NumPy: Compute the covariance matrix of two given arrays

Last update on March 25 2025 12:21:15 (UTC/GMT +8 hours)

8. Covariance Matrix of Two Arrays

Write a NumPy program to compute the covariance matrix of two given arrays.

Sample Solution:

Python Code:

# Importing the NumPy library
import numpy as np

# Creating an array 'x' containing elements [0, 1, 2]
x = np.array([0, 1, 2])

# Creating an array 'y' containing elements [2, 1, 0]
y = np.array([2, 1, 0])

# Displaying the original array 'x'
print("\nOriginal array1:")
print(x)

# Displaying the original array 'y'
print("\nOriginal array1:")
print(y)

# Calculating the covariance matrix of arrays 'x' and 'y' using np.cov()
print("\nCovariance matrix of the said arrays:\n", np.cov(x, y)) 

Sample Output:

Original array1:
[0 1 2]

Original array1:
[2 1 0]

Covariance matrix of the said arrays:
 [[ 1. -1.]
 [-1.  1.]]

Explanation:

In the above exercise –

x = np.array([0, 1, 2]): This code creates a NumPy array x containing the values 0, 1, and 2.

y = np.array([2, 1, 0]): This code creates a NumPy array y containing the values 2, 1, and 0. print(np.cov(x, y)): This code calculates the covariance matrix of the arrays x and y using the np.cov() function, and then prints it to the console.

For more Practice: Solve these Related Problems:

• Write a function that calculates the covariance matrix of two 1D arrays using np.cov and ensures the matrix is symmetric.
• Create a program that computes the covariance of two 2D arrays after flattening them into 1D arrays.
• Implement a solution that normalizes two arrays before computing their covariance and compares the output with np.cov.
• Develop a method that computes covariance manually using the formula E[XY] - E[X]E[Y] and validates it against np.cov.

Python-Numpy Code Editor:

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