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"""
Test cdflib functions versus mpmath, if available.
The following functions still need tests:
- ncfdtr
- ncfdtri
- ncfdtridfn
- ncfdtridfd
- ncfdtrinc
- nbdtrik
- nbdtrin
- pdtrik
- nctdtr
- nctdtrit
- nctdtridf
- nctdtrinc
"""
import itertools
import numpy as np
from numpy.testing import assert_equal, assert_allclose
import pytest
import scipy.special as sp
from scipy.special._testutils import (
MissingModule, check_version, FuncData)
from scipy.special._mptestutils import (
Arg, IntArg, get_args, mpf2float, assert_mpmath_equal)
try:
import mpmath
except ImportError:
mpmath = MissingModule('mpmath')
class ProbArg:
"""Generate a set of probabilities on [0, 1]."""
def __init__(self):
# Include the endpoints for compatibility with Arg et. al.
self.a = 0
self.b = 1
def values(self, n):
"""Return an array containing approximately n numbers."""
m = max(1, n//3)
v1 = np.logspace(-30, np.log10(0.3), m)
v2 = np.linspace(0.3, 0.7, m + 1, endpoint=False)[1:]
v3 = 1 - np.logspace(np.log10(0.3), -15, m)
v = np.r_[v1, v2, v3]
return np.unique(v)
class EndpointFilter:
def __init__(self, a, b, rtol, atol):
self.a = a
self.b = b
self.rtol = rtol
self.atol = atol
def __call__(self, x):
mask1 = np.abs(x - self.a) < self.rtol*np.abs(self.a) + self.atol
mask2 = np.abs(x - self.b) < self.rtol*np.abs(self.b) + self.atol
return np.where(mask1 | mask2, False, True)
class _CDFData:
def __init__(self, spfunc, mpfunc, index, argspec, spfunc_first=True,
dps=20, n=5000, rtol=None, atol=None,
endpt_rtol=None, endpt_atol=None):
self.spfunc = spfunc
self.mpfunc = mpfunc
self.index = index
self.argspec = argspec
self.spfunc_first = spfunc_first
self.dps = dps
self.n = n
self.rtol = rtol
self.atol = atol
if not isinstance(argspec, list):
self.endpt_rtol = None
self.endpt_atol = None
elif endpt_rtol is not None or endpt_atol is not None:
if isinstance(endpt_rtol, list):
self.endpt_rtol = endpt_rtol
else:
self.endpt_rtol = [endpt_rtol]*len(self.argspec)
if isinstance(endpt_atol, list):
self.endpt_atol = endpt_atol
else:
self.endpt_atol = [endpt_atol]*len(self.argspec)
else:
self.endpt_rtol = None
self.endpt_atol = None
def idmap(self, *args):
if self.spfunc_first:
res = self.spfunc(*args)
if np.isnan(res):
return np.nan
args = list(args)
args[self.index] = res
with mpmath.workdps(self.dps):
res = self.mpfunc(*tuple(args))
# Imaginary parts are spurious
res = mpf2float(res.real)
else:
with mpmath.workdps(self.dps):
res = self.mpfunc(*args)
res = mpf2float(res.real)
args = list(args)
args[self.index] = res
res = self.spfunc(*tuple(args))
return res
def get_param_filter(self):
if self.endpt_rtol is None and self.endpt_atol is None:
return None
filters = []
for rtol, atol, spec in zip(self.endpt_rtol, self.endpt_atol, self.argspec):
if rtol is None and atol is None:
filters.append(None)
continue
elif rtol is None:
rtol = 0.0
elif atol is None:
atol = 0.0
filters.append(EndpointFilter(spec.a, spec.b, rtol, atol))
return filters
def check(self):
# Generate values for the arguments
args = get_args(self.argspec, self.n)
param_filter = self.get_param_filter()
param_columns = tuple(range(args.shape[1]))
result_columns = args.shape[1]
args = np.hstack((args, args[:, self.index].reshape(args.shape[0], 1)))
FuncData(self.idmap, args,
param_columns=param_columns, result_columns=result_columns,
rtol=self.rtol, atol=self.atol, vectorized=False,
param_filter=param_filter).check()
def _assert_inverts(*a, **kw):
d = _CDFData(*a, **kw)
d.check()
def _binomial_cdf(k, n, p):
k, n, p = mpmath.mpf(k), mpmath.mpf(n), mpmath.mpf(p)
if k <= 0:
return mpmath.mpf(0)
elif k >= n:
return mpmath.mpf(1)
onemp = mpmath.fsub(1, p, exact=True)
return mpmath.betainc(n - k, k + 1, x2=onemp, regularized=True)
def _f_cdf(dfn, dfd, x):
if x < 0:
return mpmath.mpf(0)
dfn, dfd, x = mpmath.mpf(dfn), mpmath.mpf(dfd), mpmath.mpf(x)
ub = dfn*x/(dfn*x + dfd)
res = mpmath.betainc(dfn/2, dfd/2, x2=ub, regularized=True)
return res
def _student_t_cdf(df, t, dps=None):
if dps is None:
dps = mpmath.mp.dps
with mpmath.workdps(dps):
df, t = mpmath.mpf(df), mpmath.mpf(t)
fac = mpmath.hyp2f1(0.5, 0.5*(df + 1), 1.5, -t**2/df)
fac *= t*mpmath.gamma(0.5*(df + 1))
fac /= mpmath.sqrt(mpmath.pi*df)*mpmath.gamma(0.5*df)
return 0.5 + fac
def _noncentral_chi_pdf(t, df, nc):
res = mpmath.besseli(df/2 - 1, mpmath.sqrt(nc*t))
res *= mpmath.exp(-(t + nc)/2)*(t/nc)**(df/4 - 1/2)/2
return res
def _noncentral_chi_cdf(x, df, nc, dps=None):
if dps is None:
dps = mpmath.mp.dps
x, df, nc = mpmath.mpf(x), mpmath.mpf(df), mpmath.mpf(nc)
with mpmath.workdps(dps):
res = mpmath.quad(lambda t: _noncentral_chi_pdf(t, df, nc), [0, x])
return res
def _tukey_lmbda_quantile(p, lmbda):
# For lmbda != 0
return (p**lmbda - (1 - p)**lmbda)/lmbda
@pytest.mark.slow
@check_version(mpmath, '0.19')
class TestCDFlib:
@pytest.mark.xfail(run=False)
def test_bdtrik(self):
_assert_inverts(
sp.bdtrik,
_binomial_cdf,
0, [ProbArg(), IntArg(1, 1000), ProbArg()],
rtol=1e-4)
def test_bdtrin(self):
_assert_inverts(
sp.bdtrin,
_binomial_cdf,
1, [IntArg(1, 1000), ProbArg(), ProbArg()],
rtol=1e-4, endpt_atol=[None, None, 1e-6])
def test_btdtria(self):
_assert_inverts(
sp.btdtria,
lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
0, [ProbArg(), Arg(0, 1e2, inclusive_a=False),
Arg(0, 1, inclusive_a=False, inclusive_b=False)],
rtol=1e-6)
def test_btdtrib(self):
# Use small values of a or mpmath doesn't converge
_assert_inverts(
sp.btdtrib,
lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
1,
[Arg(0, 1e2, inclusive_a=False), ProbArg(),
Arg(0, 1, inclusive_a=False, inclusive_b=False)],
rtol=1e-7,
endpt_atol=[None, 1e-18, 1e-15])
@pytest.mark.xfail(run=False)
def test_fdtridfd(self):
_assert_inverts(
sp.fdtridfd,
_f_cdf,
1,
[IntArg(1, 100), ProbArg(), Arg(0, 100, inclusive_a=False)],
rtol=1e-7)
def test_gdtria(self):
_assert_inverts(
sp.gdtria,
lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
0,
[ProbArg(), Arg(0, 1e3, inclusive_a=False),
Arg(0, 1e4, inclusive_a=False)],
rtol=1e-7,
endpt_atol=[None, 1e-7, 1e-10])
def test_gdtrib(self):
# Use small values of a and x or mpmath doesn't converge
_assert_inverts(
sp.gdtrib,
lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
1,
[Arg(0, 1e2, inclusive_a=False), ProbArg(),
Arg(0, 1e3, inclusive_a=False)],
rtol=1e-5)
def test_gdtrix(self):
_assert_inverts(
sp.gdtrix,
lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
2,
[Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
ProbArg()],
rtol=1e-7,
endpt_atol=[None, 1e-7, 1e-10])
# Overall nrdtrimn and nrdtrisd are not performing well with infeasible/edge
# combinations of sigma and x, hence restricted the domains to still use the
# testing machinery, also see gh-20069
# nrdtrimn signature: p, sd, x
# nrdtrisd signature: mn, p, x
def test_nrdtrimn(self):
_assert_inverts(
sp.nrdtrimn,
lambda x, y, z: mpmath.ncdf(z, x, y),
0,
[ProbArg(), # CDF value p
Arg(0.1, np.inf, inclusive_a=False, inclusive_b=False), # sigma
Arg(-1e10, 1e10)], # x
rtol=1e-5)
def test_nrdtrisd(self):
_assert_inverts(
sp.nrdtrisd,
lambda x, y, z: mpmath.ncdf(z, x, y),
1,
[Arg(-np.inf, 10, inclusive_a=False, inclusive_b=False), # mn
ProbArg(), # CDF value p
Arg(10, 1e100)], # x
rtol=1e-5)
def test_stdtr(self):
# Ideally the left endpoint for Arg() should be 0.
assert_mpmath_equal(
sp.stdtr,
_student_t_cdf,
[IntArg(1, 100), Arg(1e-10, np.inf)], rtol=1e-7)
@pytest.mark.xfail(run=False)
def test_stdtridf(self):
_assert_inverts(
sp.stdtridf,
_student_t_cdf,
0, [ProbArg(), Arg()], rtol=1e-7)
def test_stdtrit(self):
_assert_inverts(
sp.stdtrit,
_student_t_cdf,
1, [IntArg(1, 100), ProbArg()], rtol=1e-7,
endpt_atol=[None, 1e-10])
def test_chdtriv(self):
_assert_inverts(
sp.chdtriv,
lambda v, x: mpmath.gammainc(v/2, b=x/2, regularized=True),
0, [ProbArg(), IntArg(1, 100)], rtol=1e-4)
@pytest.mark.xfail(run=False)
def test_chndtridf(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtridf,
_noncentral_chi_cdf,
1, [Arg(0, 100, inclusive_a=False), ProbArg(),
Arg(0, 100, inclusive_a=False)],
n=1000, rtol=1e-4, atol=1e-15)
@pytest.mark.xfail(run=False)
def test_chndtrinc(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtrinc,
_noncentral_chi_cdf,
2, [Arg(0, 100, inclusive_a=False), IntArg(1, 100), ProbArg()],
n=1000, rtol=1e-4, atol=1e-15)
def test_chndtrix(self):
# Use a larger atol since mpmath is doing numerical integration
_assert_inverts(
sp.chndtrix,
_noncentral_chi_cdf,
0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
n=1000, rtol=1e-4, atol=1e-15,
endpt_atol=[1e-6, None, None])
def test_tklmbda_zero_shape(self):
# When lmbda = 0 the CDF has a simple closed form
one = mpmath.mpf(1)
assert_mpmath_equal(
lambda x: sp.tklmbda(x, 0),
lambda x: one/(mpmath.exp(-x) + one),
[Arg()], rtol=1e-7)
def test_tklmbda_neg_shape(self):
_assert_inverts(
sp.tklmbda,
_tukey_lmbda_quantile,
0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
spfunc_first=False, rtol=1e-5,
endpt_atol=[1e-9, 1e-5])
@pytest.mark.xfail(run=False)
def test_tklmbda_pos_shape(self):
_assert_inverts(
sp.tklmbda,
_tukey_lmbda_quantile,
0, [ProbArg(), Arg(0, 100, inclusive_a=False)],
spfunc_first=False, rtol=1e-5)
# The values of lmdba are chosen so that 1/lmbda is exact.
@pytest.mark.parametrize('lmbda', [0.5, 1.0, 8.0])
def test_tklmbda_lmbda1(self, lmbda):
bound = 1/lmbda
assert_equal(sp.tklmbda([-bound, bound], lmbda), [0.0, 1.0])
funcs = [
("btdtria", 3),
("btdtrib", 3),
("bdtrik", 3),
("bdtrin", 3),
("chdtriv", 2),
("chndtr", 3),
("chndtrix", 3),
("chndtridf", 3),
("chndtrinc", 3),
("fdtridfd", 3),
("ncfdtr", 4),
("ncfdtri", 4),
("ncfdtridfn", 4),
("ncfdtridfd", 4),
("ncfdtrinc", 4),
("gdtrix", 3),
("gdtrib", 3),
("gdtria", 3),
("nbdtrik", 3),
("nbdtrin", 3),
("nrdtrimn", 3),
("nrdtrisd", 3),
("pdtrik", 2),
("stdtr", 2),
("stdtrit", 2),
("stdtridf", 2),
("nctdtr", 3),
("nctdtrit", 3),
("nctdtridf", 3),
("nctdtrinc", 3),
("tklmbda", 2),
]
@pytest.mark.parametrize('func,numargs', funcs, ids=[x[0] for x in funcs])
def test_nonfinite(func, numargs):
rng = np.random.default_rng(1701299355559735)
func = getattr(sp, func)
args_choices = [(float(x), np.nan, np.inf, -np.inf) for x in rng.random(numargs)]
for args in itertools.product(*args_choices):
res = func(*args)
if any(np.isnan(x) for x in args):
# Nan inputs should result to nan output
assert_equal(res, np.nan)
else:
# All other inputs should return something (but not
# raise exceptions or cause hangs)
pass
def test_chndtrix_gh2158():
# test that gh-2158 is resolved; previously this blew up
res = sp.chndtrix(0.999999, 2, np.arange(20.)+1e-6)
# Generated in R
# options(digits=16)
# ncp <- seq(0, 19) + 1e-6
# print(qchisq(0.999999, df = 2, ncp = ncp))
res_exp = [27.63103493142305, 35.25728589950540, 39.97396073236288,
43.88033702110538, 47.35206403482798, 50.54112500166103,
53.52720257322766, 56.35830042867810, 59.06600769498512,
61.67243118946381, 64.19376191277179, 66.64228141346548,
69.02756927200180, 71.35726934749408, 73.63759723904816,
75.87368842650227, 78.06984431185720, 80.22971052389806,
82.35640899964173, 84.45263768373256]
assert_allclose(res, res_exp)
@pytest.mark.xfail_on_32bit("32bit fails due to algorithm threshold")
def test_nctdtr_gh19896():
# test that gh-19896 is resolved.
# Compared to SciPy 1.11 results from Fortran code.
dfarr = [0.98, 9.8, 98, 980]
pnoncarr = [-3.8, 0.38, 3.8, 38]
tarr = [0.0015, 0.15, 1.5, 15]
resarr = [0.9999276519560749, 0.9999276519560749, 0.9999908831755221,
0.9999990265452424, 0.3524153312279712, 0.39749697267251416,
0.7168629634895805, 0.9656246449259646, 7.234804392512006e-05,
7.234804392512006e-05, 0.03538804607509127, 0.795482701508521,
0.0, 0.0, 0.0,
0.011927908523093889, 0.9999276519560749, 0.9999276519560749,
0.9999997441133123, 1.0, 0.3525155979118013,
0.4076312014048369, 0.8476794017035086, 0.9999999297116268,
7.234804392512006e-05, 7.234804392512006e-05, 0.013477443099785824,
0.9998501512331494, 0.0, 0.0,
0.0, 6.561112613212572e-07, 0.9999276519560749,
0.9999276519560749, 0.9999999313496014, 1.0,
0.3525281784865706, 0.40890253001898014, 0.8664672830017024,
1.0, 7.234804392512006e-05, 7.234804392512006e-05,
0.010990889489704836, 1.0, 0.0,
0.0, 0.0, 0.0,
0.9999276519560749, 0.9999276519560749, 0.9999999418789304,
1.0, 0.35252945487817355, 0.40903153246690993,
0.8684247068528264, 1.0, 7.234804392512006e-05,
7.234804392512006e-05, 0.01075068918582911, 1.0,
0.0, 0.0, 0.0, 0.0]
actarr = []
for df, p, t in itertools.product(dfarr, pnoncarr, tarr):
actarr += [sp.nctdtr(df, p, t)]
# The rtol is kept high on purpose to make it pass on 32bit systems
assert_allclose(actarr, resarr, rtol=1e-6, atol=0.0)
def test_nctdtrinc_gh19896():
# test that gh-19896 is resolved.
# Compared to SciPy 1.11 results from Fortran code.
dfarr = [0.001, 0.98, 9.8, 98, 980, 10000, 98, 9.8, 0.98, 0.001]
parr = [0.001, 0.1, 0.3, 0.8, 0.999, 0.001, 0.1, 0.3, 0.8, 0.999]
tarr = [0.0015, 0.15, 1.5, 15, 300, 0.0015, 0.15, 1.5, 15, 300]
desired = [3.090232306168629, 1.406141304556198, 2.014225177124157,
13.727067118283456, 278.9765683871208, 3.090232306168629,
1.4312427877936222, 2.014225177124157, 3.712743137978295,
-3.086951096691082]
actual = sp.nctdtrinc(dfarr, parr, tarr)
assert_allclose(actual, desired, rtol=5e-12, atol=0.0)
def test_stdtr_stdtrit_neg_inf():
# -inf was treated as +inf and values from the normal were returned
assert np.all(np.isnan(sp.stdtr(-np.inf, [-np.inf, -1.0, 0.0, 1.0, np.inf])))
assert np.all(np.isnan(sp.stdtrit(-np.inf, [0.0, 0.25, 0.5, 0.75, 1.0])))
def test_bdtrik_nbdtrik_inf():
y = np.array(
[np.nan,-np.inf,-10.0, -1.0, 0.0, .00001, .5, 0.9999, 1.0, 10.0, np.inf])
y = y[:,None]
p = np.atleast_2d(
[np.nan, -np.inf, -10.0, -1.0, 0.0, .00001, .5, 1.0, np.inf])
assert np.all(np.isnan(sp.bdtrik(y, np.inf, p)))
assert np.all(np.isnan(sp.nbdtrik(y, np.inf, p)))
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