def test_base_differential_entropy_with_axis_0_is_equal_to_default(self):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((100, 3))
entropy = stats.differential_entropy(values, axis=0)
default_entropy = stats.differential_entropy(values)
assert_allclose(entropy, default_entropy)
def test_differential_entropy_vasicek_2d_nondefault_axis(self):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
entropy = stats.differential_entropy(values, axis=1, method='vasicek')
assert_allclose(
entropy,
[1.342551, 1.341826, 1.293775],
rtol=1e-6,
)
entropy = stats.differential_entropy(values,
axis=1,
window_length=1,
method='vasicek')
assert_allclose(
entropy,
[1.122044, 1.102944, 1.129616],
rtol=1e-6,
)
entropy = stats.differential_entropy(values,
axis=1,
window_length=8,
method='vasicek')
assert_allclose(
entropy,
[1.349401, 1.338514, 1.292332],
rtol=1e-6,
)
def test_base_differential_entropy_transposed(self):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
assert_allclose(
stats.differential_entropy(values.T).T,
stats.differential_entropy(values, axis=1),
)
def test_input_validation(self):
x = np.random.rand(10)
message = "`base` must be a positive number or `None`."
with pytest.raises(ValueError, match=message):
stats.differential_entropy(x, base=-2)
message = "`method` must be one of..."
with pytest.raises(ValueError, match=message):
stats.differential_entropy(x, method='ekki-ekki')
def test_consistency(self, method):
# test that method is a consistent estimator
n = 10000 if method == 'correa' else 1000000
rvs = stats.norm.rvs(size=n, random_state=0)
expected = stats.norm.entropy()
res = stats.differential_entropy(rvs, method=method)
assert_allclose(res, expected, rtol=0.005)
def test_differential_entropy_vasicek(self):
random_state = np.random.RandomState(0)
values = random_state.standard_normal(100)
entropy = stats.differential_entropy(values, method='vasicek')
assert_allclose(entropy, 1.342551, rtol=1e-6)
entropy = stats.differential_entropy(values,
window_length=1,
method='vasicek')
assert_allclose(entropy, 1.122044, rtol=1e-6)
entropy = stats.differential_entropy(values,
window_length=8,
method='vasicek')
assert_allclose(entropy, 1.349401, rtol=1e-6)
def test_differential_entropy_raises_value_error(self):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
error_str = (
r"Window length \({window_length}\) must be positive and less "
r"than half the sample size \({sample_size}\).")
sample_size = values.shape[1]
for window_length in {-1, 0, sample_size // 2, sample_size}:
formatted_error_str = error_str.format(
window_length=window_length,
sample_size=sample_size,
)
with assert_raises(ValueError, match=formatted_error_str):
stats.differential_entropy(
values,
window_length=window_length,
axis=1,
)
def test_expon_rmse_std(self, method, expected):
# test that RMSE and standard deviation of estimators matches values
# given in differential_entropy reference [6]. Incidentally, also
# tests vectorization.
reps, n, m = 10000, 50, 7
rmse_expected, std_expected = expected
rvs = stats.expon.rvs(size=(reps, n), random_state=0)
true_entropy = stats.expon.entropy()
res = stats.differential_entropy(rvs,
window_length=m,
method=method,
axis=-1)
assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
rmse_expected,
atol=0.005)
assert_allclose(np.std(res), std_expected, atol=0.002)
def test_method_auto(self, n, method):
rvs = stats.norm.rvs(size=(n, ), random_state=0)
res1 = stats.differential_entropy(rvs)
res2 = stats.differential_entropy(rvs, method=method)
assert res1 == res2
