50 lines
1.3 KiB
Python
50 lines
1.3 KiB
Python
|
import scipy.special as sc
|
||
|
|
import numpy as np
|
||
|
|
from numpy.testing import assert_equal, assert_allclose
|
||
|
|
|
||
|
|
|
||
|
|
def test_zeta():
|
||
|
|
assert_allclose(sc.zeta(2,2), np.pi**2/6 - 1, rtol=1e-12)
|
||
|
|
|
||
|
|
|
||
|
|
def test_zetac():
|
||
|
|
# Expected values in the following were computed using Wolfram
|
||
|
|
# Alpha's `Zeta[x] - 1`
|
||
|
|
x = [-2.1, 0.8, 0.9999, 9, 50, 75]
|
||
|
|
desired = [
|
||
|
|
-0.9972705002153750,
|
||
|
|
-5.437538415895550,
|
||
|
|
-10000.42279161673,
|
||
|
|
0.002008392826082214,
|
||
|
|
8.881784210930816e-16,
|
||
|
|
2.646977960169853e-23,
|
||
|
|
]
|
||
|
|
assert_allclose(sc.zetac(x), desired, rtol=1e-12)
|
||
|
|
|
||
|
|
|
||
|
|
def test_zetac_special_cases():
|
||
|
|
assert sc.zetac(np.inf) == 0
|
||
|
|
assert np.isnan(sc.zetac(-np.inf))
|
||
|
|
assert sc.zetac(0) == -1.5
|
||
|
|
assert sc.zetac(1.0) == np.inf
|
||
|
|
|
||
|
|
assert_equal(sc.zetac([-2, -50, -100]), -1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_riemann_zeta_special_cases():
|
||
|
|
assert np.isnan(sc.zeta(np.nan))
|
||
|
|
assert sc.zeta(np.inf) == 1
|
||
|
|
assert sc.zeta(0) == -0.5
|
||
|
|
|
||
|
|
# Riemann zeta is zero add negative even integers.
|
||
|
|
assert_equal(sc.zeta([-2, -4, -6, -8, -10]), 0)
|
||
|
|
|
||
|
|
assert_allclose(sc.zeta(2), np.pi**2/6, rtol=1e-12)
|
||
|
|
assert_allclose(sc.zeta(4), np.pi**4/90, rtol=1e-12)
|
||
|
|
|
||
|
|
|
||
|
|
def test_riemann_zeta_avoid_overflow():
|
||
|
|
s = -260.00000000001
|
||
|
|
desired = -5.6966307844402683127e+297 # Computed with Mpmath
|
||
|
|
assert_allclose(sc.zeta(s), desired, atol=0, rtol=5e-14)
|