140 lines
3.1 KiB
Python
140 lines
3.1 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Created on Sun May 18 11:09:23 2014
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@author: rlabbe
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"""
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from __future__ import division
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import matplotlib.pyplot as plt
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import numpy as np
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import scipy.stats
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def plot_nonlinear_func(data, f, gaussian, num_bins=300):
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# linearize at mean to simulate EKF
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#x = gaussian[0]
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# equation of linearization
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#m = df(x)
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#b = f(x) - x*m
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# compute new mean and variance based on EKF equations
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ys = f(data)
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x0 = gaussian[0]
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in_std = np.sqrt(gaussian[1])
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y = f(x0)
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#m = np.mean(ys)
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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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out_lims = [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(2,2,4)
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plt.plot(h[0], h[1][1:], lw=4, alpha=0.5)
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print(max(h[0]))
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plt.ylim(out_lims[1], out_lims[0])
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plt.gca().xaxis.set_ticklabels([])
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plt.title('output')
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plt.axhline(np.mean(ys), ls='--', lw=2)
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plt.axhline(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_lims[1], isct, isct], color='r', lw=1)
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plt.xlim(in_lims)
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plt.ylim(out_lims)
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#plt.axis('equal')
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plt.title('function')
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# plot input
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h = np.histogram(data, num_bins, density=True)
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plt.subplot(2,2,1)
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plt.plot(h[1][1:], h[0], lw=4)
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plt.xlim(in_lims)
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plt.gca().yaxis.set_ticklabels([])
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plt.title('input')
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plt.show()
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print("fuck")
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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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if __name__ == "__main__":
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from numpy.random import normal
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import numpy as np
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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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