Numpy - Covariance Between Row Of Two Matrix

I need to compute the covariance between each row of two different matrices, i.e. the covariance between the first row of the first matrix with the first row of the second matrix,

Solution 1:

If you are handling big arrays, I would consider this:

from numba import jit
import numpy as np


m1 = np.random.rand(10000, 3)
m2 = np.random.rand(10000, 3)

@jit(nopython=True) defnb_cov(a, b): 
    return [np.cov(x)[0,1] for x in np.stack((a, b), axis=1)]

To get a runtime of

>>> %timeit nb_cov(m1, m2)
The slowest run took 94.24 times longer than the fastest. This could mean that an intermediate result is being cached.
1loop, best of5: 10.5 ms per loop

Compared with

>>> %timeit [np.cov(x)[0,1] forxin np.stack((m1, m2), axis=1)]
1loop, best of 5: 410 ms per loop

Solution 2:

You could use a list comprehension instead of a for loop, and you could eliminate zip (if you wanted to) by concatenating the two arrays along a third dimension.

import numpy as np

m1 = np.array([[1,2,3],[2,2,2]])
m2 = np.array([[2.56, 2.89, 3.76],[1,2,3.95]])

# List comprehension on zipped arrays.
out2 = [np.cov(a, b)[0][1] for a, b in zip(m1, m2)]
print(out2)
# [0.5999999999999999, 0.0]

# List comprehension on concatenated arrays.
big_array = np.concatenate((m1[:, np.newaxis, :],
                            m2[:, np.newaxis, :]), axis=1)

out3 = [np.cov(X)[0][1] for X in big_array]
print(out3)
# [0.5999999999999999, 0.0]