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-dimentional arrays, I get back a 2x2 matrix of results. I

Answer 1

Thanks to unutbu for the explanation. By default numpy.cov calculates the sample covariance. To obtain the population covariance you can specify normalisation by the total N samples like this:

Covariance = numpy.cov(a, b, bias=True)[0][1]
print(Covariance)

or like this:

Covariance = numpy.cov(a, b, ddof=0)[0][1]
print(Covariance)

Answer 2

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)

(where, again, cov is the function you defined above.)