def test_renyi_values():
"""
Test specific values of the Renyi divergence.
"""
d1 = Distribution(['0', '1'], [0, 1])
d2 = Distribution(['0', '1'], [1/2, 1/2])
d3 = Distribution(['0', '1'], [1, 0])
assert_almost_equal(renyi_divergence(d1, d2, 1/2), np.log2(2))
assert_almost_equal(renyi_divergence(d2, d3, 1/2), np.log2(2))
assert_almost_equal(renyi_divergence(d1, d3, 1/2), np.inf)
def test_renyi_values():
"""
Test specific values of the Renyi divergence.
"""
d1 = Distribution(['0', '1'], [0, 1])
d2 = Distribution(['0', '1'], [1/2, 1/2])
d3 = Distribution(['0', '1'], [1, 0])
assert renyi_divergence(d1, d2, 1/2) == pytest.approx(np.log2(2))
assert renyi_divergence(d2, d3, 1/2) == pytest.approx(np.log2(2))
assert renyi_divergence(d1, d3, 1/2) == pytest.approx(np.inf)
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_renyi(alpha):
"""
Consistency test for Renyi entropy and Renyi divergence
"""
dist1 = Distribution(['0', '1', '2'], [1/4, 1/2, 1/4])
uniform = Distribution(['0', '1', '2'], [1/3, 1/3, 1/3])
h = renyi_entropy(dist1, alpha)
h_u = renyi_entropy(uniform, alpha)
div = renyi_divergence(dist1, uniform, alpha)
assert h == pytest.approx(h_u - div)
def test_renyi(alpha):
"""
Consistency test for Renyi entropy and Renyi divergence
"""
dist1 = Distribution(['0', '1', '2'], [1/4, 1/2, 1/4])
uniform = Distribution(['0', '1', '2'], [1/3, 1/3, 1/3])
h = renyi_entropy(dist1, alpha)
h_u = renyi_entropy(uniform, alpha)
div = renyi_divergence(dist1, uniform, alpha)
assert h == pytest.approx(h_u - div)
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_renyi():
"""
Consistency test for Renyi entropy and Renyi divergence
"""
dist1 = Distribution(['0', '1', '2'], [1/4, 1/2, 1/4])
uniform = Distribution(['0', '1', '2'], [1/3, 1/3, 1/3])
alphas = [0, 1, 2, 0.5]
for alpha in alphas:
h = renyi_entropy(dist1, alpha)
h_u = renyi_entropy(uniform, alpha)
div = renyi_divergence(dist1, uniform, alpha)
assert_almost_equal(h, h_u - div)
def test_renyi():
"""
Consistency test for Renyi entropy and Renyi divergence
"""
dist1 = Distribution(['0', '1', '2'], [1 / 4, 1 / 2, 1 / 4])
uniform = Distribution(['0', '1', '2'], [1 / 3, 1 / 3, 1 / 3])
alphas = [0, 1, 2, 0.5]
for alpha in alphas:
h = renyi_entropy(dist1, alpha)
h_u = renyi_entropy(uniform, alpha)
div = renyi_divergence(dist1, uniform, alpha)
assert_almost_equal(h, h_u - div)
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, dist2 in product(dists, repeat=2):
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))
