Cartesian product of x and y array points into single array of 2

ghz 7months ago ⋅ 49 views

Cartesian product of x and y array points into single array of 2D points

I have two numpy arrays that define the x and y axes of a grid. For example:

x = numpy.array([1,2,3])
y = numpy.array([4,5])

I'd like to generate the Cartesian product of these arrays to generate:

array([[1,4],[2,4],[3,4],[1,5],[2,5],[3,5]])

In a way that's not terribly inefficient since I need to do this many times in a loop. I'm assuming that converting them to a Python list and using itertools.product and back to a numpy array is not the most efficient form.

Answers

To generate the Cartesian product of two NumPy arrays efficiently, you can use the numpy.meshgrid function combined with numpy.vstack and numpy.ravel. This approach avoids converting to Python lists and using itertools.product, making it more efficient.

Here's how you can achieve this:

import numpy as np

x = np.array([1, 2, 3])
y = np.array([4, 5])

# Generate meshgrid
xx, yy = np.meshgrid(x, y)

# Flatten the grid and combine
cartesian_product = np.vstack([xx.ravel(), yy.ravel()]).T

print(cartesian_product)

Explanation

  1. Meshgrid Creation:

    • np.meshgrid(x, y) generates two 2D arrays where xx contains the x-coordinates and yy contains the y-coordinates of the grid.

  2. Flattening and Stacking:

    • xx.ravel() and yy.ravel() flatten the 2D arrays into 1D arrays.
    • np.vstack([xx.ravel(), yy.ravel()]).T stacks the flattened arrays vertically and then transposes the result to get the desired shape.

Example Output

The cartesian_product will be:

array([[1, 4],
       [2, 4],
       [3, 4],
       [1, 5],
       [2, 5],
       [3, 5]])

This method is efficient and leverages NumPy's vectorized operations to perform the Cartesian product computation without explicit loops in Python. This should work well even for large arrays and in scenarios where you need to perform this operation many times in a loop.

#numpy