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