def test_alpha_symmetry(alpha, dists):
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
for dist1, dist2 in product(dists, repeat=2):
assert alpha_divergence(dist1, dist2, alpha) == pytest.approx(
alpha_divergence(dist2, dist1, -alpha))
assert (1. - alpha) * hellinger_divergence(
dist1, dist2, alpha) == pytest.approx(
alpha * hellinger_divergence(dist2, dist1, 1. - alpha))
assert (1. - alpha) * renyi_divergence(
dist1, dist2, alpha) == pytest.approx(
alpha * renyi_divergence(dist2, dist1, 1. - alpha))
def test_alpha_symmetry(alpha, dists):
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
for dist1, dist2 in product(dists, repeat=2):
assert alpha_divergence(dist1, dist2, alpha) == pytest.approx(alpha_divergence(dist2, dist1, -alpha))
assert (1.-alpha)*hellinger_divergence(dist1, dist2, alpha) == pytest.approx(alpha*hellinger_divergence(dist2, dist1, 1.-alpha))
assert (1.-alpha)*renyi_divergence(dist1, dist2, alpha) == pytest.approx(alpha*renyi_divergence(dist2, dist1, 1.-alpha))
def test_alpha_symmetry():
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
alphas = [-1, 0, 0.5, 1, 2]
test_dists = [get_dists_2(), get_dists_3()]
for alpha in alphas:
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha),
alpha_divergence(dist2, dist1, -alpha))
assert_almost_equal(
(1. - alpha) *
hellinger_divergence(dist1, dist2, alpha),
alpha * hellinger_divergence(dist2, dist1, 1. - alpha))
assert_almost_equal(
(1. - alpha) * renyi_divergence(dist1, dist2, alpha),
alpha * renyi_divergence(dist2, dist1, 1. - alpha))
def test_alpha_symmetry():
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar symmetry for the Hellinger divergence.
"""
alphas = [-1, 0, 0.5, 1, 2]
test_dists = [get_dists_2(), get_dists_3()]
for alpha in alphas:
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha), alpha_divergence(dist2, dist1, -alpha))
assert_almost_equal((1.-alpha)*hellinger_divergence(dist1, dist2, alpha), alpha*hellinger_divergence(dist2, dist1, 1.-alpha))