ai-content-maker/.venv/Lib/site-packages/scipy/special/tests/test_data.py

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2024-05-03 04:18:51 +03:00
import importlib.resources
import numpy as np
from numpy.testing import suppress_warnings
import pytest
from scipy.special import (
lpn, lpmn, lpmv, lqn, lqmn, sph_harm, eval_legendre, eval_hermite,
eval_laguerre, eval_genlaguerre, binom, cbrt, expm1, log1p, zeta,
jn, jv, jvp, yn, yv, yvp, iv, ivp, kn, kv, kvp,
gamma, gammaln, gammainc, gammaincc, gammaincinv, gammainccinv, digamma,
beta, betainc, betaincinv, poch,
ellipe, ellipeinc, ellipk, ellipkm1, ellipkinc,
elliprc, elliprd, elliprf, elliprg, elliprj,
erf, erfc, erfinv, erfcinv, exp1, expi, expn,
bdtrik, btdtr, btdtri, btdtria, btdtrib, chndtr, gdtr, gdtrc, gdtrix, gdtrib,
nbdtrik, pdtrik, owens_t,
mathieu_a, mathieu_b, mathieu_cem, mathieu_sem, mathieu_modcem1,
mathieu_modsem1, mathieu_modcem2, mathieu_modsem2,
ellip_harm, ellip_harm_2, spherical_jn, spherical_yn, wright_bessel
)
from scipy.integrate import IntegrationWarning
from scipy.special._testutils import FuncData
# The npz files are generated, and hence may live in the build dir. We can only
# access them through `importlib.resources`, not an explicit path from `__file__`
_datadir = importlib.resources.files('scipy.special.tests.data')
_boost_npz = _datadir.joinpath('boost.npz')
with importlib.resources.as_file(_boost_npz) as f:
DATASETS_BOOST = np.load(f)
_gsl_npz = _datadir.joinpath('gsl.npz')
with importlib.resources.as_file(_gsl_npz) as f:
DATASETS_GSL = np.load(f)
_local_npz = _datadir.joinpath('local.npz')
with importlib.resources.as_file(_local_npz) as f:
DATASETS_LOCAL = np.load(f)
def data(func, dataname, *a, **kw):
kw.setdefault('dataname', dataname)
return FuncData(func, DATASETS_BOOST[dataname], *a, **kw)
def data_gsl(func, dataname, *a, **kw):
kw.setdefault('dataname', dataname)
return FuncData(func, DATASETS_GSL[dataname], *a, **kw)
def data_local(func, dataname, *a, **kw):
kw.setdefault('dataname', dataname)
return FuncData(func, DATASETS_LOCAL[dataname], *a, **kw)
def ellipk_(k):
return ellipk(k*k)
def ellipkinc_(f, k):
return ellipkinc(f, k*k)
def ellipe_(k):
return ellipe(k*k)
def ellipeinc_(f, k):
return ellipeinc(f, k*k)
def zeta_(x):
return zeta(x, 1.)
def assoc_legendre_p_boost_(nu, mu, x):
# the boost test data is for integer orders only
return lpmv(mu, nu.astype(int), x)
def legendre_p_via_assoc_(nu, x):
return lpmv(0, nu, x)
def lpn_(n, x):
return lpn(n.astype('l'), x)[0][-1]
def lqn_(n, x):
return lqn(n.astype('l'), x)[0][-1]
def legendre_p_via_lpmn(n, x):
return lpmn(0, n, x)[0][0,-1]
def legendre_q_via_lqmn(n, x):
return lqmn(0, n, x)[0][0,-1]
def mathieu_ce_rad(m, q, x):
return mathieu_cem(m, q, x*180/np.pi)[0]
def mathieu_se_rad(m, q, x):
return mathieu_sem(m, q, x*180/np.pi)[0]
def mathieu_mc1_scaled(m, q, x):
# GSL follows a different normalization.
# We follow Abramowitz & Stegun, they apparently something else.
return mathieu_modcem1(m, q, x)[0] * np.sqrt(np.pi/2)
def mathieu_ms1_scaled(m, q, x):
return mathieu_modsem1(m, q, x)[0] * np.sqrt(np.pi/2)
def mathieu_mc2_scaled(m, q, x):
return mathieu_modcem2(m, q, x)[0] * np.sqrt(np.pi/2)
def mathieu_ms2_scaled(m, q, x):
return mathieu_modsem2(m, q, x)[0] * np.sqrt(np.pi/2)
def eval_legendre_ld(n, x):
return eval_legendre(n.astype('l'), x)
def eval_legendre_dd(n, x):
return eval_legendre(n.astype('d'), x)
def eval_hermite_ld(n, x):
return eval_hermite(n.astype('l'), x)
def eval_laguerre_ld(n, x):
return eval_laguerre(n.astype('l'), x)
def eval_laguerre_dd(n, x):
return eval_laguerre(n.astype('d'), x)
def eval_genlaguerre_ldd(n, a, x):
return eval_genlaguerre(n.astype('l'), a, x)
def eval_genlaguerre_ddd(n, a, x):
return eval_genlaguerre(n.astype('d'), a, x)
def bdtrik_comp(y, n, p):
return bdtrik(1-y, n, p)
def btdtri_comp(a, b, p):
return btdtri(a, b, 1-p)
def btdtria_comp(p, b, x):
return btdtria(1-p, b, x)
def btdtrib_comp(a, p, x):
return btdtrib(a, 1-p, x)
def gdtr_(p, x):
return gdtr(1.0, p, x)
def gdtrc_(p, x):
return gdtrc(1.0, p, x)
def gdtrix_(b, p):
return gdtrix(1.0, b, p)
def gdtrix_comp(b, p):
return gdtrix(1.0, b, 1-p)
def gdtrib_(p, x):
return gdtrib(1.0, p, x)
def gdtrib_comp(p, x):
return gdtrib(1.0, 1-p, x)
def nbdtrik_comp(y, n, p):
return nbdtrik(1-y, n, p)
def pdtrik_comp(p, m):
return pdtrik(1-p, m)
def poch_(z, m):
return 1.0 / poch(z, m)
def poch_minus(z, m):
return 1.0 / poch(z, -m)
def spherical_jn_(n, x):
return spherical_jn(n.astype('l'), x)
def spherical_yn_(n, x):
return spherical_yn(n.astype('l'), x)
def sph_harm_(m, n, theta, phi):
y = sph_harm(m, n, theta, phi)
return (y.real, y.imag)
def cexpm1(x, y):
z = expm1(x + 1j*y)
return z.real, z.imag
def clog1p(x, y):
z = log1p(x + 1j*y)
return z.real, z.imag
BOOST_TESTS = [
data(assoc_legendre_p_boost_, 'assoc_legendre_p_ipp-assoc_legendre_p',
(0,1,2), 3, rtol=1e-11),
data(legendre_p_via_assoc_, 'legendre_p_ipp-legendre_p',
(0,1), 2, rtol=1e-11),
data(legendre_p_via_assoc_, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 2, rtol=9.6e-14),
data(legendre_p_via_lpmn, 'legendre_p_ipp-legendre_p',
(0,1), 2, rtol=5e-14, vectorized=False),
data(legendre_p_via_lpmn, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 2, rtol=9.6e-14, vectorized=False),
data(lpn_, 'legendre_p_ipp-legendre_p',
(0,1), 2, rtol=5e-14, vectorized=False),
data(lpn_, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 2, rtol=3e-13, vectorized=False),
data(eval_legendre_ld, 'legendre_p_ipp-legendre_p',
(0,1), 2, rtol=6e-14),
data(eval_legendre_ld, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 2, rtol=2e-13),
data(eval_legendre_dd, 'legendre_p_ipp-legendre_p',
(0,1), 2, rtol=2e-14),
data(eval_legendre_dd, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 2, rtol=2e-13),
data(lqn_, 'legendre_p_ipp-legendre_p',
(0,1), 3, rtol=2e-14, vectorized=False),
data(lqn_, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 3, rtol=2e-12, vectorized=False),
data(legendre_q_via_lqmn, 'legendre_p_ipp-legendre_p',
(0,1), 3, rtol=2e-14, vectorized=False),
data(legendre_q_via_lqmn, 'legendre_p_large_ipp-legendre_p_large',
(0,1), 3, rtol=2e-12, vectorized=False),
data(beta, 'beta_exp_data_ipp-beta_exp_data',
(0,1), 2, rtol=1e-13),
data(beta, 'beta_exp_data_ipp-beta_exp_data',
(0,1), 2, rtol=1e-13),
data(beta, 'beta_med_data_ipp-beta_med_data',
(0,1), 2, rtol=5e-13),
data(betainc, 'ibeta_small_data_ipp-ibeta_small_data',
(0,1,2), 5, rtol=6e-15),
data(betainc, 'ibeta_data_ipp-ibeta_data',
(0,1,2), 5, rtol=5e-13),
data(betainc, 'ibeta_int_data_ipp-ibeta_int_data',
(0,1,2), 5, rtol=2e-14),
data(betainc, 'ibeta_large_data_ipp-ibeta_large_data',
(0,1,2), 5, rtol=4e-10),
data(betaincinv, 'ibeta_inv_data_ipp-ibeta_inv_data',
(0,1,2), 3, rtol=1e-5),
data(btdtr, 'ibeta_small_data_ipp-ibeta_small_data',
(0,1,2), 5, rtol=6e-15),
data(btdtr, 'ibeta_data_ipp-ibeta_data',
(0,1,2), 5, rtol=4e-13),
data(btdtr, 'ibeta_int_data_ipp-ibeta_int_data',
(0,1,2), 5, rtol=2e-14),
data(btdtr, 'ibeta_large_data_ipp-ibeta_large_data',
(0,1,2), 5, rtol=4e-10),
data(btdtri, 'ibeta_inv_data_ipp-ibeta_inv_data',
(0,1,2), 3, rtol=1e-5),
data(btdtri_comp, 'ibeta_inv_data_ipp-ibeta_inv_data',
(0,1,2), 4, rtol=8e-7),
data(btdtria, 'ibeta_inva_data_ipp-ibeta_inva_data',
(2,0,1), 3, rtol=5e-9),
data(btdtria_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
(2,0,1), 4, rtol=5e-9),
data(btdtrib, 'ibeta_inva_data_ipp-ibeta_inva_data',
(0,2,1), 5, rtol=5e-9),
data(btdtrib_comp, 'ibeta_inva_data_ipp-ibeta_inva_data',
(0,2,1), 6, rtol=5e-9),
data(binom, 'binomial_data_ipp-binomial_data',
(0,1), 2, rtol=1e-13),
data(binom, 'binomial_large_data_ipp-binomial_large_data',
(0,1), 2, rtol=5e-13),
data(bdtrik, 'binomial_quantile_ipp-binomial_quantile_data',
(2,0,1), 3, rtol=5e-9),
data(bdtrik_comp, 'binomial_quantile_ipp-binomial_quantile_data',
(2,0,1), 4, rtol=5e-9),
data(nbdtrik, 'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
(2,0,1), 3, rtol=4e-9),
data(nbdtrik_comp,
'negative_binomial_quantile_ipp-negative_binomial_quantile_data',
(2,0,1), 4, rtol=4e-9),
data(pdtrik, 'poisson_quantile_ipp-poisson_quantile_data',
(1,0), 2, rtol=3e-9),
data(pdtrik_comp, 'poisson_quantile_ipp-poisson_quantile_data',
(1,0), 3, rtol=4e-9),
data(cbrt, 'cbrt_data_ipp-cbrt_data', 1, 0),
data(digamma, 'digamma_data_ipp-digamma_data', 0, 1),
data(digamma, 'digamma_data_ipp-digamma_data', 0j, 1),
data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0, 1, rtol=2e-13),
data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0j, 1, rtol=1e-13),
data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0, 1, rtol=1e-15),
data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0j, 1, rtol=1e-15),
data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0, 1, rtol=1e-15),
data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0j, 1, rtol=1e-14),
data(ellipk_, 'ellint_k_data_ipp-ellint_k_data', 0, 1),
data(ellipkinc_, 'ellint_f_data_ipp-ellint_f_data', (0,1), 2, rtol=1e-14),
data(ellipe_, 'ellint_e_data_ipp-ellint_e_data', 0, 1),
data(ellipeinc_, 'ellint_e2_data_ipp-ellint_e2_data', (0,1), 2, rtol=1e-14),
data(erf, 'erf_data_ipp-erf_data', 0, 1),
data(erf, 'erf_data_ipp-erf_data', 0j, 1, rtol=1e-13),
data(erfc, 'erf_data_ipp-erf_data', 0, 2, rtol=6e-15),
data(erf, 'erf_large_data_ipp-erf_large_data', 0, 1),
data(erf, 'erf_large_data_ipp-erf_large_data', 0j, 1),
data(erfc, 'erf_large_data_ipp-erf_large_data', 0, 2, rtol=4e-14),
data(erf, 'erf_small_data_ipp-erf_small_data', 0, 1),
data(erf, 'erf_small_data_ipp-erf_small_data', 0j, 1, rtol=1e-13),
data(erfc, 'erf_small_data_ipp-erf_small_data', 0, 2),
data(erfinv, 'erf_inv_data_ipp-erf_inv_data', 0, 1),
data(erfcinv, 'erfc_inv_data_ipp-erfc_inv_data', 0, 1),
data(erfcinv, 'erfc_inv_big_data_ipp-erfc_inv_big_data', 0, 1,
param_filter=(lambda s: s > 0)),
data(exp1, 'expint_1_data_ipp-expint_1_data', 1, 2, rtol=1e-13),
data(exp1, 'expint_1_data_ipp-expint_1_data', 1j, 2, rtol=5e-9),
data(expi, 'expinti_data_ipp-expinti_data', 0, 1, rtol=1e-13),
data(expi, 'expinti_data_double_ipp-expinti_data_double', 0, 1, rtol=1e-13),
data(expi, 'expinti_data_long_ipp-expinti_data_long', 0, 1),
data(expn, 'expint_small_data_ipp-expint_small_data', (0,1), 2),
data(expn, 'expint_data_ipp-expint_data', (0,1), 2, rtol=1e-14),
data(gamma, 'test_gamma_data_ipp-near_0', 0, 1),
data(gamma, 'test_gamma_data_ipp-near_1', 0, 1),
data(gamma, 'test_gamma_data_ipp-near_2', 0, 1),
data(gamma, 'test_gamma_data_ipp-near_m10', 0, 1),
data(gamma, 'test_gamma_data_ipp-near_m55', 0, 1, rtol=7e-12),
data(gamma, 'test_gamma_data_ipp-factorials', 0, 1, rtol=4e-14),
data(gamma, 'test_gamma_data_ipp-near_0', 0j, 1, rtol=2e-9),
data(gamma, 'test_gamma_data_ipp-near_1', 0j, 1, rtol=2e-9),
data(gamma, 'test_gamma_data_ipp-near_2', 0j, 1, rtol=2e-9),
data(gamma, 'test_gamma_data_ipp-near_m10', 0j, 1, rtol=2e-9),
data(gamma, 'test_gamma_data_ipp-near_m55', 0j, 1, rtol=2e-9),
data(gamma, 'test_gamma_data_ipp-factorials', 0j, 1, rtol=2e-13),
data(gammaln, 'test_gamma_data_ipp-near_0', 0, 2, rtol=5e-11),
data(gammaln, 'test_gamma_data_ipp-near_1', 0, 2, rtol=5e-11),
data(gammaln, 'test_gamma_data_ipp-near_2', 0, 2, rtol=2e-10),
data(gammaln, 'test_gamma_data_ipp-near_m10', 0, 2, rtol=5e-11),
data(gammaln, 'test_gamma_data_ipp-near_m55', 0, 2, rtol=5e-11),
data(gammaln, 'test_gamma_data_ipp-factorials', 0, 2),
data(gammainc, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=5e-15),
data(gammainc, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
data(gammainc, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
data(gammainc, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=1e-12),
data(gdtr_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=1e-13),
data(gdtr_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
data(gdtr_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
data(gdtr_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=2e-9),
data(gammaincc, 'igamma_small_data_ipp-igamma_small_data',
(0,1), 3, rtol=1e-13),
data(gammaincc, 'igamma_med_data_ipp-igamma_med_data',
(0,1), 3, rtol=2e-13),
data(gammaincc, 'igamma_int_data_ipp-igamma_int_data',
(0,1), 3, rtol=4e-14),
data(gammaincc, 'igamma_big_data_ipp-igamma_big_data',
(0,1), 3, rtol=1e-11),
data(gdtrc_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 3, rtol=1e-13),
data(gdtrc_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 3, rtol=2e-13),
data(gdtrc_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 3, rtol=4e-14),
data(gdtrc_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 3, rtol=1e-11),
data(gdtrib_, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 2, rtol=5e-9),
data(gdtrib_comp, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 3, rtol=5e-9),
data(poch_, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
(0,1), 2, rtol=2e-13),
data(poch_, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
(0,1), 2,),
data(poch_, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
(0,1), 2,),
data(poch_minus, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data',
(0,1), 3, rtol=2e-13),
data(poch_minus, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int',
(0,1), 3),
data(poch_minus, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2',
(0,1), 3),
data(eval_hermite_ld, 'hermite_ipp-hermite',
(0,1), 2, rtol=2e-14),
data(eval_laguerre_ld, 'laguerre2_ipp-laguerre2',
(0,1), 2, rtol=7e-12),
data(eval_laguerre_dd, 'laguerre2_ipp-laguerre2',
(0,1), 2, knownfailure='hyp2f1 insufficiently accurate.'),
data(eval_genlaguerre_ldd, 'laguerre3_ipp-laguerre3',
(0,1,2), 3, rtol=2e-13),
data(eval_genlaguerre_ddd, 'laguerre3_ipp-laguerre3',
(0,1,2), 3, knownfailure='hyp2f1 insufficiently accurate.'),
data(log1p, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 1),
data(expm1, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 2),
data(iv, 'bessel_i_data_ipp-bessel_i_data',
(0,1), 2, rtol=1e-12),
data(iv, 'bessel_i_data_ipp-bessel_i_data',
(0,1j), 2, rtol=2e-10, atol=1e-306),
data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
(0,1), 2, rtol=1e-9),
data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data',
(0,1j), 2, rtol=2e-10),
data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
(0,1), 2, rtol=1.2e-13),
data(ivp, 'bessel_i_prime_int_data_ipp-bessel_i_prime_int_data',
(0,1j), 2, rtol=1.2e-13, atol=1e-300),
data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1), 2, rtol=6e-11),
data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1j), 2, rtol=6e-11),
data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1), 2, rtol=1e-12),
data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1j), 2, rtol=1e-12),
data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
(0,1), 2, rtol=1e-13),
data(jvp, 'bessel_j_prime_int_data_ipp-bessel_j_prime_int_data',
(0,1j), 2, rtol=1e-13),
data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
(0,1), 2, rtol=1e-11),
data(jvp, 'bessel_j_prime_large_data_ipp-bessel_j_prime_large_data',
(0,1j), 2, rtol=2e-11),
data(kn, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1j), 2, rtol=1e-12),
data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1), 2, rtol=1e-12),
data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1j), 2, rtol=1e-12),
data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
(0,1), 2, rtol=3e-14),
data(kvp, 'bessel_k_prime_int_data_ipp-bessel_k_prime_int_data',
(0,1j), 2, rtol=3e-14),
data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1), 2, rtol=7e-14),
data(kvp, 'bessel_k_prime_data_ipp-bessel_k_prime_data', (0,1j), 2, rtol=7e-14),
data(yn, 'bessel_y01_data_ipp-bessel_y01_data', (0,1), 2, rtol=1e-12),
data(yn, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1j), 2, rtol=1e-12),
data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1), 2, rtol=1e-10),
data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1j), 2, rtol=1e-10),
data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
(0, 1), 2, rtol=4e-9),
data(yvp, 'bessel_yv_prime_data_ipp-bessel_yv_prime_data',
(0, 1j), 2, rtol=4e-9),
data(zeta_, 'zeta_data_ipp-zeta_data', 0, 1,
param_filter=(lambda s: s > 1)),
data(zeta_, 'zeta_neg_data_ipp-zeta_neg_data', 0, 1,
param_filter=(lambda s: s > 1)),
data(zeta_, 'zeta_1_up_data_ipp-zeta_1_up_data', 0, 1,
param_filter=(lambda s: s > 1)),
data(zeta_, 'zeta_1_below_data_ipp-zeta_1_below_data', 0, 1,
param_filter=(lambda s: s > 1)),
data(gammaincinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
(0,1), 2, rtol=1e-11),
data(gammaincinv, 'gamma_inv_data_ipp-gamma_inv_data',
(0,1), 2, rtol=1e-14),
data(gammaincinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
(0,1), 2, rtol=1e-11),
data(gammainccinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
(0,1), 3, rtol=1e-12),
data(gammainccinv, 'gamma_inv_data_ipp-gamma_inv_data',
(0,1), 3, rtol=1e-14),
data(gammainccinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
(0,1), 3, rtol=1e-14),
data(gdtrix_, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
(0,1), 2, rtol=3e-13, knownfailure='gdtrix unflow some points'),
data(gdtrix_, 'gamma_inv_data_ipp-gamma_inv_data',
(0,1), 2, rtol=3e-15),
data(gdtrix_, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
(0,1), 2),
data(gdtrix_comp, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
(0,1), 2, knownfailure='gdtrix bad some points'),
data(gdtrix_comp, 'gamma_inv_data_ipp-gamma_inv_data',
(0,1), 3, rtol=6e-15),
data(gdtrix_comp, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
(0,1), 3),
data(chndtr, 'nccs_ipp-nccs',
(2,0,1), 3, rtol=3e-5),
data(chndtr, 'nccs_big_ipp-nccs_big',
(2,0,1), 3, rtol=5e-4, knownfailure='chndtr inaccurate some points'),
data(sph_harm_, 'spherical_harmonic_ipp-spherical_harmonic',
(1,0,3,2), (4,5), rtol=5e-11,
param_filter=(lambda p: np.ones(p.shape, '?'),
lambda p: np.ones(p.shape, '?'),
lambda p: np.logical_and(p < 2*np.pi, p >= 0),
lambda p: np.logical_and(p < np.pi, p >= 0))),
data(spherical_jn_, 'sph_bessel_data_ipp-sph_bessel_data',
(0,1), 2, rtol=1e-13),
data(spherical_yn_, 'sph_neumann_data_ipp-sph_neumann_data',
(0,1), 2, rtol=8e-15),
data(owens_t, 'owens_t_ipp-owens_t',
(0, 1), 2, rtol=5e-14),
data(owens_t, 'owens_t_large_data_ipp-owens_t_large_data',
(0, 1), 2, rtol=8e-12),
# -- test data exists in boost but is not used in scipy --
# ibeta_derivative_data_ipp/ibeta_derivative_data.txt
# ibeta_derivative_int_data_ipp/ibeta_derivative_int_data.txt
# ibeta_derivative_large_data_ipp/ibeta_derivative_large_data.txt
# ibeta_derivative_small_data_ipp/ibeta_derivative_small_data.txt
# bessel_y01_prime_data_ipp/bessel_y01_prime_data.txt
# bessel_yn_prime_data_ipp/bessel_yn_prime_data.txt
# sph_bessel_prime_data_ipp/sph_bessel_prime_data.txt
# sph_neumann_prime_data_ipp/sph_neumann_prime_data.txt
# ellint_d2_data_ipp/ellint_d2_data.txt
# ellint_d_data_ipp/ellint_d_data.txt
# ellint_pi2_data_ipp/ellint_pi2_data.txt
# ellint_pi3_data_ipp/ellint_pi3_data.txt
# ellint_pi3_large_data_ipp/ellint_pi3_large_data.txt
data(elliprc, 'ellint_rc_data_ipp-ellint_rc_data', (0, 1), 2,
rtol=5e-16),
data(elliprd, 'ellint_rd_data_ipp-ellint_rd_data', (0, 1, 2), 3,
rtol=5e-16),
data(elliprd, 'ellint_rd_0xy_ipp-ellint_rd_0xy', (0, 1, 2), 3,
rtol=5e-16),
data(elliprd, 'ellint_rd_0yy_ipp-ellint_rd_0yy', (0, 1, 2), 3,
rtol=5e-16),
data(elliprd, 'ellint_rd_xxx_ipp-ellint_rd_xxx', (0, 1, 2), 3,
rtol=5e-16),
# Some of the following rtol for elliprd may be larger than 5e-16 to
# work around some hard cases in the Boost test where we get slightly
# larger error than the ideal bound when the x (==y) input is close to
# zero.
# Also the accuracy on 32-bit builds with g++ may suffer from excess
# loss of precision; see GCC bugzilla 323
# https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323
data(elliprd, 'ellint_rd_xxz_ipp-ellint_rd_xxz', (0, 1, 2), 3,
rtol=6.5e-16),
data(elliprd, 'ellint_rd_xyy_ipp-ellint_rd_xyy', (0, 1, 2), 3,
rtol=6e-16),
data(elliprf, 'ellint_rf_data_ipp-ellint_rf_data', (0, 1, 2), 3,
rtol=5e-16),
data(elliprf, 'ellint_rf_xxx_ipp-ellint_rf_xxx', (0, 1, 2), 3,
rtol=5e-16),
data(elliprf, 'ellint_rf_xyy_ipp-ellint_rf_xyy', (0, 1, 2), 3,
rtol=5e-16),
data(elliprf, 'ellint_rf_xy0_ipp-ellint_rf_xy0', (0, 1, 2), 3,
rtol=5e-16),
data(elliprf, 'ellint_rf_0yy_ipp-ellint_rf_0yy', (0, 1, 2), 3,
rtol=5e-16),
# The accuracy of R_G is primarily limited by R_D that is used
# internally. It is generally worse than R_D. Notice that we increased
# the rtol for R_G here. The cases with duplicate arguments are
# slightly less likely to be unbalanced (at least two arguments are
# already balanced) so the error bound is slightly better. Again,
# precision with g++ 32-bit is even worse.
data(elliprg, 'ellint_rg_ipp-ellint_rg', (0, 1, 2), 3,
rtol=8.0e-16),
data(elliprg, 'ellint_rg_xxx_ipp-ellint_rg_xxx', (0, 1, 2), 3,
rtol=6e-16),
data(elliprg, 'ellint_rg_xyy_ipp-ellint_rg_xyy', (0, 1, 2), 3,
rtol=7.5e-16),
data(elliprg, 'ellint_rg_xy0_ipp-ellint_rg_xy0', (0, 1, 2), 3,
rtol=5e-16),
data(elliprg, 'ellint_rg_00x_ipp-ellint_rg_00x', (0, 1, 2), 3,
rtol=5e-16),
data(elliprj, 'ellint_rj_data_ipp-ellint_rj_data', (0, 1, 2, 3), 4,
rtol=5e-16, atol=1e-25,
param_filter=(lambda s: s <= 5e-26,)),
# ellint_rc_data_ipp/ellint_rc_data.txt
# ellint_rd_0xy_ipp/ellint_rd_0xy.txt
# ellint_rd_0yy_ipp/ellint_rd_0yy.txt
# ellint_rd_data_ipp/ellint_rd_data.txt
# ellint_rd_xxx_ipp/ellint_rd_xxx.txt
# ellint_rd_xxz_ipp/ellint_rd_xxz.txt
# ellint_rd_xyy_ipp/ellint_rd_xyy.txt
# ellint_rf_0yy_ipp/ellint_rf_0yy.txt
# ellint_rf_data_ipp/ellint_rf_data.txt
# ellint_rf_xxx_ipp/ellint_rf_xxx.txt
# ellint_rf_xy0_ipp/ellint_rf_xy0.txt
# ellint_rf_xyy_ipp/ellint_rf_xyy.txt
# ellint_rg_00x_ipp/ellint_rg_00x.txt
# ellint_rg_ipp/ellint_rg.txt
# ellint_rg_xxx_ipp/ellint_rg_xxx.txt
# ellint_rg_xy0_ipp/ellint_rg_xy0.txt
# ellint_rg_xyy_ipp/ellint_rg_xyy.txt
# ellint_rj_data_ipp/ellint_rj_data.txt
# ellint_rj_e2_ipp/ellint_rj_e2.txt
# ellint_rj_e3_ipp/ellint_rj_e3.txt
# ellint_rj_e4_ipp/ellint_rj_e4.txt
# ellint_rj_zp_ipp/ellint_rj_zp.txt
# jacobi_elliptic_ipp/jacobi_elliptic.txt
# jacobi_elliptic_small_ipp/jacobi_elliptic_small.txt
# jacobi_large_phi_ipp/jacobi_large_phi.txt
# jacobi_near_1_ipp/jacobi_near_1.txt
# jacobi_zeta_big_phi_ipp/jacobi_zeta_big_phi.txt
# jacobi_zeta_data_ipp/jacobi_zeta_data.txt
# heuman_lambda_data_ipp/heuman_lambda_data.txt
# hypergeometric_0F2_ipp/hypergeometric_0F2.txt
# hypergeometric_1F1_big_ipp/hypergeometric_1F1_big.txt
# hypergeometric_1F1_ipp/hypergeometric_1F1.txt
# hypergeometric_1F1_small_random_ipp/hypergeometric_1F1_small_random.txt
# hypergeometric_1F2_ipp/hypergeometric_1F2.txt
# hypergeometric_1f1_large_regularized_ipp/hypergeometric_1f1_large_regularized.txt # noqa: E501
# hypergeometric_1f1_log_large_unsolved_ipp/hypergeometric_1f1_log_large_unsolved.txt # noqa: E501
# hypergeometric_2F0_half_ipp/hypergeometric_2F0_half.txt
# hypergeometric_2F0_integer_a2_ipp/hypergeometric_2F0_integer_a2.txt
# hypergeometric_2F0_ipp/hypergeometric_2F0.txt
# hypergeometric_2F0_large_z_ipp/hypergeometric_2F0_large_z.txt
# hypergeometric_2F1_ipp/hypergeometric_2F1.txt
# hypergeometric_2F2_ipp/hypergeometric_2F2.txt
# ncbeta_big_ipp/ncbeta_big.txt
# nct_small_delta_ipp/nct_small_delta.txt
# nct_asym_ipp/nct_asym.txt
# ncbeta_ipp/ncbeta.txt
# powm1_data_ipp/powm1_big_data.txt
# powm1_sqrtp1m1_test_hpp/sqrtp1m1_data.txt
# sinc_data_ipp/sinc_data.txt
# test_gamma_data_ipp/gammap1m1_data.txt
# tgamma_ratio_data_ipp/tgamma_ratio_data.txt
# trig_data_ipp/trig_data.txt
# trig_data2_ipp/trig_data2.txt
]
@pytest.mark.parametrize('test', BOOST_TESTS, ids=repr)
def test_boost(test):
# Filter deprecation warnings of any deprecated functions.
if test.func in [btdtr, btdtri, btdtri_comp]:
with pytest.deprecated_call():
_test_factory(test)
else:
_test_factory(test)
GSL_TESTS = [
data_gsl(mathieu_a, 'mathieu_ab', (0, 1), 2, rtol=1e-13, atol=1e-13),
data_gsl(mathieu_b, 'mathieu_ab', (0, 1), 3, rtol=1e-13, atol=1e-13),
# Also the GSL output has limited accuracy...
data_gsl(mathieu_ce_rad, 'mathieu_ce_se', (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
data_gsl(mathieu_se_rad, 'mathieu_ce_se', (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
data_gsl(mathieu_mc1_scaled, 'mathieu_mc_ms',
(0, 1, 2), 3, rtol=1e-7, atol=1e-13),
data_gsl(mathieu_ms1_scaled, 'mathieu_mc_ms',
(0, 1, 2), 4, rtol=1e-7, atol=1e-13),
data_gsl(mathieu_mc2_scaled, 'mathieu_mc_ms',
(0, 1, 2), 5, rtol=1e-7, atol=1e-13),
data_gsl(mathieu_ms2_scaled, 'mathieu_mc_ms',
(0, 1, 2), 6, rtol=1e-7, atol=1e-13),
]
@pytest.mark.parametrize('test', GSL_TESTS, ids=repr)
def test_gsl(test):
_test_factory(test)
LOCAL_TESTS = [
data_local(ellipkinc, 'ellipkinc_neg_m', (0, 1), 2),
data_local(ellipkm1, 'ellipkm1', 0, 1),
data_local(ellipeinc, 'ellipeinc_neg_m', (0, 1), 2),
data_local(clog1p, 'log1p_expm1_complex', (0,1), (2,3), rtol=1e-14),
data_local(cexpm1, 'log1p_expm1_complex', (0,1), (4,5), rtol=1e-14),
data_local(gammainc, 'gammainc', (0, 1), 2, rtol=1e-12),
data_local(gammaincc, 'gammaincc', (0, 1), 2, rtol=1e-11),
data_local(ellip_harm_2, 'ellip',(0, 1, 2, 3, 4), 6, rtol=1e-10, atol=1e-13),
data_local(ellip_harm, 'ellip',(0, 1, 2, 3, 4), 5, rtol=1e-10, atol=1e-13),
data_local(wright_bessel, 'wright_bessel', (0, 1, 2), 3, rtol=1e-11),
]
@pytest.mark.parametrize('test', LOCAL_TESTS, ids=repr)
def test_local(test):
_test_factory(test)
def _test_factory(test, dtype=np.float64):
"""Boost test"""
with suppress_warnings() as sup:
sup.filter(IntegrationWarning, "The occurrence of roundoff error is detected")
with np.errstate(all='ignore'):
test.check(dtype=dtype)