How to get single value covariance using Numpy's cov function?

General Discussions
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1

I’m trying to calculate Python Covariance using Numpy’s cov function. When I pass it two one-dimensional arrays, it returns a 2x2 matrix of results. However, I believe covariance should be a single number in this case, and I’m unsure how to interpret the output.

Here’s a simple implementation I wrote:

import numpy as np

def cov(a, b):
    if len(a) != len(b):
        return

    a_mean = np.mean(a)
    b_mean = np.mean(b)

    total = 0
    for i in range(len(a)):
        total += ((a[i] - a_mean) * (b[i] - b_mean))

    return total / (len(a) - 1)

This implementation works, but I assume the Numpy version is more efficient. How can I make Numpy’s cov function behave like the one I wrote, and return a single number rather than a matrix?

2

I’ve worked with numpy a lot, and when you have two 1-dimensional sequences, you can access the python covariance between them using numpy.cov(a, b)[0][1]. This essentially gives you the covariance value you’re looking for. Think of the 2x2 matrix that np.cov(a, b) returns:

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

And cov(a, b) is what you need from this matrix. It’s pretty much the same as what you’d get from a custom cov(a, b) function. This is a simple and efficient way to calculate the covariance in Python.

3

That’s a great point! But, let me add that you can make it even more precise by using np.cov(a, b, ddof=0)[0][1]. By setting ddof=0, you ensure that the calculation is done using the population covariance (division by n instead of n-1). This is important in case you’re working with a full dataset rather than a sample. Using this approach will give you the accurate python covariance for your two sequences.

4

Good additions there! Now, if you’re also interested in a normalized version of covariance, you could consider using np.corrcoef(a, b)[0][1]. This gives you the correlation coefficient, which scales the covariance by the standard deviations of a and b. It’s a quick way to assess how strongly related the two datasets are. So, if you’re looking for something beyond just python covariance, this could be a useful approach, especially when you’re comparing datasets with different scales.