Compute the covariance matrix of two given NumPy arrays

Last Updated : 29 Aug, 2020

In NumPy for computing the covariance matrix of two given arrays with help of numpy.cov(). In this, we will pass the two arrays and it will return the covariance matrix of two given arrays.

Syntax: numpy.cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None)

Example 1:

Python

import numpy as np


array1 = np.array([0, 1, 1])
array2 = np.array([2, 2, 1])

# Original array1
print(array1)

# Original array2
print(array2)

# Covariance matrix
print("\nCovariance matrix of the said arrays:\n",
      np.cov(array1, array2))

Output:

[0 1 1]
[2 2 1]

Covariance matrix of the said arrays:
 [[ 0.33333333 -0.16666667]
 [-0.16666667  0.33333333]]

Example 2:

Python

import numpy as np


array1 = np.array([2, 1, 1, 4])
array2 = np.array([2, 2, 1, 1])

# Original array1
print(array1)

# Original array2
print(array2)

# Covariance matrix
print("\nCovariance matrix of the said arrays:\n", 
      np.cov(array1, array2))

Output:

[2 1 1 4]
[2 2 1 1]

Covariance matrix of the said arrays:
 [[ 2.         -0.33333333]
 [-0.33333333  0.33333333]]

Example 3:

Python

import numpy as np


array1 = np.array([1, 2])
array2 = np.array([1, 2])

# Original array1
print(array1)

# Original array2
print(array2)

# Covariance matrix
print("\nCovariance matrix of the said arrays:\n", 
      np.cov(array1, array2))

Output

[1 2]
[1 2]

Covariance matrix of the said arrays:
 [[0.5 0.5]
 [0.5 0.5]]

Example 4:

Python

import numpy as np 
  
x = [1.23, 2.12, 3.34, 4.5] 
y = [2.56, 2.89, 3.76, 3.95] 
  
# find out covariance with respect 
# rows 
cov_mat = np.stack((x, y), axis = 1)  
  
print("shape of matrix x and y:", 
      np.shape(cov_mat)) 

print("shape of covariance matrix:",
      np.shape(np.cov(cov_mat))) 

print(np.cov(cov_mat))

Output

shape of matrix x and y: (4, 2)
shape of covariance matrix: (4, 4)
[[ 0.88445  0.51205  0.2793  -0.36575]
 [ 0.51205  0.29645  0.1617  -0.21175]
 [ 0.2793   0.1617   0.0882  -0.1155 ]
 [-0.36575 -0.21175 -0.1155   0.15125]]