def test_wright_data_grid_less_accurate(a, b, x, phi, accuracy):
"""Test cases of test_data that do not reach relative accuracy of 1e-11
Here we test for reduced accuracy or even nan.
"""
if np.isnan(accuracy):
assert np.isnan(wright_bessel(a, b, x))
else:
assert_allclose(wright_bessel(a, b, x), phi, rtol=accuracy)
def test_wright_functional(a, b, x):
"""Test functional relation of wright_bessel.
Phi(a, b-1, z) = a*z*Phi(a, b+a, z) + (b-1)*Phi(a, b, z)
Note that d/dx Phi(a, b, x) = Phi(a, b-1, x)
See Eq. (22) of
B. Stankovic, On the Function of E. M. Wright,
Publ. de l' Institut Mathematique, Beograd,
Nouvelle S`er. 10 (1970), 113-124.
"""
assert_allclose(wright_bessel(a, b - 1, x),
a * x * wright_bessel(a, b + a, x) +
(b - 1) * wright_bessel(a, b, x),
rtol=1e-8,
atol=1e-8)
def test_wright_bessel_iv(b, x):
"""Test relation of wright_bessel and modified bessel function iv.
iv(z) = (1/2*z)**v * Phi(1, v+1; 1/4*z**2).
See https://dlmf.nist.gov/10.46.E2
"""
if x != 0:
v = b - 1
wb = wright_bessel(1, v + 1, x**2 / 4.)
# Note: iv(v, x) has precision of less than 1e-12 for some cases
# e.g v=1-1e-6 and x=1e-06)
assert_allclose(np.power(x / 2., v) * wb,
sc.iv(v, x),
rtol=1e-11,
atol=1e-11)
def test_wright_data_grid_failures(a, b, x, phi):
"""Test cases of test_data that do not reach relative accuracy of 1e-11"""
assert_allclose(wright_bessel(a, b, x), phi, rtol=1e-11)
def test_wright_bessel_zero(a, b):
"""Test at x = 0."""
assert_equal(wright_bessel(a, b, 0.), rgamma(b))