daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Removed Matplotlib deprecation warning

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needed to use new kwarg density.
This commit is contained in:
Roger Labbe committed 2018-07-14 08:46:40 -07:00
1 parent c15a693aa6
commit 8507d8baae
2 files changed
+373 -366
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11-Extended-Kalman-Filters.ipynb
+34 -34
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@@ -319,9 +319,9 @@
"outputs": [
{
"data": {
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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f12ef42e8>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -403,9 +403,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f15cd6978>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -705,9 +705,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f154194a8>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -715,9 +715,9 @@
},
{
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f16d4a588>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -725,9 +725,9 @@
},
{
"data": {
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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f16d8bba8>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -863,9 +863,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f16d15198>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1493,9 +1493,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17cf84e0>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1505,7 +1505,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Final P: [0.023 0.043 0.002]\n"
"Final P: [0.024 0.043 0.002]\n"
]
}
],
@@ -1538,9 +1538,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17e4d630>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1550,7 +1550,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Final P: [0.02 0.02 0.002]\n"
"Final P: [0.021 0.02 0.002]\n"
]
}
],
@@ -1580,9 +1580,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17cf86a0>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1592,7 +1592,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Final P: [0.019 0.047 0. ]\n"
"Final P: [0.021 0.046 0. ]\n"
]
}
],
@@ -1619,9 +1619,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17f691d0>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1631,7 +1631,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Final P: [0.262 0.805 0.004]\n"
"Final P: [0.273 0.875 0.004]\n"
]
}
],
@@ -1658,9 +1658,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17fd27f0>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1670,7 +1670,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Final P: [0.008 0.009 0.001]\n"
"Final P: [0.009 0.009 0.001]\n"
]
}
],
@@ -1720,9 +1720,9 @@
"outputs": [
{
"data": {
"image/png": 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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x24f17cf8da0>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1732,7 +1732,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"actual mean=1.30, std=1.12\n",
"actual mean=1.30, std=1.13\n",
"EKF mean=1.00, std=0.95\n"
]
}
@@ -1751,14 +1751,14 @@
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x24f18194f28>"
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
@@ -1802,7 +1802,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
"version": "3.6.5"
}
},
"nbformat": 4,
kf_book/nonlinear_plots.py
+339 -332
View File
@@ -1,332 +1,339 @@
# -*- coding: utf-8 -*-
"""Copyright 2015 Roger R Labbe Jr.
Code supporting the book
Kalman and Bayesian Filters in Python
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
This is licensed under an MIT license. See the LICENSE.txt file
for more information.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import math
from matplotlib import cm
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from numpy.random import normal, multivariate_normal
import scipy.stats
from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform
from filterpy.stats import multivariate_gaussian
def plot_nonlinear_func(data, f, out_lim=None, num_bins=300):
ys = f(data)
x0 = np.mean(data)
in_std = np.std(data)
y = f(x0)
std = np.std(ys)
in_lims = [x0 - in_std*3, x0 + in_std*3]
if out_lim is None:
out_lim = [y - std*3, y + std*3]
# plot output
h = np.histogram(ys, num_bins, density=False)
plt.subplot(221)
plt.plot(h[1][1:], h[0], lw=2, alpha=0.8)
if out_lim is not None:
plt.xlim(out_lim[0], out_lim[1])
plt.gca().yaxis.set_ticklabels([])
plt.title('Output')
plt.axvline(np.mean(ys), ls='--', lw=2)
plt.axvline(f(x0), lw=1)
norm = scipy.stats.norm(y, in_std)
'''min_x = norm.ppf(0.001)
max_x = norm.ppf(0.999)
xs = np.arange(min_x, max_x, (max_x - min_x) / 1000)
pdf = norm.pdf(xs)
plt.plot(pdf * max(h[0])/max(pdf), xs, lw=1, color='k')
print(max(norm.pdf(xs)))'''
# 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, 'k')
isct = f(x0)
plt.plot([x0, x0, in_lims[1]], [out_lim[1], isct, isct], color='r', lw=1)
plt.xlim(in_lims)
plt.ylim(out_lim)
#plt.axis('equal')
plt.title('f(x)')
# plot input
h = np.histogram(data, num_bins, density=True)
plt.subplot(2,2,4)
plt.plot(h[0], h[1][1:], lw=2)
#plt.ylim(in_lims)
plt.gca().xaxis.set_ticklabels([])
plt.title('Input')
plt.tight_layout()
plt.show()
def plot_ekf_vs_mc():
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)
mean_ekf = fx(mean)
slope = dfx(mean)
std_ekf = abs(slope*std)
norm = scipy.stats.norm(mean_ekf, std_ekf)
xs = np.linspace(-3, 5, 200)
plt.plot(xs, norm.pdf(xs), lw=2, ls='--', color='b')
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(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')
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)
# -*- coding: utf-8 -*-
"""Copyright 2015 Roger R Labbe Jr.
Code supporting the book
Kalman and Bayesian Filters in Python
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
This is licensed under an MIT license. See the LICENSE.txt file
for more information.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import math
from matplotlib import cm
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from numpy.random import normal, multivariate_normal
import scipy.stats
from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform
from filterpy.stats import multivariate_gaussian
def plot_nonlinear_func(data, f, out_lim=None, num_bins=300):
ys = f(data)
x0 = np.mean(data)
in_std = np.std(data)
y = f(x0)
std = np.std(ys)
in_lims = [x0 - in_std*3, x0 + in_std*3]
if out_lim is None:
out_lim = [y - std*3, y + std*3]
# plot output
h = np.histogram(ys, num_bins, density=False)
plt.subplot(221)
plt.plot(h[1][1:], h[0], lw=2, alpha=0.8)
if out_lim is not None:
plt.xlim(out_lim[0], out_lim[1])
plt.gca().yaxis.set_ticklabels([])
plt.title('Output')
plt.axvline(np.mean(ys), ls='--', lw=2)
plt.axvline(f(x0), lw=1)
norm = scipy.stats.norm(y, in_std)
'''min_x = norm.ppf(0.001)
max_x = norm.ppf(0.999)
xs = np.arange(min_x, max_x, (max_x - min_x) / 1000)
pdf = norm.pdf(xs)
plt.plot(pdf * max(h[0])/max(pdf), xs, lw=1, color='k')
print(max(norm.pdf(xs)))'''
# 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, 'k')
isct = f(x0)
plt.plot([x0, x0, in_lims[1]], [out_lim[1], isct, isct], color='r', lw=1)
plt.xlim(in_lims)
plt.ylim(out_lim)
#plt.axis('equal')
plt.title('f(x)')
# plot input
h = np.histogram(data, num_bins, density=True)
plt.subplot(2,2,4)
plt.plot(h[0], h[1][1:], lw=2)
#plt.ylim(in_lims)
plt.gca().xaxis.set_ticklabels([])
plt.title('Input')
plt.tight_layout()
plt.show()
def plot_ekf_vs_mc():
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)
mean_ekf = fx(mean)
slope = dfx(mean)
std_ekf = abs(slope*std)
norm = scipy.stats.norm(mean_ekf, std_ekf)
xs = np.linspace(-3, 5, 200)
plt.plot(xs, norm.pdf(xs), lw=2, ls='--', 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(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)