Calculating Covariance with Python and Numpy

Question

I am trying to figure out how to calculate covariance with the Python Numpy function cov. When I pass it two one-dimensional arrays, I get back a 2x2 matrix of results. I don't know what to do with that. I'm not great at statistics, but I believe covariance in such a situation should be a single number. This is what I am looking for. I wrote my own:

def cov(a, b): 

if len(a) != len(b): 

return 

a_mean = np.mean(a) 

b_mean = np.mean(b) 

sum = 0 

for i in range(0, len(a)): 

sum += ((a[i] - a_mean) * (b[i] - b_mean)) 

return sum/(len(a)-1)

That works, but I figure the Numpy version is much more efficient if I could figure out how to use it.

Does anybody know how to make the Numpy cov function perform like the one I wrote?

Thanks,

Answer 1

To calculate the covariance with python and numpy when a and b are 1-dimensional sequences, numpy.cov(a,b)[0][1] is equivalent to your cov(a,b).

The 2x2 array returned by np.cov(a,b) has elements equal to

cov(a,a) cov(a,b) 

cov(a,b) cov(b,b)