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Formatting and experiments.

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Let this check in get away from me. Bunch of small formatting sttuf
in the various chapters, some experimental animations and code, etc.
Not a clearly delineated check in.
This commit is contained in:
Roger Labbe committed 2015-05-09 10:21:36 -07:00
1 parent a3cd023d3b
commit 752320ad01
11 files changed
+13069 -12640
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01_g-h_filter.ipynb
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06_Multivariate_Kalman_Filters.ipynb
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09_Nonlinear_Filtering.ipynb
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10_Unscented_Kalman_Filter.ipynb
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12_Designing_Nonlinear_Kalman_Filters.ipynb
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animations/Gaussians_Animations.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
"@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
"@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
"\n",
" div.cell{\n",
" width: 850px;\n",
" margin-left: 0% !important;\n",
" margin-right: auto;\n",
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" div.text_cell code {\n",
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" ol{\n",
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" text-decoration: none;\n",
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" .rendered_html :active {\n",
" text-decoration: none;\n",
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" .warning{\n",
" color: rgb( 240, 20, 20 )\n",
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" background: #fcfcfc;\n",
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" font-family: 'Open sans',verdana,arial,sans-serif;\n",
" width:680px;\n",
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"source": [
"from __future__ import division, print_function\n",
"%matplotlib inline\n",
"import sys\n",
"sys.path.insert(0,'..') # allow us to format the book\n",
"sys.path.insert(0,'../code') \n",
"# use same formatting as rest of book so that the plots are\n",
"# consistant with that look and feel.\n",
"import book_format\n",
"book_format.load_style(directory='..')"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc3f902ea58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from gif_animate import animate\n",
"from stats import gaussian\n",
"import matplotlib.pylab as pylab\n",
"from matplotlib import animation\n",
"\n",
"\n",
"def plt_g (mu, variance):\n",
" xs = np.arange(2,8,0.05)\n",
" ys = [gaussian (x, mu, variance) for x in xs]\n",
" plt.plot (xs, ys)\n",
" plt.ylim((0,1))\n",
"\n",
"\n",
"mu = 2\n",
"sigma = 0.6\n",
"def ganimate(frame):\n",
" global mu, sigma\n",
" if frame < 25:\n",
" mu += .2\n",
" elif frame == 25:\n",
" mu = 5\n",
" elif frame < 37:\n",
" sigma -= 0.05\n",
" else:\n",
" sigma += 0.05\n",
"\n",
" plt.cla()\n",
" plt_g(mu,sigma)\n",
"\n",
"animate('04_gaussian_animate.gif', ganimate, \n",
" frames=80, interval=50, figsize=(6,4))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='04_gaussian_animate.gif'>"
]
}
],
"metadata": {
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{
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{
"cell_type": "code",
"execution_count": 1,
"metadata": {
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},
"outputs": [
{
"data": {
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"@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
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" }\n",
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" background: #fcfcfc;\n",
" border-left: 5px solid #c76c0c;\n",
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" width:680px;\n",
" padding: 10px 10px 10px 10px;\n",
" text-align:justify;\n",
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],
"source": [
"from __future__ import division, print_function\n",
"%matplotlib inline\n",
"import sys\n",
"sys.path.insert(0,'..') # allow us to format the book\n",
"sys.path.insert(0,'../code') \n",
"# use same formatting as rest of book so that the plots are\n",
"# consistant with that look and feel.\n",
"import book_format\n",
"book_format.load_style(directory='..')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
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"text/plain": [
"<matplotlib.figure.Figure at 0x8474eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from gif_animate import animate\n",
"from stats import gaussian\n",
"import matplotlib.pylab as pylab\n",
"from matplotlib import animation\n",
"import matplotlib\n",
"\n",
"def plt_g (mu, variance):\n",
" xs = np.arange(2,8,0.05)\n",
" ys = [gaussian (x, mu, variance) for x in xs]\n",
" plt.plot (xs, ys)\n",
" plt.ylim((0,1))\n",
"\n",
"\n",
"mu = 2\n",
"sigma = 0.6\n",
"def ganimate(frame):\n",
" global mu, sigma\n",
" if frame < 25:\n",
" mu += .2\n",
" elif frame == 25:\n",
" mu = 5\n",
" elif frame < 37:\n",
" sigma -= 0.05\n",
" else:\n",
" sigma += 0.05\n",
"\n",
" plt.cla()\n",
" plt_g(mu,sigma)\n",
"\n",
"animate('04_gaussian_animate.gif', ganimate, \n",
" frames=80, interval=50, figsize=(6,4))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='04_gaussian_animate.gif'>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
animations/particle_animate.ipynb
+342
View File
@@ -0,0 +1,342 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"<style>\n",
"@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
"@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
"@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
"\n",
" div.cell{\n",
" width: 850px;\n",
" margin-left: 0% !important;\n",
" margin-right: auto;\n",
" }\n",
" div.text_cell code {\n",
" background: transparent;\n",
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" font-weight: 600;\n",
" font-size: 11pt;\n",
" font-style: bold;\n",
" font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
" }\n",
" h1 {\n",
" font-family: 'Open sans',verdana,arial,sans-serif;\n",
"\t}\n",
"\t\n",
" div.input_area {\n",
" background: #F6F6F9;\n",
" border: 1px solid #586e75;\n",
" }\n",
"\n",
" .text_cell_render h1 {\n",
" font-weight: 200;\n",
" font-size: 30pt;\n",
" line-height: 100%;\n",
" color:#c76c0c;\n",
" margin-bottom: 0.5em;\n",
" margin-top: 1em;\n",
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" white-space: wrap;\n",
" } \n",
" h2 {\n",
" font-family: 'Open sans',verdana,arial,sans-serif;\n",
" }\n",
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" line-height: 100%;\n",
" color:#c76c0c;\n",
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" margin-top: 1.5em;\n",
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" white-space: wrap;\n",
" } \n",
" h3 {\n",
" font-family: 'Open sans',verdana,arial,sans-serif;\n",
" }\n",
" .text_cell_render h3 {\n",
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" font-size: 14pt;\n",
" line-height: 100%;\n",
" color:#d77c0c;\n",
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" font-weight: 100;\n",
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" color:#d77c0c;\n",
" margin-bottom: 0.5em;\n",
" margin-top: 0.5em;\n",
" display: block;\n",
" white-space: nowrap;\n",
" }\n",
" h5 {\n",
" font-family: 'Open sans',verdana,arial,sans-serif;\n",
" }\n",
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" font-weight: 200;\n",
" font-style: normal;\n",
" color: #1d3b84;\n",
" font-size: 16pt;\n",
" margin-bottom: 0em;\n",
" margin-top: 0.5em;\n",
" display: block;\n",
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" font-family: 'Arimo',verdana,arial,sans-serif;\n",
" line-height: 125%;\n",
" font-size: 120%;\n",
" width:740px;\n",
" margin-left:auto;\n",
" margin-right:auto;\n",
" text-align:justify;\n",
" text-justify:inter-word;\n",
" }\n",
" div.output_subarea.output_text.output_pyout {\n",
" overflow-x: auto;\n",
" overflow-y: scroll;\n",
" max-height: 50000px;\n",
" }\n",
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" overflow-x: auto;\n",
" overflow-y: scroll;\n",
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" }\n",
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" margin-bottom:0.2em;\n",
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" code{\n",
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" }\n",
" .rendered_html code{\n",
" background-color: transparent;\n",
" }\n",
" ul{\n",
" margin: 2em;\n",
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" ul li{\n",
" padding-left: 0.5em; \n",
" margin-bottom: 0.5em; \n",
" margin-top: 0.5em; \n",
" }\n",
" ul li li{\n",
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" ol{\n",
" margin: 2em;\n",
" }\n",
" ol li{\n",
" padding-left: 0.5em; \n",
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" }\n",
" ul li{\n",
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" margin-bottom: 0.5em; \n",
" margin-top: 0.2em; \n",
" }\n",
" a:link{\n",
" font-weight: bold;\n",
" color:#447adb;\n",
" }\n",
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" font-weight: bold;\n",
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" color:#447adb;\n",
" }\n",
" .rendered_html :link {\n",
" text-decoration: underline; \n",
" }\n",
" .rendered_html :hover {\n",
" text-decoration: none; \n",
" }\n",
" .rendered_html :visited {\n",
" text-decoration: none;\n",
" }\n",
" .rendered_html :focus {\n",
" text-decoration: none;\n",
" }\n",
" .rendered_html :active {\n",
" text-decoration: none;\n",
" }\n",
" .warning{\n",
" color: rgb( 240, 20, 20 )\n",
" } \n",
" hr {\n",
" color: #f3f3f3;\n",
" background-color: #f3f3f3;\n",
" height: 1px;\n",
" }\n",
" blockquote{\n",
" display:block;\n",
" background: #fcfcfc;\n",
" border-left: 5px solid #c76c0c;\n",
" font-family: 'Open sans',verdana,arial,sans-serif;\n",
" width:680px;\n",
" padding: 10px 10px 10px 10px;\n",
" text-align:justify;\n",
" text-justify:inter-word;\n",
" }\n",
" blockquote p {\n",
" margin-bottom: 0;\n",
" line-height: 125%;\n",
" font-size: 100%;\n",
" }\n",
"</style>\n",
"<script>\n",
" MathJax.Hub.Config({\n",
" TeX: {\n",
" extensions: [\"AMSmath.js\"]\n",
" },\n",
" tex2jax: {\n",
" inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
" displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
" },\n",
" displayAlign: 'center', // Change this to 'center' to center equations.\n",
" \"HTML-CSS\": {\n",
" scale:85,\n",
" styles: {'.MathJax_Display': {\"margin\": 4}}\n",
" }\n",
" });\n",
"</script>\n"
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"<IPython.core.display.HTML object>"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from __future__ import division, print_function\n",
"%matplotlib inline\n",
"import sys\n",
"sys.path.insert(0,'..') # allow us to format the book\n",
"sys.path.insert(0,'../code') \n",
"# use same formatting as rest of book so that the plots are\n",
"# consistant with that look and feel.\n",
"import book_format\n",
"book_format.load_style(directory='..')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x5a2cda0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from random import uniform\n",
"import matplotlib.pylab as pylab\n",
"from matplotlib import animation\n",
"from gif_animate import animate\n",
"import matplotlib as mpl\n",
"from math import pi\n",
"\n",
"def make_particle():\n",
" return [uniform(0,100), uniform(0,100), uniform(0, 2), uniform(0, 2*pi)]\n",
"\n",
"\n",
"def move(particles, t=1.):\n",
" vx = particles[:, 2]*np.cos(particles[:, 3])\n",
" vy = particles[:, 2]*np.sin(particles[:, 3])\n",
" particles[:, 0] = (particles[:, 0] + vx*t) % 100\n",
" particles[:, 1] = (particles[:, 1] + vy*t) % 100\n",
" \n",
"particles = np.asarray([make_particle() for i in range(1000)])\n",
"\n",
"def panimate(frame):\n",
" move(particles, t=1.)\n",
"\n",
" plt.cla()\n",
" plt.scatter(particles[:, 0], particles[:, 1])\n",
" plt.xlim(0, 100)\n",
" plt.ylim(0, 100)\n",
" plt.gca().get_xaxis().set_ticks([])\n",
" plt.gca().get_yaxis().set_ticks([])\n",
"\n",
" \n",
"animate('13_particle_move.gif', panimate, \n",
" frames=500, interval=50, figsize=(4, 4))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"<img src='13_particle_move.gif'>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
code/nonlinear_plots.py
+78 -62
View File
@@ -1,62 +1,78 @@
# -*- coding: utf-8 -*-
"""
Created on Sun May 18 11:09:23 2014
@author: rlabbe
"""
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
def plot_transfer_func(data, f, lims, num_bins=1000):
ys = f(data)
h = np.histogram(ys, num_bins, density=False)
#plot output
plt.subplot(2,2,1)
plt.plot(h[0], h[1][1:], lw=4)
plt.ylim(lims)
plt.gca().xaxis.set_ticklabels([])
plt.title('output')
plt.axhline(np.mean(ys), ls='--', lw=2)
# plot transfer function
plt.subplot(2,2,2)
x = np.arange(lims[0], lims[1],0.1)
y = f(x)
plt.plot (x,y)
isct = f(0)
plt.plot([0,0,lims[0]],[lims[0],isct,isct],c='r')
plt.xlim(lims)
plt.ylim(lims)
plt.title('transfer function')
# plot input
h = np.histogram(data, num_bins, density=True)
plt.subplot(2,2,4)
plt.plot(h[1][1:], h[0], lw=4)
plt.xlim(lims)
plt.gca().yaxis.set_ticklabels([])
plt.title('input')
plt.show()
if __name__ == "__main__":
from numpy.random import normal
import numpy as np
data = normal(loc=0.0, scale=1, size=500000)
def g(x):
return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x
plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
# -*- coding: utf-8 -*-
"""
Created on Sun May 18 11:09:23 2014
@author: rlabbe
"""
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
def plot_transfer_func(data, f, gaussian, num_bins=300):
ys = f(data)
x0 = gaussian[0]
in_std = np.sqrt(gaussian[1])
y = f(x0)
m = np.mean(ys)
std = np.std(ys)
in_lims = [x0-in_std*3, x0+in_std*3]
out_lims = [y-std*3, y+std*3]
#plot output
h = np.histogram(ys, num_bins, density=False)
plt.subplot(2,2,4)
plt.plot(h[0], h[1][1:], lw=4)
plt.ylim(out_lims[1], out_lims[0])
plt.gca().xaxis.set_ticklabels([])
plt.title('output')
plt.axhline(np.mean(ys), ls='--', lw=2)
plt.axhline(f(x0), lw=1)
# plot transfer function
plt.subplot(2,2,3)
x = np.arange(in_lims[0], in_lims[1], 0.1)
y = f(x)
plt.plot (x,y)
isct = f(x0)
plt.plot([x0, x0, in_lims[1]], [out_lims[1], isct, isct], color='r', lw=1)
plt.xlim(in_lims)
plt.ylim(out_lims)
#plt.axis('equal')
plt.title('function')
# plot input
h = np.histogram(data, num_bins, density=True)
plt.subplot(2,2,1)
plt.plot(h[1][1:], h[0], lw=4)
plt.xlim(in_lims)
plt.gca().yaxis.set_ticklabels([])
plt.title('input')
plt.show()
if __name__ == "__main__":
from numpy.random import normal
import numpy as np
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_transfer_func (data, g, gaussian=x0,
num_bins=100)
experiments/bicycle.py
+43 -46
View File
@@ -1,46 +1,43 @@
# -*- coding: utf-8 -*-
"""
Created on Tue Apr 28 08:19:21 2015
@author: Roger
"""
from math import *
import numpy as np
import matplotlib.pyplot as plt
wheelbase = 100 #inches
vel = 20 *12 # fps to inches per sec
steering_angle = radians(1)
t = 1 # second
orientation = 0. # radians
pos = np.array([0., 0.])
for i in range(100):
#if abs(steering_angle) > 1.e-8:
dist = vel*t
turn_radius = tan(steering_angle)
radius = wheelbase / tan(steering_angle)
arc_len = dist / (2*pi*radius)
turn_angle = 2*pi * arc_len
cx = pos[0] - (sin(orientation) * radius)
cy = pos[1] + (cos(orientation) * radius)
orientation = (orientation + turn_angle) % (2.0 * pi)
pos[0] = cx + (sin(orientation) * radius)
pos[1] = cy - (cos(orientation) * radius)
plt.scatter(pos[0], pos[1])
plt.axis('equal')
# -*- coding: utf-8 -*-
"""
Created on Tue Apr 28 08:19:21 2015
@author: Roger
"""
from math import *
import numpy as np
import matplotlib.pyplot as plt
wheelbase = 100 #inches
vel = 20 *12 # fps to inches per sec
steering_angle = radians(1)
t = 1 # second
orientation = 0. # radians
pos = np.array([0., 0.]
for i in range(100):
#if abs(steering_angle) > 1.e-8:
dist = vel*t
turn_radius = tan(steering_angle)
radius = wheelbase / tan(steering_angle)
arc_len = dist / (2*pi*radius)
turn_angle = 2*pi * arc_len
cx = pos[0] - (sin(orientation) * radius)
cy = pos[1] + (cos(orientation) * radius)
orientation = (orientation + turn_angle) % (2.0 * pi)
pos[0] = cx + (sin(orientation) * radius)
pos[1] = cy - (cos(orientation) * radius)
plt.scatter(pos[0], pos[1])
plt.axis('equal')