(phi)
assert vec.y == rho * sympy.sin(phi)
assert vec.phi == phi
assert vec.rho == rho
assert isinstance(vec.azimuthal, vector.backends.sympy.AzimuthalSympyRhoPhi)
assert vec.azimuthal.elements == (rho, phi)
# 3D coords
for vec_cls in (vector.VectorSympy3D, vector.VectorSympy4D):
coords = {"x": x, "y": y, "z": z}
if vec_cls == vector.VectorSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.z == z
assert vec.eta == sympy.asinh(z / sympy.sqrt(x**2 + y**2))
assert vec.theta == sympy.acos(z / sympy.sqrt(x**2 + y**2 + z**2))
assert isinstance(vec.longitudinal, vector.backends.sympy.LongitudinalSympyZ)
assert vec.longitudinal.elements == (z,)
coords = {"x": x, "y": y, "eta": eta}
if vec_cls == vector.VectorSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.z == sympy.sqrt(x**2 + y**2) * sympy.sinh(eta)
assert vec.eta == eta
assert vec.theta == 2.0 * sympy.atan(sympy.exp(-eta))
assert isinstance(vec.longitudinal, vector.backends.sympy.LongitudinalSympyEta)
assert vec.longitudinal.elements == (eta,)
coords = {"x": x, "y": y, "theta": theta}
if vec_cls == vector.VectorSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.z == sympy.sqrt(x**2 + y**2) / sympy.tan(theta)
assert vec.eta == -sympy.log(sympy.tan(0.5 * theta))
assert vec.theta == theta
assert isinstance(
vec.longitudinal, vector.backends.sympy.LongitudinalSympyTheta
)
assert vec.longitudinal.elements == (theta,)
# 4D coords
for vec_cls in (vector.VectorSympy4D,):
coords = {"x": x, "y": y, "z": z, "t": t}
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.t == t
assert vec.tau == sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
assert isinstance(vec.temporal, vector.backends.sympy.TemporalSympyT)
assert vec.temporal.elements == (t,)
coords = {"x": x, "y": y, "z": z, "tau": tau}
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.t == sympy.sqrt(tau**2 + x**2 + y**2 + z**2)
assert vec.tau == tau
assert isinstance(vec.temporal, vector.backends.sympy.TemporalSympyTau)
assert vec.temporal.elements == (tau,)
# momentum
# 2D coords
for vec_cls in (
vector.MomentumSympy2D,
vector.MomentumSympy3D,
vector.MomentumSympy4D,
):
coords = {"px": px, "py": py}
if vec_cls in (vector.MomentumSympy3D, vector.MomentumSympy4D):
coords["z"] = z
if vec_cls == vector.MomentumSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.px == px
assert vec.py == py
assert vec.phi == sympy.atan2(py, px)
assert vec.rho == sympy.sqrt(px**2 + py**2)
assert vec.pt == sympy.sqrt(px**2 + py**2)
assert isinstance(vec.azimuthal, vector.backends.sympy.AzimuthalSympyXY)
assert vec.azimuthal.elements == (px, py)
coords = {"pt": pt, "phi": phi}
if vec_cls in (vector.MomentumSympy3D, vector.MomentumSympy4D):
coords["z"] = z
if vec_cls == vector.MomentumSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.px == pt * sympy.cos(phi)
assert vec.py == pt * sympy.sin(phi)
assert vec.phi == phi
assert vec.rho == pt
assert vec.pt == pt
assert isinstance(vec.azimuthal, vector.backends.sympy.AzimuthalSympyRhoPhi)
assert vec.azimuthal.elements == (pt, phi)
# 3D coords
for vec_cls in (vector.MomentumSympy3D, vector.MomentumSympy4D):
coords = {"px": px, "py": py, "pz": pz}
if vec_cls == vector.MomentumSympy4D:
coords["t"] = t
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.pz == pz
assert vec.eta == sympy.asinh(pz / sympy.sqrt(px**2 + py**2))
assert vec.theta == sympy.acos(pz / sympy.sqrt(px**2 + py**2 + pz**2))
assert isinstance(vec.longitudinal, vector.backends.sympy.LongitudinalSympyZ)
assert vec.longitudinal.elements == (pz,)
# 4D coords
for vec_cls in (vector.MomentumSympy4D,):
coords = {"px": px, "py": py, "pz": pz, "E": E}
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.m == sympy.sqrt(sympy.Abs(px**2 + py**2 + pz**2 - E**2))
assert sympy.sqrt(sympy.Abs(px**2 + py**2 + pz**2 - E**2)) == vec.M
assert vec.mass == sympy.sqrt(sympy.Abs(px**2 + py**2 + pz**2 - E**2))
assert vec.e == E
assert vec.E == E
assert vec.energy == E
assert isinstance(vec.temporal, vector.backends.sympy.TemporalSympyT)
assert vec.temporal.elements == (E,)
coords = {"px": px, "py": py, "pz": pz, "M": M}
vec = vec_cls(**coords)
with pytest.raises(TypeError):
vec = vec_cls(bad=1, **coords)
assert vec.m == M
assert vec.M == M
assert vec.mass == M
assert vec.e == sympy.sqrt(M**2 + px**2 + py**2 + pz**2)
assert sympy.sqrt(M**2 + px**2 + py**2 + pz**2) == vec.E
assert vec.energy == sympy.sqrt(M**2 + px**2 + py**2 + pz**2)
assert isinstance(vec.temporal, vector.backends.sympy.TemporalSympyTau)
assert vec.temporal.elements == (M,)
def test_type_checks():
with pytest.raises(TypeError):
vector.VectorSympy2D(x=1, y=2)
with pytest.raises(TypeError):
vector.VectorSympy2D()
with pytest.raises(TypeError):
vector.VectorSympy3D(x=1, y=2, z=3)
with pytest.raises(TypeError):
vector.VectorSympy3D()
with pytest.raises(TypeError):
vector.VectorSympy4D(x=1, y=2, z=3, t=4)
with pytest.raises(TypeError):
vector.VectorSympy4D()
nx, ny, nz = sympy.symbols("nx ny nz")
def test_eq():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 == v1 # noqa: PLR0124
assert not v1 == v2 # noqa: SIM201
with pytest.raises(TypeError):
v1.equal(v2.to_Vector3D())
def test_ne():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert not v1 != v1 # noqa: PLR0124,SIM202
assert v1 != v2
with pytest.raises(TypeError):
v1.not_equal(v2.to_Vector3D())
def test_abs():
v1 = vector.VectorSympy2D(x=x, y=y)
assert abs(v1) == sympy.sqrt(x**2 + y**2)
v2 = vector.VectorSympy3D(x=x, y=y, z=z)
assert abs(v2) == sympy.sqrt(x**2 + y**2 + z**2)
v3 = vector.VectorSympy4D(x=x, y=y, z=z, t=t)
assert abs(v3) == sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
def test_add():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 + v2 == vector.VectorSympy2D(x=x + nx, y=y + ny)
assert v1 + v2.to_Vector3D().like(v1) == vector.VectorSympy2D(x=x + nx, y=y + ny)
v1 += v2
assert v1 == vector.VectorSympy2D(x=x + nx, y=y + ny)
with pytest.raises(TypeError):
v1 + 5
with pytest.raises(TypeError):
5 + v1
with pytest.raises(TypeError):
v1 + v2.to_Vector3D()
def test_sub():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 - v2 == vector.VectorSympy2D(x=x - nx, y=y - ny)
v1 -= v2
assert v1 == vector.VectorSympy2D(x=x - nx, y=y - ny)
with pytest.raises(TypeError):
v1 - 5
with pytest.raises(TypeError):
5 - v1
with pytest.raises(TypeError):
v1 - v2.to_Vector3D()
def test_mul():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 * 10 == vector.VectorSympy2D(x=x * 10, y=y * 10)
assert 10 * v1 == vector.VectorSympy2D(x=10 * x, y=10 * y)
v1 *= 10
assert v1 == vector.VectorSympy2D(x=10 * x, y=10 * y)
with pytest.raises(TypeError):
v1 * v2
def test_neg():
v1 = vector.VectorSympy2D(x=x, y=y)
assert -v1 == vector.VectorSympy2D(x=-x, y=-y)
def test_pos():
v1 = vector.VectorSympy2D(x=x, y=y)
assert +v1 == vector.VectorSympy2D(x=x, y=y)
def test_truediv():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 / 10 == vector.VectorSympy2D(x=0.1 * x, y=0.1 * y)
v1 /= 10
assert v1 == vector.VectorSympy2D(x=0.1 * x, y=0.1 * y)
with pytest.raises(TypeError):
10 / v1
with pytest.raises(TypeError):
v1 / v2
def test_pow():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1**2 == x**2 + y**2
with pytest.raises(TypeError):
2**v1
with pytest.raises(TypeError):
v1**v2
def test_matmul():
v1 = vector.VectorSympy2D(x=x, y=y)
v2 = vector.VectorSympy2D(x=nx, y=ny)
assert v1 @ v2 == x * nx + y * ny
assert v2 @ v1 == x * nx + y * ny
with pytest.raises(TypeError):
v1 @ 5
def test_reprs():
assert (
vector.backends.sympy.AzimuthalSympyXY(x, y).__repr__()
== "AzimuthalSympyXY(x=x, y=y)"
)
assert (
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi).__repr__()
== "AzimuthalSympyRhoPhi(rho=rho, phi=phi)"
)
assert (
vector.backends.sympy.LongitudinalSympyZ(z).__repr__()
== "LongitudinalSympyZ(z=z)"
)
assert (
vector.backends.sympy.LongitudinalSympyEta(eta).__repr__()
== "LongitudinalSympyEta(eta=eta)"
)
assert (
vector.backends.sympy.LongitudinalSympyTheta(theta).__repr__()
== "LongitudinalSympyTheta(theta=theta)"
)
assert vector.backends.sympy.TemporalSympyT(t).__repr__() == "TemporalSympyT(t=t)"
assert (
vector.backends.sympy.TemporalSympyTau(tau).__repr__()
== "TemporalSympyTau(tau=tau)"
)
assert vector.VectorSympy2D(x=x, y=y).__repr__() == "VectorSympy2D(x=x, y=y)"
assert (
vector.VectorSympy3D(x=x, y=y, z=z).__repr__() == "VectorSympy3D(x=x, y=y, z=z)"
)
assert (
vector.VectorSympy4D(x=x, y=y, z=z, t=t).__repr__()
== "VectorSympy4D(x=x, y=y, z=z, t=t)"
)
assert (
vector.MomentumSympy2D(px=px, py=py).__repr__()
== "MomentumSympy2D(px=px, py=py)"
)
assert (
vector.MomentumSympy3D(px=px, py=py, pz=pz).__repr__()
== "MomentumSympy3D(px=px, py=py, pz=pz)"
)
assert (
vector.MomentumSympy4D(px=px, py=py, pz=pz, M=M).__repr__()
== "MomentumSympy4D(px=px, py=py, pz=pz, mass=M)"
)
def test_setters():
v = vector.VectorSympy2D(x=x, y=y)
v.x = 2 * x
assert v.x == 2 * x
v.y = 2 * y
assert v.y == 2 * y
v.rho = 2 * rho
assert v.rho == 2 * rho
v.phi = 2 * phi
assert v.phi == 2 * phi
v = vector.MomentumSympy2D(px=px, py=py)
v.px = 2 * px
assert v.px == 2 * px
v.py = 2 * py
assert v.py == 2 * py
v.pt = 2 * pt
assert v.pt == 2 * pt
v = vector.VectorSympy3D(x=x, y=y, z=z)
v.x = 2 * x
assert v.x == 2 * x
v.y = 2 * y
assert v.y == 2 * y
v.z = 2 * z
assert v.z == 2 * z
v.eta = 2 * eta
assert v.eta == 2 * eta
v.theta = 2 * theta
assert v.theta == 2 * theta
v = vector.MomentumSympy3D(px=px, py=py, pz=pz)
v.px = 2 * px
assert v.px == 2 * px
v.py = 2 * py
assert v.py == 2 * py
v.pt = 2 * pt
assert v.pt == 2 * pt
v.pz = 2 * pz
assert v.pz == 2 * pz
v = vector.VectorSympy4D(x=x, y=y, z=z, t=t)
v.x = 2 * x
assert v.x == 2 * x
v.y = 2 * y
assert v.y == 2 * y
v.z = 2 * z
assert v.z == 2 * z
v.eta = 2 * eta
assert v.eta == 2 * eta
v.theta = 2 * theta
assert v.theta == 2 * theta
v.t = 2 * t
assert v.t == 2 * t
v.tau = 2 * tau
assert v.tau == 2 * tau
v = vector.MomentumSympy4D(px=px, py=py, pz=pz, m=M)
v.px = 2 * px
assert v.px == 2 * px
v.py = 2 * py
assert v.py == 2 * py
v.pt = 2 * pt
assert v.pt == 2 * pt
v.pz = 2 * pz
assert v.pz == 2 * pz
v.m = 2 * m
assert v.m == 2 * m
v.mass = 2 * mass
assert v.mass == 2 * mass
v.M = 2 * M
assert v.M == 2 * M
v.e = 2 * e
assert v.e == 2 * e
v.energy = 2 * energy
assert v.energy == 2 * energy
v.E = 2 * E
assert v.E == 2 * E
|
