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488 lines
16 KiB
Python
488 lines
16 KiB
Python
from scipy import stats
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import numpy as np
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from numpy.testing import (assert_almost_equal, assert_,
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assert_array_almost_equal, assert_array_almost_equal_nulp, assert_allclose)
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import pytest
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from pytest import raises as assert_raises
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def test_kde_1d():
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#some basic tests comparing to normal distribution
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np.random.seed(8765678)
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n_basesample = 500
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xn = np.random.randn(n_basesample)
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xnmean = xn.mean()
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xnstd = xn.std(ddof=1)
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# get kde for original sample
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gkde = stats.gaussian_kde(xn)
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# evaluate the density function for the kde for some points
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xs = np.linspace(-7,7,501)
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kdepdf = gkde.evaluate(xs)
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normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
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intervall = xs[1] - xs[0]
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assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
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prob1 = gkde.integrate_box_1d(xnmean, np.inf)
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prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
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assert_almost_equal(prob1, 0.5, decimal=1)
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assert_almost_equal(prob2, 0.5, decimal=1)
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assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
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assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
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assert_almost_equal(gkde.integrate_kde(gkde),
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(kdepdf**2).sum()*intervall, decimal=2)
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assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
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(kdepdf*normpdf).sum()*intervall, decimal=2)
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def test_kde_1d_weighted():
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#some basic tests comparing to normal distribution
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np.random.seed(8765678)
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n_basesample = 500
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xn = np.random.randn(n_basesample)
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wn = np.random.rand(n_basesample)
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xnmean = np.average(xn, weights=wn)
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xnstd = np.sqrt(np.average((xn-xnmean)**2, weights=wn))
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# get kde for original sample
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gkde = stats.gaussian_kde(xn, weights=wn)
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# evaluate the density function for the kde for some points
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xs = np.linspace(-7,7,501)
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kdepdf = gkde.evaluate(xs)
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normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
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intervall = xs[1] - xs[0]
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assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
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prob1 = gkde.integrate_box_1d(xnmean, np.inf)
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prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
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assert_almost_equal(prob1, 0.5, decimal=1)
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assert_almost_equal(prob2, 0.5, decimal=1)
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assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
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assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
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assert_almost_equal(gkde.integrate_kde(gkde),
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(kdepdf**2).sum()*intervall, decimal=2)
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assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
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(kdepdf*normpdf).sum()*intervall, decimal=2)
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@pytest.mark.slow
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def test_kde_2d():
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#some basic tests comparing to normal distribution
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np.random.seed(8765678)
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n_basesample = 500
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mean = np.array([1.0, 3.0])
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covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
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# Need transpose (shape (2, 500)) for kde
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xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
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# get kde for original sample
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gkde = stats.gaussian_kde(xn)
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# evaluate the density function for the kde for some points
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x, y = np.mgrid[-7:7:500j, -7:7:500j]
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grid_coords = np.vstack([x.ravel(), y.ravel()])
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kdepdf = gkde.evaluate(grid_coords)
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kdepdf = kdepdf.reshape(500, 500)
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normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]), mean=mean, cov=covariance)
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intervall = y.ravel()[1] - y.ravel()[0]
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assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
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small = -1e100
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large = 1e100
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prob1 = gkde.integrate_box([small, mean[1]], [large, large])
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prob2 = gkde.integrate_box([small, small], [large, mean[1]])
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assert_almost_equal(prob1, 0.5, decimal=1)
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assert_almost_equal(prob2, 0.5, decimal=1)
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assert_almost_equal(gkde.integrate_kde(gkde),
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(kdepdf**2).sum()*(intervall**2), decimal=2)
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assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
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(kdepdf*normpdf).sum()*(intervall**2), decimal=2)
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@pytest.mark.slow
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def test_kde_2d_weighted():
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#some basic tests comparing to normal distribution
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np.random.seed(8765678)
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n_basesample = 500
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mean = np.array([1.0, 3.0])
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covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
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# Need transpose (shape (2, 500)) for kde
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xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
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wn = np.random.rand(n_basesample)
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# get kde for original sample
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gkde = stats.gaussian_kde(xn, weights=wn)
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# evaluate the density function for the kde for some points
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x, y = np.mgrid[-7:7:500j, -7:7:500j]
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grid_coords = np.vstack([x.ravel(), y.ravel()])
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kdepdf = gkde.evaluate(grid_coords)
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kdepdf = kdepdf.reshape(500, 500)
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normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]), mean=mean, cov=covariance)
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intervall = y.ravel()[1] - y.ravel()[0]
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assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
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small = -1e100
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large = 1e100
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prob1 = gkde.integrate_box([small, mean[1]], [large, large])
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prob2 = gkde.integrate_box([small, small], [large, mean[1]])
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assert_almost_equal(prob1, 0.5, decimal=1)
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assert_almost_equal(prob2, 0.5, decimal=1)
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assert_almost_equal(gkde.integrate_kde(gkde),
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(kdepdf**2).sum()*(intervall**2), decimal=2)
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assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
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(kdepdf*normpdf).sum()*(intervall**2), decimal=2)
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def test_kde_bandwidth_method():
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def scotts_factor(kde_obj):
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"""Same as default, just check that it works."""
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return np.power(kde_obj.n, -1./(kde_obj.d+4))
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np.random.seed(8765678)
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n_basesample = 50
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xn = np.random.randn(n_basesample)
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# Default
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gkde = stats.gaussian_kde(xn)
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# Supply a callable
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gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
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# Supply a scalar
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gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
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xs = np.linspace(-7,7,51)
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kdepdf = gkde.evaluate(xs)
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kdepdf2 = gkde2.evaluate(xs)
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assert_almost_equal(kdepdf, kdepdf2)
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kdepdf3 = gkde3.evaluate(xs)
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assert_almost_equal(kdepdf, kdepdf3)
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assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
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def test_kde_bandwidth_method_weighted():
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def scotts_factor(kde_obj):
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"""Same as default, just check that it works."""
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return np.power(kde_obj.neff, -1./(kde_obj.d+4))
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np.random.seed(8765678)
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n_basesample = 50
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xn = np.random.randn(n_basesample)
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# Default
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gkde = stats.gaussian_kde(xn)
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# Supply a callable
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gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
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# Supply a scalar
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gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
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xs = np.linspace(-7,7,51)
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kdepdf = gkde.evaluate(xs)
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kdepdf2 = gkde2.evaluate(xs)
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assert_almost_equal(kdepdf, kdepdf2)
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kdepdf3 = gkde3.evaluate(xs)
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assert_almost_equal(kdepdf, kdepdf3)
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assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
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# Subclasses that should stay working (extracted from various sources).
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# Unfortunately the earlier design of gaussian_kde made it necessary for users
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# to create these kinds of subclasses, or call _compute_covariance() directly.
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class _kde_subclass1(stats.gaussian_kde):
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def __init__(self, dataset):
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self.dataset = np.atleast_2d(dataset)
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self.d, self.n = self.dataset.shape
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self.covariance_factor = self.scotts_factor
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self._compute_covariance()
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class _kde_subclass2(stats.gaussian_kde):
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def __init__(self, dataset):
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self.covariance_factor = self.scotts_factor
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super(_kde_subclass2, self).__init__(dataset)
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class _kde_subclass3(stats.gaussian_kde):
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def __init__(self, dataset, covariance):
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self.covariance = covariance
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stats.gaussian_kde.__init__(self, dataset)
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def _compute_covariance(self):
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self.inv_cov = np.linalg.inv(self.covariance)
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self._norm_factor = np.sqrt(np.linalg.det(2 * np.pi * self.covariance))
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class _kde_subclass4(stats.gaussian_kde):
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def covariance_factor(self):
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return 0.5 * self.silverman_factor()
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def test_gaussian_kde_subclassing():
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x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
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xs = np.linspace(-10, 10, num=50)
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# gaussian_kde itself
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kde = stats.gaussian_kde(x1)
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ys = kde(xs)
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# subclass 1
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kde1 = _kde_subclass1(x1)
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y1 = kde1(xs)
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assert_array_almost_equal_nulp(ys, y1, nulp=10)
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# subclass 2
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kde2 = _kde_subclass2(x1)
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y2 = kde2(xs)
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assert_array_almost_equal_nulp(ys, y2, nulp=10)
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# subclass 3
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kde3 = _kde_subclass3(x1, kde.covariance)
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y3 = kde3(xs)
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assert_array_almost_equal_nulp(ys, y3, nulp=10)
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# subclass 4
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kde4 = _kde_subclass4(x1)
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y4 = kde4(x1)
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y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
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assert_array_almost_equal(y_expected, y4, decimal=6)
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# Not a subclass, but check for use of _compute_covariance()
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kde5 = kde
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kde5.covariance_factor = lambda: kde.factor
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kde5._compute_covariance()
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y5 = kde5(xs)
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assert_array_almost_equal_nulp(ys, y5, nulp=10)
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def test_gaussian_kde_covariance_caching():
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x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
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xs = np.linspace(-10, 10, num=5)
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# These expected values are from scipy 0.10, before some changes to
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# gaussian_kde. They were not compared with any external reference.
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y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
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# Set the bandwidth, then reset it to the default.
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kde = stats.gaussian_kde(x1)
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kde.set_bandwidth(bw_method=0.5)
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kde.set_bandwidth(bw_method='scott')
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y2 = kde(xs)
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assert_array_almost_equal(y_expected, y2, decimal=7)
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def test_gaussian_kde_monkeypatch():
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"""Ugly, but people may rely on this. See scipy pull request 123,
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specifically the linked ML thread "Width of the Gaussian in stats.kde".
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If it is necessary to break this later on, that is to be discussed on ML.
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"""
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x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
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xs = np.linspace(-10, 10, num=50)
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# The old monkeypatched version to get at Silverman's Rule.
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kde = stats.gaussian_kde(x1)
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kde.covariance_factor = kde.silverman_factor
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kde._compute_covariance()
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y1 = kde(xs)
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# The new saner version.
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kde2 = stats.gaussian_kde(x1, bw_method='silverman')
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y2 = kde2(xs)
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assert_array_almost_equal_nulp(y1, y2, nulp=10)
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def test_kde_integer_input():
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"""Regression test for #1181."""
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x1 = np.arange(5)
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kde = stats.gaussian_kde(x1)
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y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
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assert_array_almost_equal(kde(x1), y_expected, decimal=6)
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_ftypes = ['float32', 'float64', 'float96', 'float128', 'int32', 'int64']
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@pytest.mark.parametrize("bw_type", _ftypes + ["scott", "silverman"])
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@pytest.mark.parametrize("weights_type", _ftypes)
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@pytest.mark.parametrize("dataset_type", _ftypes)
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@pytest.mark.parametrize("point_type", _ftypes)
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def test_kde_output_dtype(point_type, dataset_type, weights_type, bw_type):
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# Check whether the datatypes are available
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point_type = getattr(np, point_type, None)
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dataset_type = getattr(np, weights_type, None)
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weights_type = getattr(np, weights_type, None)
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if bw_type in ["scott", "silverman"]:
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bw = bw_type
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else:
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bw_type = getattr(np, bw_type, None)
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bw = bw_type(3) if bw_type else None
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if any(dt is None for dt in [point_type, dataset_type, weights_type, bw]):
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pytest.skip()
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weights = np.arange(5, dtype=weights_type)
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dataset = np.arange(5, dtype=dataset_type)
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k = stats.kde.gaussian_kde(dataset, bw_method=bw, weights=weights)
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points = np.arange(5, dtype=point_type)
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result = k(points)
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# weights are always cast to float64
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assert result.dtype == np.result_type(dataset, points, np.float64(weights),
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k.factor)
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def test_pdf_logpdf():
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np.random.seed(1)
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n_basesample = 50
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xn = np.random.randn(n_basesample)
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# Default
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gkde = stats.gaussian_kde(xn)
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xs = np.linspace(-15, 12, 25)
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pdf = gkde.evaluate(xs)
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pdf2 = gkde.pdf(xs)
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assert_almost_equal(pdf, pdf2, decimal=12)
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logpdf = np.log(pdf)
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logpdf2 = gkde.logpdf(xs)
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assert_almost_equal(logpdf, logpdf2, decimal=12)
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# There are more points than data
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gkde = stats.gaussian_kde(xs)
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pdf = np.log(gkde.evaluate(xn))
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pdf2 = gkde.logpdf(xn)
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assert_almost_equal(pdf, pdf2, decimal=12)
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def test_pdf_logpdf_weighted():
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np.random.seed(1)
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n_basesample = 50
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xn = np.random.randn(n_basesample)
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wn = np.random.rand(n_basesample)
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# Default
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gkde = stats.gaussian_kde(xn, weights=wn)
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xs = np.linspace(-15, 12, 25)
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pdf = gkde.evaluate(xs)
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pdf2 = gkde.pdf(xs)
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assert_almost_equal(pdf, pdf2, decimal=12)
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logpdf = np.log(pdf)
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logpdf2 = gkde.logpdf(xs)
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assert_almost_equal(logpdf, logpdf2, decimal=12)
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# There are more points than data
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gkde = stats.gaussian_kde(xs, weights=np.random.rand(len(xs)))
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pdf = np.log(gkde.evaluate(xn))
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pdf2 = gkde.logpdf(xn)
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assert_almost_equal(pdf, pdf2, decimal=12)
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def test_logpdf_overflow():
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# regression test for gh-12988; testing against linalg instability for
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# very high dimensionality kde
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np.random.seed(1)
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n_dimensions = 2500
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n_samples = 5000
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xn = np.array([np.random.randn(n_samples) + (n) for n in range(
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0, n_dimensions)])
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# Default
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gkde = stats.gaussian_kde(xn)
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logpdf = gkde.logpdf(np.arange(0, n_dimensions))
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np.testing.assert_equal(np.isneginf(logpdf[0]), False)
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np.testing.assert_equal(np.isnan(logpdf[0]), False)
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def test_weights_intact():
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# regression test for gh-9709: weights are not modified
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np.random.seed(12345)
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vals = np.random.lognormal(size=100)
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weights = np.random.choice([1.0, 10.0, 100], size=vals.size)
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orig_weights = weights.copy()
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stats.gaussian_kde(np.log10(vals), weights=weights)
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assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
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def test_weights_integer():
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# integer weights are OK, cf gh-9709 (comment)
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np.random.seed(12345)
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values = [0.2, 13.5, 21.0, 75.0, 99.0]
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weights = [1, 2, 4, 8, 16] # a list of integers
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pdf_i = stats.gaussian_kde(values, weights=weights)
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pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
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|
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xn = [0.3, 11, 88]
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assert_allclose(pdf_i.evaluate(xn),
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pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
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|
|
|
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def test_seed():
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# Test the seed option of the resample method
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def test_seed_sub(gkde_trail):
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n_sample = 200
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# The results should be different without using seed
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samp1 = gkde_trail.resample(n_sample)
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samp2 = gkde_trail.resample(n_sample)
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assert_raises(
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AssertionError, assert_allclose, samp1, samp2, atol=1e-13
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|
)
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# Use integer seed
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seed = 831
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samp1 = gkde_trail.resample(n_sample, seed=seed)
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samp2 = gkde_trail.resample(n_sample, seed=seed)
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assert_allclose(samp1, samp2, atol=1e-13)
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|
# Use RandomState
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|
rstate1 = np.random.RandomState(seed=138)
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|
samp1 = gkde_trail.resample(n_sample, seed=rstate1)
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|
rstate2 = np.random.RandomState(seed=138)
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|
samp2 = gkde_trail.resample(n_sample, seed=rstate2)
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assert_allclose(samp1, samp2, atol=1e-13)
|
|
|
|
# check that np.random.Generator can be used (numpy >= 1.17)
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|
if hasattr(np.random, 'default_rng'):
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|
# obtain a np.random.Generator object
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|
rng = np.random.default_rng(1234)
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|
gkde_trail.resample(n_sample, seed=rng)
|
|
|
|
np.random.seed(8765678)
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|
n_basesample = 500
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|
wn = np.random.rand(n_basesample)
|
|
# Test 1D case
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|
xn_1d = np.random.randn(n_basesample)
|
|
|
|
gkde_1d = stats.gaussian_kde(xn_1d)
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|
test_seed_sub(gkde_1d)
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|
gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
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|
test_seed_sub(gkde_1d_weighted)
|
|
|
|
# Test 2D case
|
|
mean = np.array([1.0, 3.0])
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|
covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
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|
xn_2d = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
|
|
|
|
gkde_2d = stats.gaussian_kde(xn_2d)
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|
test_seed_sub(gkde_2d)
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|
gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
|
|
test_seed_sub(gkde_2d_weighted)
|