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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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