609 lines
20 KiB
Python
609 lines
20 KiB
Python
from scipy import stats, linalg, integrate
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import numpy as np
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from numpy.testing import (assert_almost_equal, assert_, assert_equal,
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assert_array_almost_equal,
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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]),
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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]),
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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().__init__(dataset)
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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 was removed because we have no obligation to maintain support
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# for user invocation of private methods
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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("dtype", _ftypes)
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def test_kde_output_dtype(dtype, bw_type):
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# Check whether the datatypes are available
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dtype = getattr(np, dtype, 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 [dtype, bw]):
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pytest.skip()
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weights = np.arange(5, dtype=dtype)
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dataset = np.arange(5, dtype=dtype)
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k = stats.gaussian_kde(dataset, bw_method=bw, weights=weights)
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points = np.arange(5, dtype=dtype)
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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_validation():
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rng = np.random.default_rng(64202298293133848336925499069837723291)
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xn = rng.standard_normal((2, 10))
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gkde = stats.gaussian_kde(xn)
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xs = rng.standard_normal((3, 10))
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msg = "points have dimension 3, dataset has dimension 2"
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with pytest.raises(ValueError, match=msg):
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gkde.logpdf(xs)
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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_marginal_1_axis():
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rng = np.random.default_rng(6111799263660870475)
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n_data = 50
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n_dim = 10
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dataset = rng.normal(size=(n_dim, n_data))
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points = rng.normal(size=(n_dim, 3))
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dimensions = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9]) # dimensions to keep
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kde = stats.gaussian_kde(dataset)
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marginal = kde.marginal(dimensions)
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pdf = marginal.pdf(points[dimensions])
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def marginal_pdf_single(point):
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def f(x):
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x = np.concatenate(([x], point[dimensions]))
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return kde.pdf(x)[0]
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return integrate.quad(f, -np.inf, np.inf)[0]
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def marginal_pdf(points):
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return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
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ref = marginal_pdf(points)
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assert_allclose(pdf, ref, rtol=1e-6)
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@pytest.mark.xslow
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def test_marginal_2_axis():
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rng = np.random.default_rng(6111799263660870475)
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n_data = 30
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n_dim = 4
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dataset = rng.normal(size=(n_dim, n_data))
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points = rng.normal(size=(n_dim, 3))
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dimensions = np.array([1, 3]) # dimensions to keep
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kde = stats.gaussian_kde(dataset)
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marginal = kde.marginal(dimensions)
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pdf = marginal.pdf(points[dimensions])
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def marginal_pdf(points):
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def marginal_pdf_single(point):
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def f(y, x):
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w, z = point[dimensions]
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x = np.array([x, w, y, z])
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return kde.pdf(x)[0]
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return integrate.dblquad(f, -np.inf, np.inf, -np.inf, np.inf)[0]
|
|
|
|
return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
|
|
|
|
ref = marginal_pdf(points)
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|
|
|
assert_allclose(pdf, ref, rtol=1e-6)
|
|
|
|
|
|
def test_marginal_iv():
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# test input validation
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|
rng = np.random.default_rng(6111799263660870475)
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n_data = 30
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|
n_dim = 4
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|
dataset = rng.normal(size=(n_dim, n_data))
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|
points = rng.normal(size=(n_dim, 3))
|
|
|
|
kde = stats.gaussian_kde(dataset)
|
|
|
|
# check that positive and negative indices are equivalent
|
|
dimensions1 = [-1, 1]
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|
marginal1 = kde.marginal(dimensions1)
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|
pdf1 = marginal1.pdf(points[dimensions1])
|
|
|
|
dimensions2 = [3, -3]
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|
marginal2 = kde.marginal(dimensions2)
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|
pdf2 = marginal2.pdf(points[dimensions2])
|
|
|
|
assert_equal(pdf1, pdf2)
|
|
|
|
# IV for non-integer dimensions
|
|
message = "Elements of `dimensions` must be integers..."
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|
with pytest.raises(ValueError, match=message):
|
|
kde.marginal([1, 2.5])
|
|
|
|
# IV for uniquenes
|
|
message = "All elements of `dimensions` must be unique."
|
|
with pytest.raises(ValueError, match=message):
|
|
kde.marginal([1, 2, 2])
|
|
|
|
# IV for non-integer dimensions
|
|
message = (r"Dimensions \[-5 6\] are invalid for a distribution in 4...")
|
|
with pytest.raises(ValueError, match=message):
|
|
kde.marginal([1, -5, 6])
|
|
|
|
|
|
@pytest.mark.xslow
|
|
def test_logpdf_overflow():
|
|
# regression test for gh-12988; testing against linalg instability for
|
|
# very high dimensionality kde
|
|
np.random.seed(1)
|
|
n_dimensions = 2500
|
|
n_samples = 5000
|
|
xn = np.array([np.random.randn(n_samples) + (n) for n in range(
|
|
0, n_dimensions)])
|
|
|
|
# Default
|
|
gkde = stats.gaussian_kde(xn)
|
|
|
|
logpdf = gkde.logpdf(np.arange(0, n_dimensions))
|
|
np.testing.assert_equal(np.isneginf(logpdf[0]), False)
|
|
np.testing.assert_equal(np.isnan(logpdf[0]), False)
|
|
|
|
|
|
def test_weights_intact():
|
|
# regression test for gh-9709: weights are not modified
|
|
np.random.seed(12345)
|
|
vals = np.random.lognormal(size=100)
|
|
weights = np.random.choice([1.0, 10.0, 100], size=vals.size)
|
|
orig_weights = weights.copy()
|
|
|
|
stats.gaussian_kde(np.log10(vals), weights=weights)
|
|
assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
|
|
|
|
|
|
def test_weights_integer():
|
|
# integer weights are OK, cf gh-9709 (comment)
|
|
np.random.seed(12345)
|
|
values = [0.2, 13.5, 21.0, 75.0, 99.0]
|
|
weights = [1, 2, 4, 8, 16] # a list of integers
|
|
pdf_i = stats.gaussian_kde(values, weights=weights)
|
|
pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
|
|
|
|
xn = [0.3, 11, 88]
|
|
assert_allclose(pdf_i.evaluate(xn),
|
|
pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
|
|
|
|
|
|
def test_seed():
|
|
# Test the seed option of the resample method
|
|
def test_seed_sub(gkde_trail):
|
|
n_sample = 200
|
|
# The results should be different without using seed
|
|
samp1 = gkde_trail.resample(n_sample)
|
|
samp2 = gkde_trail.resample(n_sample)
|
|
assert_raises(
|
|
AssertionError, assert_allclose, samp1, samp2, atol=1e-13
|
|
)
|
|
# Use integer seed
|
|
seed = 831
|
|
samp1 = gkde_trail.resample(n_sample, seed=seed)
|
|
samp2 = gkde_trail.resample(n_sample, seed=seed)
|
|
assert_allclose(samp1, samp2, atol=1e-13)
|
|
# Use RandomState
|
|
rstate1 = np.random.RandomState(seed=138)
|
|
samp1 = gkde_trail.resample(n_sample, seed=rstate1)
|
|
rstate2 = np.random.RandomState(seed=138)
|
|
samp2 = gkde_trail.resample(n_sample, seed=rstate2)
|
|
assert_allclose(samp1, samp2, atol=1e-13)
|
|
|
|
# check that np.random.Generator can be used (numpy >= 1.17)
|
|
if hasattr(np.random, 'default_rng'):
|
|
# obtain a np.random.Generator object
|
|
rng = np.random.default_rng(1234)
|
|
gkde_trail.resample(n_sample, seed=rng)
|
|
|
|
np.random.seed(8765678)
|
|
n_basesample = 500
|
|
wn = np.random.rand(n_basesample)
|
|
# Test 1D case
|
|
xn_1d = np.random.randn(n_basesample)
|
|
|
|
gkde_1d = stats.gaussian_kde(xn_1d)
|
|
test_seed_sub(gkde_1d)
|
|
gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
|
|
test_seed_sub(gkde_1d_weighted)
|
|
|
|
# Test 2D case
|
|
mean = np.array([1.0, 3.0])
|
|
covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
|
|
xn_2d = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
|
|
|
|
gkde_2d = stats.gaussian_kde(xn_2d)
|
|
test_seed_sub(gkde_2d)
|
|
gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
|
|
test_seed_sub(gkde_2d_weighted)
|
|
|
|
|
|
def test_singular_data_covariance_gh10205():
|
|
# When the data lie in a lower-dimensional subspace and this causes
|
|
# and exception, check that the error message is informative.
|
|
rng = np.random.default_rng(2321583144339784787)
|
|
mu = np.array([1, 10, 20])
|
|
sigma = np.array([[4, 10, 0], [10, 25, 0], [0, 0, 100]])
|
|
data = rng.multivariate_normal(mu, sigma, 1000)
|
|
try: # doesn't raise any error on some platforms, and that's OK
|
|
stats.gaussian_kde(data.T)
|
|
except linalg.LinAlgError:
|
|
msg = "The data appears to lie in a lower-dimensional subspace..."
|
|
with assert_raises(linalg.LinAlgError, match=msg):
|
|
stats.gaussian_kde(data.T)
|
|
|
|
|
|
def test_fewer_points_than_dimensions_gh17436():
|
|
# When the number of points is fewer than the number of dimensions, the
|
|
# the covariance matrix would be singular, and the exception tested in
|
|
# test_singular_data_covariance_gh10205 would occur. However, sometimes
|
|
# this occurs when the user passes in the transpose of what `gaussian_kde`
|
|
# expects. This can result in a huge covariance matrix, so bail early.
|
|
rng = np.random.default_rng(2046127537594925772)
|
|
rvs = rng.multivariate_normal(np.zeros(3), np.eye(3), size=5)
|
|
message = "Number of dimensions is greater than number of samples..."
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.gaussian_kde(rvs)
|