def test_entropy_subadditivity(dist):
"""
H(X1, ...) <= sum(H(X_i))
"""
h = H(dist)
h_sum = sum(H(dist.marginal(rv)) for rv in dist.rvs)
assert h <= h_sum + epsilon
def test_conditional_entropy(dist):
"""
H(X|Y) <= H(X)
"""
ch = H(dist, [0], [1])
h = H(dist, [0])
assert ch <= h + epsilon
def test_entropy_upper_bound(dist):
"""
H(X) <= log(|X|)
"""
h = H(dist)
logX = np.log2(len(dist.outcomes))
assert h <= logX + epsilon
def test_wolf():
"""
Test against value from publication.
"""
d = Wolfs_dice()
entropy = H(d, 'W') / np.log2(np.e)
assert entropy == pytest.approx(1.784990, abs=1e-6)
def test_fanos_inequality(dist):
"""
H(X|Y) <= hb(P_e) + P_e log(|X| - 1)
"""
dist1 = SD.from_distribution(dist.marginal([0]))
dist2 = SD.from_distribution(dist.marginal([1]))
ce = H(dist, [0], [1])
X = len(set().union(dist1.outcomes, dist2.outcomes))
eq_dist = dist1 == dist2
P_e = eq_dist[False] if False in eq_dist else 0
hb = H(SD([P_e, 1 - P_e]))
assert ce <= hb + P_e * np.log2(X - 1) + epsilon
def test_minent_1():
"""
Test minent
"""
d = uniform(['000', '001', '010', '011', '100', '101', '110', '111'])
meo = MinEntOptimizer(d, [[0], [1], [2]])
meo.optimize()
dp = meo.construct_dist()
assert H(dp) == pytest.approx(1)
def test_H2():
""" Test the various entropies of two independent events """
d = D(['00', '01', '10', '11'], [1 / 4] * 4)
assert_almost_equal(H(d), 2)
assert_almost_equal(H(d, [0]), 1)
assert_almost_equal(H(d, [1]), 1)
assert_almost_equal(H(d, [0], [1]), 1)
assert_almost_equal(H(d, [1], [0]), 1)
assert_almost_equal(H(d, [0], [0]), 0)
assert_almost_equal(H(d, [0], [0, 1]), 0)
def test_H2():
""" Test the various entropies of two independent events """
d = D(['00', '01', '10', '11'], [1 / 4] * 4)
assert H(d) == pytest.approx(2)
assert H(d, [0]) == pytest.approx(1)
assert H(d, [1]) == pytest.approx(1)
assert H(d, [0], [1]) == pytest.approx(1)
assert H(d, [1], [0]) == pytest.approx(1)
assert H(d, [0], [0]) == pytest.approx(0)
assert H(d, [0], [0, 1]) == pytest.approx(0)
def test_maxent_3():
"""
Test the RdnUnqXor distribution.
"""
X00, X01, X02, Y01, Y02 = 'rR', 'aA', [0, 1], 'bB', [0, 1]
inputs = product(X00, X01, X02, Y01, Y02)
events = [(x00 + x01 + str(x02), x00 + y01 + str(y02),
x00 + x01 + y01 + str(x02 ^ y02))
for x00, x01, x02, y01, y02 in inputs]
RdnUnqXor = uniform(events)
d = maxent_dist(RdnUnqXor, [[0, 1], [0, 2], [1, 2]])
assert H(d) == pytest.approx(6)
def test_H3():
""" Test the various entropies of two independent events with names """
d = D(['00', '01', '10', '11'], [1 / 4] * 4)
d.set_rv_names('XY')
assert_almost_equal(H(d), 2)
assert_almost_equal(H(d, ['X']), 1)
assert_almost_equal(H(d, ['Y']), 1)
assert_almost_equal(H(d, ['X'], ['Y']), 1)
assert_almost_equal(H(d, ['Y'], ['X']), 1)
assert_almost_equal(H(d, ['X'], ['X']), 0)
assert_almost_equal(H(d, ['X'], ['X', 'Y']), 0)
def test_H3():
""" Test the various entropies of two independent events with names """
d = D(['00', '01', '10', '11'], [1 / 4] * 4)
d.set_rv_names('XY')
assert H(d) == pytest.approx(2)
assert H(d, ['X']) == pytest.approx(1)
assert H(d, ['Y']) == pytest.approx(1)
assert H(d, ['X'], ['Y']) == pytest.approx(1)
assert H(d, ['Y'], ['X']) == pytest.approx(1)
assert H(d, ['X'], ['X']) == pytest.approx(0)
assert H(d, ['X'], ['X', 'Y']) == pytest.approx(0)
def test_coi7():
""" Test that H = I for one variable """
outcomes = "ABC"
pmf = [1 / 3] * 3
d = D(outcomes, pmf)
assert H(d) == pytest.approx(I(d))
def test_H7():
""" Test H for uniform distributions using SDs in various bases """
for i in range(2, 10):
d = uniform(i)
d.set_base(i)
yield assert_almost_equal, H(d), 1
def test_H1():
""" Test H of a fair coin """
d = D(['H', 'T'], [1 / 2, 1 / 2])
assert_almost_equal(H(d), 1)
def test_H1():
""" Test H of a fair coin """
d = D(['H', 'T'], [1 / 2, 1 / 2])
assert H(d) == pytest.approx(1)
def test_H4():
""" Test H for uniform distributions """
for i in range(2, 10):
d = D.from_distribution(uniform(i))
yield assert_almost_equal, H(d), np.log2(i)
def test_H5():
""" Test H for uniform distributions in various bases """
for i in range(2, 10):
d = D.from_distribution(uniform(i))
d.set_base(i)
yield assert_almost_equal, H(d), 1
def test_H6():
""" Test H for uniform distributions using ScalarDistributions """
for i in range(2, 10):
d = uniform(i)
yield assert_almost_equal, H(d), np.log2(i)
def test_H4(i):
""" Test H for uniform distributions """
d = D.from_distribution(uniform(i))
assert H(d) == pytest.approx(np.log2(i))
def test_H6(i):
""" Test H for uniform distributions using ScalarDistributions """
d = uniform(i)
assert H(d) == pytest.approx(np.log2(i))
def test_H5(i):
""" Test H for uniform distributions in various bases """
d = D.from_distribution(uniform(i))
d.set_base(i)
assert H(d) == pytest.approx(1)
def test_giant_bit1(n, k):
"""
tests for the giant bit entropy
"""
d = giant_bit(n, k)
assert H(d) == pytest.approx(np.log2(k))
def test_H7(i):
""" Test H for uniform distributions using SDs in various bases """
d = uniform(i)
d.set_base(i)
assert H(d) == pytest.approx(1)
def test_coi7():
""" Test that H = I for one variable """
outcomes = "ABC"
pmf = [1/3]*3
d = D(outcomes, pmf)
assert_almost_equal(H(d), I(d))