Скачать или смотреть Boost Your Python Code: Vectorize NumPY Dot Product Between 2D Arrays

Discover how to efficiently perform the `dot product` operation between rows of a 2D NumPY array and another 2D array without using loops, significantly improving your code's performance.
---
This video is based on the question https://stackoverflow.com/q/71640689/ asked by the user 'Openmic' ( https://stackoverflow.com/u/5175556/ ) and on the answer https://stackoverflow.com/a/71641143/ provided by the user 'hpaulj' ( https://stackoverflow.com/u/901925/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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: Vectorize NumPY Dot Product Between a 2D array and Another 2D Array per Row

Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l...
The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Boost Your Python Code: Vectorize NumPY Dot Product Between 2D Arrays

When it comes to numerical computing in Python, especially with arrays, performance is a critical consideration. If you have worked with NumPY, you may have encountered situations where you need to apply operations over rows in 2D arrays. In this guide, we will dive into a common problem faced by many Python developers: how to vectorize the dot product operation between a 2D array and another 2D array for each row without relying on loops.

The Problem

Imagine you have two matrices, A and B, and you want to multiply each row of A with B, then calculate a series of dot products. Doing this in a loop, while it works, is not efficient and can lead to longer computation times, especially with larger datasets. Let's look at the original code that utilizes a loop:

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

Intermediate and Desired Results

When you run the above code, you might see intermediate results that look like this:

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

The desired results can be extracted as:

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

As we can see, the loop produces the correct output. But how can we achieve this without using a loop?

The Solution

The key to vectorization in this case lies in leveraging NumPY's broadcasting capabilities and matrix multiplication functions. Here's a breakdown of how you can perform the dot product per row in a vectorized manner.

Step 1: Reshape the Arrays

To utilize broadcasting with NumPY, we need to reshape A to make it (4,1,3) and another form of A to make it (4,3,1). This allows us to perform matrix multiplication across all rows in one go.

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

This operation gives us the correct shape of (4, 1, 1).

Step 2: Remove Size 1 Dimensions

Next, we can simplify the output by removing the size 1 dimensions from our result using the squeeze() function.

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

Step 3: Using einsum for Flexibility

Alternatively, you can achieve the same result using NumPY's einsum function, which provides a concise way to perform tensor operations:

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

The einsum method is highly flexible and can often lead to clearer code for complex operations.

Summary of the Vectorization Process

To summarize the process of vectorizing the dot product between two 2D arrays A and B per row:

Reshape A for broadcasting.

Perform matrix multiplication without loops.

Clean up the output to get the desired results.

Key Takeaways

Efficiency: Vectorized operations are generally much faster than iterating through arrays in Python.

Readability: Using functions like einsum() can lead to clearer and more maintainable code.

Simplicity: With NumPY, complex operations can often be accomplished with a few lines of code.

By leveraging these techniques, you not only boost your code's performance but also make your codebase easier to understand and maintain. Happy coding!