def test_J11():
""" Test a property of J from result 5 of the paper """
pmf = np.array([1 / 2, 1 / 4, 1 / 8, 1 / 16, 1 / 16])
N = len(pmf)
d = SD(pmf)
q = SD(1 / (N - 1) * (1 - pmf))
j2 = (N - 1) * (H(q) - np.log2(N - 1))
assert_almost_equal(J(d), j2)
def test_J6():
""" Test a property of J from result 2 of the paper with base 10 """
for i in range(2, 10):
d = SD([1 / i] * i)
d.set_base(10)
yield assert_almost_equal, J(d), (i - 1) * (np.log10(i) -
np.log10(i - 1))
def test_J10():
""" Test a property of J from result 4 of the paper """
d = SD([1 / 2, 1 / 4, 1 / 8, 1 / 16, 1 / 16])
j = J(d)
h = H(d)
s = sum(J(p) for p in d.pmf)
assert_almost_equal(h, s - j)
def test_J10():
""" Test a property of J from result 4 of the paper """
d = SD([1/2, 1/4, 1/8, 1/16, 1/16])
j = J(d)
h = H(d)
s = sum(J(p) for p in d.pmf)
assert h == pytest.approx(s-j)
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_R5():
""" Test that R fails on SDs """
d = SD([1 / 4] * 4)
assert_raises(ditException, R, d)
def test_H1():
""" Test the entropy of a fair coin """
d = SD([1 / 2, 1 / 2])
assert H(d) == pytest.approx(1.0)
def test_p1(i):
""" Test some simple base cases using SD """
assert P(SD([1 / i] * i)) == pytest.approx(i)
def test_p2():
""" Test some simple base cases using SD with varying bases """
for i in range(2, 10):
d = SD([1 / i] * i)
d.set_base(i)
yield assert_almost_equal, P(d), i
def test_J4():
""" Test a property of J from result 2 of the paper """
for i in range(2, 10):
d = SD([1 / i] * i)
yield assert_almost_equal, J(d), (i - 1) * (np.log2(i) -
np.log2(i - 1))
def test_J2():
""" Test a simple base case using ScalarDistribution """
d = SD([1/2]*2)
assert J(d) == pytest.approx(1)
def test_H4():
""" Test entropy in base 10 """
d = SD([1 / 10] * 10)
d.set_base(10)
assert_almost_equal(H(d), 1.0)
def test_H1():
""" Test the entropy of a fair coin """
d = SD([1 / 2, 1 / 2])
assert_almost_equal(H(d), 1.0)
def test_R5():
""" Test that R fails on SDs """
d = SD([1 / 4] * 4)
with pytest.raises(ditException):
R(d)
def test_B6():
""" Test that B fails on SDs """
d = SD([1 / 4] * 4)
with pytest.raises(ditException):
B(d)
def test_tc8():
""" Test that T fails on SDs """
d = SD([1 / 3] * 3)
assert_raises(ditException, T, d)
def test_coi8():
""" Test that I fails on ScalarDistributions """
d = SD([1 / 3] * 3)
with pytest.raises(ditException):
I(d)
def test_tc8():
""" Test that T fails on SDs """
d = SD([1/3]*3)
with pytest.raises(ditException):
T(d)
def test_J2():
""" Test a simple base case using ScalarDistribution """
d = SD([1 / 2] * 2)
assert_almost_equal(J(d), 1)
def test_J7():
""" Test a property of J from result 1 of the paper """
for i in range(3, 10):
d = SD([1 / i] * i)
yield assert_true, J(d) < H(d)
def test_J4(i):
""" Test a property of J from result 2 of the paper """
d = SD([1/i]*i)
assert J(d) == pytest.approx((i-1)*(np.log2(i) - np.log2(i-1)))
def test_p1():
""" Test some simple base cases using SD """
for i in range(2, 10):
yield assert_almost_equal, P(SD([1 / i] * i)), i
def test_J8():
""" Test a property of J from result 1 of the paper using log bases """
for i in range(3, 10):
d = SD([1 / i] * i)
d.set_base(i)
yield assert_true, J(d) < H(d)
def test_J5(i):
""" Test a property of J from result 2 of the paper with a log base """
d = SD([1/i]*i)
d.set_base('e')
assert J(d) == pytest.approx((i-1)*(np.log(i)-np.log(i-1)))
def test_J6(i):
""" Test a property of J from result 2 of the paper with base 10 """
d = SD([1/i]*i)
d.set_base(10)
assert J(d) == pytest.approx((i-1)*(np.log10(i)-np.log10(i-1)))
def test_J7(i):
""" Test a property of J from result 1 of the paper """
d = SD([1/i]*i)
assert J(d) < H(d)
def test_p2(i):
""" Test some simple base cases using SD with varying bases """
d = SD([1 / i] * i)
d.set_base(i)
assert P(d) == pytest.approx(i)
def test_J8(i):
""" Test a property of J from result 1 of the paper using log bases """
d = SD([1/i]*i)
d.set_base(i)
assert J(d) < H(d)
def test_H4():
""" Test entropy in base 10 """
d = SD([1 / 10] * 10)
d.set_base(10)
assert H(d) == pytest.approx(1.0)
def test_B6():
""" Test that B fails on SDs """
d = SD([1 / 4] * 4)
assert_raises(ditException, B, d)