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import numpy as np
from numpy.testing import assert_allclose
from scipy.special._testutils import FuncData
from scipy.special import gamma, gammaln, loggamma
def test_identities1():
# test the identity exp(loggamma(z)) = gamma(z)
x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
y = x.copy()
x, y = np.meshgrid(x, y)
z = (x + 1J*y).flatten()
dataset = np.vstack((z, gamma(z))).T
def f(z):
return np.exp(loggamma(z))
FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
def test_identities2():
# test the identity loggamma(z + 1) = log(z) + loggamma(z)
x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
y = x.copy()
x, y = np.meshgrid(x, y)
z = (x + 1J*y).flatten()
dataset = np.vstack((z, np.log(z) + loggamma(z))).T
def f(z):
return loggamma(z + 1)
FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
def test_realpart():
# Test that the real parts of loggamma and gammaln agree on the
# real axis.
x = np.r_[-np.logspace(10, -10), np.logspace(-10, 10)] + 0.5
dataset = np.vstack((x, gammaln(x))).T
def f(z):
return loggamma(z).real
FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
def test_gh_6536():
z = loggamma(complex(-3.4, +0.0))
zbar = loggamma(complex(-3.4, -0.0))
assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
def test_branch_cut():
# Make sure negative zero is treated correctly
x = -np.logspace(300, -30, 100)
z = np.asarray([complex(x0, 0.0) for x0 in x])
zbar = np.asarray([complex(x0, -0.0) for x0 in x])
assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
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