def test_sqrt_beta_analytical(n, m, rng, allclose):
"""Tests pdf, cdf, and ppf of SqrtBeta distribution."""
pytest.importorskip("scipy") # beta and betainc
dt = 0.001
x = np.arange(dt, 1 + dt, dt)
dist = SqrtBeta(n, m)
pdf = dist.pdf(x)
cdf = dist.cdf(x)
ppf = dist.ppf(cdf)
# The pdf should reflect the samples
num_samples = 2500
num_bins = 5
samples = dist.sample(num_samples, rng=rng)
act_hist, _ = np.histogram(samples, bins=num_bins)
bin_points = np.linspace(0, 1, num_bins + 1)
bin_cdf = dist.cdf(bin_points)
exp_freq = bin_cdf[1:] - bin_cdf[:-1]
assert np.all(np.abs(np.asfarray(act_hist) / num_samples - exp_freq) < 0.1)
# The cdf should be the accumulated pdf
assert allclose(cdf, np.cumsum(pdf) * dt, atol=0.01)
# The ppf should give back x
assert allclose(x, ppf, atol=0.01)
def test_sqrt_beta(n, m, rng):
num_samples = 1000
num_bins = 5
vectors = rng.randn(num_samples, n + m)
vectors /= npext.norm(vectors, axis=1, keepdims=True)
expectation, _ = np.histogram(npext.norm(vectors[:, :m], axis=1), bins=num_bins)
dist = SqrtBeta(n, m)
samples = dist.sample(num_samples, 1, rng=rng)
histogram, _ = np.histogram(samples, bins=num_bins)
assert np.all(np.abs(np.asfarray(histogram - expectation) / num_samples) < 0.16)
