def test_multivariate():
from scipy.stats import multivariate_normal as mvn
from numpy.random import rand
mean = 3
var = 1.5
assert near_equal(mvn(mean,var).pdf(0.5),
multivariate_gaussian(0.5, mean, var))
mean = np.array([2.,17.])
var = np.array([[10., 1.2], [1.2, 4.]])
x = np.array([1,16])
assert near_equal(mvn(mean,var).pdf(x),
multivariate_gaussian(x, mean, var))
for i in range(100):
x = np.array([rand(), rand()])
assert near_equal(mvn(mean,var).pdf(x),
multivariate_gaussian(x, mean, var))
assert near_equal(mvn(mean,var).pdf(x),
norm_pdf_multivariate(x, mean, var))
mean = np.array([1,2,3,4])
var = np.eye(4)*rand()
x = np.array([2,3,4,5])
assert near_equal(mvn(mean,var).pdf(x),
norm_pdf_multivariate(x, mean, var))
def test_multivariate():
from scipy.stats import multivariate_normal as mvn
from numpy.random import rand
mean = 3
var = 1.5
assert near_equal(mvn(mean,var).pdf(0.5),
multivariate_gaussian(0.5, mean, var))
mean = np.array([2.,17.])
var = np.array([[10., 1.2], [1.2, 4.]])
x = np.array([1,16])
assert near_equal(mvn(mean,var).pdf(x),
multivariate_gaussian(x, mean, var))
for i in range(100):
x = np.array([rand(), rand()])
assert near_equal(mvn(mean,var).pdf(x),
multivariate_gaussian(x, mean, var))
assert near_equal(mvn(mean,var).pdf(x),
norm_pdf_multivariate(x, mean, var))
mean = np.array([1,2,3,4])
var = np.eye(4)*rand()
x = np.array([2,3,4,5])
assert near_equal(mvn(mean,var).pdf(x),
norm_pdf_multivariate(x, mean, var))
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)
