117 lines
4.5 KiB
Python
117 lines
4.5 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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import pytest
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from scipy.special._testutils import MissingModule, check_version
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from scipy.special._mptestutils import (
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Arg, IntArg, mp_assert_allclose, assert_mpmath_equal)
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from scipy.special._precompute.gammainc_asy import (
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compute_g, compute_alpha, compute_d)
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from scipy.special._precompute.gammainc_data import gammainc, gammaincc
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try:
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import sympy
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except ImportError:
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sympy = MissingModule('sympy')
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try:
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import mpmath as mp
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except ImportError:
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mp = MissingModule('mpmath')
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_is_32bit_platform = np.intp(0).itemsize < 8
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@check_version(mp, '0.19')
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def test_g():
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# Test data for the g_k. See DLMF 5.11.4.
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with mp.workdps(30):
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g = [mp.mpf(1), mp.mpf(1)/12, mp.mpf(1)/288,
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-mp.mpf(139)/51840, -mp.mpf(571)/2488320,
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mp.mpf(163879)/209018880, mp.mpf(5246819)/75246796800]
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mp_assert_allclose(compute_g(7), g)
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@pytest.mark.slow
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@check_version(mp, '0.19')
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@check_version(sympy, '0.7')
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@pytest.mark.xfail(condition=_is_32bit_platform, reason="rtol only 2e-11, see gh-6938")
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def test_alpha():
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# Test data for the alpha_k. See DLMF 8.12.14.
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with mp.workdps(30):
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alpha = [mp.mpf(0), mp.mpf(1), mp.mpf(1)/3, mp.mpf(1)/36,
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-mp.mpf(1)/270, mp.mpf(1)/4320, mp.mpf(1)/17010,
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-mp.mpf(139)/5443200, mp.mpf(1)/204120]
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mp_assert_allclose(compute_alpha(9), alpha)
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@pytest.mark.xslow
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@check_version(mp, '0.19')
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@check_version(sympy, '0.7')
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def test_d():
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# Compare the d_{k, n} to the results in appendix F of [1].
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#
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# Sources
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# -------
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# [1] DiDonato and Morris, Computation of the Incomplete Gamma
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# Function Ratios and their Inverse, ACM Transactions on
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# Mathematical Software, 1986.
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with mp.workdps(50):
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dataset = [(0, 0, -mp.mpf('0.333333333333333333333333333333')),
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(0, 12, mp.mpf('0.102618097842403080425739573227e-7')),
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(1, 0, -mp.mpf('0.185185185185185185185185185185e-2')),
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(1, 12, mp.mpf('0.119516285997781473243076536700e-7')),
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(2, 0, mp.mpf('0.413359788359788359788359788360e-2')),
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(2, 12, -mp.mpf('0.140925299108675210532930244154e-7')),
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(3, 0, mp.mpf('0.649434156378600823045267489712e-3')),
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(3, 12, -mp.mpf('0.191111684859736540606728140873e-7')),
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(4, 0, -mp.mpf('0.861888290916711698604702719929e-3')),
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(4, 12, mp.mpf('0.288658297427087836297341274604e-7')),
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(5, 0, -mp.mpf('0.336798553366358150308767592718e-3')),
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(5, 12, mp.mpf('0.482409670378941807563762631739e-7')),
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(6, 0, mp.mpf('0.531307936463992223165748542978e-3')),
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(6, 12, -mp.mpf('0.882860074633048352505085243179e-7')),
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(7, 0, mp.mpf('0.344367606892377671254279625109e-3')),
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(7, 12, -mp.mpf('0.175629733590604619378669693914e-6')),
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(8, 0, -mp.mpf('0.652623918595309418922034919727e-3')),
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(8, 12, mp.mpf('0.377358774161109793380344937299e-6')),
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(9, 0, -mp.mpf('0.596761290192746250124390067179e-3')),
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(9, 12, mp.mpf('0.870823417786464116761231237189e-6'))]
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d = compute_d(10, 13)
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res = []
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for k, n, std in dataset:
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res.append(d[k][n])
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std = map(lambda x: x[2], dataset)
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mp_assert_allclose(res, std)
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@check_version(mp, '0.19')
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def test_gammainc():
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# Quick check that the gammainc in
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# special._precompute.gammainc_data agrees with mpmath's
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# gammainc.
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assert_mpmath_equal(gammainc,
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lambda a, x: mp.gammainc(a, b=x, regularized=True),
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[Arg(0, 100, inclusive_a=False), Arg(0, 100)],
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nan_ok=False, rtol=1e-17, n=50, dps=50)
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@pytest.mark.xslow
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@check_version(mp, '0.19')
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def test_gammaincc():
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# Check that the gammaincc in special._precompute.gammainc_data
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# agrees with mpmath's gammainc.
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assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
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lambda a, x: mp.gammainc(a, a=x, regularized=True),
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[Arg(20, 100), Arg(20, 100)],
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nan_ok=False, rtol=1e-17, n=50, dps=1000)
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# Test the fast integer path
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assert_mpmath_equal(gammaincc,
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lambda a, x: mp.gammainc(a, a=x, regularized=True),
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[IntArg(1, 100), Arg(0, 100)],
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nan_ok=False, rtol=1e-17, n=50, dps=50)
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