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 = 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 = 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 = 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 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):
NumericalInverseHermite("norm")
match = "could not convert string to float"
with pytest.raises(ValueError, match=match):
NumericalInverseHermite(StandardNormal(), u_resolution='ekki')
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):
NumericalInverseHermite(stats.beta(*shapes))
# no error with coarser tol
NumericalInverseHermite(stats.beta(*shapes), u_resolution=1e-8)
def test_RVS(self, rng, size_in, size_out):
dist = StandardNormal()
fni = 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 test_ppf(self, u):
dist = StandardNormal()
rng = NumericalInverseHermite(dist, u_resolution=1e-12)
# Older versions of NumPy throw RuntimeWarnings for comparisons
# with nan.
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in greater")
sup.filter(RuntimeWarning, "invalid value encountered in "
"greater_equal")
sup.filter(RuntimeWarning, "invalid value encountered in less")
sup.filter(RuntimeWarning, "invalid value encountered in "
"less_equal")
res = rng.ppf(u)
expected = stats.norm.ppf(u)
assert_allclose(res, expected, rtol=1e-9, atol=3e-10)
assert res.shape == expected.shape
def test_custom_distribution(self):
dist1 = StandardNormal()
fni1 = NumericalInverseHermite(dist1)
dist2 = stats.norm()
fni2 = NumericalInverseHermite(dist2)
assert_allclose(fni1.rvs(random_state=0), fni2.rvs(random_state=0))
def test_u_error(self):
dist = StandardNormal()
rng = NumericalInverseHermite(dist, u_resolution=1e-10)
max_error, mae = rng.u_error()
assert max_error < 1e-10
assert mae <= max_error
with suppress_warnings() as sup:
# ignore warning about u-resolution being too small.
sup.filter(RuntimeWarning)
rng = NumericalInverseHermite(dist, u_resolution=1e-14)
max_error, mae = rng.u_error()
assert max_error < 1e-14
assert mae <= max_error
def test_with_scipy_distribution():
# test if the setup works with SciPy's rv_frozen distributions
dist = stats.norm()
urng = np.random.default_rng(0)
rng = NumericalInverseHermite(dist, random_state=urng)
u = np.linspace(0, 1, num=100)
check_cont_samples(rng, dist, dist.stats())
assert_allclose(dist.ppf(u), rng.ppf(u))
# test if it works with `loc` and `scale`
dist = stats.norm(loc=10., scale=5.)
rng = NumericalInverseHermite(dist, random_state=urng)
check_cont_samples(rng, dist, dist.stats())
assert_allclose(dist.ppf(u), rng.ppf(u))
# check for discrete distributions
dist = stats.binom(10, 0.2)
rng = DiscreteAliasUrn(dist, random_state=urng)
domain = dist.support()
pv = dist.pmf(np.arange(domain[0], domain[1] + 1))
check_discr_samples(rng, pv, dist.stats())
def test_inf_nan_domains(self, domain, err, msg):
with pytest.raises(err, match=msg):
NumericalInverseHermite(StandardNormal(), domain=domain)
def test_basic(self, dist, mv_ex, order):
rng = NumericalInverseHermite(dist, order=order, random_state=42)
check_cont_samples(rng, dist, mv_ex)
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):
NumericalInverseHermite("norm")
match = "could not convert string to float"
with pytest.raises(ValueError, match=match):
NumericalInverseHermite(StandardNormal(), u_resolution='ekki')
match = "`max_intervals' must be..."
with pytest.raises(ValueError, match=match):
NumericalInverseHermite(StandardNormal(), max_intervals=-1)
match = "`qmc_engine` must be an instance of..."
with pytest.raises(ValueError, match=match):
fni = NumericalInverseHermite(StandardNormal())
fni.qrvs(qmc_engine=0)
if NumpyVersion(np.__version__) >= '1.18.0':
# issues with QMCEngines and old NumPy
fni = 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_deprecations(self):
msg = ("`tol` has been deprecated and replaced with `u_resolution`. "
"It will be completely removed in a future release.")
with pytest.warns(DeprecationWarning, match=msg):
NumericalInverseHermite(StandardNormal(), tol=1e-12)