from scipy.stats import betabinom, hypergeom, bernoulli, boltzmann
import numpy as np
from numpy.testing import assert_almost_equal, assert_equal, assert_allclose


def test_hypergeom_logpmf():
    # symmetries test
    # f(k,N,K,n) = f(n-k,N,N-K,n) = f(K-k,N,K,N-n) = f(k,N,n,K)
    k = 5
    N = 50
    K = 10
    n = 5
    logpmf1 = hypergeom.logpmf(k, N, K, n)
    logpmf2 = hypergeom.logpmf(n - k, N, N - K, n)
    logpmf3 = hypergeom.logpmf(K - k, N, K, N - n)
    logpmf4 = hypergeom.logpmf(k, N, n, K)
    assert_almost_equal(logpmf1, logpmf2, decimal=12)
    assert_almost_equal(logpmf1, logpmf3, decimal=12)
    assert_almost_equal(logpmf1, logpmf4, decimal=12)

    # test related distribution
    # Bernoulli distribution if n = 1
    k = 1
    N = 10
    K = 7
    n = 1
    hypergeom_logpmf = hypergeom.logpmf(k, N, K, n)
    bernoulli_logpmf = bernoulli.logpmf(k, K/N)
    assert_almost_equal(hypergeom_logpmf, bernoulli_logpmf, decimal=12)


def test_boltzmann_upper_bound():
    k = np.arange(-3, 5)

    N = 1
    p = boltzmann.pmf(k, 0.123, N)
    expected = k == 0
    assert_equal(p, expected)

    lam = np.log(2)
    N = 3
    p = boltzmann.pmf(k, lam, N)
    expected = [0, 0, 0, 4/7, 2/7, 1/7, 0, 0]
    assert_allclose(p, expected, rtol=1e-13)

    c = boltzmann.cdf(k, lam, N)
    expected = [0, 0, 0, 4/7, 6/7, 1, 1, 1]
    assert_allclose(c, expected, rtol=1e-13)


def test_betabinom_a_and_b_unity():
    # test limiting case that betabinom(n, 1, 1) is a discrete uniform
    # distribution from 0 to n
    n = 20
    k = np.arange(n + 1)
    p = betabinom(n, 1, 1).pmf(k)
    expected = np.repeat(1 / (n + 1), n + 1)
    assert_almost_equal(p, expected)


def test_betabinom_bernoulli():
    # test limiting case that betabinom(1, a, b) = bernoulli(a / (a + b))
    a = 2.3
    b = 0.63
    k = np.arange(2)
    p = betabinom(1, a, b).pmf(k)
    expected = bernoulli(a / (a + b)).pmf(k)
    assert_almost_equal(p, expected)
