NumPy: Create a Cartesian product of two arrays into single array of 2D points

Last update on March 24 2025 13:39:10 (UTC/GMT +8 hours)

Create Cartesian Product of Two Arrays

Write a NumPy program to create a Cartesian product of two arrays into a single array of 2D points.

Sample Solution:

Python Code:

# Importing the NumPy library and aliasing it as 'np'
import numpy as np

# Creating a NumPy array 'x' containing integers [1, 2, 3]
x = np.array([1, 2, 3])

# Creating a NumPy array 'y' containing integers [4, 5]
y = np.array([4, 5])

# Using np.tile and np.repeat to create a grid of repeated elements from 'x' and 'y'
# The grid is created by replicating 'x' along rows and 'y' along columns
result = np.transpose([np.tile(x, len(y)), np.repeat(y, len(x))])

# Printing the resulting grid obtained by combining 'x' and 'y' elements
print(result) 

Sample Output:

[[1 4]
 [2 4]
 [3 4]
 [1 5]
 [2 5]
 [3 5]]

Explanation:

In the above code –

1. x = np.array([1,2,3]): This line creates a 1D NumPy array 'x' containing the elements [1, 2, 3].
2. y = np.array([4,5]): This line creates a 1D NumPy array 'y' containing the elements [4, 5].
3. np.tile(x, len(y)): Repeat the elements of 'x' as many times as there are elements in 'y'. In this case, 'x' will be repeated twice, resulting in the array [1, 2, 3, 1, 2, 3].
4. np.repeat(y, len(x)): Repeat each element of 'y' as many times as there are elements in 'x'. In this case, each element of 'y' will be repeated three times, resulting in the array [4, 4, 4, 5, 5, 5].
5. np.transpose(...): Combine the arrays from steps 3 and 4 by stacking them along a new axis and then transposing the result. This gives the final 2D array 'result', which contains all possible combinations of elements from 'x' and 'y':

Pictorial Presentation:

For more Practice: Solve these Related Problems:

• Write a NumPy program to compute the Cartesian product of two 1D arrays using np.meshgrid and reshape.
• Create a function that returns a 2D array of all possible pairs formed from two input arrays.
• Test the Cartesian product function with arrays of different lengths and verify the resulting shape.
• Implement the solution using np.column_stack to combine flattened meshgrid outputs.

Python-Numpy Code Editor: