What's the Fastest Way to Perform a Cartesian Product (CROSS JOIN) with Pandas DataFrames?

Performant Cartesian Product (CROSS JOIN) with Pandas

Introduction

Computing the Cartesian product, also known as CROSS JOIN, of two or more DataFrames can be a crucial operation in data analysis. However, finding the most performant method for computing this result can be challenging. This article will explore various techniques and provide a performance comparison to determine the optimal solution.

Methods

1. Many-to-Many JOIN with Temporary "Key" Column:

The most straightforward approach is to assign a temporary "key" column to both DataFrames with the same value (e.g., 1) and perform a many-to-many JOIN on the "key" column using merge. However, this method may have performance limitations for large DataFrames.

2. NumPy Cartesian Product:

NumPy offers efficient implementations of 1D Cartesian products. Several of these implementations can be utilized to build a performant Cartesian product solution for DataFrames. One notable example is @senderle's implementation.

3. Cartesian Product on Non-Mixed Indices:

This method generalizes to work on DataFrames with any type of scalar dtype. It involves computing the Cartesian product of the numeric indices of the DataFrames and using this to reindex the DataFrames.

4. Further Simplification for Two DataFrames:

When dealing with only two DataFrames, np.broadcast_arrays can be employed to achieve similar performance to the NumPy Cartesian product solution.

Performance Evaluation

Benchmarks on synthetic DataFrames with unique indices show that using @senderle's cartesian_product function results in the best overall performance. However, the simplified cartesian_product_simplified function provides almost the same level of performance when working with only two DataFrames.

Conclusion

The optimal method for computing the Cartesian product of DataFrames depends on various factors, including the size and type of data and whether the indices have mixed dtypes or are unique. Based on the performance benchmarks, using @senderle's cartesian_product function is recommended for the best performance, especially for large DataFrames or when working with multiple DataFrames. For cases involving only two DataFrames with non-mixed scalar dtypes, the simplified cartesian_product_simplified function provides excellent performance.

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