47 lines
1.2 KiB
Python
47 lines
1.2 KiB
Python
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy.testing import assert_allclose
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import scipy.special as sc
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from scipy.special._testutils import FuncData
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def test_line():
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# Test on the line a = x where a simpler asymptotic expansion
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# (analog of DLMF 8.12.15) is available.
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def gammainc_line(x):
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c = np.array([-1/3, -1/540, 25/6048, 101/155520,
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-3184811/3695155200, -2745493/8151736420])
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res = 0
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xfac = 1
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for ck in c:
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res -= ck*xfac
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xfac /= x
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res /= np.sqrt(2*np.pi*x)
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res += 0.5
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return res
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x = np.logspace(np.log10(25), 300, 500)
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a = x.copy()
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dataset = np.vstack((a, x, gammainc_line(x))).T
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FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
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def test_gammainc_roundtrip():
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a = np.logspace(-5, 10, 100)
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x = np.logspace(-5, 10, 100)
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y = sc.gammaincinv(a, sc.gammainc(a, x))
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assert_allclose(x, y, rtol=1e-10)
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def test_gammaincc_roundtrip():
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a = np.logspace(-5, 10, 100)
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x = np.logspace(-5, 10, 100)
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y = sc.gammainccinv(a, sc.gammaincc(a, x))
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assert_allclose(x, y, rtol=1e-14)
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