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]))))