import numpy as np
from matplotlib import pylab as plt
from matplotlib import mlab

mean_test = np.array([0,0])
cov_test = array([[ 0.6744121 , -0.16938146],
                  [-0.16938146,  0.21243464]])

# Semi-positive definite if all eigenvalues are 0 or
# if there exists a Cholesky decomposition
print np.linalg.eigvals(cov_test)
print np.linalg.cholesky(cov_test)

data_test = np.random.multivariate_normal(mean_test, cov_test, 1000)
 plt.scatter(data_test[:,0],data_test[:,1])

x = np.arange(-3.0, 3.0, 0.1)
y = np.arange(-3.0, 3.0, 0.1)
X, Y = np.meshgrid(x, y)
Z = mlab.bivariate_normal(X, Y,
                      cov_test[0,0], cov_test[1,1],
                      0, 0, cov_test[0,1])
print Z
plt.contour(X, Y, Z)

[[ nan  nan  nan ...,  nan  nan  nan]
 [ nan  nan  nan ...,  nan  nan  nan]
 [ nan  nan  nan ...,  nan  nan  nan]
 ...,
 [ nan  nan  nan ...,  nan  nan  nan]
 [ nan  nan  nan ...,  nan  nan  nan]
 [ nan  nan  nan ...,  nan  nan  nan]]

 ValueError: zero-size array to reduction operation minimum which has no identity

Z = mlab.bivariate_normal(X, Y,
                      cov_test[0,0], cov_test[1,1],
                      0, 0, cov_test[0,1])

Z = mlab.bivariate_normal(X, Y,
                      np.sqrt(cov_test[0,0]), np.sqrt(cov_test[1,1]),
                      0, 0, cov_test[0,1])