305 lines
12 KiB
Python
305 lines
12 KiB
Python
import math
|
|
import pytest
|
|
from pytest import raises as assert_raises
|
|
|
|
import numpy as np
|
|
from numpy.testing import assert_allclose
|
|
|
|
from scipy import stats
|
|
from scipy.conftest import array_api_compatible
|
|
from scipy._lib._array_api import xp_assert_close, xp_assert_equal, xp_assert_less
|
|
|
|
class TestEntropy:
|
|
@array_api_compatible
|
|
def test_entropy_positive(self, xp):
|
|
# See ticket #497
|
|
pk = xp.asarray([0.5, 0.2, 0.3])
|
|
qk = xp.asarray([0.1, 0.25, 0.65])
|
|
eself = stats.entropy(pk, pk)
|
|
edouble = stats.entropy(pk, qk)
|
|
xp_assert_equal(eself, xp.asarray(0.))
|
|
xp_assert_less(-edouble, xp.asarray(0.))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_base(self, xp):
|
|
pk = xp.ones(16)
|
|
S = stats.entropy(pk, base=2.)
|
|
xp_assert_less(xp.abs(S - 4.), xp.asarray(1.e-5))
|
|
|
|
qk = xp.ones(16)
|
|
qk = xp.where(xp.arange(16) < 8, xp.asarray(2.), qk)
|
|
S = stats.entropy(pk, qk)
|
|
S2 = stats.entropy(pk, qk, base=2.)
|
|
xp_assert_less(xp.abs(S/S2 - math.log(2.)), xp.asarray(1.e-5))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_zero(self, xp):
|
|
# Test for PR-479
|
|
x = xp.asarray([0., 1., 2.])
|
|
xp_assert_close(stats.entropy(x),
|
|
xp.asarray(0.63651416829481278))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_2d(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
|
|
xp_assert_close(stats.entropy(pk, qk),
|
|
xp.asarray([0.1933259, 0.18609809]))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_2d_zero(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]])
|
|
xp_assert_close(stats.entropy(pk, qk),
|
|
xp.asarray([xp.inf, 0.18609809]))
|
|
|
|
pk = xp.asarray([[0.0, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
xp_assert_close(stats.entropy(pk, qk),
|
|
xp.asarray([0.17403988, 0.18609809]))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_base_2d_nondefault_axis(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
xp_assert_close(stats.entropy(pk, axis=1),
|
|
xp.asarray([0.63651417, 0.63651417, 0.66156324]))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_2d_nondefault_axis(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
|
|
xp_assert_close(stats.entropy(pk, qk, axis=1),
|
|
xp.asarray([0.23104906, 0.23104906, 0.12770641]))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_raises_value_error(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.1, 0.2], [0.6, 0.3]])
|
|
message = "Array shapes are incompatible for broadcasting."
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.entropy(pk, qk)
|
|
|
|
@array_api_compatible
|
|
def test_base_entropy_with_axis_0_is_equal_to_default(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
xp_assert_close(stats.entropy(pk, axis=0),
|
|
stats.entropy(pk))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_with_axis_0_is_equal_to_default(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
|
|
xp_assert_close(stats.entropy(pk, qk, axis=0),
|
|
stats.entropy(pk, qk))
|
|
|
|
@array_api_compatible
|
|
def test_base_entropy_transposed(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
xp_assert_close(stats.entropy(pk.T),
|
|
stats.entropy(pk, axis=1))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_transposed(self, xp):
|
|
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
|
|
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
|
|
xp_assert_close(stats.entropy(pk.T, qk.T),
|
|
stats.entropy(pk, qk, axis=1))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_broadcasting(self, xp):
|
|
rng = np.random.default_rng(74187315492831452)
|
|
x = xp.asarray(rng.random(3))
|
|
y = xp.asarray(rng.random((2, 1)))
|
|
res = stats.entropy(x, y, axis=-1)
|
|
xp_assert_equal(res[0], stats.entropy(x, y[0, ...]))
|
|
xp_assert_equal(res[1], stats.entropy(x, y[1, ...]))
|
|
|
|
@array_api_compatible
|
|
def test_entropy_shape_mismatch(self, xp):
|
|
x = xp.ones((10, 1, 12))
|
|
y = xp.ones((11, 2))
|
|
message = "Array shapes are incompatible for broadcasting."
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.entropy(x, y)
|
|
|
|
@array_api_compatible
|
|
def test_input_validation(self, xp):
|
|
x = xp.ones(10)
|
|
message = "`base` must be a positive number."
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.entropy(x, base=-2)
|
|
|
|
|
|
class TestDifferentialEntropy:
|
|
"""
|
|
Vasicek results are compared with the R package vsgoftest.
|
|
|
|
# library(vsgoftest)
|
|
#
|
|
# samp <- c(<values>)
|
|
# entropy.estimate(x = samp, window = <window_length>)
|
|
|
|
"""
|
|
|
|
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_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_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_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_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')
|
|
|
|
@pytest.mark.parametrize('method', ['vasicek', 'van es',
|
|
'ebrahimi', 'correa'])
|
|
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)
|
|
|
|
# values from differential_entropy reference [6], table 1, n=50, m=7
|
|
norm_rmse_std_cases = { # method: (RMSE, STD)
|
|
'vasicek': (0.198, 0.109),
|
|
'van es': (0.212, 0.110),
|
|
'correa': (0.135, 0.112),
|
|
'ebrahimi': (0.128, 0.109)
|
|
}
|
|
|
|
@pytest.mark.parametrize('method, expected',
|
|
list(norm_rmse_std_cases.items()))
|
|
def test_norm_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.norm.rvs(size=(reps, n), random_state=0)
|
|
true_entropy = stats.norm.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)
|
|
|
|
# values from differential_entropy reference [6], table 2, n=50, m=7
|
|
expon_rmse_std_cases = { # method: (RMSE, STD)
|
|
'vasicek': (0.194, 0.148),
|
|
'van es': (0.179, 0.149),
|
|
'correa': (0.155, 0.152),
|
|
'ebrahimi': (0.151, 0.148)
|
|
}
|
|
|
|
@pytest.mark.parametrize('method, expected',
|
|
list(expon_rmse_std_cases.items()))
|
|
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)
|
|
|
|
@pytest.mark.parametrize('n, method', [(8, 'van es'),
|
|
(12, 'ebrahimi'),
|
|
(1001, 'vasicek')])
|
|
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
|