def test_data_processing_inequality_gk(dist):
"""
given X - Y - Z:
K(X:Z) <= K(X:Y)
"""
k_xy = K(dist, [[0], [1]])
k_xz = K(dist, [[0], [2]])
assert k_xz <= k_xy + epsilon
def test_K4():
""" Test K in a canonical example """
outcomes = ['00', '01', '10', '11', '22', '33']
pmf = [1 / 8, 1 / 8, 1 / 8, 1 / 8, 1 / 4, 1 / 4]
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.5)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1 / 3] * 3
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(0.0)
assert K(d, [[0], [1]]) == pytest.approx(0.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(0.0)
def test_K1():
""" Test K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2] * 2
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1]]) == pytest.approx(1.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.0)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1 / 3, 1 / 3, 1 / 3]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 0.0)
assert_almost_equal(K(d, [[0], [1]]), 0.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']]), 0.0)
def test_K1():
""" Test K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2, 1 / 2]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 1.0)
assert_almost_equal(K(d, [[0], [1]]), 1.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']]), 1.0)
def test_K2():
""" Test conditional K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2, 1 / 2]
d = Distribution(outcomes, pmf)
assert K(d, [[0], [1]], [0]) == pytest.approx(0.0)
assert K(d, [[0], [1]], [1]) == pytest.approx(0.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']], ['X']) == pytest.approx(0.0)
assert K(d, [['X'], ['Y']], ['Y']) == pytest.approx(0.0)
def test_K5():
""" Test K on subvariables and conditionals """
outcomes = ['000', '010', '100', '110', '221', '331']
pmf = [1 / 8, 1 / 8, 1 / 8, 1 / 8, 1 / 4, 1 / 4]
d = Distribution(outcomes, pmf)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1], [2]]) == pytest.approx(1.0)
d.set_rv_names("XYZ")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
assert K(d, [['X'], ['Y'], ['Z']]) == pytest.approx(1.0)
assert K(d, ['X', 'Y'], ['Z']) == pytest.approx(0.5)
assert K(d, ['XY', 'YZ']) == pytest.approx(2.0)
def test_cis2(dist):
"""
Test that the common informations are ordered correctly.
"""
k = K(dist)
j = J(dist)
b = B(dist)
c = C(dist)
g = G(dist)
f = F(dist)
m = M(dist)
assert k <= j + epsilon
assert j <= b + epsilon
assert b <= c + epsilon
assert c <= g + epsilon
assert g <= f + epsilon
assert f <= m + epsilon