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326 lines
9.9 KiB
Python
326 lines
9.9 KiB
Python
"""
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Created on 2. jan. 2017
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@author: pab
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"""
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from __future__ import absolute_import, division, print_function
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import scipy.stats as st
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import numpy as np
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import warnings
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from wafo.plotbackend import plotbackend as plt
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from wafo.kdetools import Kernel, TKDE, KDE, KRegression, BKRegression
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try:
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from wafo import fig
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except ImportError:
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warnings.warn('fig import only supported on Windows')
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__all__ = ['kde_demo1', 'kde_demo2', 'kde_demo3', 'kde_demo4', 'kde_demo5',
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'kreg_demo1', ]
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def kde_demo1():
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"""KDEDEMO1 Demonstrate the smoothing parameter impact on KDE.
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KDEDEMO1 shows the true density (dotted) compared to KDE based on 7
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observations (solid) and their individual kernels (dashed) for 3
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different values of the smoothing parameter, hs.
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Example
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-------
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>>> kde_demo1()
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"""
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x = np.linspace(-4, 4, 101)
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x0 = x / 2.0
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data = np.random.normal(loc=0, scale=1.0, size=7)
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kernel = Kernel('gauss')
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hs = kernel.hns(data)
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h_vec = [hs / 2, hs, 2 * hs]
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for ix, h in enumerate(h_vec):
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plt.figure(ix)
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kde = KDE(data, hs=h, kernel=kernel)
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f2 = kde(x, output='plot', title='h_s = {0:2.2f}'.format(float(h)),
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ylab='Density')
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f2.plot('k-')
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plt.plot(x, st.norm.pdf(x, 0, 1), 'k:')
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n = len(data)
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plt.plot(data, np.zeros(data.shape), 'bx')
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y = kernel(x0) / (n * h * kernel.norm_factor(d=1, n=n))
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for i in range(n):
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plt.plot(data[i] + x0 * h, y, 'b--')
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plt.plot([data[i], data[i]], [0, np.max(y)], 'b')
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plt.axis([min(x), max(x), 0, 0.5])
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def kde_demo2():
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"""Demonstrate the difference between transformation- and ordinary-KDE.
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KDEDEMO2 shows that the transformation KDE is a better estimate for
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Rayleigh distributed data around 0 than the ordinary KDE.
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Example
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-------
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>>> kde_demo2()
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"""
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data = st.rayleigh.rvs(scale=1, size=300)
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x = np.linspace(1.5e-2, 5, 55)
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kde = KDE(data)
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f = kde(output='plot', title='Ordinary KDE (hs={0:})'.format(kde.hs))
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plt.figure(0)
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f.plot()
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plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
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# plotnorm((data).^(L2)) # gives a straight line => L2 = 0.5 reasonable
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hs = Kernel('gauss').get_smoothing(data**0.5)
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tkde = TKDE(data, hs=hs, L2=0.5)
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ft = tkde(x, output='plot',
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title='Transformation KDE (hs={0:})'.format(tkde.tkde.hs))
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plt.figure(1)
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ft.plot()
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plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
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plt.figure(0)
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def kde_demo3():
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"""Demonstrate the difference between transformation and ordinary-KDE in 2D
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KDEDEMO3 shows that the transformation KDE is a better estimate for
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Rayleigh distributed data around 0 than the ordinary KDE.
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Example
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-------
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>>> kde_demo3()
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"""
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data = st.rayleigh.rvs(scale=1, size=(2, 300))
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# x = np.linspace(1.5e-3, 5, 55)
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kde = KDE(data)
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f = kde(output='plot', title='Ordinary KDE', plotflag=1)
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plt.figure(0)
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f.plot()
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plt.plot(data[0], data[1], '.')
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# plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable
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hs = Kernel('gauss').get_smoothing(data**0.5)
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tkde = TKDE(data, hs=hs, L2=0.5)
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ft = tkde.eval_grid_fast(
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output='plot', title='Transformation KDE', plotflag=1)
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plt.figure(1)
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ft.plot()
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plt.plot(data[0], data[1], '.')
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plt.figure(0)
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def kde_demo4(N=50):
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"""Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior
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for 1D multimodal distributions
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KDEDEMO4 shows that the improved Sheather-Jones plug-in smoothing is a
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better compared to normal reference rules (in this case the hns)
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Example
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-------
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>>> kde_demo4()
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"""
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data = np.hstack((st.norm.rvs(loc=5, scale=1, size=(N,)),
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st.norm.rvs(loc=-5, scale=1, size=(N,))))
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# x = np.linspace(1.5e-3, 5, 55)
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kde = KDE(data, kernel=Kernel('gauss', 'hns'))
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f = kde(output='plot', title='Ordinary KDE', plotflag=1)
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kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
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f1 = kde1(output='plot', label='Ordinary KDE', plotflag=1)
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plt.figure(0)
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f.plot('r', label='hns={0}'.format(kde.hs))
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# plt.figure(2)
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f1.plot('b', label='hisj={0}'.format(kde1.hs))
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x = np.linspace(-9, 9)
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plt.plot(x, (st.norm.pdf(x, loc=-5, scale=1) +
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st.norm.pdf(x, loc=5, scale=1)) / 2, 'k:',
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label='True density')
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plt.legend()
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def kde_demo5(N=500):
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"""Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior
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for 2D multimodal distributions
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KDEDEMO5 shows that the improved Sheather-Jones plug-in smoothing is better
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compared to normal reference rules (in this case the hns)
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Example
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-------
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>>> kde_demo5()
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"""
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data = np.hstack((st.norm.rvs(loc=5, scale=1, size=(2, N,)),
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st.norm.rvs(loc=-5, scale=1, size=(2, N,))))
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kde = KDE(data, kernel=Kernel('gauss', 'hns'))
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f = kde(output='plot', plotflag=1,
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title='Ordinary KDE, hns={0:s}'.format(str(list(kde.hs))))
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kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
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f1 = kde1(output='plot', plotflag=1,
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title='Ordinary KDE, hisj={0:s}'.format(str(list(kde1.hs))))
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plt.figure(0)
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plt.clf()
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f.plot()
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plt.plot(data[0], data[1], '.')
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plt.figure(1)
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plt.clf()
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f1.plot()
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plt.plot(data[0], data[1], '.')
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def kreg_demo1(hs=None, fast=True, fun='hisj'):
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"""Compare KRegression to KernelReg from statsmodels.nonparametric
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Example
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-------
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>>> kreg_demo1()
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"""
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N = 100
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# ei = np.random.normal(loc=0, scale=0.075, size=(N,))
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ei = np.array([
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-0.08508516, 0.10462496, 0.07694448, -0.03080661, 0.05777525,
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0.06096313, -0.16572389, 0.01838912, -0.06251845, -0.09186784,
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-0.04304887, -0.13365788, -0.0185279, -0.07289167, 0.02319097,
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0.06887854, -0.08938374, -0.15181813, 0.03307712, 0.08523183,
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-0.0378058, -0.06312874, 0.01485772, 0.06307944, -0.0632959,
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0.18963205, 0.0369126, -0.01485447, 0.04037722, 0.0085057,
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-0.06912903, 0.02073998, 0.1174351, 0.17599277, -0.06842139,
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0.12587608, 0.07698113, -0.0032394, -0.12045792, -0.03132877,
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0.05047314, 0.02013453, 0.04080741, 0.00158392, 0.10237899,
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-0.09069682, 0.09242174, -0.15445323, 0.09190278, 0.07138498,
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0.03002497, 0.02495252, 0.01286942, 0.06449978, 0.03031802,
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0.11754861, -0.02322272, 0.00455867, -0.02132251, 0.09119446,
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-0.03210086, -0.06509545, 0.07306443, 0.04330647, 0.078111,
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-0.04146907, 0.05705476, 0.02492201, -0.03200572, -0.02859788,
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-0.05893749, 0.00089538, 0.0432551, 0.04001474, 0.04888828,
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-0.17708392, 0.16478644, 0.1171006, 0.11664846, 0.01410477,
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-0.12458953, -0.11692081, 0.0413047, -0.09292439, -0.07042327,
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0.14119701, -0.05114335, 0.04994696, -0.09520663, 0.04829406,
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-0.01603065, -0.1933216, 0.19352763, 0.11819496, 0.04567619,
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-0.08348306, 0.00812816, -0.00908206, 0.14528945, 0.02901065])
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x = np.linspace(0, 1, N)
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va_1 = 0.3 ** 2
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va_2 = 0.7 ** 2
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y0 = np.exp(-x ** 2 / (2 * va_1)) + 1.3 * np.exp(-(x - 1) ** 2 / (2 * va_2))
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y = y0 + ei
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kernel = Kernel('gauss', fun=fun)
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hopt = kernel.hisj(x)
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kreg = KRegression(
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x, y, p=0, hs=hs, kernel=kernel, xmin=-2 * hopt, xmax=1 + 2 * hopt)
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if fast:
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kreg.__call__ = kreg.eval_grid_fast
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f = kreg(x, output='plot', title='Kernel regression', plotflag=1)
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plt.figure(0)
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f.plot(label='p=0')
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kreg.p = 1
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f1 = kreg(x, output='plot', title='Kernel regression', plotflag=1)
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f1.plot(label='p=1')
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# print(f1.data)
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plt.plot(x, y, '.', label='data')
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plt.plot(x, y0, 'k', label='True model')
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from statsmodels.nonparametric.kernel_regression import KernelReg
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kreg2 = KernelReg(y, x, ('c'))
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y2 = kreg2.fit(x)
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plt.plot(x, y2[0], 'm', label='statsmodel')
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plt.legend()
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# print(kreg.tkde.tkde._inv_hs)
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# print(kreg.tkde.tkde.hs)
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def _get_data(n=100, symmetric=False, loc1=1.1, scale1=0.6, scale2=1.0):
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"""
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Return test data for binomial regression demo.
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"""
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dist = st.norm
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norm1 = scale2 * (dist.pdf(-loc1, loc=-loc1, scale=scale1) +
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dist.pdf(-loc1, loc=loc1, scale=scale1))
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def fun1(x):
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return ((dist.pdf(x, loc=-loc1, scale=scale1) +
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dist.pdf(x, loc=loc1, scale=scale1)) / norm1).clip(max=1.0)
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x = np.sort(6 * np.random.rand(n, 1) - 3, axis=0)
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y = (fun1(x) > np.random.rand(n, 1)).ravel()
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# y = (np.cos(x)>2*np.random.rand(n, 1)-1).ravel()
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x = x.ravel()
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if symmetric:
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xi = np.hstack((x.ravel(), -x.ravel()))
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yi = np.hstack((y, y))
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i = np.argsort(xi)
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x = xi[i]
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y = yi[i]
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return x, y, fun1
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def check_bkregression():
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"""
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Check binomial regression
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Example
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-------
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>>> check_bkregression()
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"""
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# plt.ion()
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k = 0
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for _i, n in enumerate([50, 100, 300, 600]):
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x, y, fun1 = _get_data(n, symmetric=True, loc1=0.1,
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scale1=0.6, scale2=0.75)
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bkreg = BKRegression(x, y, a=0.05, b=0.05)
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fbest = bkreg.prb_search_best(
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hsfun='hste', alpha=0.05, color='g', label='Transit_D')
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figk = plt.figure(k)
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ax = figk.gca()
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k += 1
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# fbest.score.plot(axis=ax)
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# axsize = ax.axis()
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# ax.vlines(fbest.hs,axsize[2]+1,axsize[3])
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# ax.set(yscale='log')
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fbest.labels.title = 'N = {:d}'.format(n)
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fbest.plot(axis=ax)
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ax.plot(x, fun1(x), 'r')
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ax.legend(frameon=False, markerscale=4)
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# ax = plt.gca()
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ax.set_yticklabels(ax.get_yticks() * 100.0)
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ax.grid(True)
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# fig.tile(range(0, k))
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# plt.ioff()
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# plt.show('hold')
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if __name__ == '__main__':
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from wafo.testing import test_docstrings
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test_docstrings(__file__)
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# kde_demo5()
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# check_bkregression()
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# kreg_demo1(hs=0.04, fast=True)
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# plt.show('hold')
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