Removed Matplotlib deprecation warning
needed to use new kwarg density.
This commit is contained in:
Roger Labbe
parent
c15a693aa6
commit
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# -*- coding: utf-8 -*-
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"""Copyright 2015 Roger R Labbe Jr.
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Code supporting the book
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Kalman and Bayesian Filters in Python
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https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
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This is licensed under an MIT license. See the LICENSE.txt file
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for more information.
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"""
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from __future__ import (absolute_import, division, print_function,
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unicode_literals)
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import math
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from matplotlib import cm
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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import numpy as np
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from numpy.random import normal, multivariate_normal
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import scipy.stats
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from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform
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from filterpy.stats import multivariate_gaussian
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def plot_nonlinear_func(data, f, out_lim=None, num_bins=300):
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ys = f(data)
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x0 = np.mean(data)
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in_std = np.std(data)
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y = f(x0)
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std = np.std(ys)
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in_lims = [x0 - in_std*3, x0 + in_std*3]
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if out_lim is None:
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out_lim = [y - std*3, y + std*3]
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# plot output
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h = np.histogram(ys, num_bins, density=False)
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plt.subplot(221)
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plt.plot(h[1][1:], h[0], lw=2, alpha=0.8)
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if out_lim is not None:
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plt.xlim(out_lim[0], out_lim[1])
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plt.gca().yaxis.set_ticklabels([])
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plt.title('Output')
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plt.axvline(np.mean(ys), ls='--', lw=2)
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plt.axvline(f(x0), lw=1)
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norm = scipy.stats.norm(y, in_std)
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'''min_x = norm.ppf(0.001)
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max_x = norm.ppf(0.999)
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xs = np.arange(min_x, max_x, (max_x - min_x) / 1000)
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pdf = norm.pdf(xs)
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plt.plot(pdf * max(h[0])/max(pdf), xs, lw=1, color='k')
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print(max(norm.pdf(xs)))'''
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# plot transfer function
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plt.subplot(2, 2, 3)
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x = np.arange(in_lims[0], in_lims[1], 0.1)
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y = f(x)
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plt.plot (x, y, 'k')
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isct = f(x0)
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plt.plot([x0, x0, in_lims[1]], [out_lim[1], isct, isct], color='r', lw=1)
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plt.xlim(in_lims)
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plt.ylim(out_lim)
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#plt.axis('equal')
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plt.title('f(x)')
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# plot input
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h = np.histogram(data, num_bins, density=True)
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plt.subplot(2,2,4)
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plt.plot(h[0], h[1][1:], lw=2)
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#plt.ylim(in_lims)
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plt.gca().xaxis.set_ticklabels([])
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plt.title('Input')
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plt.tight_layout()
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plt.show()
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def plot_ekf_vs_mc():
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def fx(x):
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return x**3
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def dfx(x):
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return 3*x**2
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mean = 1
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var = .1
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std = math.sqrt(var)
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data = normal(loc=mean, scale=std, size=50000)
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d_t = fx(data)
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mean_ekf = fx(mean)
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slope = dfx(mean)
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std_ekf = abs(slope*std)
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norm = scipy.stats.norm(mean_ekf, std_ekf)
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xs = np.linspace(-3, 5, 200)
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plt.plot(xs, norm.pdf(xs), lw=2, ls='--', color='b')
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plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g')
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actual_mean = d_t.mean()
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plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo')
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plt.axvline(mean_ekf, lw=2, ls='--', color='b', label='EKF')
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plt.legend()
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plt.show()
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print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
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print('EKF mean={:.2f}, std={:.2f}'.format(mean_ekf, std_ekf))
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def plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.):
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def fx(x):
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return x**3
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def dfx(x):
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return 3*x**2
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mean = 1
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var = .1
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std = math.sqrt(var)
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data = normal(loc=mean, scale=std, size=50000)
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d_t = fx(data)
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points = MerweScaledSigmaPoints(1, alpha, beta, kappa)
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Wm, Wc = points.Wm, points.Wc
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sigmas = points.sigma_points(mean, var)
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sigmas_f = np.zeros((3, 1))
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for i in range(3):
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sigmas_f[i] = fx(sigmas[i, 0])
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### pass through unscented transform
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ukf_mean, ukf_cov = unscented_transform(sigmas_f, Wm, Wc)
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ukf_mean = ukf_mean[0]
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ukf_std = math.sqrt(ukf_cov[0])
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norm = scipy.stats.norm(ukf_mean, ukf_std)
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xs = np.linspace(-3, 5, 200)
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plt.plot(xs, norm.pdf(xs), ls='--', lw=2, color='b')
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plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g')
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actual_mean = d_t.mean()
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plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo')
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plt.axvline(ukf_mean, lw=2, ls='--', color='b', label='UKF')
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plt.legend()
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plt.show()
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print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
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print('UKF mean={:.2f}, std={:.2f}'.format(ukf_mean, ukf_std))
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def test_plot():
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import math
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from numpy.random import normal
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from scipy import stats
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global data
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def f(x):
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return 2*x + 1
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mean = 2
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var = 3
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std = math.sqrt(var)
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data = normal(loc=2, scale=std, size=50000)
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d2 = f(data)
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n = scipy.stats.norm(mean, std)
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kde1 = stats.gaussian_kde(data, bw_method='silverman')
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kde2 = stats.gaussian_kde(d2, bw_method='silverman')
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xs = np.linspace(-10, 10, num=200)
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#plt.plot(data)
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plt.plot(xs, kde1(xs))
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plt.plot(xs, kde2(xs))
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plt.plot(xs, n.pdf(xs), color='k')
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num_bins=100
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h = np.histogram(data, num_bins, density=True)
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plt.plot(h[1][1:], h[0], lw=4)
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h = np.histogram(d2, num_bins, density=True)
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plt.plot(h[1][1:], h[0], lw=4)
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def plot_bivariate_colormap(xs, ys):
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xs = np.asarray(xs)
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ys = np.asarray(ys)
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xmin = xs.min()
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xmax = xs.max()
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ymin = ys.min()
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ymax = ys.max()
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values = np.vstack([xs, ys])
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kernel = scipy.stats.gaussian_kde(values)
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X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
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positions = np.vstack([X.ravel(), Y.ravel()])
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Z = np.reshape(kernel.evaluate(positions).T, X.shape)
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plt.gca().imshow(np.rot90(Z), cmap=plt.cm.Greys,
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extent=[xmin, xmax, ymin, ymax])
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def plot_monte_carlo_mean(xs, ys, f, mean_fx, label, plot_colormap=True):
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fxs, fys = f(xs, ys)
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computed_mean_x = np.average(fxs)
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computed_mean_y = np.average(fys)
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ax = plt.subplot(121)
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ax.grid(b=False)
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plot_bivariate_colormap(xs, ys)
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plt.scatter(xs, ys, marker='.', alpha=0.02, color='k')
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ax.set_xlim(-20, 20)
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ax.set_ylim(-20, 20)
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ax = plt.subplot(122)
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ax.grid(b=False)
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plt.scatter(fxs, fys, marker='.', alpha=0.02, color='k')
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plt.scatter(mean_fx[0], mean_fx[1],
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marker='v', s=300, c='r', label=label)
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plt.scatter(computed_mean_x, computed_mean_y,
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marker='*',s=120, c='b', label='Computed Mean')
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plot_bivariate_colormap(fxs, fys)
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ax.set_xlim([-100, 100])
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ax.set_ylim([-10, 200])
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plt.legend(loc='best', scatterpoints=1)
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print ('Difference in mean x={:.3f}, y={:.3f}'.format(
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computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1]))
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def plot_cov_ellipse_colormap(cov=[[1,1],[1,1]]):
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side = np.linspace(-3, 3, 200)
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X,Y = np.meshgrid(side,side)
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pos = np.empty(X.shape + (2,))
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pos[:, :, 0] = X;
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pos[:, :, 1] = Y
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plt.axes(xticks=[], yticks=[], frameon=True)
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rv = scipy.stats.multivariate_normal((0,0), cov)
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plt.gca().grid(b=False)
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plt.gca().imshow(rv.pdf(pos), cmap=plt.cm.Greys, origin='lower')
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plt.show()
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def plot_gaussians(xs, ps, x_range, y_range, N):
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""" given a list of 2d states (x,y) and 2x2 covariance matrices, produce
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a surface plot showing all of the gaussians"""
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xs = np.asarray(xs)
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x = np.linspace (x_range[0], x_range[1], N)
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y = np.linspace (y_range[0], y_range[1], N)
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xx, yy = np.meshgrid(x, y)
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zv = np.zeros((N, N))
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for mean, cov in zip(xs, ps):
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zs = np.array([multivariate_gaussian(np.array([i ,j]), mean, cov)
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for i, j in zip(np.ravel(xx), np.ravel(yy))])
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zv += zs.reshape(xx.shape)
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ax = plt.figure().add_subplot(111, projection='3d')
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ax.plot_surface(xx, yy, zv, rstride=1, cstride=1, lw=.5, edgecolors='#191919',
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antialiased=True, shade=True, cmap=cm.autumn)
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ax.view_init(elev=40., azim=230)
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if __name__ == "__main__":
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#plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 2]])
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'''
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from numpy.random import normal
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import numpy as np
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plot_ukf_vs_mc()'''
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'''x0 = (1, 1)
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data = normal(loc=x0[0], scale=x0[1], size=500000)
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def g(x):
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return x*x
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return (np.cos(3*(x/2+0.7)))*np.sin(0.7*x)-1.6*x
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return -2*x
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#plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
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plot_nonlinear_func (data, g, gaussian=x0,
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num_bins=100)
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'''
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Ps = np.array([[[ 2.85841814, 0.71772898],
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[ 0.71772898, 0.93786824]],
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[[ 3.28939458, 0.52634978],
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[ 0.52634978, 0.13435503]],
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[[ 2.40532661, 0.29692055],
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[ 0.29692055, 0.07671416]],
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[[ 2.23084082, 0.27823192],
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[ 0.27823192, 0.07488681]]])
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Ms = np.array([[ 0.68040795, 0.17084572],
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[ 8.46201389, 1.15070342],
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[ 13.7992229 , 0.96022707],
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[ 19.95838208, 0.87524265]])
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plot_multiple_gaussians(Ms, Ps, (-5,25), (-5, 5), 75)
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# -*- coding: utf-8 -*-
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"""Copyright 2015 Roger R Labbe Jr.
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Code supporting the book
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Kalman and Bayesian Filters in Python
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https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
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This is licensed under an MIT license. See the LICENSE.txt file
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for more information.
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"""
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from __future__ import (absolute_import, division, print_function,
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unicode_literals)
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import math
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from matplotlib import cm
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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import numpy as np
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from numpy.random import normal, multivariate_normal
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import scipy.stats
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from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform
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from filterpy.stats import multivariate_gaussian
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def plot_nonlinear_func(data, f, out_lim=None, num_bins=300):
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ys = f(data)
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x0 = np.mean(data)
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in_std = np.std(data)
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y = f(x0)
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std = np.std(ys)
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in_lims = [x0 - in_std*3, x0 + in_std*3]
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if out_lim is None:
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out_lim = [y - std*3, y + std*3]
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# plot output
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h = np.histogram(ys, num_bins, density=False)
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plt.subplot(221)
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plt.plot(h[1][1:], h[0], lw=2, alpha=0.8)
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if out_lim is not None:
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plt.xlim(out_lim[0], out_lim[1])
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plt.gca().yaxis.set_ticklabels([])
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plt.title('Output')
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plt.axvline(np.mean(ys), ls='--', lw=2)
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plt.axvline(f(x0), lw=1)
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norm = scipy.stats.norm(y, in_std)
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'''min_x = norm.ppf(0.001)
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max_x = norm.ppf(0.999)
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xs = np.arange(min_x, max_x, (max_x - min_x) / 1000)
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pdf = norm.pdf(xs)
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plt.plot(pdf * max(h[0])/max(pdf), xs, lw=1, color='k')
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print(max(norm.pdf(xs)))'''
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# plot transfer function
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plt.subplot(2, 2, 3)
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x = np.arange(in_lims[0], in_lims[1], 0.1)
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y = f(x)
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plt.plot (x, y, 'k')
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isct = f(x0)
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plt.plot([x0, x0, in_lims[1]], [out_lim[1], isct, isct], color='r', lw=1)
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plt.xlim(in_lims)
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plt.ylim(out_lim)
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#plt.axis('equal')
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plt.title('f(x)')
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# plot input
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h = np.histogram(data, num_bins, density=True)
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plt.subplot(2,2,4)
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plt.plot(h[0], h[1][1:], lw=2)
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#plt.ylim(in_lims)
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plt.gca().xaxis.set_ticklabels([])
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plt.title('Input')
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plt.tight_layout()
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plt.show()
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def plot_ekf_vs_mc():
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def fx(x):
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return x**3
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def dfx(x):
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return 3*x**2
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mean = 1
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var = .1
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std = math.sqrt(var)
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data = normal(loc=mean, scale=std, size=50000)
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d_t = fx(data)
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mean_ekf = fx(mean)
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slope = dfx(mean)
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std_ekf = abs(slope*std)
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norm = scipy.stats.norm(mean_ekf, std_ekf)
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xs = np.linspace(-3, 5, 200)
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plt.plot(xs, norm.pdf(xs), lw=2, ls='--', color='b')
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try:
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plt.hist(d_t, bins=200, density=True, histtype='step', lw=2, color='g')
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except:
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# older versions of matplotlib don't have the density keyword
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plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g')
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actual_mean = d_t.mean()
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plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo')
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plt.axvline(mean_ekf, lw=2, ls='--', color='b', label='EKF')
|
||||
plt.legend()
|
||||
plt.show()
|
||||
|
||||
print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
|
||||
print('EKF mean={:.2f}, std={:.2f}'.format(mean_ekf, std_ekf))
|
||||
|
||||
|
||||
def plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.):
|
||||
|
||||
def fx(x):
|
||||
return x**3
|
||||
|
||||
def dfx(x):
|
||||
return 3*x**2
|
||||
|
||||
mean = 1
|
||||
var = .1
|
||||
std = math.sqrt(var)
|
||||
|
||||
data = normal(loc=mean, scale=std, size=50000)
|
||||
d_t = fx(data)
|
||||
|
||||
|
||||
points = MerweScaledSigmaPoints(1, alpha, beta, kappa)
|
||||
Wm, Wc = points.Wm, points.Wc
|
||||
sigmas = points.sigma_points(mean, var)
|
||||
|
||||
sigmas_f = np.zeros((3, 1))
|
||||
for i in range(3):
|
||||
sigmas_f[i] = fx(sigmas[i, 0])
|
||||
|
||||
### pass through unscented transform
|
||||
ukf_mean, ukf_cov = unscented_transform(sigmas_f, Wm, Wc)
|
||||
ukf_mean = ukf_mean[0]
|
||||
ukf_std = math.sqrt(ukf_cov[0])
|
||||
|
||||
norm = scipy.stats.norm(ukf_mean, ukf_std)
|
||||
xs = np.linspace(-3, 5, 200)
|
||||
plt.plot(xs, norm.pdf(xs), ls='--', lw=2, color='b')
|
||||
try:
|
||||
plt.hist(d_t, bins=200, density=True, histtype='step', lw=2, color='g')
|
||||
except:
|
||||
# older versions of matplotlib don't have the density keyword
|
||||
plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g')
|
||||
|
||||
actual_mean = d_t.mean()
|
||||
plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo')
|
||||
plt.axvline(ukf_mean, lw=2, ls='--', color='b', label='UKF')
|
||||
plt.legend()
|
||||
plt.show()
|
||||
|
||||
print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
|
||||
print('UKF mean={:.2f}, std={:.2f}'.format(ukf_mean, ukf_std))
|
||||
|
||||
|
||||
|
||||
def test_plot():
|
||||
import math
|
||||
from numpy.random import normal
|
||||
from scipy import stats
|
||||
global data
|
||||
|
||||
def f(x):
|
||||
return 2*x + 1
|
||||
|
||||
mean = 2
|
||||
var = 3
|
||||
std = math.sqrt(var)
|
||||
|
||||
data = normal(loc=2, scale=std, size=50000)
|
||||
|
||||
d2 = f(data)
|
||||
n = scipy.stats.norm(mean, std)
|
||||
|
||||
kde1 = stats.gaussian_kde(data, bw_method='silverman')
|
||||
kde2 = stats.gaussian_kde(d2, bw_method='silverman')
|
||||
xs = np.linspace(-10, 10, num=200)
|
||||
|
||||
#plt.plot(data)
|
||||
plt.plot(xs, kde1(xs))
|
||||
plt.plot(xs, kde2(xs))
|
||||
plt.plot(xs, n.pdf(xs), color='k')
|
||||
|
||||
num_bins=100
|
||||
h = np.histogram(data, num_bins, density=True)
|
||||
plt.plot(h[1][1:], h[0], lw=4)
|
||||
|
||||
h = np.histogram(d2, num_bins, density=True)
|
||||
plt.plot(h[1][1:], h[0], lw=4)
|
||||
|
||||
|
||||
def plot_bivariate_colormap(xs, ys):
|
||||
xs = np.asarray(xs)
|
||||
ys = np.asarray(ys)
|
||||
xmin = xs.min()
|
||||
xmax = xs.max()
|
||||
ymin = ys.min()
|
||||
ymax = ys.max()
|
||||
values = np.vstack([xs, ys])
|
||||
kernel = scipy.stats.gaussian_kde(values)
|
||||
X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
|
||||
positions = np.vstack([X.ravel(), Y.ravel()])
|
||||
|
||||
Z = np.reshape(kernel.evaluate(positions).T, X.shape)
|
||||
plt.gca().imshow(np.rot90(Z), cmap=plt.cm.Greys,
|
||||
extent=[xmin, xmax, ymin, ymax])
|
||||
|
||||
|
||||
|
||||
def plot_monte_carlo_mean(xs, ys, f, mean_fx, label, plot_colormap=True):
|
||||
fxs, fys = f(xs, ys)
|
||||
|
||||
computed_mean_x = np.average(fxs)
|
||||
computed_mean_y = np.average(fys)
|
||||
|
||||
ax = plt.subplot(121)
|
||||
ax.grid(b=False)
|
||||
|
||||
plot_bivariate_colormap(xs, ys)
|
||||
|
||||
plt.scatter(xs, ys, marker='.', alpha=0.02, color='k')
|
||||
ax.set_xlim(-20, 20)
|
||||
ax.set_ylim(-20, 20)
|
||||
|
||||
ax = plt.subplot(122)
|
||||
ax.grid(b=False)
|
||||
|
||||
plt.scatter(fxs, fys, marker='.', alpha=0.02, color='k')
|
||||
plt.scatter(mean_fx[0], mean_fx[1],
|
||||
marker='v', s=300, c='r', label=label)
|
||||
plt.scatter(computed_mean_x, computed_mean_y,
|
||||
marker='*',s=120, c='b', label='Computed Mean')
|
||||
|
||||
plot_bivariate_colormap(fxs, fys)
|
||||
ax.set_xlim([-100, 100])
|
||||
ax.set_ylim([-10, 200])
|
||||
plt.legend(loc='best', scatterpoints=1)
|
||||
print ('Difference in mean x={:.3f}, y={:.3f}'.format(
|
||||
computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1]))
|
||||
|
||||
|
||||
def plot_cov_ellipse_colormap(cov=[[1,1],[1,1]]):
|
||||
side = np.linspace(-3, 3, 200)
|
||||
X,Y = np.meshgrid(side,side)
|
||||
|
||||
pos = np.empty(X.shape + (2,))
|
||||
pos[:, :, 0] = X;
|
||||
pos[:, :, 1] = Y
|
||||
plt.axes(xticks=[], yticks=[], frameon=True)
|
||||
rv = scipy.stats.multivariate_normal((0,0), cov)
|
||||
plt.gca().grid(b=False)
|
||||
plt.gca().imshow(rv.pdf(pos), cmap=plt.cm.Greys, origin='lower')
|
||||
plt.show()
|
||||
|
||||
|
||||
def plot_gaussians(xs, ps, x_range, y_range, N):
|
||||
""" given a list of 2d states (x,y) and 2x2 covariance matrices, produce
|
||||
a surface plot showing all of the gaussians"""
|
||||
|
||||
xs = np.asarray(xs)
|
||||
x = np.linspace (x_range[0], x_range[1], N)
|
||||
y = np.linspace (y_range[0], y_range[1], N)
|
||||
xx, yy = np.meshgrid(x, y)
|
||||
zv = np.zeros((N, N))
|
||||
|
||||
for mean, cov in zip(xs, ps):
|
||||
zs = np.array([multivariate_gaussian(np.array([i ,j]), mean, cov)
|
||||
for i, j in zip(np.ravel(xx), np.ravel(yy))])
|
||||
zv += zs.reshape(xx.shape)
|
||||
|
||||
ax = plt.figure().add_subplot(111, projection='3d')
|
||||
ax.plot_surface(xx, yy, zv, rstride=1, cstride=1, lw=.5, edgecolors='#191919',
|
||||
antialiased=True, shade=True, cmap=cm.autumn)
|
||||
ax.view_init(elev=40., azim=230)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
#plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 2]])
|
||||
'''
|
||||
from numpy.random import normal
|
||||
import numpy as np
|
||||
|
||||
plot_ukf_vs_mc()'''
|
||||
|
||||
'''x0 = (1, 1)
|
||||
data = normal(loc=x0[0], scale=x0[1], size=500000)
|
||||
|
||||
def g(x):
|
||||
return x*x
|
||||
return (np.cos(3*(x/2+0.7)))*np.sin(0.7*x)-1.6*x
|
||||
return -2*x
|
||||
|
||||
|
||||
#plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
|
||||
plot_nonlinear_func (data, g, gaussian=x0,
|
||||
num_bins=100)
|
||||
'''
|
||||
|
||||
Ps = np.array([[[ 2.85841814, 0.71772898],
|
||||
[ 0.71772898, 0.93786824]],
|
||||
|
||||
[[ 3.28939458, 0.52634978],
|
||||
[ 0.52634978, 0.13435503]],
|
||||
|
||||
[[ 2.40532661, 0.29692055],
|
||||
[ 0.29692055, 0.07671416]],
|
||||
|
||||
[[ 2.23084082, 0.27823192],
|
||||
[ 0.27823192, 0.07488681]]])
|
||||
|
||||
Ms = np.array([[ 0.68040795, 0.17084572],
|
||||
[ 8.46201389, 1.15070342],
|
||||
[ 13.7992229 , 0.96022707],
|
||||
[ 19.95838208, 0.87524265]])
|
||||
|
||||
plot_multiple_gaussians(Ms, Ps, (-5,25), (-5, 5), 75)
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user