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