# Copyright (c) 2019, 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, z, t = sympy.symbols("x y rho phi z t", real=True, positive=True)
values = {x: 3, y: 4, rho: 5, phi: 0, z: 10, t: 20}


def test_xy_z_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyZ(z),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity == 0.5 * sympy.log((t + z) / (t - z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_xy_z_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyZ(z),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
        ),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log(
        (-z - sympy.sqrt(x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)))
        / (z - sympy.sqrt(x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)))
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_xy_theta_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyTheta(
            sympy.acos(z / sympy.sqrt(x**2 + y**2 + z**2))
        ),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log((t + z) / (t - z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_xy_theta_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyTheta(
            sympy.acos(z / sympy.sqrt(x**2 + y**2 + z**2))
        ),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
        ),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log(
        (-z - sympy.sqrt(x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)))
        / (z - sympy.sqrt(x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)))
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_xy_eta_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyEta(
            sympy.asinh(z / sympy.sqrt(x**2 + y**2))
        ),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log((t + z) / (t - z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_xy_eta_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyXY(x, y),
        vector.backends.sympy.LongitudinalSympyEta(
            sympy.asinh(z / sympy.sqrt(x**2 + y**2))
        ),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
        ),
    )
    # TODO: why won't sympy equate the expressions without double
    # simplifying?
    assert (
        sympy.simplify(
            vec.rapidity.simplify()
            - 0.5
            * sympy.log(
                (
                    -z
                    - sympy.sqrt(
                        (
                            0.25
                            * (x**2 + y**2)
                            * (
                                sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                                + 1
                            )
                            ** 2
                            + sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                            * sympy.Abs(-(t**2) + x**2 + y**2 + z**2)
                        )
                        * sympy.exp(-2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                    )
                )
                / (
                    z
                    - sympy.sqrt(
                        (
                            0.25
                            * (x**2 + y**2)
                            * (
                                sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                                + 1
                            )
                            ** 2
                            + sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                            * sympy.Abs(-(t**2) + x**2 + y**2 + z**2)
                        )
                        * sympy.exp(-2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
                    )
                )
            )
        )
        == 0
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_z_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyZ(z),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log((t + z) / (t - z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_z_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyZ(z),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
        ),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log(
        (-z - sympy.sqrt(rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)))
        / (z - sympy.sqrt(rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)))
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_theta_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyTheta(
            sympy.acos(z / sympy.sqrt(rho**2 + z**2))
        ),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log((-t - z) / (-t + z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_theta_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyTheta(
            sympy.acos(z / sympy.sqrt(rho**2 + z**2))
        ),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
        ),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log(
        (-z - sympy.sqrt(rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)))
        / (z - sympy.sqrt(rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)))
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_eta_t():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyEta(sympy.asinh(z / rho)),
        vector.backends.sympy.TemporalSympyT(t),
    )
    assert vec.rapidity.simplify() == 0.5 * sympy.log((t + z) / (t - z))
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)


def test_rhophi_eta_tau():
    vec = vector.VectorSympy4D(
        vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
        vector.backends.sympy.LongitudinalSympyEta(sympy.asinh(z / rho)),
        vector.backends.sympy.TemporalSympyTau(
            sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
        ),
    )
    assert vec.rapidity == 0.5 * sympy.log(
        (
            z
            + sympy.sqrt(
                rho**2
                * (0.5 + 0.5 * sympy.exp(-2 * sympy.asinh(z / rho))) ** 2
                * sympy.exp(2 * sympy.asinh(z / rho))
                + sympy.Abs(rho**2 - t**2 + z**2)
            )
        )
        / (
            -z
            + sympy.sqrt(
                rho**2
                * (0.5 + 0.5 * sympy.exp(-2 * sympy.asinh(z / rho))) ** 2
                * sympy.exp(2 * sympy.asinh(z / rho))
                + sympy.Abs(rho**2 - t**2 + z**2)
            )
        )
    )
    assert vec.rapidity.subs(values).evalf() == pytest.approx(0.5493061443340549)
