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from __future__ import division, print_function, absolute_import
import os
import numpy as np
from numpy import arccosh, arcsinh, arctanh
from scipy.special import (
erf, erfc, log1p, expm1,
jn, jv, yn, yv, iv, kv, kn, gamma, gammaln, digamma, beta, cbrt,
ellipe, ellipeinc, ellipk, ellipkm1, ellipj, erfinv, erfcinv, exp1, expi,
expn, zeta, gammaincinv, lpmv, mathieu_a, mathieu_b, mathieu_cem, mathieu_sem,
mathieu_modcem1, mathieu_modsem1, mathieu_modcem2, mathieu_modsem2,
)
from scipy.special._testutils import FuncData
DATASETS_BOOST = np.load(os.path.join(os.path.dirname(__file__),
"data", "boost.npz"))
DATASETS_GSL = np.load(os.path.join(os.path.dirname(__file__),
"data", "gsl.npz"))
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 ellipk_(k):
return ellipk(k*k)
def ellipe_(k):
return ellipe(k*k)
def ellipeinc_(f, k):
return ellipeinc(f, k*k)
def ellipj_(k):
return ellipj(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 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 test_boost():
TESTS = [
data(arccosh, 'acosh_data_ipp-acosh_data', 0, 1, rtol=5e-13),
data(arccosh, 'acosh_data_ipp-acosh_data', 0j, 1, rtol=5e-14),
data(arcsinh, 'asinh_data_ipp-asinh_data', 0, 1, rtol=1e-11),
data(arcsinh, 'asinh_data_ipp-asinh_data', 0j, 1, rtol=1e-11),
data(arctanh, 'atanh_data_ipp-atanh_data', 0, 1, rtol=1e-11),
data(arctanh, 'atanh_data_ipp-atanh_data', 0j, 1, rtol=1e-11),
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(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_small_data_ipp-beta_small_data', (0,1), 2),
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=1e-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-11),
data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0j, 1, rtol=1e-11),
data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0, 1),
data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0j, 1),
data(ellipk_, 'ellint_k_data_ipp-ellint_k_data', 0, 1),
data(ellipkm1, '-ellipkm1', 0, 1),
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),
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),
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),
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(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-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(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(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(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(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(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(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_data_ipp-gamma_inv_data', (0,1), 2,
rtol=1e-12),
data(gammaincinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data',
(0,1), 2, rtol=1e-11),
# XXX: the data file needs reformatting...
#data(gammaincinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data',
# (0,1), 2),
# -- not used yet:
# assoc_legendre_p.txt
# binomial_data.txt
# binomial_large_data.txt
# binomial_quantile_data.txt
# ellint_f_data.txt
# ellint_pi2_data.txt
# ellint_pi3_data.txt
# ellint_pi3_large_data.txt
# ellint_rc_data.txt
# ellint_rd_data.txt
# ellint_rf_data.txt
# ellint_rj_data.txt
# expinti_data_long.txt
# factorials.txt
# gammap1m1_data.txt
# hermite.txt
# ibeta_data.txt
# ibeta_int_data.txt
# ibeta_inv_data.txt
# ibeta_inva_data.txt
# ibeta_large_data.txt
# ibeta_small_data.txt
# igamma_big_data.txt
# igamma_int_data.txt
# igamma_inva_data.txt
# igamma_med_data.txt
# igamma_small_data.txt
# laguerre2.txt
# laguerre3.txt
# legendre_p.txt
# legendre_p_large.txt
# ncbeta.txt
# ncbeta_big.txt
# nccs.txt
# near_0.txt
# near_1.txt
# near_2.txt
# near_m10.txt
# near_m55.txt
# negative_binomial_quantile_data.txt
# poisson_quantile_data.txt
# sph_bessel_data.txt
# sph_neumann_data.txt
# spherical_harmonic.txt
# tgamma_delta_ratio_data.txt
# tgamma_delta_ratio_int.txt
# tgamma_delta_ratio_int2.txt
# tgamma_ratio_data.txt
]
for test in TESTS:
yield _test_factory, test
def 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),
]
for test in TESTS:
yield _test_factory, test
def _test_factory(test, dtype=np.double):
"""Boost test"""
olderr = np.seterr(all='ignore')
try:
test.check(dtype=dtype)
finally:
np.seterr(**olderr)
|
