45 lines
1.4 KiB
Python
45 lines
1.4 KiB
Python
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy import pi, log, sqrt
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from numpy.testing import assert_, assert_equal
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from scipy.special._testutils import FuncData
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import scipy.special as sc
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# Euler-Mascheroni constant
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euler = 0.57721566490153286
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def test_consistency():
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# Make sure the implementation of digamma for real arguments
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# agrees with the implementation of digamma for complex arguments.
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# It's all poles after -1e16
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x = np.r_[-np.logspace(15, -30, 200), np.logspace(-30, 300, 200)]
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dataset = np.vstack((x + 0j, sc.digamma(x))).T
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FuncData(sc.digamma, dataset, 0, 1, rtol=5e-14, nan_ok=True).check()
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def test_special_values():
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# Test special values from Gauss's digamma theorem. See
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#
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# https://en.wikipedia.org/wiki/Digamma_function
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dataset = [(1, -euler),
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(0.5, -2*log(2) - euler),
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(1/3, -pi/(2*sqrt(3)) - 3*log(3)/2 - euler),
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(1/4, -pi/2 - 3*log(2) - euler),
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(1/6, -pi*sqrt(3)/2 - 2*log(2) - 3*log(3)/2 - euler),
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(1/8, -pi/2 - 4*log(2) - (pi + log(2 + sqrt(2)) - log(2 - sqrt(2)))/sqrt(2) - euler)]
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dataset = np.asarray(dataset)
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FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
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def test_nonfinite():
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pts = [0.0, -0.0, np.inf]
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std = [-np.inf, np.inf, np.inf]
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assert_equal(sc.digamma(pts), std)
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assert_(all(np.isnan(sc.digamma([-np.inf, -1]))))
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