33 lines
1.1 KiB
Python
33 lines
1.1 KiB
Python
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import numpy as np
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from numpy import sqrt, log, pi
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from scipy.special._testutils import FuncData
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from scipy.special import spence
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def test_consistency():
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# Make sure the implementation of spence for real arguments
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# agrees with the implementation of spence for imaginary arguments.
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x = np.logspace(-30, 300, 200)
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dataset = np.vstack((x + 0j, spence(x))).T
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FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
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def test_special_points():
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# Check against known values of Spence's function.
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phi = (1 + sqrt(5))/2
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dataset = [(1, 0),
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(2, -pi**2/12),
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(0.5, pi**2/12 - log(2)**2/2),
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(0, pi**2/6),
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(-1, pi**2/4 - 1j*pi*log(2)),
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((-1 + sqrt(5))/2, pi**2/15 - log(phi)**2),
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((3 - sqrt(5))/2, pi**2/10 - log(phi)**2),
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(phi, -pi**2/15 + log(phi)**2/2),
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# Corrected from Zagier, "The Dilogarithm Function"
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((3 + sqrt(5))/2, -pi**2/10 - log(phi)**2)]
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dataset = np.asarray(dataset)
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FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
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