288 lines
11 KiB
Python
288 lines
11 KiB
Python
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import numpy as np
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from numpy.testing import assert_equal, assert_allclose
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# avoid new uses of the following; prefer assert/np.testing.assert_allclose
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from numpy.testing import (assert_, assert_almost_equal,
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assert_array_almost_equal)
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import pytest
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from pytest import raises as assert_raises
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import scipy.stats as stats
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class TestEntropy:
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def test_entropy_positive(self):
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# See ticket #497
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pk = [0.5, 0.2, 0.3]
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qk = [0.1, 0.25, 0.65]
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eself = stats.entropy(pk, pk)
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edouble = stats.entropy(pk, qk)
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assert_(0.0 == eself)
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assert_(edouble >= 0.0)
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def test_entropy_base(self):
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pk = np.ones(16, float)
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S = stats.entropy(pk, base=2.)
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assert_(abs(S - 4.) < 1.e-5)
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qk = np.ones(16, float)
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qk[:8] = 2.
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S = stats.entropy(pk, qk)
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S2 = stats.entropy(pk, qk, base=2.)
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assert_(abs(S/S2 - np.log(2.)) < 1.e-5)
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def test_entropy_zero(self):
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# Test for PR-479
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assert_almost_equal(stats.entropy([0, 1, 2]), 0.63651416829481278,
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decimal=12)
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def test_entropy_2d(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
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assert_array_almost_equal(stats.entropy(pk, qk),
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[0.1933259, 0.18609809])
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def test_entropy_2d_zero(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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qk = [[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]]
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assert_array_almost_equal(stats.entropy(pk, qk),
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[np.inf, 0.18609809])
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pk[0][0] = 0.0
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assert_array_almost_equal(stats.entropy(pk, qk),
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[0.17403988, 0.18609809])
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def test_entropy_base_2d_nondefault_axis(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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assert_array_almost_equal(stats.entropy(pk, axis=1),
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[0.63651417, 0.63651417, 0.66156324])
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def test_entropy_2d_nondefault_axis(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
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assert_array_almost_equal(stats.entropy(pk, qk, axis=1),
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[0.231049, 0.231049, 0.127706])
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def test_entropy_raises_value_error(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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qk = [[0.1, 0.2], [0.6, 0.3]]
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assert_raises(ValueError, stats.entropy, pk, qk)
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def test_base_entropy_with_axis_0_is_equal_to_default(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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assert_array_almost_equal(stats.entropy(pk, axis=0),
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stats.entropy(pk))
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def test_entropy_with_axis_0_is_equal_to_default(self):
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pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
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qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
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assert_array_almost_equal(stats.entropy(pk, qk, axis=0),
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stats.entropy(pk, qk))
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def test_base_entropy_transposed(self):
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pk = np.array([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
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assert_array_almost_equal(stats.entropy(pk.T).T,
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stats.entropy(pk, axis=1))
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def test_entropy_transposed(self):
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pk = np.array([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
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qk = np.array([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
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assert_array_almost_equal(stats.entropy(pk.T, qk.T).T,
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stats.entropy(pk, qk, axis=1))
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def test_entropy_broadcasting(self):
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np.random.rand(0)
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x = np.random.rand(3)
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y = np.random.rand(2, 1)
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res = stats.entropy(x, y, axis=-1)
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assert_equal(res[0], stats.entropy(x, y[0]))
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assert_equal(res[1], stats.entropy(x, y[1]))
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def test_entropy_shape_mismatch(self):
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x = np.random.rand(10, 1, 12)
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y = np.random.rand(11, 2)
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message = "shape mismatch: objects cannot be broadcast"
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with pytest.raises(ValueError, match=message):
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stats.entropy(x, y)
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def test_input_validation(self):
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x = np.random.rand(10)
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message = "`base` must be a positive number."
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with pytest.raises(ValueError, match=message):
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stats.entropy(x, base=-2)
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class TestDifferentialEntropy:
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"""
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Vasicek results are compared with the R package vsgoftest.
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# library(vsgoftest)
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#
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# samp <- c(<values>)
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# entropy.estimate(x = samp, window = <window_length>)
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"""
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def test_differential_entropy_vasicek(self):
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random_state = np.random.RandomState(0)
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values = random_state.standard_normal(100)
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entropy = stats.differential_entropy(values, method='vasicek')
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assert_allclose(entropy, 1.342551, rtol=1e-6)
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entropy = stats.differential_entropy(values, window_length=1,
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method='vasicek')
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assert_allclose(entropy, 1.122044, rtol=1e-6)
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entropy = stats.differential_entropy(values, window_length=8,
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method='vasicek')
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assert_allclose(entropy, 1.349401, rtol=1e-6)
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def test_differential_entropy_vasicek_2d_nondefault_axis(self):
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random_state = np.random.RandomState(0)
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values = random_state.standard_normal((3, 100))
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entropy = stats.differential_entropy(values, axis=1, method='vasicek')
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assert_allclose(
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entropy,
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[1.342551, 1.341826, 1.293775],
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rtol=1e-6,
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)
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entropy = stats.differential_entropy(values, axis=1, window_length=1,
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method='vasicek')
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assert_allclose(
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entropy,
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[1.122044, 1.102944, 1.129616],
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rtol=1e-6,
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)
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entropy = stats.differential_entropy(values, axis=1, window_length=8,
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method='vasicek')
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assert_allclose(
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entropy,
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[1.349401, 1.338514, 1.292332],
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rtol=1e-6,
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)
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def test_differential_entropy_raises_value_error(self):
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random_state = np.random.RandomState(0)
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values = random_state.standard_normal((3, 100))
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error_str = (
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r"Window length \({window_length}\) must be positive and less "
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r"than half the sample size \({sample_size}\)."
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)
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sample_size = values.shape[1]
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for window_length in {-1, 0, sample_size//2, sample_size}:
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formatted_error_str = error_str.format(
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window_length=window_length,
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sample_size=sample_size,
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)
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with assert_raises(ValueError, match=formatted_error_str):
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stats.differential_entropy(
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values,
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window_length=window_length,
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axis=1,
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)
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def test_base_differential_entropy_with_axis_0_is_equal_to_default(self):
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random_state = np.random.RandomState(0)
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values = random_state.standard_normal((100, 3))
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entropy = stats.differential_entropy(values, axis=0)
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default_entropy = stats.differential_entropy(values)
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assert_allclose(entropy, default_entropy)
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def test_base_differential_entropy_transposed(self):
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random_state = np.random.RandomState(0)
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values = random_state.standard_normal((3, 100))
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assert_allclose(
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stats.differential_entropy(values.T).T,
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stats.differential_entropy(values, axis=1),
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)
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def test_input_validation(self):
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x = np.random.rand(10)
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message = "`base` must be a positive number or `None`."
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with pytest.raises(ValueError, match=message):
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stats.differential_entropy(x, base=-2)
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message = "`method` must be one of..."
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with pytest.raises(ValueError, match=message):
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stats.differential_entropy(x, method='ekki-ekki')
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@pytest.mark.parametrize('method', ['vasicek', 'van es',
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'ebrahimi', 'correa'])
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def test_consistency(self, method):
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# test that method is a consistent estimator
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n = 10000 if method == 'correa' else 1000000
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rvs = stats.norm.rvs(size=n, random_state=0)
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expected = stats.norm.entropy()
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res = stats.differential_entropy(rvs, method=method)
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assert_allclose(res, expected, rtol=0.005)
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# values from differential_entropy reference [6], table 1, n=50, m=7
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norm_rmse_std_cases = { # method: (RMSE, STD)
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'vasicek': (0.198, 0.109),
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'van es': (0.212, 0.110),
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'correa': (0.135, 0.112),
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'ebrahimi': (0.128, 0.109)
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}
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@pytest.mark.parametrize('method, expected',
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list(norm_rmse_std_cases.items()))
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def test_norm_rmse_std(self, method, expected):
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# test that RMSE and standard deviation of estimators matches values
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# given in differential_entropy reference [6]. Incidentally, also
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# tests vectorization.
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reps, n, m = 10000, 50, 7
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rmse_expected, std_expected = expected
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rvs = stats.norm.rvs(size=(reps, n), random_state=0)
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true_entropy = stats.norm.entropy()
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res = stats.differential_entropy(rvs, window_length=m,
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method=method, axis=-1)
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assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
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rmse_expected, atol=0.005)
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assert_allclose(np.std(res), std_expected, atol=0.002)
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# values from differential_entropy reference [6], table 2, n=50, m=7
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expon_rmse_std_cases = { # method: (RMSE, STD)
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'vasicek': (0.194, 0.148),
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'van es': (0.179, 0.149),
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'correa': (0.155, 0.152),
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'ebrahimi': (0.151, 0.148)
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}
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@pytest.mark.parametrize('method, expected',
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list(expon_rmse_std_cases.items()))
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def test_expon_rmse_std(self, method, expected):
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# test that RMSE and standard deviation of estimators matches values
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# given in differential_entropy reference [6]. Incidentally, also
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# tests vectorization.
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reps, n, m = 10000, 50, 7
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rmse_expected, std_expected = expected
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rvs = stats.expon.rvs(size=(reps, n), random_state=0)
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true_entropy = stats.expon.entropy()
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res = stats.differential_entropy(rvs, window_length=m,
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method=method, axis=-1)
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assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
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rmse_expected, atol=0.005)
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assert_allclose(np.std(res), std_expected, atol=0.002)
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@pytest.mark.parametrize('n, method', [(8, 'van es'),
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(12, 'ebrahimi'),
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(1001, 'vasicek')])
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def test_method_auto(self, n, method):
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rvs = stats.norm.rvs(size=(n,), random_state=0)
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res1 = stats.differential_entropy(rvs)
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res2 = stats.differential_entropy(rvs, method=method)
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assert res1 == res2
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