1358 lines
50 KiB
Python
1358 lines
50 KiB
Python
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import threading
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import pickle
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import pytest
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from copy import deepcopy
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import platform
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import sys
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import math
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import numpy as np
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from numpy.testing import assert_allclose, assert_equal, suppress_warnings
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from numpy.lib import NumpyVersion
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from scipy.stats.sampling import (
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TransformedDensityRejection,
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DiscreteAliasUrn,
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DiscreteGuideTable,
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NumericalInversePolynomial,
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NumericalInverseHermite,
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SimpleRatioUniforms,
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UNURANError
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)
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from scipy import stats
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from scipy import special
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from scipy.stats import chisquare, cramervonmises
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from scipy.stats._distr_params import distdiscrete, distcont
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from scipy._lib._util import check_random_state
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# common test data: this data can be shared between all the tests.
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# Normal distribution shared between all the continuous methods
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class StandardNormal:
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def pdf(self, x):
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# normalization constant needed for NumericalInverseHermite
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return 1./np.sqrt(2.*np.pi) * np.exp(-0.5 * x*x)
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def dpdf(self, x):
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return 1./np.sqrt(2.*np.pi) * -x * np.exp(-0.5 * x*x)
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def cdf(self, x):
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return special.ndtr(x)
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all_methods = [
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("TransformedDensityRejection", {"dist": StandardNormal()}),
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("DiscreteAliasUrn", {"dist": [0.02, 0.18, 0.8]}),
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("DiscreteGuideTable", {"dist": [0.02, 0.18, 0.8]}),
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("NumericalInversePolynomial", {"dist": StandardNormal()}),
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("NumericalInverseHermite", {"dist": StandardNormal()}),
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("SimpleRatioUniforms", {"dist": StandardNormal(), "mode": 0})
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]
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if (sys.implementation.name == 'pypy'
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and sys.implementation.version < (7, 3, 10)):
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# changed in PyPy for v7.3.10
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floaterr = r"unsupported operand type for float\(\): 'list'"
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else:
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floaterr = r"must be real number, not list"
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# Make sure an internal error occurs in UNU.RAN when invalid callbacks are
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# passed. Moreover, different generators throw different error messages.
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# So, in case of an `UNURANError`, we do not validate the error message.
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bad_pdfs_common = [
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# Negative PDF
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(lambda x: -x, UNURANError, r"..."),
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# Returning wrong type
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(lambda x: [], TypeError, floaterr),
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# Undefined name inside the function
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(lambda x: foo, NameError, r"name 'foo' is not defined"), # type: ignore[name-defined] # noqa
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# Infinite value returned => Overflow error.
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(lambda x: np.inf, UNURANError, r"..."),
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# NaN value => internal error in UNU.RAN
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(lambda x: np.nan, UNURANError, r"..."),
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# signature of PDF wrong
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(lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
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]
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# same approach for dpdf
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bad_dpdf_common = [
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# Infinite value returned.
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(lambda x: np.inf, UNURANError, r"..."),
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# NaN value => internal error in UNU.RAN
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(lambda x: np.nan, UNURANError, r"..."),
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# Returning wrong type
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(lambda x: [], TypeError, floaterr),
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# Undefined name inside the function
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(lambda x: foo, NameError, r"name 'foo' is not defined"), # type: ignore[name-defined] # noqa
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# signature of dPDF wrong
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(lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
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]
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# same approach for logpdf
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bad_logpdfs_common = [
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# Returning wrong type
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(lambda x: [], TypeError, floaterr),
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# Undefined name inside the function
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(lambda x: foo, NameError, r"name 'foo' is not defined"), # type: ignore[name-defined] # noqa
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# Infinite value returned => Overflow error.
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(lambda x: np.inf, UNURANError, r"..."),
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# NaN value => internal error in UNU.RAN
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(lambda x: np.nan, UNURANError, r"..."),
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# signature of logpdf wrong
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(lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
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]
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bad_pv_common = [
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([], r"must contain at least one element"),
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([[1.0, 0.0]], r"wrong number of dimensions \(expected 1, got 2\)"),
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([0.2, 0.4, np.nan, 0.8], r"must contain only finite / non-nan values"),
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([0.2, 0.4, np.inf, 0.8], r"must contain only finite / non-nan values"),
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([0.0, 0.0], r"must contain at least one non-zero value"),
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]
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# size of the domains is incorrect
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bad_sized_domains = [
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# > 2 elements in the domain
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((1, 2, 3), ValueError, r"must be a length 2 tuple"),
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# empty domain
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((), ValueError, r"must be a length 2 tuple")
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]
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# domain values are incorrect
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bad_domains = [
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((2, 1), UNURANError, r"left >= right"),
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((1, 1), UNURANError, r"left >= right"),
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]
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# infinite and nan values present in domain.
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inf_nan_domains = [
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# left >= right
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((10, 10), UNURANError, r"left >= right"),
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((np.inf, np.inf), UNURANError, r"left >= right"),
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((-np.inf, -np.inf), UNURANError, r"left >= right"),
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((np.inf, -np.inf), UNURANError, r"left >= right"),
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# Also include nans in some of the domains.
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((-np.inf, np.nan), ValueError, r"only non-nan values"),
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((np.nan, np.inf), ValueError, r"only non-nan values")
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]
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# `nan` values present in domain. Some distributions don't support
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# infinite tails, so don't mix the nan values with infinities.
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nan_domains = [
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((0, np.nan), ValueError, r"only non-nan values"),
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((np.nan, np.nan), ValueError, r"only non-nan values")
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]
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# all the methods should throw errors for nan, bad sized, and bad valued
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# domains.
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@pytest.mark.parametrize("domain, err, msg",
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bad_domains + bad_sized_domains +
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nan_domains) # type: ignore[operator]
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@pytest.mark.parametrize("method, kwargs", all_methods)
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def test_bad_domain(domain, err, msg, method, kwargs):
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Method = getattr(stats.sampling, method)
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with pytest.raises(err, match=msg):
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Method(**kwargs, domain=domain)
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@pytest.mark.parametrize("method, kwargs", all_methods)
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def test_random_state(method, kwargs):
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Method = getattr(stats.sampling, method)
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# simple seed that works for any version of NumPy
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seed = 123
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rng1 = Method(**kwargs, random_state=seed)
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rng2 = Method(**kwargs, random_state=seed)
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assert_equal(rng1.rvs(100), rng2.rvs(100))
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# global seed
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np.random.seed(123)
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rng1 = Method(**kwargs)
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rvs1 = rng1.rvs(100)
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np.random.seed(None)
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rng2 = Method(**kwargs, random_state=123)
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rvs2 = rng2.rvs(100)
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assert_equal(rvs1, rvs2)
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# Generator seed for new NumPy
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# when a RandomState is given, it should take the bitgen_t
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# member of the class and create a Generator instance.
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seed1 = np.random.RandomState(np.random.MT19937(123))
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seed2 = np.random.Generator(np.random.MT19937(123))
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rng1 = Method(**kwargs, random_state=seed1)
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rng2 = Method(**kwargs, random_state=seed2)
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assert_equal(rng1.rvs(100), rng2.rvs(100))
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def test_set_random_state():
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rng1 = TransformedDensityRejection(StandardNormal(), random_state=123)
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rng2 = TransformedDensityRejection(StandardNormal())
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rng2.set_random_state(123)
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assert_equal(rng1.rvs(100), rng2.rvs(100))
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rng = TransformedDensityRejection(StandardNormal(), random_state=123)
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rvs1 = rng.rvs(100)
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rng.set_random_state(123)
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rvs2 = rng.rvs(100)
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assert_equal(rvs1, rvs2)
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def test_threading_behaviour():
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# Test if the API is thread-safe.
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# This verifies if the lock mechanism and the use of `PyErr_Occurred`
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# is correct.
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errors = {"err1": None, "err2": None}
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class Distribution:
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def __init__(self, pdf_msg):
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self.pdf_msg = pdf_msg
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def pdf(self, x):
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if 49.9 < x < 50.0:
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raise ValueError(self.pdf_msg)
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return x
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def dpdf(self, x):
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return 1
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def func1():
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dist = Distribution('foo')
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rng = TransformedDensityRejection(dist, domain=(10, 100),
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random_state=12)
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try:
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rng.rvs(100000)
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except ValueError as e:
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errors['err1'] = e.args[0]
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def func2():
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dist = Distribution('bar')
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rng = TransformedDensityRejection(dist, domain=(10, 100),
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random_state=2)
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try:
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rng.rvs(100000)
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except ValueError as e:
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errors['err2'] = e.args[0]
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t1 = threading.Thread(target=func1)
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t2 = threading.Thread(target=func2)
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t1.start()
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t2.start()
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t1.join()
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t2.join()
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assert errors['err1'] == 'foo'
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assert errors['err2'] == 'bar'
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@pytest.mark.parametrize("method, kwargs", all_methods)
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def test_pickle(method, kwargs):
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Method = getattr(stats.sampling, method)
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rng1 = Method(**kwargs, random_state=123)
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obj = pickle.dumps(rng1)
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rng2 = pickle.loads(obj)
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assert_equal(rng1.rvs(100), rng2.rvs(100))
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@pytest.mark.parametrize("size", [None, 0, (0, ), 1, (10, 3), (2, 3, 4, 5),
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(0, 0), (0, 1)])
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def test_rvs_size(size):
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# As the `rvs` method is present in the base class and shared between
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# all the classes, we can just test with one of the methods.
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rng = TransformedDensityRejection(StandardNormal())
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if size is None:
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assert np.isscalar(rng.rvs(size))
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else:
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if np.isscalar(size):
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size = (size, )
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assert rng.rvs(size).shape == size
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def test_with_scipy_distribution():
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# test if the setup works with SciPy's rv_frozen distributions
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dist = stats.norm()
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urng = np.random.default_rng(0)
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rng = NumericalInverseHermite(dist, random_state=urng)
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u = np.linspace(0, 1, num=100)
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check_cont_samples(rng, dist, dist.stats())
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assert_allclose(dist.ppf(u), rng.ppf(u))
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# test if it works with `loc` and `scale`
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dist = stats.norm(loc=10., scale=5.)
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rng = NumericalInverseHermite(dist, random_state=urng)
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check_cont_samples(rng, dist, dist.stats())
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assert_allclose(dist.ppf(u), rng.ppf(u))
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# check for discrete distributions
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dist = stats.binom(10, 0.2)
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rng = DiscreteAliasUrn(dist, random_state=urng)
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domain = dist.support()
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pv = dist.pmf(np.arange(domain[0], domain[1]+1))
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check_discr_samples(rng, pv, dist.stats())
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def check_cont_samples(rng, dist, mv_ex):
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rvs = rng.rvs(100000)
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mv = rvs.mean(), rvs.var()
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# test the moments only if the variance is finite
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if np.isfinite(mv_ex[1]):
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assert_allclose(mv, mv_ex, rtol=1e-7, atol=1e-1)
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# Cramer Von Mises test for goodness-of-fit
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rvs = rng.rvs(500)
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dist.cdf = np.vectorize(dist.cdf)
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pval = cramervonmises(rvs, dist.cdf).pvalue
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assert pval > 0.1
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def check_discr_samples(rng, pv, mv_ex):
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rvs = rng.rvs(100000)
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# test if the first few moments match
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mv = rvs.mean(), rvs.var()
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assert_allclose(mv, mv_ex, rtol=1e-3, atol=1e-1)
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# normalize
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pv = pv / pv.sum()
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# chi-squared test for goodness-of-fit
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obs_freqs = np.zeros_like(pv)
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_, freqs = np.unique(rvs, return_counts=True)
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freqs = freqs / freqs.sum()
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obs_freqs[:freqs.size] = freqs
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pval = chisquare(obs_freqs, pv).pvalue
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assert pval > 0.1
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def test_warning_center_not_in_domain():
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# UNURAN will warn if the center provided or the one computed w/o the
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# domain is outside of the domain
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msg = "102 : center moved into domain of distribution"
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with pytest.warns(RuntimeWarning, match=msg):
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NumericalInversePolynomial(StandardNormal(), center=0, domain=(3, 5))
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with pytest.warns(RuntimeWarning, match=msg):
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NumericalInversePolynomial(StandardNormal(), domain=(3, 5))
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@pytest.mark.parametrize('method', ["SimpleRatioUniforms",
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"NumericalInversePolynomial",
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"TransformedDensityRejection"])
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def test_error_mode_not_in_domain(method):
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# UNURAN raises an error if the mode is not in the domain
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# the behavior is different compared to the case that center is not in the
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# domain. mode is supposed to be the exact value, center can be an
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# approximate value
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Method = getattr(stats.sampling, method)
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msg = "17 : mode not in domain"
|
||
|
|
with pytest.raises(UNURANError, match=msg):
|
||
|
|
Method(StandardNormal(), mode=0, domain=(3, 5))
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('method', ["NumericalInverseHermite",
|
||
|
|
"NumericalInversePolynomial"])
|
||
|
|
class TestQRVS:
|
||
|
|
def test_input_validation(self, method):
|
||
|
|
match = "`qmc_engine` must be an instance of..."
|
||
|
|
with pytest.raises(ValueError, match=match):
|
||
|
|
Method = getattr(stats.sampling, method)
|
||
|
|
gen = Method(StandardNormal())
|
||
|
|
gen.qrvs(qmc_engine=0)
|
||
|
|
|
||
|
|
# issues with QMCEngines and old NumPy
|
||
|
|
Method = getattr(stats.sampling, method)
|
||
|
|
gen = Method(StandardNormal())
|
||
|
|
|
||
|
|
match = "`d` must be consistent with dimension of `qmc_engine`."
|
||
|
|
with pytest.raises(ValueError, match=match):
|
||
|
|
gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
|
||
|
|
|
||
|
|
qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
|
||
|
|
# `size=None` should not add anything to the shape, `size=1` should
|
||
|
|
sizes = [(None, tuple()), (1, (1,)), (4, (4,)),
|
||
|
|
((4,), (4,)), ((2, 4), (2, 4))] # type: ignore
|
||
|
|
# Neither `d=None` nor `d=1` should add anything to the shape
|
||
|
|
ds = [(None, tuple()), (1, tuple()), (3, (3,))]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('qrng', qrngs)
|
||
|
|
@pytest.mark.parametrize('size_in, size_out', sizes)
|
||
|
|
@pytest.mark.parametrize('d_in, d_out', ds)
|
||
|
|
def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
|
||
|
|
d_in, d_out, method):
|
||
|
|
w32 = sys.platform == "win32" and platform.architecture()[0] == "32bit"
|
||
|
|
if w32 and method == "NumericalInversePolynomial":
|
||
|
|
pytest.xfail("NumericalInversePolynomial.qrvs fails for Win "
|
||
|
|
"32-bit")
|
||
|
|
|
||
|
|
dist = StandardNormal()
|
||
|
|
Method = getattr(stats.sampling, method)
|
||
|
|
gen = Method(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):
|
||
|
|
gen.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 = gen.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_QRVS_size_tuple(self, method):
|
||
|
|
# 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.
|
||
|
|
|
||
|
|
dist = StandardNormal()
|
||
|
|
Method = getattr(stats.sampling, method)
|
||
|
|
gen = Method(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 = gen.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)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTransformedDensityRejection:
|
||
|
|
# Simple Custom Distribution
|
||
|
|
class dist0:
|
||
|
|
def pdf(self, x):
|
||
|
|
return 3/4 * (1-x*x)
|
||
|
|
|
||
|
|
def dpdf(self, x):
|
||
|
|
return 3/4 * (-2*x)
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return 3/4 * (x - x**3/3 + 2/3)
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -1, 1
|
||
|
|
|
||
|
|
# Standard Normal Distribution
|
||
|
|
class dist1:
|
||
|
|
def pdf(self, x):
|
||
|
|
return stats.norm._pdf(x / 0.1)
|
||
|
|
|
||
|
|
def dpdf(self, x):
|
||
|
|
return -x / 0.01 * stats.norm._pdf(x / 0.1)
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return stats.norm._cdf(x / 0.1)
|
||
|
|
|
||
|
|
# pdf with piecewise linear function as transformed density
|
||
|
|
# with T = -1/sqrt with shift. Taken from UNU.RAN test suite
|
||
|
|
# (from file t_tdr_ps.c)
|
||
|
|
class dist2:
|
||
|
|
def __init__(self, shift):
|
||
|
|
self.shift = shift
|
||
|
|
|
||
|
|
def pdf(self, x):
|
||
|
|
x -= self.shift
|
||
|
|
y = 1. / (abs(x) + 1.)
|
||
|
|
return 0.5 * y * y
|
||
|
|
|
||
|
|
def dpdf(self, x):
|
||
|
|
x -= self.shift
|
||
|
|
y = 1. / (abs(x) + 1.)
|
||
|
|
y = y * y * y
|
||
|
|
return y if (x < 0.) else -y
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
x -= self.shift
|
||
|
|
if x <= 0.:
|
||
|
|
return 0.5 / (1. - x)
|
||
|
|
else:
|
||
|
|
return 1. - 0.5 / (1. + x)
|
||
|
|
|
||
|
|
dists = [dist0(), dist1(), dist2(0.), dist2(10000.)]
|
||
|
|
|
||
|
|
# exact mean and variance of the distributions in the list dists
|
||
|
|
mv0 = [0., 4./15.]
|
||
|
|
mv1 = [0., 0.01]
|
||
|
|
mv2 = [0., np.inf]
|
||
|
|
mv3 = [10000., np.inf]
|
||
|
|
mvs = [mv0, mv1, mv2, mv3]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("dist, mv_ex",
|
||
|
|
zip(dists, mvs))
|
||
|
|
def test_basic(self, dist, mv_ex):
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
# filter the warnings thrown by UNU.RAN
|
||
|
|
sup.filter(RuntimeWarning)
|
||
|
|
rng = TransformedDensityRejection(dist, random_state=42)
|
||
|
|
check_cont_samples(rng, dist, mv_ex)
|
||
|
|
|
||
|
|
# PDF 0 everywhere => bad construction points
|
||
|
|
bad_pdfs = [(lambda x: 0, UNURANError, r"50 : bad construction points.")]
|
||
|
|
bad_pdfs += bad_pdfs_common # type: ignore[arg-type]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pdf, err, msg", bad_pdfs)
|
||
|
|
def test_bad_pdf(self, pdf, err, msg):
|
||
|
|
class dist:
|
||
|
|
pass
|
||
|
|
dist.pdf = pdf
|
||
|
|
dist.dpdf = lambda x: 1 # an arbitrary dPDF
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
TransformedDensityRejection(dist)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("dpdf, err, msg", bad_dpdf_common)
|
||
|
|
def test_bad_dpdf(self, dpdf, err, msg):
|
||
|
|
class dist:
|
||
|
|
pass
|
||
|
|
dist.pdf = lambda x: x
|
||
|
|
dist.dpdf = dpdf
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
TransformedDensityRejection(dist, domain=(1, 10))
|
||
|
|
|
||
|
|
# test domains with inf + nan in them. need to write a custom test for
|
||
|
|
# this because not all methods support infinite tails.
|
||
|
|
@pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
|
||
|
|
def test_inf_nan_domains(self, domain, err, msg):
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
TransformedDensityRejection(StandardNormal(), domain=domain)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("construction_points", [-1, 0, 0.1])
|
||
|
|
def test_bad_construction_points_scalar(self, construction_points):
|
||
|
|
with pytest.raises(ValueError, match=r"`construction_points` must be "
|
||
|
|
r"a positive integer."):
|
||
|
|
TransformedDensityRejection(
|
||
|
|
StandardNormal(), construction_points=construction_points
|
||
|
|
)
|
||
|
|
|
||
|
|
def test_bad_construction_points_array(self):
|
||
|
|
# empty array
|
||
|
|
construction_points = []
|
||
|
|
with pytest.raises(ValueError, match=r"`construction_points` must "
|
||
|
|
r"either be a "
|
||
|
|
r"scalar or a non-empty array."):
|
||
|
|
TransformedDensityRejection(
|
||
|
|
StandardNormal(), construction_points=construction_points
|
||
|
|
)
|
||
|
|
|
||
|
|
# construction_points not monotonically increasing
|
||
|
|
construction_points = [1, 1, 1, 1, 1, 1]
|
||
|
|
with pytest.warns(RuntimeWarning, match=r"33 : starting points not "
|
||
|
|
r"strictly monotonically "
|
||
|
|
r"increasing"):
|
||
|
|
TransformedDensityRejection(
|
||
|
|
StandardNormal(), construction_points=construction_points
|
||
|
|
)
|
||
|
|
|
||
|
|
# construction_points containing nans
|
||
|
|
construction_points = [np.nan, np.nan, np.nan]
|
||
|
|
with pytest.raises(UNURANError, match=r"50 : bad construction "
|
||
|
|
r"points."):
|
||
|
|
TransformedDensityRejection(
|
||
|
|
StandardNormal(), construction_points=construction_points
|
||
|
|
)
|
||
|
|
|
||
|
|
# construction_points out of domain
|
||
|
|
construction_points = [-10, 10]
|
||
|
|
with pytest.warns(RuntimeWarning, match=r"50 : starting point out of "
|
||
|
|
r"domain"):
|
||
|
|
TransformedDensityRejection(
|
||
|
|
StandardNormal(), domain=(-3, 3),
|
||
|
|
construction_points=construction_points
|
||
|
|
)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("c", [-1., np.nan, np.inf, 0.1, 1.])
|
||
|
|
def test_bad_c(self, c):
|
||
|
|
msg = r"`c` must either be -0.5 or 0."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
TransformedDensityRejection(StandardNormal(), c=-1.)
|
||
|
|
|
||
|
|
u = [np.linspace(0, 1, num=1000), [], [[]], [np.nan],
|
||
|
|
[-np.inf, np.nan, np.inf], 0,
|
||
|
|
[[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("u", u)
|
||
|
|
def test_ppf_hat(self, u):
|
||
|
|
# Increase the `max_squeeze_hat_ratio` so the ppf_hat is more
|
||
|
|
# accurate.
|
||
|
|
rng = TransformedDensityRejection(StandardNormal(),
|
||
|
|
max_squeeze_hat_ratio=0.9999)
|
||
|
|
# 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_hat(u)
|
||
|
|
expected = stats.norm.ppf(u)
|
||
|
|
assert_allclose(res, expected, rtol=1e-3, atol=1e-5)
|
||
|
|
assert res.shape == expected.shape
|
||
|
|
|
||
|
|
def test_bad_dist(self):
|
||
|
|
# Empty distribution
|
||
|
|
class dist:
|
||
|
|
...
|
||
|
|
|
||
|
|
msg = r"`pdf` required but not found."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
TransformedDensityRejection(dist)
|
||
|
|
|
||
|
|
# dPDF not present in dist
|
||
|
|
class dist:
|
||
|
|
pdf = lambda x: 1-x*x # noqa: E731
|
||
|
|
|
||
|
|
msg = r"`dpdf` required but not found."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
TransformedDensityRejection(dist)
|
||
|
|
|
||
|
|
|
||
|
|
class TestDiscreteAliasUrn:
|
||
|
|
# DAU fails on these probably because of large domains and small
|
||
|
|
# computation errors in PMF. Mean/SD match but chi-squared test fails.
|
||
|
|
basic_fail_dists = {
|
||
|
|
'nchypergeom_fisher', # numerical erros on tails
|
||
|
|
'nchypergeom_wallenius', # numerical erros on tails
|
||
|
|
'randint' # fails on 32-bit ubuntu
|
||
|
|
}
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("distname, params", distdiscrete)
|
||
|
|
def test_basic(self, distname, params):
|
||
|
|
if distname in self.basic_fail_dists:
|
||
|
|
msg = ("DAU fails on these probably because of large domains "
|
||
|
|
"and small computation errors in PMF.")
|
||
|
|
pytest.skip(msg)
|
||
|
|
if not isinstance(distname, str):
|
||
|
|
dist = distname
|
||
|
|
else:
|
||
|
|
dist = getattr(stats, distname)
|
||
|
|
dist = dist(*params)
|
||
|
|
domain = dist.support()
|
||
|
|
if not np.isfinite(domain[1] - domain[0]):
|
||
|
|
# DAU only works with finite domain. So, skip the distributions
|
||
|
|
# with infinite tails.
|
||
|
|
pytest.skip("DAU only works with a finite domain.")
|
||
|
|
k = np.arange(domain[0], domain[1]+1)
|
||
|
|
pv = dist.pmf(k)
|
||
|
|
mv_ex = dist.stats('mv')
|
||
|
|
rng = DiscreteAliasUrn(dist, random_state=42)
|
||
|
|
check_discr_samples(rng, pv, mv_ex)
|
||
|
|
|
||
|
|
# Can't use bad_pmf_common here as we evaluate PMF early on to avoid
|
||
|
|
# unhelpful errors from UNU.RAN.
|
||
|
|
bad_pmf = [
|
||
|
|
# inf returned
|
||
|
|
(lambda x: np.inf, ValueError,
|
||
|
|
r"must contain only finite / non-nan values"),
|
||
|
|
# nan returned
|
||
|
|
(lambda x: np.nan, ValueError,
|
||
|
|
r"must contain only finite / non-nan values"),
|
||
|
|
# all zeros
|
||
|
|
(lambda x: 0.0, ValueError,
|
||
|
|
r"must contain at least one non-zero value"),
|
||
|
|
# Undefined name inside the function
|
||
|
|
(lambda x: foo, NameError, # type: ignore[name-defined] # noqa
|
||
|
|
r"name 'foo' is not defined"),
|
||
|
|
# Returning wrong type.
|
||
|
|
(lambda x: [], ValueError,
|
||
|
|
r"setting an array element with a sequence."),
|
||
|
|
# probabilities < 0
|
||
|
|
(lambda x: -x, UNURANError,
|
||
|
|
r"50 : probability < 0"),
|
||
|
|
# signature of PMF wrong
|
||
|
|
(lambda: 1.0, TypeError,
|
||
|
|
r"takes 0 positional arguments but 1 was given")
|
||
|
|
]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pmf, err, msg", bad_pmf)
|
||
|
|
def test_bad_pmf(self, pmf, err, msg):
|
||
|
|
class dist:
|
||
|
|
pass
|
||
|
|
dist.pmf = pmf
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
DiscreteAliasUrn(dist, domain=(1, 10))
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pv", [[0.18, 0.02, 0.8],
|
||
|
|
[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]])
|
||
|
|
def test_sampling_with_pv(self, pv):
|
||
|
|
pv = np.asarray(pv, dtype=np.float64)
|
||
|
|
rng = DiscreteAliasUrn(pv, random_state=123)
|
||
|
|
rvs = rng.rvs(100_000)
|
||
|
|
pv = pv / pv.sum()
|
||
|
|
variates = np.arange(0, len(pv))
|
||
|
|
# test if the first few moments match
|
||
|
|
m_expected = np.average(variates, weights=pv)
|
||
|
|
v_expected = np.average((variates - m_expected) ** 2, weights=pv)
|
||
|
|
mv_expected = m_expected, v_expected
|
||
|
|
check_discr_samples(rng, pv, mv_expected)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pv, msg", bad_pv_common)
|
||
|
|
def test_bad_pv(self, pv, msg):
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
DiscreteAliasUrn(pv)
|
||
|
|
|
||
|
|
# DAU doesn't support infinite tails. So, it should throw an error when
|
||
|
|
# inf is present in the domain.
|
||
|
|
inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
|
||
|
|
(0, np.inf), (-np.inf, 0)]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("domain", inf_domain)
|
||
|
|
def test_inf_domain(self, domain):
|
||
|
|
with pytest.raises(ValueError, match=r"must be finite"):
|
||
|
|
DiscreteAliasUrn(stats.binom(10, 0.2), domain=domain)
|
||
|
|
|
||
|
|
def test_bad_urn_factor(self):
|
||
|
|
with pytest.warns(RuntimeWarning, match=r"relative urn size < 1."):
|
||
|
|
DiscreteAliasUrn([0.5, 0.5], urn_factor=-1)
|
||
|
|
|
||
|
|
def test_bad_args(self):
|
||
|
|
msg = (r"`domain` must be provided when the "
|
||
|
|
r"probability vector is not available.")
|
||
|
|
|
||
|
|
class dist:
|
||
|
|
def pmf(self, x):
|
||
|
|
return x
|
||
|
|
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
DiscreteAliasUrn(dist)
|
||
|
|
|
||
|
|
|
||
|
|
class TestNumericalInversePolynomial:
|
||
|
|
# Simple Custom Distribution
|
||
|
|
class dist0:
|
||
|
|
def pdf(self, x):
|
||
|
|
return 3/4 * (1-x*x)
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return 3/4 * (x - x**3/3 + 2/3)
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -1, 1
|
||
|
|
|
||
|
|
# Standard Normal Distribution
|
||
|
|
class dist1:
|
||
|
|
def pdf(self, x):
|
||
|
|
return stats.norm._pdf(x / 0.1)
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return stats.norm._cdf(x / 0.1)
|
||
|
|
|
||
|
|
# Sin 2 distribution
|
||
|
|
# / 0.05 + 0.45*(1 +sin(2 Pi x)) if |x| <= 1
|
||
|
|
# f(x) = <
|
||
|
|
# \ 0 otherwise
|
||
|
|
# Taken from UNU.RAN test suite (from file t_pinv.c)
|
||
|
|
class dist2:
|
||
|
|
def pdf(self, x):
|
||
|
|
return 0.05 + 0.45 * (1 + np.sin(2*np.pi*x))
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return (0.05*(x + 1) +
|
||
|
|
0.9*(1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) /
|
||
|
|
(4.*np.pi))
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -1, 1
|
||
|
|
|
||
|
|
# Sin 10 distribution
|
||
|
|
# / 0.05 + 0.45*(1 +sin(2 Pi x)) if |x| <= 5
|
||
|
|
# f(x) = <
|
||
|
|
# \ 0 otherwise
|
||
|
|
# Taken from UNU.RAN test suite (from file t_pinv.c)
|
||
|
|
class dist3:
|
||
|
|
def pdf(self, x):
|
||
|
|
return 0.2 * (0.05 + 0.45 * (1 + np.sin(2*np.pi*x)))
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return x/10. + 0.5 + 0.09/(2*np.pi) * (np.cos(10*np.pi) -
|
||
|
|
np.cos(2*np.pi*x))
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -5, 5
|
||
|
|
|
||
|
|
dists = [dist0(), dist1(), dist2(), dist3()]
|
||
|
|
|
||
|
|
# exact mean and variance of the distributions in the list dists
|
||
|
|
mv0 = [0., 4./15.]
|
||
|
|
mv1 = [0., 0.01]
|
||
|
|
mv2 = [-0.45/np.pi, 2/3*0.5 - 0.45**2/np.pi**2]
|
||
|
|
mv3 = [-0.45/np.pi, 0.2 * 250/3 * 0.5 - 0.45**2/np.pi**2]
|
||
|
|
mvs = [mv0, mv1, mv2, mv3]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("dist, mv_ex",
|
||
|
|
zip(dists, mvs))
|
||
|
|
def test_basic(self, dist, mv_ex):
|
||
|
|
rng = NumericalInversePolynomial(dist, random_state=42)
|
||
|
|
check_cont_samples(rng, dist, mv_ex)
|
||
|
|
|
||
|
|
very_slow_dists = ['studentized_range', 'trapezoid', 'triang', 'vonmises',
|
||
|
|
'levy_stable', 'kappa4', 'ksone', 'kstwo', 'levy_l',
|
||
|
|
'gausshyper', 'anglit']
|
||
|
|
# for these distributions, some assertions fail due to minor
|
||
|
|
# numerical differences. They can be avoided either by changing
|
||
|
|
# the seed or by increasing the u_resolution.
|
||
|
|
fail_dists = ['ncf', 'pareto', 'chi2', 'fatiguelife', 'halfgennorm',
|
||
|
|
'gibrat', 'lognorm', 'ncx2', 't']
|
||
|
|
|
||
|
|
@pytest.mark.xslow
|
||
|
|
@pytest.mark.parametrize("distname, params", distcont)
|
||
|
|
def test_basic_all_scipy_dists(self, distname, params):
|
||
|
|
if distname in self.very_slow_dists:
|
||
|
|
pytest.skip(f"PINV too slow for {distname}")
|
||
|
|
if distname in self.fail_dists:
|
||
|
|
pytest.skip(f"PINV fails for {distname}")
|
||
|
|
dist = (getattr(stats, distname)
|
||
|
|
if isinstance(distname, str)
|
||
|
|
else distname)
|
||
|
|
dist = dist(*params)
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning)
|
||
|
|
rng = NumericalInversePolynomial(dist, random_state=42)
|
||
|
|
check_cont_samples(rng, dist, [dist.mean(), dist.var()])
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pdf, err, msg", bad_pdfs_common)
|
||
|
|
def test_bad_pdf(self, pdf, err, msg):
|
||
|
|
class dist:
|
||
|
|
pass
|
||
|
|
dist.pdf = pdf
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
NumericalInversePolynomial(dist, domain=[0, 5])
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("logpdf, err, msg", bad_logpdfs_common)
|
||
|
|
def test_bad_logpdf(self, logpdf, err, msg):
|
||
|
|
class dist:
|
||
|
|
pass
|
||
|
|
dist.logpdf = logpdf
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
NumericalInversePolynomial(dist, domain=[0, 5])
|
||
|
|
|
||
|
|
# test domains with inf + nan in them. need to write a custom test for
|
||
|
|
# this because not all methods support infinite tails.
|
||
|
|
@pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
|
||
|
|
def test_inf_nan_domains(self, domain, err, msg):
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
NumericalInversePolynomial(StandardNormal(), domain=domain)
|
||
|
|
|
||
|
|
u = [
|
||
|
|
# test if quantile 0 and 1 return -inf and inf respectively and check
|
||
|
|
# the correctness of the PPF for equidistant points between 0 and 1.
|
||
|
|
np.linspace(0, 1, num=10000),
|
||
|
|
# test the PPF method for empty arrays
|
||
|
|
[], [[]],
|
||
|
|
# test if nans and infs return nan result.
|
||
|
|
[np.nan], [-np.inf, np.nan, np.inf],
|
||
|
|
# test if a scalar is returned for a scalar input.
|
||
|
|
0,
|
||
|
|
# test for arrays with nans, values greater than 1 and less than 0,
|
||
|
|
# and some valid values.
|
||
|
|
[[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
|
||
|
|
]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("u", u)
|
||
|
|
def test_ppf(self, u):
|
||
|
|
dist = StandardNormal()
|
||
|
|
rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
|
||
|
|
# 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-11, atol=1e-11)
|
||
|
|
assert res.shape == expected.shape
|
||
|
|
|
||
|
|
x = [np.linspace(-10, 10, num=10000), [], [[]], [np.nan],
|
||
|
|
[-np.inf, np.nan, np.inf], 0,
|
||
|
|
[[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-np.inf, 3, 4]]]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("x", x)
|
||
|
|
def test_cdf(self, x):
|
||
|
|
dist = StandardNormal()
|
||
|
|
rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
|
||
|
|
# 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.cdf(x)
|
||
|
|
expected = stats.norm.cdf(x)
|
||
|
|
assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
|
||
|
|
assert res.shape == expected.shape
|
||
|
|
|
||
|
|
def test_u_error(self):
|
||
|
|
dist = StandardNormal()
|
||
|
|
rng = NumericalInversePolynomial(dist, u_resolution=1e-10)
|
||
|
|
max_error, mae = rng.u_error()
|
||
|
|
assert max_error < 1e-10
|
||
|
|
assert mae <= max_error
|
||
|
|
rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
|
||
|
|
max_error, mae = rng.u_error()
|
||
|
|
assert max_error < 1e-14
|
||
|
|
assert mae <= max_error
|
||
|
|
|
||
|
|
bad_orders = [1, 4.5, 20, np.inf, np.nan]
|
||
|
|
bad_u_resolution = [1e-20, 1e-1, np.inf, np.nan]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("order", bad_orders)
|
||
|
|
def test_bad_orders(self, order):
|
||
|
|
dist = StandardNormal()
|
||
|
|
|
||
|
|
msg = r"`order` must be an integer in the range \[3, 17\]."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
NumericalInversePolynomial(dist, order=order)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("u_resolution", bad_u_resolution)
|
||
|
|
def test_bad_u_resolution(self, u_resolution):
|
||
|
|
msg = r"`u_resolution` must be between 1e-15 and 1e-5."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
NumericalInversePolynomial(StandardNormal(),
|
||
|
|
u_resolution=u_resolution)
|
||
|
|
|
||
|
|
def test_bad_args(self):
|
||
|
|
|
||
|
|
class BadDist:
|
||
|
|
def cdf(self, x):
|
||
|
|
return stats.norm._cdf(x)
|
||
|
|
|
||
|
|
dist = BadDist()
|
||
|
|
msg = r"Either of the methods `pdf` or `logpdf` must be specified"
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
rng = NumericalInversePolynomial(dist)
|
||
|
|
|
||
|
|
dist = StandardNormal()
|
||
|
|
rng = NumericalInversePolynomial(dist)
|
||
|
|
msg = r"`sample_size` must be greater than or equal to 1000."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
rng.u_error(10)
|
||
|
|
|
||
|
|
class Distribution:
|
||
|
|
def pdf(self, x):
|
||
|
|
return np.exp(-0.5 * x*x)
|
||
|
|
|
||
|
|
dist = Distribution()
|
||
|
|
rng = NumericalInversePolynomial(dist)
|
||
|
|
msg = r"Exact CDF required but not found."
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
rng.u_error()
|
||
|
|
|
||
|
|
def test_logpdf_pdf_consistency(self):
|
||
|
|
# 1. check that PINV works with pdf and logpdf only
|
||
|
|
# 2. check that generated ppf is the same (up to a small tolerance)
|
||
|
|
|
||
|
|
class MyDist:
|
||
|
|
pass
|
||
|
|
|
||
|
|
# create genrator from dist with only pdf
|
||
|
|
dist_pdf = MyDist()
|
||
|
|
dist_pdf.pdf = lambda x: math.exp(-x*x/2)
|
||
|
|
rng1 = NumericalInversePolynomial(dist_pdf)
|
||
|
|
|
||
|
|
# create dist with only logpdf
|
||
|
|
dist_logpdf = MyDist()
|
||
|
|
dist_logpdf.logpdf = lambda x: -x*x/2
|
||
|
|
rng2 = NumericalInversePolynomial(dist_logpdf)
|
||
|
|
|
||
|
|
q = np.linspace(1e-5, 1-1e-5, num=100)
|
||
|
|
assert_allclose(rng1.ppf(q), rng2.ppf(q))
|
||
|
|
|
||
|
|
|
||
|
|
class TestNumericalInverseHermite:
|
||
|
|
# / (1 +sin(2 Pi x))/2 if |x| <= 1
|
||
|
|
# f(x) = <
|
||
|
|
# \ 0 otherwise
|
||
|
|
# Taken from UNU.RAN test suite (from file t_hinv.c)
|
||
|
|
class dist0:
|
||
|
|
def pdf(self, x):
|
||
|
|
return 0.5*(1. + np.sin(2.*np.pi*x))
|
||
|
|
|
||
|
|
def dpdf(self, x):
|
||
|
|
return np.pi*np.cos(2.*np.pi*x)
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
return (1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) / (4.*np.pi)
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -1, 1
|
||
|
|
|
||
|
|
# / Max(sin(2 Pi x)),0)Pi/2 if -1 < x <0.5
|
||
|
|
# f(x) = <
|
||
|
|
# \ 0 otherwise
|
||
|
|
# Taken from UNU.RAN test suite (from file t_hinv.c)
|
||
|
|
class dist1:
|
||
|
|
def pdf(self, x):
|
||
|
|
if (x <= -0.5):
|
||
|
|
return np.sin((2. * np.pi) * x) * 0.5 * np.pi
|
||
|
|
if (x < 0.):
|
||
|
|
return 0.
|
||
|
|
if (x <= 0.5):
|
||
|
|
return np.sin((2. * np.pi) * x) * 0.5 * np.pi
|
||
|
|
|
||
|
|
def dpdf(self, x):
|
||
|
|
if (x <= -0.5):
|
||
|
|
return np.cos((2. * np.pi) * x) * np.pi * np.pi
|
||
|
|
if (x < 0.):
|
||
|
|
return 0.
|
||
|
|
if (x <= 0.5):
|
||
|
|
return np.cos((2. * np.pi) * x) * np.pi * np.pi
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
if (x <= -0.5):
|
||
|
|
return 0.25 * (1 - np.cos((2. * np.pi) * x))
|
||
|
|
if (x < 0.):
|
||
|
|
return 0.5
|
||
|
|
if (x <= 0.5):
|
||
|
|
return 0.75 - 0.25 * np.cos((2. * np.pi) * x)
|
||
|
|
|
||
|
|
def support(self):
|
||
|
|
return -1, 0.5
|
||
|
|
|
||
|
|
dists = [dist0(), dist1()]
|
||
|
|
|
||
|
|
# exact mean and variance of the distributions in the list dists
|
||
|
|
mv0 = [-1/(2*np.pi), 1/3 - 1/(4*np.pi*np.pi)]
|
||
|
|
mv1 = [-1/4, 3/8-1/(2*np.pi*np.pi) - 1/16]
|
||
|
|
mvs = [mv0, mv1]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("dist, mv_ex",
|
||
|
|
zip(dists, mvs))
|
||
|
|
@pytest.mark.parametrize("order", [3, 5])
|
||
|
|
def test_basic(self, dist, mv_ex, order):
|
||
|
|
rng = NumericalInverseHermite(dist, order=order, random_state=42)
|
||
|
|
check_cont_samples(rng, dist, mv_ex)
|
||
|
|
|
||
|
|
# test domains with inf + nan in them. need to write a custom test for
|
||
|
|
# this because not all methods support infinite tails.
|
||
|
|
@pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
|
||
|
|
def test_inf_nan_domains(self, domain, err, msg):
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
NumericalInverseHermite(StandardNormal(), domain=domain)
|
||
|
|
|
||
|
|
def basic_test_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)
|
||
|
|
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
|
||
|
|
|
||
|
|
@pytest.mark.filterwarnings('ignore::RuntimeWarning')
|
||
|
|
@pytest.mark.xslow
|
||
|
|
@pytest.mark.parametrize(("distname", "shapes"), distcont)
|
||
|
|
def test_basic_all_scipy_dists(self, distname, shapes):
|
||
|
|
# if distname == "truncnorm":
|
||
|
|
# pytest.skip("Tested separately")
|
||
|
|
self.basic_test_all_scipy_dists(distname, shapes)
|
||
|
|
|
||
|
|
@pytest.mark.filterwarnings('ignore::RuntimeWarning')
|
||
|
|
def test_basic_truncnorm_gh17155(self):
|
||
|
|
self.basic_test_all_scipy_dists("truncnorm", (0.1, 2))
|
||
|
|
|
||
|
|
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')
|
||
|
|
|
||
|
|
rngs = [None, 0, np.random.RandomState(0)]
|
||
|
|
rngs.append(np.random.default_rng(0)) # type: ignore
|
||
|
|
sizes = [(None, tuple()), (8, (8,)), ((4, 5, 6), (4, 5, 6))]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('rng', rngs)
|
||
|
|
@pytest.mark.parametrize('size_in, size_out', sizes)
|
||
|
|
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_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_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))
|
||
|
|
|
||
|
|
u = [
|
||
|
|
# check the correctness of the PPF for equidistant points between
|
||
|
|
# 0.02 and 0.98.
|
||
|
|
np.linspace(0., 1., num=10000),
|
||
|
|
# test the PPF method for empty arrays
|
||
|
|
[], [[]],
|
||
|
|
# test if nans and infs return nan result.
|
||
|
|
[np.nan], [-np.inf, np.nan, np.inf],
|
||
|
|
# test if a scalar is returned for a scalar input.
|
||
|
|
0,
|
||
|
|
# test for arrays with nans, values greater than 1 and less than 0,
|
||
|
|
# and some valid values.
|
||
|
|
[[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
|
||
|
|
]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("u", u)
|
||
|
|
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_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
|
||
|
|
|
||
|
|
|
||
|
|
class TestDiscreteGuideTable:
|
||
|
|
basic_fail_dists = {
|
||
|
|
'nchypergeom_fisher', # numerical errors on tails
|
||
|
|
'nchypergeom_wallenius', # numerical errors on tails
|
||
|
|
'randint' # fails on 32-bit ubuntu
|
||
|
|
}
|
||
|
|
|
||
|
|
def test_guide_factor_gt3_raises_warning(self):
|
||
|
|
pv = [0.1, 0.3, 0.6]
|
||
|
|
urng = np.random.default_rng()
|
||
|
|
with pytest.warns(RuntimeWarning):
|
||
|
|
DiscreteGuideTable(pv, random_state=urng, guide_factor=7)
|
||
|
|
|
||
|
|
def test_guide_factor_zero_raises_warning(self):
|
||
|
|
pv = [0.1, 0.3, 0.6]
|
||
|
|
urng = np.random.default_rng()
|
||
|
|
with pytest.warns(RuntimeWarning):
|
||
|
|
DiscreteGuideTable(pv, random_state=urng, guide_factor=0)
|
||
|
|
|
||
|
|
def test_negative_guide_factor_raises_warning(self):
|
||
|
|
# This occurs from the UNU.RAN wrapper automatically.
|
||
|
|
# however it already gives a useful warning
|
||
|
|
# Here we just test that a warning is raised.
|
||
|
|
pv = [0.1, 0.3, 0.6]
|
||
|
|
urng = np.random.default_rng()
|
||
|
|
with pytest.warns(RuntimeWarning):
|
||
|
|
DiscreteGuideTable(pv, random_state=urng, guide_factor=-1)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("distname, params", distdiscrete)
|
||
|
|
def test_basic(self, distname, params):
|
||
|
|
if distname in self.basic_fail_dists:
|
||
|
|
msg = ("DGT fails on these probably because of large domains "
|
||
|
|
"and small computation errors in PMF.")
|
||
|
|
pytest.skip(msg)
|
||
|
|
|
||
|
|
if not isinstance(distname, str):
|
||
|
|
dist = distname
|
||
|
|
else:
|
||
|
|
dist = getattr(stats, distname)
|
||
|
|
|
||
|
|
dist = dist(*params)
|
||
|
|
domain = dist.support()
|
||
|
|
|
||
|
|
if not np.isfinite(domain[1] - domain[0]):
|
||
|
|
# DGT only works with finite domain. So, skip the distributions
|
||
|
|
# with infinite tails.
|
||
|
|
pytest.skip("DGT only works with a finite domain.")
|
||
|
|
|
||
|
|
k = np.arange(domain[0], domain[1]+1)
|
||
|
|
pv = dist.pmf(k)
|
||
|
|
mv_ex = dist.stats('mv')
|
||
|
|
rng = DiscreteGuideTable(dist, random_state=42)
|
||
|
|
check_discr_samples(rng, pv, mv_ex)
|
||
|
|
|
||
|
|
u = [
|
||
|
|
# the correctness of the PPF for equidistant points between 0 and 1.
|
||
|
|
np.linspace(0, 1, num=10000),
|
||
|
|
# test the PPF method for empty arrays
|
||
|
|
[], [[]],
|
||
|
|
# test if nans and infs return nan result.
|
||
|
|
[np.nan], [-np.inf, np.nan, np.inf],
|
||
|
|
# test if a scalar is returned for a scalar input.
|
||
|
|
0,
|
||
|
|
# test for arrays with nans, values greater than 1 and less than 0,
|
||
|
|
# and some valid values.
|
||
|
|
[[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
|
||
|
|
]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('u', u)
|
||
|
|
def test_ppf(self, u):
|
||
|
|
n, p = 4, 0.1
|
||
|
|
dist = stats.binom(n, p)
|
||
|
|
rng = DiscreteGuideTable(dist, random_state=42)
|
||
|
|
|
||
|
|
# 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.binom.ppf(u, n, p)
|
||
|
|
assert_equal(res.shape, expected.shape)
|
||
|
|
assert_equal(res, expected)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("pv, msg", bad_pv_common)
|
||
|
|
def test_bad_pv(self, pv, msg):
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
DiscreteGuideTable(pv)
|
||
|
|
|
||
|
|
# DGT doesn't support infinite tails. So, it should throw an error when
|
||
|
|
# inf is present in the domain.
|
||
|
|
inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
|
||
|
|
(0, np.inf), (-np.inf, 0)]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("domain", inf_domain)
|
||
|
|
def test_inf_domain(self, domain):
|
||
|
|
with pytest.raises(ValueError, match=r"must be finite"):
|
||
|
|
DiscreteGuideTable(stats.binom(10, 0.2), domain=domain)
|
||
|
|
|
||
|
|
|
||
|
|
class TestSimpleRatioUniforms:
|
||
|
|
# pdf with piecewise linear function as transformed density
|
||
|
|
# with T = -1/sqrt with shift. Taken from UNU.RAN test suite
|
||
|
|
# (from file t_srou.c)
|
||
|
|
class dist:
|
||
|
|
def __init__(self, shift):
|
||
|
|
self.shift = shift
|
||
|
|
self.mode = shift
|
||
|
|
|
||
|
|
def pdf(self, x):
|
||
|
|
x -= self.shift
|
||
|
|
y = 1. / (abs(x) + 1.)
|
||
|
|
return 0.5 * y * y
|
||
|
|
|
||
|
|
def cdf(self, x):
|
||
|
|
x -= self.shift
|
||
|
|
if x <= 0.:
|
||
|
|
return 0.5 / (1. - x)
|
||
|
|
else:
|
||
|
|
return 1. - 0.5 / (1. + x)
|
||
|
|
|
||
|
|
dists = [dist(0.), dist(10000.)]
|
||
|
|
|
||
|
|
# exact mean and variance of the distributions in the list dists
|
||
|
|
mv1 = [0., np.inf]
|
||
|
|
mv2 = [10000., np.inf]
|
||
|
|
mvs = [mv1, mv2]
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("dist, mv_ex",
|
||
|
|
zip(dists, mvs))
|
||
|
|
def test_basic(self, dist, mv_ex):
|
||
|
|
rng = SimpleRatioUniforms(dist, mode=dist.mode, random_state=42)
|
||
|
|
check_cont_samples(rng, dist, mv_ex)
|
||
|
|
rng = SimpleRatioUniforms(dist, mode=dist.mode,
|
||
|
|
cdf_at_mode=dist.cdf(dist.mode),
|
||
|
|
random_state=42)
|
||
|
|
check_cont_samples(rng, dist, mv_ex)
|
||
|
|
|
||
|
|
# test domains with inf + nan in them. need to write a custom test for
|
||
|
|
# this because not all methods support infinite tails.
|
||
|
|
@pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
|
||
|
|
def test_inf_nan_domains(self, domain, err, msg):
|
||
|
|
with pytest.raises(err, match=msg):
|
||
|
|
SimpleRatioUniforms(StandardNormal(), domain=domain)
|
||
|
|
|
||
|
|
def test_bad_args(self):
|
||
|
|
# pdf_area < 0
|
||
|
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with pytest.raises(ValueError, match=r"`pdf_area` must be > 0"):
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SimpleRatioUniforms(StandardNormal(), mode=0, pdf_area=-1)
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