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