def kde_demo5(N=500):
"""Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior
for 2D multimodal distributions
KDEDEMO5 shows that the improved Sheather-Jones plug-in smoothing is better
compared to normal reference rules (in this case the hns)
Examples
--------
>>> kde_demo5()
"""
data = np.hstack((st.norm.rvs(loc=5, scale=1, size=(2, N,)),
st.norm.rvs(loc=-5, scale=1, size=(2, N,))))
kde = KDE(data, kernel=Kernel('gauss', 'hns'))
f = kde(output='plot', plotflag=1,
title='Ordinary KDE, hns={0:s}'.format(str(list(kde.hs))))
kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
f1 = kde1(output='plot', plotflag=1,
title='Ordinary KDE, hisj={0:s}'.format(str(list(kde1.hs))))
plt.figure(0)
plt.clf()
f.plot()
plt.plot(data[0], data[1], '.')
plt.figure(1)
plt.clf()
f1.plot()
plt.plot(data[0], data[1], '.')
def kde_demo4(N=50):
"""Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior
for 1D multimodal distributions
KDEDEMO4 shows that the improved Sheather-Jones plug-in smoothing is a
better compared to normal reference rules (in this case the hns)
Examples
--------
>>> kde_demo4()
"""
data = np.hstack((st.norm.rvs(loc=5, scale=1, size=(N,)),
st.norm.rvs(loc=-5, scale=1, size=(N,))))
# x = np.linspace(1.5e-3, 5, 55)
kde = KDE(data, kernel=Kernel('gauss', 'hns'))
f = kde(output='plot', title='Ordinary KDE', plotflag=1)
kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
f1 = kde1(output='plot', label='Ordinary KDE', plotflag=1)
plt.figure(0)
f.plot('r', label='hns={0}'.format(kde.hs))
# plt.figure(2)
f1.plot('b', label='hisj={0}'.format(kde1.hs))
x = np.linspace(-9, 9)
plt.plot(x, (st.norm.pdf(x, loc=-5, scale=1) +
st.norm.pdf(x, loc=5, scale=1)) / 2, 'k:',
label='True density')
plt.legend()
def kde_demo3():
"""Demonstrate the difference between transformation and ordinary-KDE in 2D
KDEDEMO3 shows that the transformation KDE is a better estimate for
Rayleigh distributed data around 0 than the ordinary KDE.
Examples
--------
>>> kde_demo3()
"""
data = st.rayleigh.rvs(scale=1, size=(2, 300))
# x = np.linspace(1.5e-3, 5, 55)
kde = KDE(data)
f = kde(output='plot', title='Ordinary KDE', plotflag=1)
plt.figure(0)
f.plot()
plt.plot(data[0], data[1], '.')
# plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable
hs = Kernel('gauss').get_smoothing(data**0.5)
tkde = TKDE(data, hs=hs, L2=0.5)
ft = tkde.eval_grid_fast(
output='plot', title='Transformation KDE', plotflag=1)
plt.figure(1)
ft.plot()
plt.plot(data[0], data[1], '.')
plt.figure(0)
def kde_demo2():
"""Demonstrate the difference between transformation- and ordinary-KDE.
KDEDEMO2 shows that the transformation KDE is a better estimate for
Rayleigh distributed data around 0 than the ordinary KDE.
Examples
--------
>>> kde_demo2()
"""
data = st.rayleigh.rvs(scale=1, size=300)
x = np.linspace(1.5e-2, 5, 55)
kde = KDE(data)
f = kde(output='plot', title='Ordinary KDE (hs={0:})'.format(kde.hs))
plt.figure(0)
f.plot()
plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
# plotnorm((data).^(L2)) # gives a straight line => L2 = 0.5 reasonable
hs = Kernel('gauss').get_smoothing(data**0.5)
tkde = TKDE(data, hs=hs, L2=0.5)
ft = tkde(x, output='plot',
title='Transformation KDE (hs={0:})'.format(tkde.tkde.hs))
plt.figure(1)
ft.plot()
plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
plt.figure(0)
def kde_demo1():
"""KDEDEMO1 Demonstrate the smoothing parameter impact on KDE.
KDEDEMO1 shows the true density (dotted) compared to KDE based on 7
observations (solid) and their individual kernels (dashed) for 3
different values of the smoothing parameter, hs.
Examples
--------
>>> kde_demo1()
"""
x = np.linspace(-4, 4, 101)
x0 = x / 2.0
data = np.random.normal(loc=0, scale=1.0, size=7)
kernel = Kernel('gauss')
hs = kernel.hns(data)
h_vec = [hs / 2, hs, 2 * hs]
for ix, h in enumerate(h_vec):
plt.figure(ix)
kde = KDE(data, hs=h, kernel=kernel)
f2 = kde(x, output='plot', title='h_s = {0:2.2f}'.format(float(h)),
ylab='Density')
f2.plot('k-')
plt.plot(x, st.norm.pdf(x, 0, 1), 'k:')
n = len(data)
plt.plot(data, np.zeros(data.shape), 'bx')
y = kernel(x0) / (n * h * kernel.norm_factor(d=1, n=n))
for i in range(n):
plt.plot(data[i] + x0 * h, y, 'b--')
plt.plot([data[i], data[i]], [0, np.max(y)], 'b')
plt.axis([min(x), max(x), 0, 0.5])