85 lines
2.6 KiB
Python
85 lines
2.6 KiB
Python
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import numpy as np
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from numpy.testing import assert_allclose
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import pytest
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from scipy.special._ufuncs import _cosine_cdf, _cosine_invcdf
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# These values are (x, p) where p is the expected exact value of
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# _cosine_cdf(x). These values will be tested for exact agreement.
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_coscdf_exact = [
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(-4.0, 0.0),
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(0, 0.5),
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(np.pi, 1.0),
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(4.0, 1.0),
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]
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@pytest.mark.parametrize("x, expected", _coscdf_exact)
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def test_cosine_cdf_exact(x, expected):
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assert _cosine_cdf(x) == expected
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# These values are (x, p), where p is the expected value of
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# _cosine_cdf(x). The expected values were computed with mpmath using
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# 50 digits of precision. These values will be tested for agreement
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# with the computed values using a very small relative tolerance.
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# The value at -np.pi is not 0, because -np.pi does not equal -π.
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_coscdf_close = [
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(3.1409, 0.999999999991185),
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(2.25, 0.9819328173287907),
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# -1.6 is the threshold below which the Pade approximant is used.
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(-1.599, 0.08641959838382553),
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(-1.601, 0.086110582992713),
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(-2.0, 0.0369709335961611),
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(-3.0, 7.522387241801384e-05),
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(-3.1415, 2.109869685443648e-14),
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(-3.14159, 4.956444476505336e-19),
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(-np.pi, 4.871934450264861e-50),
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]
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@pytest.mark.parametrize("x, expected", _coscdf_close)
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def test_cosine_cdf(x, expected):
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assert_allclose(_cosine_cdf(x), expected, rtol=5e-15)
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# These values are (p, x) where x is the expected exact value of
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# _cosine_invcdf(p). These values will be tested for exact agreement.
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_cosinvcdf_exact = [
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(0.0, -np.pi),
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(0.5, 0.0),
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(1.0, np.pi),
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]
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@pytest.mark.parametrize("p, expected", _cosinvcdf_exact)
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def test_cosine_invcdf_exact(p, expected):
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assert _cosine_invcdf(p) == expected
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def test_cosine_invcdf_invalid_p():
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# Check that p values outside of [0, 1] return nan.
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assert np.isnan(_cosine_invcdf([-0.1, 1.1])).all()
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# These values are (p, x), where x is the expected value of _cosine_invcdf(p).
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# The expected values were computed with mpmath using 50 digits of precision.
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_cosinvcdf_close = [
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(1e-50, -np.pi),
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(1e-14, -3.1415204137058454),
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(1e-08, -3.1343686589124524),
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(0.0018001, -2.732563923138336),
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(0.010, -2.41276589008678),
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(0.060, -1.7881244975330157),
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(0.125, -1.3752523669869274),
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(0.250, -0.831711193579736),
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(0.400, -0.3167954512395289),
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(0.419, -0.25586025626919906),
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(0.421, -0.24947570750445663),
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(0.750, 0.831711193579736),
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(0.940, 1.7881244975330153),
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(0.9999999996, 3.1391220839917167),
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]
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@pytest.mark.parametrize("p, expected", _cosinvcdf_close)
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def test_cosine_invcdf(p, expected):
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assert_allclose(_cosine_invcdf(p), expected, rtol=1e-14)
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