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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, rho, phi, theta = sympy.symbols("x y rho phi theta", real=True, positive=True)
values = {x: 3, y: 4, rho: 5, phi: 0, theta: 0.4636476090008061}
def test_xy_z():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(x, y),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(
sympy.sqrt(x**2 + y**2) / sympy.tan(theta)
),
)
assert vec.theta.simplify() == sympy.acos(
sympy.Abs(sympy.cos(theta) * sympy.tan(theta)) / sympy.tan(theta)
)
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
def test_xy_theta():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(x, y),
longitudinal=vector.backends.sympy.LongitudinalSympyTheta(theta),
)
assert vec.theta == theta
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
def test_xy_eta():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyXY(x, y),
longitudinal=vector.backends.sympy.LongitudinalSympyEta(
-sympy.log(sympy.tan(0.5 * theta))
),
)
assert vec.theta.simplify() == 2.0 * sympy.atan(sympy.tan(0.5 * theta))
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
def test_rhophi_z():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
longitudinal=vector.backends.sympy.LongitudinalSympyZ(rho / sympy.tan(theta)),
)
assert vec.theta.simplify() == sympy.acos(
sympy.Abs(sympy.cos(theta) * sympy.tan(theta)) / sympy.tan(theta)
)
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
def test_rhophi_theta():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
longitudinal=vector.backends.sympy.LongitudinalSympyTheta(theta),
)
assert vec.theta == theta
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
def test_rhophi_eta():
vec = vector.VectorSympy3D(
azimuthal=vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
longitudinal=vector.backends.sympy.LongitudinalSympyEta(
-sympy.log(sympy.tan(0.5 * theta))
),
)
assert vec.theta.simplify() == 2.0 * sympy.atan(sympy.tan(0.5 * theta))
assert vec.theta.subs(values).evalf() == pytest.approx(0.4636476090008061)
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