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