54 lines
1.8 KiB
Python
54 lines
1.8 KiB
Python
import numpy as np
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from numpy.testing import assert_equal, assert_allclose
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import scipy.special as sc
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def test_symmetries():
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np.random.seed(1234)
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a, h = np.random.rand(100), np.random.rand(100)
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assert_equal(sc.owens_t(h, a), sc.owens_t(-h, a))
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assert_equal(sc.owens_t(h, a), -sc.owens_t(h, -a))
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def test_special_cases():
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assert_equal(sc.owens_t(5, 0), 0)
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assert_allclose(sc.owens_t(0, 5), 0.5*np.arctan(5)/np.pi,
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rtol=5e-14)
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# Target value is 0.5*Phi(5)*(1 - Phi(5)) for Phi the CDF of the
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# standard normal distribution
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assert_allclose(sc.owens_t(5, 1), 1.4332574485503512543e-07,
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rtol=5e-14)
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def test_nans():
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assert_equal(sc.owens_t(20, np.nan), np.nan)
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assert_equal(sc.owens_t(np.nan, 20), np.nan)
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assert_equal(sc.owens_t(np.nan, np.nan), np.nan)
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def test_infs():
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h, a = 0, np.inf
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# T(0, a) = 1/2π * arctan(a)
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res = 1/(2*np.pi) * np.arctan(a)
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assert_allclose(sc.owens_t(h, a), res, rtol=5e-14)
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assert_allclose(sc.owens_t(h, -a), -res, rtol=5e-14)
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h = 1
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# Refer Owens T function definition in Wikipedia
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# https://en.wikipedia.org/wiki/Owen%27s_T_function
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# Value approximated through Numerical Integration
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# using scipy.integrate.quad
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# quad(lambda x: 1/(2*pi)*(exp(-0.5*(1*1)*(1+x*x))/(1+x*x)), 0, inf)
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res = 0.07932762696572854
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assert_allclose(sc.owens_t(h, np.inf), res, rtol=5e-14)
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assert_allclose(sc.owens_t(h, -np.inf), -res, rtol=5e-14)
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assert_equal(sc.owens_t(np.inf, 1), 0)
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assert_equal(sc.owens_t(-np.inf, 1), 0)
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assert_equal(sc.owens_t(np.inf, np.inf), 0)
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assert_equal(sc.owens_t(-np.inf, np.inf), 0)
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assert_equal(sc.owens_t(np.inf, -np.inf), -0.0)
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assert_equal(sc.owens_t(-np.inf, -np.inf), -0.0)
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