def test_hypercontractivity_coefficient_tensorization(dist1, dist2):
"""
Test tensorization:
hc(X X' : Y Y') = max(hc(X:Y), hc(X', Y'))
"""
import dit
dit.ditParams['repr.print'] = True
mixed = dist1.__matmul__(dist2)
hc_mixed = hypercontractivity_coefficient(mixed, [[0, 2], [1, 3]])
hc_a = hypercontractivity_coefficient(dist1, [[0], [1]])
hc_b = hypercontractivity_coefficient(dist2, [[0], [1]])
assert hc_mixed == pytest.approx(max(hc_a, hc_b), abs=1e-2)
def test_hypercontractivity_coefficient2():
"""
Test against a known value.
"""
d = Distribution(['00', '01', '10', '11'], [1 / 4] * 4)
hc = hypercontractivity_coefficient(d, [[0], [1]])
assert hc == pytest.approx(0.0)
def test_mi_hc(dist):
"""
given U - X - Y:
I[U:Y] <= s*(X||Y)*I[U:X]
"""
a = I(dist, [[0], [2]])
b = hypercontractivity_coefficient(dist, [[1], [2]], niter=20)
c = I(dist, [[0], [1]])
assert a <= b * c + epsilon
def test_mi_hc(dist):
"""
given U - X - Y:
I[U:Y] <= s*(X||Y)*I[U:X]
"""
a = I(dist, [[0], [2]])
b = hypercontractivity_coefficient(dist, [[1], [2]], niter=20)
c = I(dist, [[0], [1]])
assert a <= b*c + epsilon
def test_hypercontractivity_coefficient_failure(rvs):
""" Test that hypercontractivity_coefficient fails with len(rvs) != 2 """
with pytest.raises(ditException):
hypercontractivity_coefficient(dyadic, rvs)
def test_hypercontractivity_coefficient(dist, rvs):
""" Test against known values """
assert hypercontractivity_coefficient(dist, rvs) == pytest.approx(1.0)
