110 lines
4.5 KiB
Python
110 lines
4.5 KiB
Python
|
import numpy as np # np is actually used, in the decorators below.
|
||
|
|
import pytest
|
||
|
|
|
||
|
|
from scipy.special._testutils import MissingModule, check_version
|
||
|
|
from scipy.special._mptestutils import (
|
||
|
|
Arg, IntArg, mp_assert_allclose, assert_mpmath_equal)
|
||
|
|
from scipy.special._precompute.gammainc_asy import (
|
||
|
|
compute_g, compute_alpha, compute_d)
|
||
|
|
from scipy.special._precompute.gammainc_data import gammainc, gammaincc
|
||
|
|
|
||
|
|
try:
|
||
|
|
import sympy # type: ignore[import]
|
||
|
|
except ImportError:
|
||
|
|
sympy = MissingModule('sympy')
|
||
|
|
|
||
|
|
try:
|
||
|
|
import mpmath as mp # type: ignore[import]
|
||
|
|
except ImportError:
|
||
|
|
mp = MissingModule('mpmath')
|
||
|
|
|
||
|
|
|
||
|
|
@check_version(mp, '0.19')
|
||
|
|
def test_g():
|
||
|
|
# Test data for the g_k. See DLMF 5.11.4.
|
||
|
|
with mp.workdps(30):
|
||
|
|
g = [mp.mpf(1), mp.mpf(1)/12, mp.mpf(1)/288,
|
||
|
|
-mp.mpf(139)/51840, -mp.mpf(571)/2488320,
|
||
|
|
mp.mpf(163879)/209018880, mp.mpf(5246819)/75246796800]
|
||
|
|
mp_assert_allclose(compute_g(7), g)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
@check_version(mp, '0.19')
|
||
|
|
@check_version(sympy, '0.7')
|
||
|
|
@pytest.mark.xfail_on_32bit("rtol only 2e-11, see gh-6938")
|
||
|
|
def test_alpha():
|
||
|
|
# Test data for the alpha_k. See DLMF 8.12.14.
|
||
|
|
with mp.workdps(30):
|
||
|
|
alpha = [mp.mpf(0), mp.mpf(1), mp.mpf(1)/3, mp.mpf(1)/36,
|
||
|
|
-mp.mpf(1)/270, mp.mpf(1)/4320, mp.mpf(1)/17010,
|
||
|
|
-mp.mpf(139)/5443200, mp.mpf(1)/204120]
|
||
|
|
mp_assert_allclose(compute_alpha(9), alpha)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.xslow
|
||
|
|
@check_version(mp, '0.19')
|
||
|
|
@check_version(sympy, '0.7')
|
||
|
|
def test_d():
|
||
|
|
# Compare the d_{k, n} to the results in appendix F of [1].
|
||
|
|
#
|
||
|
|
# Sources
|
||
|
|
# -------
|
||
|
|
# [1] DiDonato and Morris, Computation of the Incomplete Gamma
|
||
|
|
# Function Ratios and their Inverse, ACM Transactions on
|
||
|
|
# Mathematical Software, 1986.
|
||
|
|
|
||
|
|
with mp.workdps(50):
|
||
|
|
dataset = [(0, 0, -mp.mpf('0.333333333333333333333333333333')),
|
||
|
|
(0, 12, mp.mpf('0.102618097842403080425739573227e-7')),
|
||
|
|
(1, 0, -mp.mpf('0.185185185185185185185185185185e-2')),
|
||
|
|
(1, 12, mp.mpf('0.119516285997781473243076536700e-7')),
|
||
|
|
(2, 0, mp.mpf('0.413359788359788359788359788360e-2')),
|
||
|
|
(2, 12, -mp.mpf('0.140925299108675210532930244154e-7')),
|
||
|
|
(3, 0, mp.mpf('0.649434156378600823045267489712e-3')),
|
||
|
|
(3, 12, -mp.mpf('0.191111684859736540606728140873e-7')),
|
||
|
|
(4, 0, -mp.mpf('0.861888290916711698604702719929e-3')),
|
||
|
|
(4, 12, mp.mpf('0.288658297427087836297341274604e-7')),
|
||
|
|
(5, 0, -mp.mpf('0.336798553366358150308767592718e-3')),
|
||
|
|
(5, 12, mp.mpf('0.482409670378941807563762631739e-7')),
|
||
|
|
(6, 0, mp.mpf('0.531307936463992223165748542978e-3')),
|
||
|
|
(6, 12, -mp.mpf('0.882860074633048352505085243179e-7')),
|
||
|
|
(7, 0, mp.mpf('0.344367606892377671254279625109e-3')),
|
||
|
|
(7, 12, -mp.mpf('0.175629733590604619378669693914e-6')),
|
||
|
|
(8, 0, -mp.mpf('0.652623918595309418922034919727e-3')),
|
||
|
|
(8, 12, mp.mpf('0.377358774161109793380344937299e-6')),
|
||
|
|
(9, 0, -mp.mpf('0.596761290192746250124390067179e-3')),
|
||
|
|
(9, 12, mp.mpf('0.870823417786464116761231237189e-6'))]
|
||
|
|
d = compute_d(10, 13)
|
||
|
|
res = [d[k][n] for k, n, std in dataset]
|
||
|
|
std = map(lambda x: x[2], dataset)
|
||
|
|
mp_assert_allclose(res, std)
|
||
|
|
|
||
|
|
|
||
|
|
@check_version(mp, '0.19')
|
||
|
|
def test_gammainc():
|
||
|
|
# Quick check that the gammainc in
|
||
|
|
# special._precompute.gammainc_data agrees with mpmath's
|
||
|
|
# gammainc.
|
||
|
|
assert_mpmath_equal(gammainc,
|
||
|
|
lambda a, x: mp.gammainc(a, b=x, regularized=True),
|
||
|
|
[Arg(0, 100, inclusive_a=False), Arg(0, 100)],
|
||
|
|
nan_ok=False, rtol=1e-17, n=50, dps=50)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.xslow
|
||
|
|
@check_version(mp, '0.19')
|
||
|
|
def test_gammaincc():
|
||
|
|
# Check that the gammaincc in special._precompute.gammainc_data
|
||
|
|
# agrees with mpmath's gammainc.
|
||
|
|
assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
|
||
|
|
lambda a, x: mp.gammainc(a, a=x, regularized=True),
|
||
|
|
[Arg(20, 100), Arg(20, 100)],
|
||
|
|
nan_ok=False, rtol=1e-17, n=50, dps=1000)
|
||
|
|
|
||
|
|
# Test the fast integer path
|
||
|
|
assert_mpmath_equal(gammaincc,
|
||
|
|
lambda a, x: mp.gammainc(a, a=x, regularized=True),
|
||
|
|
[IntArg(1, 100), Arg(0, 100)],
|
||
|
|
nan_ok=False, rtol=1e-17, n=50, dps=50)
|