# sambal --- Sample balls, spheres, spherical caps
# Copyright © 2021 Arun I <arunisaac@systemreboot.net>
# Copyright © 2021 Murugesan Venkatapathi <murugesh@iisc.ac.in>
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see
# <https://www.gnu.org/licenses/>.

import pytest
from numpy import arccos, dot, ones, pi, sin, where
from numpy.linalg import norm
from numpy.random import default_rng
from scipy.special import betainc
from scipy.stats import kstest
from sambal import random_on_cap

# Set seed of random number generator.
rng = default_rng(0)

def planar_angle2solid_angle_fraction(planar_angle, dim):
    """Return the solid angle fraction for a given planar angle."""
    alpha = (dim - 1) / 2
    beta = 1/2
    return where(planar_angle < pi/2,
                 0.5*betainc(alpha, beta, sin(planar_angle)**2),
                 1 - 0.5*betainc(alpha, beta, sin(planar_angle)**2))

def make_uniform_cdf(maximum_planar_angle, dim):
    """Return the CDF of theta uniformly distributed on the spherical
cap.

    """
    def cdf(theta):
        return where(theta > maximum_planar_angle, 1,
                     planar_angle2solid_angle_fraction(theta, dim)
                     / planar_angle2solid_angle_fraction(maximum_planar_angle, dim))
    return cdf

dimensions = [10, 100, 1000, 5000]
testdata = [*[(dim, 0.35*pi) for dim in dimensions],
            *[(dim, 0.65*pi) for dim in dimensions]]

@pytest.mark.parametrize("dim,maximum_planar_angle", testdata)
def test_random_on_cap(dim, maximum_planar_angle):
    axis = ones(dim)
    axis = axis / norm(axis)
    thetas = [arccos(dot(random_on_cap(axis, maximum_planar_angle, rng), axis))
              for i in range(1000)]
    assert kstest(thetas, make_uniform_cdf(maximum_planar_angle, dim)).statistic < 0.05