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- 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)
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