How to Efficiently Fill an ndarray in a Diagonal Way Using NumPy

Learn how to create and fill a NumPy array diagonally with efficient techniques. Discover how to optimize your NumPy array manipulation!
---

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: How to fill ndarray in a diagonal way?

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
How to Efficiently Fill an ndarray in a Diagonal Way Using NumPy

When dealing with arrays in NumPy, you might come across situations where you need to fill an ndarray shape such as (a, b, c, b) in a diagonal manner. Specifically, you want to set the values to 1 where the second and the last dimension indices match and set them to 0 otherwise. While you may have a working solution, the quest for a more elegant and performant technique can lead to many discoveries. In this guide, we’ll explore efficient ways to create and fill your ndarray diagonally.

The Problem Statement

Let's clarify the task at hand. You have a multi-dimensional array structured as (a, b, c, b). Your goal is to fill this array based on the following criteria:

Set the value of the array to 1 if the index of the second dimension equals the index of the last dimension.

Set the value to 0 otherwise.

Initially, you might implement a solution like this:

[[See Video to Reveal this Text or Code Snippet]]

Although this works perfectly, you might be on the lookout for a more concise and efficient method.

Improved Solutions

There are a couple of alternative solutions that are not only cleaner but can also improve performance. Let’s dive into them:

The first solution utilizes broadcasting with an identity matrix. This allows for an elegant assignment of values.

[[See Video to Reveal this Text or Code Snippet]]

Explanation:

By using slicing with None, we effectively add extra dimensions to the identity matrix, enabling broadcasting to the shape (a, b, c, b).

This method is efficient and clearly communicates the intention of filling the ndarray diagonally.

2. Using Tiling and Reshaping

If you prefer a one-liner solution, you can tile the identity array and reshape it as follows:

[[See Video to Reveal this Text or Code Snippet]]

Explanation:

The subsequent reshape rearranges the array to the desired shape of (a, b, c, b).

This method is also straightforward and benefits from NumPy's efficient handling of array operations.

Performance Comparison

It’s always helpful to measure performance for optimization purposes. Here’s the timing comparison for the different solutions:

Original Method: 3.14 µs ± 46.9 ns per loop

Broadcasting Method: 1.82 µs ± 21.7 ns per loop

Tiling Method: 4.5 µs ± 47 ns per loop

The broadcasting method stands out as the most efficient, followed closely by the original approach.

Conclusion

Choosing the right method for filling an ndarray can significantly influence both performance and readability of your code. Using broadcasting with an identity matrix or tiling and reshaping are both effective and cleaner solutions. Adopting these strategies can enhance your workflow when working with NumPy arrays, allowing you to focus more on problem-solving and less on verbose implementations.

For any further questions or if you have suggestions for improvements, feel free to leave a comment below!