def test_input_validation(self):
match = r"`order` must be either 1, 3, or 5."
with pytest.raises(ValueError, match=match):
NumericalInverseHermite(StandardNormal(), order=2)
match = "`cdf` required but not found"
with pytest.raises(ValueError, match=match):
stats.NumericalInverseHermite("norm")
match = "could not convert string to float"
with pytest.raises(ValueError, match=match):
stats.NumericalInverseHermite(StandardNormal(),
u_resolution='ekki')
match = "`max_intervals' must be..."
with pytest.raises(ValueError, match=match):
stats.NumericalInverseHermite(StandardNormal(), max_intervals=-1)
match = "`qmc_engine` must be an instance of..."
with pytest.raises(ValueError, match=match):
fni = stats.NumericalInverseHermite(StandardNormal())
fni.qrvs(qmc_engine=0)
if NumpyVersion(np.__version__) >= '1.18.0':
# issues with QMCEngines and old NumPy
fni = stats.NumericalInverseHermite(StandardNormal())
match = "`d` must be consistent with dimension of `qmc_engine`."
with pytest.raises(ValueError, match=match):
fni.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
def test_custom_distribution(self):
dist1 = StandardNormal()
fni1 = stats.NumericalInverseHermite(dist1)
dist2 = stats.norm()
fni2 = stats.NumericalInverseHermite(dist2)
assert_allclose(fni1.rvs(random_state=0), fni2.rvs(random_state=0))
def test_inaccurate_CDF(self):
# CDF function with inaccurate tail cannot be inverted; see gh-13319
# https://github.com/scipy/scipy/pull/13319#discussion_r626188955
shapes = (2.3098496451481823, 0.6268795430096368)
match = ("98 : one or more intervals very short; possibly due to "
"numerical problems with a pole or very flat tail")
# fails with default tol
with pytest.warns(RuntimeWarning, match=match):
stats.NumericalInverseHermite(stats.beta(*shapes))
# no error with coarser tol
stats.NumericalInverseHermite(stats.beta(*shapes), u_resolution=1e-8)
def test_basic_all_scipy_dists(self, distname, shapes):
slow_dists = {'ksone', 'kstwo', 'levy_stable', 'skewnorm'}
fail_dists = {
'beta', 'gausshyper', 'geninvgauss', 'ncf', 'nct', 'norminvgauss',
'genhyperbolic', 'studentized_range', 'vonmises', 'kappa4',
'invgauss', 'wald'
}
if distname in slow_dists:
pytest.skip("Distribution is too slow")
if distname in fail_dists:
# specific reasons documented in gh-13319
# https://github.com/scipy/scipy/pull/13319#discussion_r626188955
pytest.xfail("Fails - usually due to inaccurate CDF/PDF")
np.random.seed(0)
dist = getattr(stats, distname)(*shapes)
with np.testing.suppress_warnings() as sup:
sup.filter(RuntimeWarning, "overflow encountered")
sup.filter(RuntimeWarning, "divide by zero")
sup.filter(RuntimeWarning, "invalid value encountered")
fni = stats.NumericalInverseHermite(dist)
x = np.random.rand(10)
p_tol = np.max(np.abs(dist.ppf(x) - fni.ppf(x)) / np.abs(dist.ppf(x)))
u_tol = np.max(np.abs(dist.cdf(fni.ppf(x)) - x))
assert p_tol < 1e-8
assert u_tol < 1e-12
def test_QRVS_size_tuple(self):
# QMCEngine samples are always of shape (n, d). When `size` is a tuple,
# we set `n = prod(size)` in the call to qmc_engine.random, transform
# the sample, and reshape it to the final dimensions. When we reshape,
# we need to be careful, because the _columns_ of the sample returned
# by a QMCEngine are "independent"-ish, but the elements within the
# columns are not. We need to make sure that this doesn't get mixed up
# by reshaping: qrvs[..., i] should remain "independent"-ish of
# qrvs[..., i+1], but the elements within qrvs[..., i] should be
# transformed from the same low-discrepancy sequence.
if NumpyVersion(np.__version__) <= '1.18.0':
pytest.skip("QMC doesn't play well with old NumPy")
dist = StandardNormal()
fni = stats.NumericalInverseHermite(dist)
size = (3, 4)
d = 5
qrng = stats.qmc.Halton(d, seed=0)
qrng2 = stats.qmc.Halton(d, seed=0)
uniform = qrng2.random(np.prod(size))
qrvs = fni.qrvs(size=size, d=d, qmc_engine=qrng)
qrvs2 = stats.norm.ppf(uniform)
for i in range(d):
sample = qrvs[..., i]
sample2 = qrvs2[:, i].reshape(size)
assert_allclose(sample, sample2, atol=1e-12)
def test_QRVS(self, qrng, size_in, size_out, d_in, d_out):
dist = StandardNormal()
fni = stats.NumericalInverseHermite(dist)
# If d and qrng.d are inconsistent, an error is raised
if d_in is not None and qrng is not None and qrng.d != d_in:
match = "`d` must be consistent with dimension of `qmc_engine`."
with pytest.raises(ValueError, match=match):
fni.qrvs(size_in, d=d_in, qmc_engine=qrng)
return
# Sometimes d is really determined by qrng
if d_in is None and qrng is not None and qrng.d != 1:
d_out = (qrng.d, )
shape_expected = size_out + d_out
qrng2 = deepcopy(qrng)
qrvs = fni.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
if size_in is not None:
assert (qrvs.shape == shape_expected)
if qrng2 is not None:
uniform = qrng2.random(np.prod(size_in) or 1)
qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
assert_allclose(qrvs, qrvs2, atol=1e-12)
def setup(self, dist, order):
self.urng = np.random.default_rng(0xb235b58c1f616c59c18d8568f77d44d1)
with np.testing.suppress_warnings() as sup:
sup.filter(RuntimeWarning)
try:
self.rng = stats.NumericalInverseHermite(
dist, order=order, random_state=self.urng)
except stats.UNURANError:
raise NotImplementedError(f"setup failed for {dist}")
def test_RVS(self, rng, size_in, size_out):
dist = StandardNormal()
fni = stats.NumericalInverseHermite(dist)
rng2 = deepcopy(rng)
rvs = fni.rvs(size=size_in, random_state=rng)
if size_in is not None:
assert (rvs.shape == size_out)
if rng2 is not None:
rng2 = check_random_state(rng2)
uniform = rng2.uniform(size=size_in)
rvs2 = stats.norm.ppf(uniform)
assert_allclose(rvs, rvs2)
def time_fni(self, distcase):
distname, shapes = distcase
slow_dists = {'ksone', 'kstwo', 'levy_stable', 'skewnorm'}
fail_dists = {'beta', 'gausshyper', 'geninvgauss', 'ncf', 'nct',
'norminvgauss', 'genhyperbolic', 'studentized_range'}
if distname in slow_dists or distname in fail_dists:
raise NotImplementedError("skipped")
dist = getattr(stats, distname)(*shapes)
with np.testing.suppress_warnings() as sup:
sup.filter(RuntimeWarning, "overflow encountered")
sup.filter(RuntimeWarning, "divide by zero")
sup.filter(RuntimeWarning, "invalid value encountered")
stats.NumericalInverseHermite(dist)
def time_hinv_setup(self, dist, order):
with np.testing.suppress_warnings() as sup:
sup.filter(RuntimeWarning)
stats.NumericalInverseHermite(dist,
order=order,
random_state=self.urng)