def test_BR1():
""" Test that B + R = H """
d = D(['000', '001', '010', '100', '111'], [1 / 5] * 5)
assert B(d) + R(d) == pytest.approx(H(d))
def test_B1():
""" Test B for two dependent variables """
d = D(['00', '11'], [1/2, 1/2])
assert B(d) == pytest.approx(1)
def test_B3():
""" Test B for four dependent variables """
d = D(['0000', '1111'], [1/2, 1/2])
assert B(d) == pytest.approx(1)
assert B(d, [[0], [1, 2]], [3]) == pytest.approx(0)
def test_BR1():
""" Test that B + R = H """
d = D(['000', '001', '010', '100', '111'], [1 / 5] * 5)
assert_almost_equal(B(d) + R(d), H(d))
def test_p4():
""" Test some simple base cases using D with varying bases """
for i in range(2, 10):
d = D([str(_) for _ in range(i)], [1 / i] * i)
d.set_base(i)
yield assert_almost_equal, P(d), i
def test_R1():
""" Test R for dependent variables """
d = D(['00', '11'], [1 / 2, 1 / 2])
assert_almost_equal(R(d), 0)
def test_R3():
""" Test R for a generic distribution """
d = D(['000', '011', '101', '110'], [1 / 4] * 4)
assert_almost_equal(R(d), 0)
assert_almost_equal(R(d, [[0, 1], [2]]), 1)
def conditional_uniform2():
events = [(a - 2, b - 2) for a, b, in product(range(5), range(5))
if a <= b]
probs = [1 / (3 - a) / 5 for a, _ in events]
d = D(events, probs)
return d
def test_H1():
""" Test H of a fair coin """
d = D(['H', 'T'], [1 / 2] * 2)
assert H(d) == pytest.approx(1)
def test_tse2(n):
""" Test TSE for giant bit distributions """
d = D(['0' * n, '1' * n], [1 / 2, 1 / 2])
tse = TSE(d)
assert tse == pytest.approx((n - 1) / 2)
def miwin():
d3 = [1, 2, 5, 6, 7, 9]
d4 = [1, 3, 4, 5, 8, 9]
d5 = [2, 3, 4, 6, 7, 8]
d = D(list(product(d3, d4, d5)), [1 / 6**3] * 6**3)
return d
def test_caekl_3():
"""
Test a known value.
"""
d = D(['000', '011', '101', '110'], [1/4]*4)
assert J(d) == pytest.approx(0.5)
def test_mode2():
""" Test mode on a generic distribution """
d = D([(0, 0), (1, 0), (2, 1), (3, 1)], [1 / 8, 1 / 8, 3 / 8, 3 / 8])
modes = [np.array([2, 3]), np.array([1])]
for m1, m2 in zip(mode(d), modes):
assert np.allclose(m1, m2)
def test_median2():
""" Test median on a generic distribution """
d = D([(0, 0), (1, 0), (2, 1), (3, 1)], [1 / 8, 1 / 8, 3 / 8, 3 / 8])
assert np.allclose(median(d), [2, 1])
def test_B3():
""" Test B for four dependent variables """
d = D(['0000', '1111'], [1 / 2, 1 / 2])
assert_almost_equal(B(d), 1)
assert_almost_equal(B(d, [[0], [1, 2]], [3]), 0)
"""
Tests for dit.multivariate.exact_common_information
"""
from __future__ import division
import pytest
from dit import Distribution as D
from dit.multivariate import exact_common_information as G
from dit.multivariate.common_informations.exact_common_information import ExactCommonInformation
from dit.shannon import entropy
outcomes = ['0000', '0001', '0110', '0111', '1010', '1011', '1100', '1101']
pmf = [1 / 8] * 8
xor = D(outcomes, pmf)
sbec = lambda p: D(['00', '0e', '1e', '11'], [(1 - p) / 2, p / 2, p / 2,
(1 - p) / 2])
G_sbec = lambda p: min(1, entropy(p) + 1 - p)
@pytest.mark.slow
@pytest.mark.flaky(reruns=5)
@pytest.mark.parametrize(('rvs', 'crvs', 'val'), [
(None, None, 2.0),
([[0], [1], [2]], None, 2.0),
([[0], [1]], [2, 3], 1.0),
([[0], [1]], [2], 1.0),
([[0], [1]], None, 0.0),
])
def test_B5():
""" Test B = I for two variables """
d = D(['00', '01', '11'], [1 / 3] * 3)
assert_almost_equal(B(d), I(d, [0], [1]))
def test_I1():
""" Test mutual information of independent variables """
outcomes = ['00', '01', '10', '11']
pmf = [1/4]*4
d = D(outcomes, pmf)
assert I(d, [0], [1]) == pytest.approx(0.0)
def test_R2():
""" Test R for independent variables """
d = D(['00', '01', '10', '11'], [1 / 4] * 4)
assert_almost_equal(R(d), 2)
assert_almost_equal(R(d, [[0], [1]]), 2)
def test_I2():
""" Test mutual information of dependent variables """
outcomes = ['00', '11']
pmf = [1/2]*2
d = D(outcomes, pmf)
assert I(d, [0], [1]) == pytest.approx(1.0)
def test_R4():
""" Test that R = H - I in two variables """
d = D(['00', '01', '11'], [1 / 3] * 3)
assert_almost_equal(R(d), H(d) - I(d, [0], [1]))
def test_I3():
""" Test mutual information of overlapping variables """
outcomes = ['000', '011', '101', '110']
pmf = [1/4]*4
d = D(outcomes, pmf)
assert I(d, [0, 1], [1, 2]) == pytest.approx(2.0)
def test_p3():
""" Test some simple base cases using D """
for i in range(2, 10):
d = D([str(_) for _ in range(i)], [1 / i] * i)
yield assert_almost_equal, P(d), i
def test_ii1(i):
""" Test II for giant bit distributions """
outcomes = ['0' * i, '1' * i]
pmf = [1 / 2, 1 / 2]
d = D(outcomes, pmf)
assert interaction_information(d) == pytest.approx((-1)**i)
def test_p6():
""" Test some joint and conditional perplexities """
d = D(['00', '11'], [1 / 2] * 2)
assert_almost_equal(P(d), 2)
assert_almost_equal(P(d, [0], [1]), 1)
assert_almost_equal(P(d, [1], [0]), 1)
def test_B1():
""" Test B for two dependent variables """
d = D(['00', '11'], [1 / 2, 1 / 2])
assert_almost_equal(B(d), 1)
def test_B2():
""" Test B for three dependent variables """
d = D(['000', '111'], [1/2, 1/2])
assert B(d) == pytest.approx(1)
assert B(d, [[0], [1]], [2]) == pytest.approx(0)
def test_B2():
""" Test B for three dependent variables """
d = D(['000', '111'], [1 / 2, 1 / 2])
assert_almost_equal(B(d), 1)
assert_almost_equal(B(d, [[0], [1]], [2]), 0)
def test_B5():
""" Test B = I for two variables """
d = D(['00', '01', '11'], [1/3]*3)
assert B(d) == pytest.approx(I(d, [0], [1]))
def test_R4():
""" Test that R = H - I in two variables """
d = D(['00', '01', '11'], [1 / 3] * 3)
assert R(d) == pytest.approx(H(d) - I(d, [0], [1]))
