dists = distribution_structures(size=3, alphabet=2, uniform=False)
example = find(dists, predicate)
assert coinformation(example) <= -1 / 2
@pytest.mark.flaky(reruns=5)
def test_distribution_structures6():
"""
A test for the distribution_structures strategy.
"""
dists = distribution_structures(size=3, alphabet=2, uniform=True)
example = find(dists, predicate)
assert coinformation(example) <= -1 / 2
@given(dist=markov_chains(alphabets=3))
def test_markov_chains1(dist):
"""
Test the markov_chains strategy.
"""
assert coinformation(dist, [[0], [2]], [1]) == pytest.approx(0.0, abs=1e-7)
@given(dist=markov_chains(alphabets=(2, 2, 2)))
def test_markov_chains2(dist):
"""
Test the markov_chains strategy.
"""
assert coinformation(dist, [[0], [2]], [1]) == pytest.approx(0.0, abs=1e-7)
@given(dist=distributions(alphabets=((2, 4), ) * 4))
def test_zhang_yeung_inequality(dist):
"""
2I(C:D) <= I(A:B)+I(A:CD)+3I(C:D|A)+I(C:D|B)
"""
I_a_b = I(dist, [[0], [1]])
I_c_d = I(dist, [[2], [3]])
I_a_cd = I(dist, [[0], [2, 3]])
I_c_d_g_a = I(dist, [[2], [3]], [0])
I_c_d_g_b = I(dist, [[2], [3]], [1])
assert 2 * I_c_d <= I_a_b + I_a_cd + 3 * I_c_d_g_a + I_c_d_g_b + epsilon
@given(dist=markov_chains(alphabets=((2, 4), ) * 3))
def test_data_processing_inequality(dist):
"""
given X - Y - Z:
I(X:Z) <= I(X:Y)
"""
i_xy = I(dist, [[0], [1]])
i_xz = I(dist, [[0], [2]])
assert i_xz <= i_xy + epsilon
@given(dist=markov_chains(alphabets=((2, 4), ) * 3))
def test_data_processing_inequality_mc(dist):
"""
given X - Y - Z:
rho(X:Z) <= rho(X:Y)
@given(dist=distributions(alphabets=((2, 4),)*4))
def test_zhang_yeung_inequality(dist):
"""
2I(C:D) <= I(A:B)+I(A:CD)+3I(C:D|A)+I(C:D|B)
"""
I_a_b = I(dist, [[0], [1]])
I_c_d = I(dist, [[2], [3]])
I_a_cd = I(dist, [[0], [2, 3]])
I_c_d_g_a = I(dist, [[2], [3]], [0])
I_c_d_g_b = I(dist, [[2], [3]], [1])
assert 2*I_c_d <= I_a_b + I_a_cd + 3*I_c_d_g_a + I_c_d_g_b + epsilon
@given(dist=markov_chains(alphabets=((2, 4),)*3))
def test_data_processing_inequality(dist):
"""
given X - Y - Z:
I(X:Z) <= I(X:Y)
"""
i_xy = I(dist, [[0], [1]])
i_xz = I(dist, [[0], [2]])
assert i_xz <= i_xy + epsilon
@given(dist=markov_chains(alphabets=((2, 4),)*3))
def test_data_processing_inequality_mc(dist):
"""
given X - Y - Z:
rho(X:Z) <= rho(X:Y)
def test_markov_chains1():
"""
Test the markov_chains strategy.
"""
dist = markov_chains(alphabets=3).example()
assert coinformation(dist, [[0], [2]], [1]) == pytest.approx(0.0, abs=1e-7)
def test_markov_chains1():
"""
Test the markov_chains strategy.
"""
dist = markov_chains(alphabets=3).example()
assert coinformation(dist, [[0], [2]], [1]) == pytest.approx(0.0, abs=1e-7)
