Calculating Covariance with Python and Numpy

Solution 1:

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.)

Solution 2:

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:

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

or like this:

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

Solution 3:

Note that starting in Python 3.10, one can obtain the covariance directly from the standard library.

Using statistics.covariance which is a measure (the number you're looking for) of the joint variability of two inputs:

from statistics import covariance

# x = [1, 2, 3, 4, 5, 6, 7, 8, 9]
# y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
covariance(x, y)
# 0.75