def show_x_error_chart(count):
""" displays x=123 with covariances showing error"""
plt.cla()
plt.gca().autoscale(tight=True)
cov = np.array([[0.03, 0], [0, 8]])
e = stats.covariance_ellipse(cov)
cov2 = np.array([[0.03, 0], [0, 4]])
e2 = stats.covariance_ellipse(cov2)
cov3 = np.array([[12, 11.95], [11.95, 12]])
e3 = stats.covariance_ellipse(cov3)
sigma = [1, 4, 9]
if count >= 1:
stats.plot_covariance_ellipse((0, 0), ellipse=e, variance=sigma)
if count == 2 or count == 3:
stats.plot_covariance_ellipse((5, 5), ellipse=e, variance=sigma)
if count == 3:
stats.plot_covariance_ellipse((5, 5),
ellipse=e3,
variance=sigma,
edgecolor='r')
if count == 4:
M1 = np.array([[5, 5]]).T
m4, cov4 = stats.multivariate_multiply(M1, cov2, M1, cov3)
e4 = stats.covariance_ellipse(cov4)
stats.plot_covariance_ellipse((5, 5),
ellipse=e,
variance=sigma,
alpha=0.25)
stats.plot_covariance_ellipse((5, 5),
ellipse=e3,
variance=sigma,
edgecolor='r',
alpha=0.25)
stats.plot_covariance_ellipse(m4[:, 0], ellipse=e4, variance=sigma)
#plt.ylim([0,11])
#plt.xticks(np.arange(1,4,1))
plt.xlabel("Position")
plt.ylabel("Velocity")
plt.show()
def show_x_error_chart(count):
""" displays x=123 with covariances showing error"""
plt.cla()
plt.gca().autoscale(tight=True)
cov = np.array([[0.03,0], [0,8]])
e = stats.covariance_ellipse (cov)
cov2 = np.array([[0.03,0], [0,4]])
e2 = stats.covariance_ellipse (cov2)
cov3 = np.array([[12,11.95], [11.95,12]])
e3 = stats.covariance_ellipse (cov3)
sigma=[1, 4, 9]
if count >= 1:
stats.plot_covariance_ellipse ((0,0), ellipse=e, variance=sigma)
if count == 2 or count == 3:
stats.plot_covariance_ellipse ((5,5), ellipse=e, variance=sigma)
if count == 3:
stats.plot_covariance_ellipse ((5,5), ellipse=e3, variance=sigma,
edgecolor='r')
if count == 4:
M1 = np.array([[5, 5]]).T
m4, cov4 = stats.multivariate_multiply(M1, cov2, M1, cov3)
e4 = stats.covariance_ellipse (cov4)
stats.plot_covariance_ellipse ((5,5), ellipse=e, variance=sigma,
alpha=0.25)
stats.plot_covariance_ellipse ((5,5), ellipse=e3, variance=sigma,
edgecolor='r', alpha=0.25)
stats.plot_covariance_ellipse (m4[:,0], ellipse=e4, variance=sigma)
#plt.ylim([0,11])
#plt.xticks(np.arange(1,4,1))
plt.xlabel("Position")
plt.ylabel("Velocity")
plt.show()
def show_x_with_unobserved():
""" shows x=1,2,3 with velocity superimposed on top """
# plot velocity
sigma=[0.5,1.,1.5,2]
cov = np.array([[1,1],[1,1.1]])
stats.plot_covariance_ellipse ((2,2), cov=cov, variance=sigma, axis_equal=False)
# plot positions
cov = np.array([[0.003,0], [0,12]])
sigma=[0.5,1.,1.5,2]
e = stats.covariance_ellipse (cov)
stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)
# plot intersection cirle
isct = Ellipse(xy=(2,2), width=.2, height=1.2, edgecolor='r', fc='None', lw=4)
plt.gca().add_artist(isct)
plt.ylim([0,11])
plt.xlim([0,4])
plt.xticks(np.arange(1,4,1))
plt.xlabel("Position")
plt.ylabel("Time")
plt.show()
def show_x_error_chart():
""" displays x=123 with covariances showing error"""
cov = np.array([[0.003, 0], [0, 12]])
sigma = [0.5, 1., 1.5, 2]
e = stats.covariance_ellipse(cov)
stats.plot_covariance_ellipse((1, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
stats.plot_covariance_ellipse((2, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
stats.plot_covariance_ellipse((3, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
plt.ylim([0, 11])
plt.xticks(np.arange(1, 4, 1))
plt.xlabel("Position")
plt.ylabel("Time")
plt.show()
def plot_3d_sampled_covariance(mean, cov):
""" plots a 2x2 covariance matrix positioned at mean. mean will be plotted
in x and y, and the probability in the z axis.
Parameters
----------
mean : 2x1 tuple-like object
mean for x and y coordinates. For example (2.3, 7.5)
cov : 2x2 nd.array
the covariance matrix
"""
# compute width and height of covariance ellipse so we can choose
# appropriate ranges for x and y
o,w,h = stats.covariance_ellipse(cov,3)
# rotate width and height to x,y axis
wx = abs(w*np.cos(o) + h*np.sin(o))*1.2
wy = abs(h*np.cos(o) - w*np.sin(o))*1.2
# ensure axis are of the same size so everything is plotted with the same
# scale
if wx > wy:
w = wx
else:
w = wy
minx = mean[0] - w
maxx = mean[0] + w
miny = mean[1] - w
maxy = mean[1] + w
count = 1000
x,y = multivariate_normal(mean=mean, cov=cov, size=count).T
xs = np.arange(minx, maxx, (maxx-minx)/40.)
ys = np.arange(miny, maxy, (maxy-miny)/40.)
xv, yv = np.meshgrid (xs, ys)
zs = np.array([100.* stats.multivariate_gaussian(np.array([xx,yy]),mean,cov) \
for xx,yy in zip(np.ravel(xv), np.ravel(yv))])
zv = zs.reshape(xv.shape)
ax = plt.figure().add_subplot(111, projection='3d')
ax.scatter(x,y, [0]*count, marker='.')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)
ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)
def plot_3d_sampled_covariance(mean, cov):
""" plots a 2x2 covariance matrix positioned at mean. mean will be plotted
in x and y, and the probability in the z axis.
Parameters
----------
mean : 2x1 tuple-like object
mean for x and y coordinates. For example (2.3, 7.5)
cov : 2x2 nd.array
the covariance matrix
"""
# compute width and height of covariance ellipse so we can choose
# appropriate ranges for x and y
o, w, h = stats.covariance_ellipse(cov, 3)
# rotate width and height to x,y axis
wx = abs(w * np.cos(o) + h * np.sin(o)) * 1.2
wy = abs(h * np.cos(o) - w * np.sin(o)) * 1.2
# ensure axis are of the same size so everything is plotted with the same
# scale
if wx > wy:
w = wx
else:
w = wy
minx = mean[0] - w
maxx = mean[0] + w
miny = mean[1] - w
maxy = mean[1] + w
count = 1000
x, y = multivariate_normal(mean=mean, cov=cov, size=count).T
xs = np.arange(minx, maxx, (maxx - minx) / 40.)
ys = np.arange(miny, maxy, (maxy - miny) / 40.)
xv, yv = np.meshgrid(xs, ys)
zs = np.array([100.* stats.multivariate_gaussian(np.array([xx,yy]),mean,cov) \
for xx,yy in zip(np.ravel(xv), np.ravel(yv))])
zv = zs.reshape(xv.shape)
ax = plt.figure().add_subplot(111, projection='3d')
ax.scatter(x, y, [0] * count, marker='.')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.contour(xv, yv, zv, zdir='x', offset=minx - 1, cmap=cm.autumn)
ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)
def show_x_with_unobserved():
""" shows x=1,2,3 with velocity superimposed on top """
# plot velocity
sigma = [0.5, 1., 1.5, 2]
cov = np.array([[1, 1], [1, 1.1]])
stats.plot_covariance_ellipse((2, 2),
cov=cov,
variance=sigma,
axis_equal=False)
# plot positions
cov = np.array([[0.003, 0], [0, 12]])
sigma = [0.5, 1., 1.5, 2]
e = stats.covariance_ellipse(cov)
stats.plot_covariance_ellipse((1, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
stats.plot_covariance_ellipse((2, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
stats.plot_covariance_ellipse((3, 1),
ellipse=e,
variance=sigma,
axis_equal=False)
# plot intersection cirle
isct = Ellipse(xy=(2, 2),
width=.2,
height=1.2,
edgecolor='r',
fc='None',
lw=4)
plt.gca().add_artist(isct)
plt.ylim([0, 11])
plt.xlim([0, 4])
plt.xticks(np.arange(1, 4, 1))
plt.xlabel("Position")
plt.ylabel("Time")
plt.show()
def show_x_error_chart():
""" displays x=123 with covariances showing error"""
cov = np.array([[0.003,0], [0,12]])
sigma=[0.5,1.,1.5,2]
e = stats.covariance_ellipse (cov)
stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)
plt.ylim([0,11])
plt.xticks(np.arange(1,4,1))
plt.xlabel("Position")
plt.ylabel("Time")
plt.show()