def test_kde_1d():
#some basic tests comparing to normal distribution
np.random.seed(8765678)
n_basesample = 500
xn = np.random.randn(n_basesample)
xnmean = xn.mean()
xnstd = xn.std(ddof=1)
# get kde for original sample
gkde = stats.gaussian_kde(xn)
# evaluate the density function for the kde for some points
xs = np.linspace(-7,7,501)
kdepdf = gkde.evaluate(xs)
normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
intervall = xs[1] - xs[0]
assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
prob1 = gkde.integrate_box_1d(xnmean, np.inf)
prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
assert_almost_equal(prob1, 0.5, decimal=1)
assert_almost_equal(prob2, 0.5, decimal=1)
assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
assert_almost_equal(gkde.integrate_kde(gkde),
(kdepdf**2).sum()*intervall, decimal=2)
assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
(kdepdf*normpdf).sum()*intervall, decimal=2)
def test_kde_1d():
#some basic tests comparing to normal distribution
np.random.seed(8765678)
n_basesample = 500
xn = np.random.randn(n_basesample)
xnmean = xn.mean()
xnstd = xn.std(ddof=1)
# get kde for original sample
gkde = stats.gaussian_kde(xn)
# evaluate the density function for the kde for some points
xs = np.linspace(-7,7,501)
kdepdf = gkde.evaluate(xs)
normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
intervall = xs[1] - xs[0]
assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
prob1 = gkde.integrate_box_1d(xnmean, np.inf)
prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
assert_almost_equal(prob1, 0.5, decimal=1)
assert_almost_equal(prob2, 0.5, decimal=1)
assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
assert_almost_equal(gkde.integrate_kde(gkde),
(kdepdf**2).sum()*intervall, decimal=2)
assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
(kdepdf*normpdf).sum()*intervall, decimal=2)
def test_gaussian_kde_monkeypatch():
"""Ugly, but people may rely on this. See scipy pull request 123,
specifically the linked ML thread "Width of the Gaussian in stats.kde".
If it is necessary to break this later on, that is to be discussed on ML.
"""
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=50)
# The old monkeypatched version to get at Silverman's Rule.
kde = stats.gaussian_kde(x1)
kde.covariance_factor = kde.silverman_factor
kde._compute_covariance()
y1 = kde(xs)
# The new saner version.
kde2 = stats.gaussian_kde(x1, bw_method='silverman')
y2 = kde2(xs)
assert_array_almost_equal_nulp(y1, y2, nulp=10)
def test_gaussian_kde_monkeypatch():
"""Ugly, but people may rely on this. See scipy pull request 123,
specifically the linked ML thread "Width of the Gaussian in stats.kde".
If it is necessary to break this later on, that is to be discussed on ML.
"""
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=50)
# The old monkeypatched version to get at Silverman's Rule.
kde = stats.gaussian_kde(x1)
kde.covariance_factor = kde.silverman_factor
kde._compute_covariance()
y1 = kde(xs)
# The new saner version.
kde2 = stats.gaussian_kde(x1, bw_method='silverman')
y2 = kde2(xs)
assert_array_almost_equal_nulp(y1, y2, nulp=10)
def test_gaussian_kde_covariance_caching():
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=5)
# These expected values are from scipy 0.10, before some changes to
# gaussian_kde. They were not compared with any external reference.
y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
# Set the bandwidth, then reset it to the default.
kde = stats.gaussian_kde(x1)
kde.set_bandwidth(bw_method=0.5)
kde.set_bandwidth(bw_method='scott')
y2 = kde(xs)
assert_array_almost_equal(y_expected, y2, decimal=7)
def test_gaussian_kde_covariance_caching():
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=5)
# These expected values are from scipy 0.10, before some changes to
# gaussian_kde. They were not compared with any external reference.
y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
# Set the bandwidth, then reset it to the default.
kde = stats.gaussian_kde(x1)
kde.set_bandwidth(bw_method=0.5)
kde.set_bandwidth(bw_method='scott')
y2 = kde(xs)
assert_array_almost_equal(y_expected, y2, decimal=7)
def test_kde_bandwidth_method():
def scotts_factor(kde_obj):
"""Same as default, just check that it works."""
return np.power(kde_obj.n, -1./(kde_obj.d+4))
np.random.seed(8765678)
n_basesample = 50
xn = np.random.randn(n_basesample)
# Default
gkde = stats.gaussian_kde(xn)
# Supply a callable
gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
# Supply a scalar
gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
xs = np.linspace(-7,7,51)
kdepdf = gkde.evaluate(xs)
kdepdf2 = gkde2.evaluate(xs)
assert_almost_equal(kdepdf, kdepdf2)
kdepdf3 = gkde3.evaluate(xs)
assert_almost_equal(kdepdf, kdepdf3)
assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
def test_kde_bandwidth_method():
def scotts_factor(kde_obj):
"""Same as default, just check that it works."""
return np.power(kde_obj.n, -1./(kde_obj.d+4))
np.random.seed(8765678)
n_basesample = 50
xn = np.random.randn(n_basesample)
# Default
gkde = stats.gaussian_kde(xn)
# Supply a callable
gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
# Supply a scalar
gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
xs = np.linspace(-7,7,51)
kdepdf = gkde.evaluate(xs)
kdepdf2 = gkde2.evaluate(xs)
assert_almost_equal(kdepdf, kdepdf2)
kdepdf3 = gkde3.evaluate(xs)
assert_almost_equal(kdepdf, kdepdf3)
assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
def test_pdf_logpdf():
np.random.seed(1)
n_basesample = 50
xn = np.random.randn(n_basesample)
# Default
gkde = stats.gaussian_kde(xn)
xs = np.linspace(-15, 12, 25)
pdf = gkde.evaluate(xs)
pdf2 = gkde.pdf(xs)
assert_almost_equal(pdf, pdf2, decimal=12)
logpdf = np.log(pdf)
logpdf2 = gkde.logpdf(xs)
assert_almost_equal(logpdf, logpdf2, decimal=12)
def test_pdf_logpdf():
np.random.seed(1)
n_basesample = 50
xn = np.random.randn(n_basesample)
# Default
gkde = stats.gaussian_kde(xn)
xs = np.linspace(-15, 12, 25)
pdf = gkde.evaluate(xs)
pdf2 = gkde.pdf(xs)
assert_almost_equal(pdf, pdf2, decimal=12)
logpdf = np.log(pdf)
logpdf2 = gkde.logpdf(xs)
assert_almost_equal(logpdf, logpdf2, decimal=12)
def test_gaussian_kde_subclassing():
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=50)
# gaussian_kde itself
kde = stats.gaussian_kde(x1)
ys = kde(xs)
# subclass 1
kde1 = _kde_subclass1(x1)
y1 = kde1(xs)
assert_array_almost_equal_nulp(ys, y1, nulp=10)
# subclass 2
kde2 = _kde_subclass2(x1)
y2 = kde2(xs)
assert_array_almost_equal_nulp(ys, y2, nulp=10)
# subclass 3
kde3 = _kde_subclass3(x1, kde.covariance)
y3 = kde3(xs)
assert_array_almost_equal_nulp(ys, y3, nulp=10)
# subclass 4
kde4 = _kde_subclass4(x1)
y4 = kde4(x1)
y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
assert_array_almost_equal(y_expected, y4, decimal=6)
# Not a subclass, but check for use of _compute_covariance()
kde5 = kde
kde5.covariance_factor = lambda: kde.factor
kde5._compute_covariance()
y5 = kde5(xs)
assert_array_almost_equal_nulp(ys, y5, nulp=10)
def test_gaussian_kde_subclassing():
x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
xs = np.linspace(-10, 10, num=50)
# gaussian_kde itself
kde = stats.gaussian_kde(x1)
ys = kde(xs)
# subclass 1
kde1 = _kde_subclass1(x1)
y1 = kde1(xs)
assert_array_almost_equal_nulp(ys, y1, nulp=10)
# subclass 2
kde2 = _kde_subclass2(x1)
y2 = kde2(xs)
assert_array_almost_equal_nulp(ys, y2, nulp=10)
# subclass 3
kde3 = _kde_subclass3(x1, kde.covariance)
y3 = kde3(xs)
assert_array_almost_equal_nulp(ys, y3, nulp=10)
# subclass 4
kde4 = _kde_subclass4(x1)
y4 = kde4(x1)
y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
assert_array_almost_equal(y_expected, y4, decimal=6)
# Not a subclass, but check for use of _compute_covariance()
kde5 = kde
kde5.covariance_factor = lambda: kde.factor
kde5._compute_covariance()
y5 = kde5(xs)
assert_array_almost_equal_nulp(ys, y5, nulp=10)
def test_kde_integer_input():
"""Regression test for #1181."""
x1 = np.arange(5)
kde = stats.gaussian_kde(x1)
y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
assert_array_almost_equal(kde(x1), y_expected, decimal=6)
def test_kde_integer_input():
"""Regression test for #1181."""
x1 = np.arange(5)
kde = stats.gaussian_kde(x1)
y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
assert_array_almost_equal(kde(x1), y_expected, decimal=6)
