daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Switched to interactive plots!

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Using %matplotlib notebook to render plots.

I made the g-h filter chapter work. There is a very good chance
I broke the other chapters. Need to push to really find out.
This commit is contained in:
Roger Labbe 2016-02-27 17:10:09 -08:00
parent 26cf805dc3
commit 6aea84f6b1
17 changed files with 19161 additions and 728 deletions
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19204
01-g-h-filter.ipynb
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File diff suppressed because one or more lines are too long

29
book_format.py
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@ -28,6 +28,11 @@ import os.path
import sys
import warnings
try:
import seaborn
except:
pass
# version 1.4.3 of matplotlib has a bug that makes
# it issue a spurious warning on every plot that
# clutters the notebook output
@ -56,6 +61,15 @@ def test_filterpy_version():
# chapter so the reader can see that they need to update FilterPy.
test_filterpy_version()
pylab.rcParams['figure.max_open_warning'] = 50
def end_interactive(fig):
""" end interaction in a plot created with %matplotlib notebook """
import time
plt.gcf().canvas.draw()
time.sleep(0.1)
plt.close(fig)
def equal_axis():
pylab.rcParams['figure.figsize'] = 10,10
@ -78,6 +92,7 @@ def figsize(x=11, y=4):
yield
pylab.rcParams['figure.figsize'] = size
@contextmanager
def numpy_precision(precision):
old = np.get_printoptions()['precision']
@ -127,11 +142,15 @@ def load_style(directory = '.', name='code/custom.css'):
# matplotlib has deprecated the use of axes.color_cycle as of version
version = [int(version_no) for version_no in matplotlib.__version__.split('.')]
if version[0] > 1 or (version[0] == 1 and version[1] >= 5):
style["axes.prop_cycle"] = "cycler('color', ['#6d904f','#013afe', '#202020','#fc4f30','#e5ae38','#A60628','#30a2da','#008080','#7A68A6','#CF4457','#188487','#E24A33'])"
style.pop("axes.color_cycle", None)
plt.rcParams.update(style)
try:
import seaborn
except:
version = [int(version_no) for version_no in matplotlib.__version__.split('.')]
if version[0] > 1 or (version[0] == 1 and version[1] >= 5):
style["axes.prop_cycle"] = "cycler('color', ['#6d904f','#013afe', '#202020','#fc4f30','#e5ae38','#A60628','#30a2da','#008080','#7A68A6','#CF4457','#188487','#E24A33'])"
style.pop("axes.color_cycle", None)
plt.rcParams.update(style)
reset_axis ()
np.set_printoptions(suppress=True,precision=3, linewidth=70,
formatter={'float':lambda x:' {:.3}'.format(x)})

332
code/book_plots.py
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@ -19,6 +19,37 @@ from __future__ import (absolute_import, division, print_function,
import matplotlib.pyplot as plt
import numpy as np
from contextlib import contextmanager
import sys
sys.path.insert(0, '..')
from book_format import figsize
try:
import seaborn
except:
pass
def end_interactive(fig):
""" end interaction in a plot created with %matplotlib notebook """
import time
plt.gcf().canvas.draw()
time.sleep(0.1)
plt.close(fig)
@contextmanager
def interactive_plot(close=True, fig=None):
if fig is None:
fig = plt.figure()
yield
if close:
end_interactive(fig)
def plot_errorbars(bars, xlims, ylims=(0, 2)):
@ -34,6 +65,240 @@ def plot_errorbars(bars, xlims, ylims=(0, 2)):
plt.show()
def plot_errorbar1():
with figsize(y=2):
plt.figure()
plot_errorbars([(160, 8, 'A'), (170, 8, 'B')],
xlims=(145, 185), ylims=(-1, 1))
plt.show()
plt.savefig('../figs/gh_errorbar1.png', pad_inches=0.)
def plot_errorbar2():
with figsize(y=2):
plt.figure()
plot_errorbars([(160, 3, 'A'), (170, 9, 'B')],
xlims=(145, 185), ylims=(-1, 1))
plt.savefig('../figs/gh_errorbar2.png', pad_inches=0.)
def plot_errorbar3():
with figsize(y=2):
plt.figure()
plot_errorbars([(160, 1, 'A'), (170, 9, 'B')],
xlims=(145, 185), ylims=(-1, 1))
plt.savefig('../figs/gh_errorbar3.png', pad_inches=0.1)
def plot_hypothesis1():
with figsize(y=2.5):
plt.figure()
plt.errorbar([1, 2, 3], [170, 161, 169],
xerr=0, yerr=10, fmt='bo', capthick=2, capsize=10)
plt.plot([1, 3], [180, 160], color='g', ls='--')
plt.plot([1, 3], [170, 170], color='g', ls='--')
plt.plot([1, 3], [160, 175], color='g', ls='--')
plt.plot([1, 2, 3], [180, 152, 179], color='g', ls='--')
plt.xlim(0,4); plt.ylim(150, 185)
plt.xlabel('day')
plt.ylabel('lbs')
plt.tight_layout()
plt.savefig('../figs/gh_hypothesis1.png', pad_inches=0.1)
def plot_hypothesis2():
with figsize(y=2.5):
plt.figure()
plt.errorbar(range(1, 11), [169, 170, 169,171, 170, 171, 169, 170, 169, 170],
xerr=0, yerr=6, fmt='bo', capthick=2, capsize=10)
plt.plot([1, 10], [169, 170.5], color='g', ls='--')
plt.xlim(0, 11); plt.ylim(150, 185)
plt.xlabel('day')
plt.ylabel('lbs')
plt.savefig('../figs/gh_hypothesis2.png', pad_inches=0.1)
def plot_hypothesis3():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
with figsize(y=2.5):
plt.figure()
plt.errorbar(range(1, 13), weights,
xerr=0, yerr=6, fmt='o', capthick=2, capsize=10)
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
plt.savefig('../figs/gh_hypothesis3.png', pad_inches=0.1)
def plot_hypothesis4():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
with figsize(y=2.5):
plt.figure()
ave = np.sum(weights) / len(weights)
plt.errorbar(range(1,13), weights, label='weights',
yerr=6, fmt='o', capthick=2, capsize=10)
plt.plot([1, 12], [ave,ave], c='r', label='hypothesis')
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
show_legend()
plt.savefig('../figs/gh_hypothesis4.png', pad_inches=0.1)
def plot_hypothesis5():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
xs = range(1, len(weights)+1)
line = np.poly1d(np.polyfit(xs, weights, 1))
with figsize(y=2.5):
plt.figure()
plt.errorbar(range(1, 13), weights, label='weights',
yerr=5, fmt='o', capthick=2, capsize=10)
plt.plot (xs, line(xs), c='r', label='hypothesis')
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
show_legend()
plt.savefig('../figs/gh_hypothesis5.png', pad_inches=0.1)
def plot_estimate_chart_1():
with figsize(y=2.5):
plt.figure()
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->', ec='r',shrinkA=6, lw=3,shrinkB=5))
plt.scatter ([0], [158], c='b')
plt.scatter ([1], [159], c='r')
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.tight_layout()
plt.savefig('../figs/gh_estimate1.png', pad_inches=0.1)
def plot_estimate_chart_2():
with figsize(y=2.5):
plt.figure()
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->',
ec='r', lw=3, shrinkA=6, shrinkB=5))
plt.scatter ([0], [158.0], c='k',s=128)
plt.scatter ([1], [164.2], c='b',s=128)
plt.scatter ([1], [159], c='r', s=128)
plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red')
plt.text (1.0, 164.4, "measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue')
plt.text (0, 157.8, "estimate ($\hat{x}_{t-1}$)", ha='center', va='top',fontsize=18)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.savefig('../figs/gh_estimate2.png', pad_inches=0.1)
def plot_estimate_chart_3():
with figsize(y=2.5):
plt.figure()
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->',
ec='r', lw=3, shrinkA=6, shrinkB=5))
ax.annotate('', xy=[1,159], xytext=[1,164.2],
arrowprops=dict(arrowstyle='-',
ec='k', lw=3, shrinkA=8, shrinkB=8))
est_y = ((164.2-158)*.8 + 158)
plt.scatter ([0,1], [158.0,est_y], c='k',s=128)
plt.scatter ([1], [164.2], c='b',s=128)
plt.scatter ([1], [159], c='r', s=128)
plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red')
plt.text (1.0, 164.4, "measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue')
plt.text (0, 157.8, "estimate ($\hat{x}_{t-1}$)", ha='center', va='top',fontsize=18)
plt.text (0.95, est_y, "new estimate ($\hat{x}_{t}$)", ha='right', va='center',fontsize=18)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.savefig('../figs/gh_estimate3.png', pad_inches=0.1)
def create_predict_update_chart(box_bg = '#CCCCCC',
arrow1 = '#88CCFF',
arrow2 = '#88FF88'):
plt.close('all')
plt.figure(figsize=(4, 2.), facecolor='w')
#plt.figure(figsize=(14,12.5), facecolor='w')
ax = plt.axes((0, 0, 1, 1),
xticks=[], yticks=[], frameon=False)
pc = Circle((4,5), 0.7, fc=box_bg)
uc = Circle((6,5), 0.7, fc=box_bg)
ax.add_patch (pc)
ax.add_patch (uc)
plt.text(4,5, "Predict\nStep",ha='center', va='center', fontsize=12)
plt.text(6,5, "Update\nStep",ha='center', va='center', fontsize=12)
#btm arrow from update to predict
ax.annotate('',
xy=(4.1, 4.5), xycoords='data',
xytext=(6, 4.5), textcoords='data',
size=20,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none",
patchB=pc,
patchA=uc,
connectionstyle="arc3,rad=-0.5"))
#top arrow from predict to update
ax.annotate('',
xy=(6, 5.5), xycoords='data',
xytext=(4.1, 5.5), textcoords='data',
size=20,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none",
patchB=uc,
patchA=pc,
connectionstyle="arc3,rad=-0.5"))
ax.annotate('Measurement ($\mathbf{z_k}$)',
xy=(6.3, 5.6), xycoords='data',
xytext=(6,6), textcoords='data',
size=14,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
# arrow from predict to state estimate
ax.annotate('',
xy=(4.0, 3.8), xycoords='data',
xytext=(4.0,4.3), textcoords='data',
size=12,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
ax.annotate('Initial\nConditions ($\mathbf{x_0}$)',
xy=(4.05, 5.7), xycoords='data',
xytext=(2.5, 6.5), textcoords='data',
size=14,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
plt.text (4, 3.7,'State Estimate ($\mathbf{\hat{x}_k}$)',
ha='center', va='center', fontsize=14)
plt.axis('equal')
plt.xlim(2,10)
plt.savefig('../figs/gh_predict_update.png', pad_inches=0.1)
def show_legend():
@ -42,32 +307,32 @@ def show_legend():
def bar_plot(pos, x=None, ylim=(0,1), title=None, c='#30a2da',
**kwargs):
""" plot the values in `pos` as a bar plot.
""" plot the values in `pos` as a bar plot.
**Parameters**
pos : list-like
list of values to plot as bars
x : list-like, optional
If provided, specifies the x value for each value in pos. If not
provided, the first pos element is plotted at x == 0, the second
at 1, etc.
ylim : (lower, upper), default = (0,1)
specifies the lower and upper limits for the y-axis
title : str, optional
If specified, provides a title for the plot
c : color, default='#30a2da'
Color for the bars
**kwargs : keywords, optional
extra keyword arguments passed to ax.bar()
extra keyword arguments passed to ax.bar()
"""
ax = plt.gca()
if x is None:
x = np.arange(len(pos))
@ -83,11 +348,11 @@ def plot_belief_vs_prior(belief, prior, **kwargs):
""" plots two discrete probability distributions side by side, with
titles "belief" and "prior"
"""
plt.subplot(121)
bar_plot(belief, title='belief', **kwargs)
plt.subplot(122)
bar_plot(prior, title='prior', **kwargs)
bar_plot(prior, title='prior', **kwargs)
def plot_prior_vs_posterior(prior, posterior, reverse=False, **kwargs):
@ -96,15 +361,15 @@ def plot_prior_vs_posterior(prior, posterior, reverse=False, **kwargs):
"""
if reverse:
plt.subplot(121)
bar_plot(posterior, title='posterior', **kwargs)
bar_plot(posterior, title='posterior', **kwargs)
plt.subplot(122)
bar_plot(prior, title='prior', **kwargs)
else:
plt.subplot(121)
bar_plot(prior, title='prior', **kwargs)
plt.subplot(122)
bar_plot(posterior, title='posterior', **kwargs)
bar_plot(posterior, title='posterior', **kwargs)
def set_labels(title=None, x=None, y=None):
""" helps make code in book shorter. Optional set title, xlabel and ylabel
@ -156,16 +421,16 @@ def plot_measurements(xs, ys=None, color='k', lw=2, label='Measurements',
plt.autoscale(tight=True)
if lines:
if ys is not None:
plt.plot(xs, ys, color=color, lw=lw, ls='--', label=label, **kwargs)
return plt.plot(xs, ys, color=color, lw=lw, ls='--', label=label, **kwargs)
else:
plt.plot(xs, color=color, lw=lw, ls='--', label=label, **kwargs)
return plt.plot(xs, color=color, lw=lw, ls='--', label=label, **kwargs)
else:
if ys is not None:
plt.scatter(xs, ys, edgecolor=color, facecolor='none',
lw=2, label=label, **kwargs)
return plt.scatter(xs, ys, edgecolor=color, facecolor='none',
lw=2, label=label, **kwargs),
else:
plt.scatter(range(len(xs)), xs, edgecolor=color, facecolor='none',
lw=2, label=label, **kwargs)
return plt.scatter(range(len(xs)), xs, edgecolor=color, facecolor='none',
lw=2, label=label, **kwargs),
def plot_residual_limits(Ps, stds=1.):
@ -184,9 +449,9 @@ def plot_residual_limits(Ps, stds=1.):
def plot_track(xs, ys=None, label='Track', c='k', lw=2, **kwargs):
if ys is not None:
plt.plot(xs, ys, color=c, lw=lw, ls=':', label=label, **kwargs)
return plt.plot(xs, ys, color=c, lw=lw, ls=':', label=label, **kwargs)
else:
plt.plot(xs, color=c, lw=lw, ls=':', label=label, **kwargs)
return plt.plot(xs, color=c, lw=lw, ls=':', label=label, **kwargs)
def plot_filter(xs, ys=None, c='#013afe', label='Filter', var=None, **kwargs):
@ -267,7 +532,22 @@ def hinton(W, maxweight=None):
if __name__ == "__main__":
p = [0.2245871, 0.06288015, 0.06109133, 0.0581008, 0.09334062, 0.2245871,
plot_errorbar1()
plot_errorbar2()
plot_errorbar3()
plot_hypothesis1()
plot_hypothesis2()
plot_hypothesis3()
plot_hypothesis4()
plot_hypothesis5()
plot_estimate_chart_1()
plot_estimate_chart_2()
plot_estimate_chart_3()
create_predict_update_chart()
plt.close('all')
'''p = [0.2245871, 0.06288015, 0.06109133, 0.0581008, 0.09334062, 0.2245871,
0.06288015, 0.06109133, 0.0581008, 0.09334062]*2
bar_plot(p)
plot_measurements(p)
plot_measurements(p)'''

42
code/custom.css
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@ -24,7 +24,7 @@
font-family: 'Source Code Pro', Consolas, monocco, monospace;
}
div.cell{
width: 850px;
//width: 950px;
margin-left: 0% !important;
margin-right: auto;
}
@ -38,7 +38,7 @@
//font-family: 'Chivo',verdana,arial,sans-serif;
//font-family: 'Cardo',verdana,arial,sans-serif;
//font-family: 'Arvo',verdana,arial,sans-serif;
//font-family: 'Poppins',verdana,arial,sans-serif;
//font-family: 'Poppins',verdana,arial,sans-serif;
//font-family: 'Ubuntu',verdana,arial,sans-serif;
//font-family: 'Fontin',verdana,arial,sans-serif;
//font-family: 'Raleway',verdana,arial,sans-serif;
@ -62,10 +62,10 @@
h1 {
font-family: 'Open sans',verdana,arial,sans-serif;
}
div.input_area {
background: #F6F6F9;
border: 1px solid #586e75;
border: 1px solid #586e75;
}
.text_cell_render h1 {
@ -78,7 +78,7 @@
display: block;
white-space: wrap;
text-align: left;
}
}
h2 {
font-family: 'Open sans',verdana,arial,sans-serif;
text-align: left;
@ -94,7 +94,7 @@
display: block;
white-space: wrap;
text-align: left;
}
}
h3 {
font-family: 'Open sans',verdana,arial,sans-serif;
}
@ -161,27 +161,27 @@
margin: 2em;
}
ul li{
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.5em;
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.5em;
}
ul li li{
padding-left: 0.2em;
margin-bottom: 0.2em;
margin-top: 0.2em;
padding-left: 0.2em;
margin-bottom: 0.2em;
margin-top: 0.2em;
}
ol{
margin: 2em;
}
ol li{
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.5em;
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.5em;
}
ul li{
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.2em;
padding-left: 0.5em;
margin-bottom: 0.5em;
margin-top: 0.2em;
}
a:link{
color:#447adb;
@ -200,10 +200,10 @@
color:#447adb;
}
.rendered_html :link {
text-decoration: underline;
text-decoration: underline;
}
.rendered_html :hover {
text-decoration: none;
text-decoration: none;
}
.rendered_html :visited {
text-decoration: none;
@ -216,7 +216,7 @@
}
.warning{
color: rgb( 240, 20, 20 )
}
}
hr {
color: #f3f3f3;
background-color: #f3f3f3;

282
code/gh_internal.py
View File

@ -16,243 +16,99 @@ for more information.
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import book_format
import sys
sys.path.insert(0, '..')
import book_plots
import numpy as np
from matplotlib.patches import Circle, Rectangle, Polygon, Arrow, FancyArrow
import pylab as plt
def plot_errorbar1():
with book_format.figsize(y=1.5):
book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')],
xlims=(145, 185), ylims=(-1, 2))
def plot_errorbar2():
with book_format.figsize(y=1.5):
book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')],
xlims=(145, 185), ylims=(-1, 2))
def plot_errorbar3():
with book_format.figsize(y=1.5):
book_plots.plot_errorbars([(160, 1, 'A'), (170, 9, 'B')],
xlims=(145, 185), ylims=(-1, 2))
import time
def plot_gh_results(weights, estimates, predictions):
def plot_gh_results(weights, estimates, predictions, time_step=0):
n = len(weights)
if time_step > 0:
rng = range(1, n+1)
else:
rng = range(n, n+1)
xs = list(range(n+1))
book_plots.plot_filter(xs, estimates, marker='o')
book_plots.plot_measurements(xs[1:], weights, color='k', label='Scale', lines=False)
book_plots.plot_track([0, n], [160, 160+n], c='k', label='Actual Weight')
book_plots.plot_track(xs[1:], predictions, c='r', label='Predictions', marker='v')
book_plots.show_legend()
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
act, = book_plots.plot_track([0, n], [160, 160+n], c='k')
plt.gcf().canvas.draw()
for i in rng:
xs = list(range(i+1))
#plt.cla()
pred, = book_plots.plot_track(xs[1:], predictions[:i], c='r', marker='v')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
scale, = book_plots.plot_measurements(xs[1:], weights[:i], color='k', lines=False)
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
book_plots.plot_filter(xs[:i+1], estimates[:i+1], marker='o')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
plt.legend([act, scale, pred], ['Actual Weight', 'Measurement', 'Predictions'], loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
plt.xlim([0, n])
plt.show()
def print_results(estimates, prediction, weight):
print('previous: {:.2f}, prediction: {:.2f} estimate {:.2f}'.format(
estimates[-2], prediction, weight))
def create_predict_update_chart(box_bg = '#CCCCCC',
arrow1 = '#88CCFF',
arrow2 = '#88FF88'):
plt.figure(figsize=(3,3), facecolor='w')
ax = plt.axes((0, 0, 1, 1),
xticks=[], yticks=[], frameon=False)
#ax.set_xlim(0, 10)
#ax.set_ylim(0, 10)
pc = Circle((4,5), 0.5, fc=box_bg)
uc = Circle((6,5), 0.5, fc=box_bg)
ax.add_patch (pc)
ax.add_patch (uc)
plt.text(4,5, "Predict\nStep",ha='center', va='center', fontsize=14)
plt.text(6,5, "Update\nStep",ha='center', va='center', fontsize=14)
#btm
ax.annotate('',
xy=(4.1, 4.5), xycoords='data',
xytext=(6, 4.5), textcoords='data',
size=20,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none",
patchB=pc,
patchA=uc,
connectionstyle="arc3,rad=-0.5"))
#top
ax.annotate('',
xy=(6, 5.5), xycoords='data',
xytext=(4.1, 5.5), textcoords='data',
size=20,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none",
patchB=uc,
patchA=pc,
connectionstyle="arc3,rad=-0.5"))
ax.annotate('Measurement ($\mathbf{z_k}$)',
xy=(6.3, 5.4), xycoords='data',
xytext=(6,6), textcoords='data',
size=18,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
ax.annotate('',
xy=(4.0, 3.5), xycoords='data',
xytext=(4.0,4.5), textcoords='data',
size=18,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
ax.annotate('Initial\nConditions ($\mathbf{x_0}$)',
xy=(4.0, 5.5), xycoords='data',
xytext=(2.5,6.5), textcoords='data',
size=18,
arrowprops=dict(arrowstyle="simple",
fc="0.6", ec="none"))
plt.text (4,3.4,'State Estimate ($\mathbf{\hat{x}_k}$)',
ha='center', va='center', fontsize=18)
plt.axis('equal')
#plt.axis([0,8,0,8])
#plt.show()
def plot_estimate_chart_1():
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->', ec='r',shrinkA=6, lw=3,shrinkB=5))
plt.scatter ([0], [158], c='b')
plt.scatter ([1], [159], c='r')
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.show()
def plot_estimate_chart_2():
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->',
ec='r', lw=3, shrinkA=6, shrinkB=5))
plt.scatter ([0], [158.0], c='k',s=128)
plt.scatter ([1], [164.2], c='b',s=128)
plt.scatter ([1], [159], c='r', s=128)
plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red')
plt.text (1.0, 164.4, "measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue')
plt.text (0, 157.8, "estimate ($\hat{x}_{t-1}$)", ha='center', va='top',fontsize=18)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.show()
def plot_estimate_chart_3():
ax = plt.axes()
ax.annotate('', xy=[1,159], xytext=[0,158],
arrowprops=dict(arrowstyle='->',
ec='r', lw=3, shrinkA=6, shrinkB=5))
ax.annotate('', xy=[1,159], xytext=[1,164.2],
arrowprops=dict(arrowstyle='-',
ec='k', lw=3, shrinkA=8, shrinkB=8))
est_y = ((164.2-158)*.8 + 158)
plt.scatter ([0,1], [158.0,est_y], c='k',s=128)
plt.scatter ([1], [164.2], c='b',s=128)
plt.scatter ([1], [159], c='r', s=128)
plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red')
plt.text (1.0, 164.4, "measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue')
plt.text (0, 157.8, "estimate ($\hat{x}_{t-1}$)", ha='center', va='top',fontsize=18)
plt.text (0.95, est_y, "new estimate ($\hat{x}_{t}$)", ha='right', va='center',fontsize=18)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
ax.xaxis.grid(True, which="major", linestyle='dotted')
ax.yaxis.grid(True, which="major", linestyle='dotted')
plt.show()
def plot_hypothesis():
plt.errorbar([1, 2, 3], [170, 161, 169],
xerr=0, yerr=10, fmt='bo', capthick=2, capsize=10)
plt.plot([1, 3], [180, 160], color='g', ls='--')
plt.plot([1, 3], [170, 170], color='g', ls='--')
plt.plot([1, 3], [160, 175], color='g', ls='--')
plt.plot([1, 2, 3], [180, 152, 179], color='g', ls='--')
plt.xlim(0,4); plt.ylim(150, 185)
plt.xlabel('day')
plt.ylabel('lbs')
plt.tight_layout()
plt.show()
def plot_hypothesis2():
plt.errorbar(range(1, 11), [169, 170, 169,171, 170, 171, 169, 170, 169, 170],
xerr=0, yerr=6, fmt='bo', capthick=2, capsize=10)
plt.plot([1, 10], [169, 170.5], color='g', ls='--')
plt.xlim(0, 11); plt.ylim(150, 185)
plt.xlabel('day')
plt.ylabel('lbs')
plt.show()
def plot_hypothesis3():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
plt.errorbar(range(1, 13), weights,
xerr=0, yerr=6, fmt='o', capthick=2, capsize=10)
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
plt.show()
def plot_hypothesis4():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
ave = np.sum(weights) / len(weights)
plt.errorbar(range(1,13), weights, label='weights',
yerr=6, fmt='o', capthick=2, capsize=10)
plt.plot([1, 12], [ave,ave], c='r', label='hypothesis')
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
book_plots.show_legend()
plt.show()
def plot_hypothesis5():
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
xs = range(1, len(weights)+1)
line = np.poly1d(np.polyfit(xs, weights, 1))
plt.errorbar(range(1, 13), weights, label='weights',
yerr=5, fmt='o', capthick=2, capsize=10)
plt.plot (xs, line(xs), c='r', label='hypothesis')
plt.xlim(0, 13); plt.ylim(145, 185)
plt.xlabel('day')
plt.ylabel('weight (lbs)')
book_plots.show_legend()
plt.show()
def plot_g_h_results(measurements, filtered_data,
title='', z_label='Measurements', **kwargs):
title='', z_label='Measurements',
**kwargs):
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
book_plots.show_legend()
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
return
import time
if not interactive:
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
book_plots.show_legend()
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
else:
for i in range(2, len(measurements)):
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
book_plots.show_legend()
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
plt.gca().canvas.draw()
time.sleep(0.5)
if __name__ == '__main__':
create_predict_update_chart()
import seaborn
plot_errorbar1()
#create_predict_update_chart()

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