How to Efficiently Perform a CROSS JOIN in Pandas?

Performant Cross Join (CROSS JOIN) with Pandas

In this post, we explore the most efficient methods for performing a Cartesian product (CROSS JOIN) operation in Pandas.

Baseline Method: Temporary Key Column

The typical approach involves assigning a temporary key column to both DataFrames, performing a many-to-many join on that key, and then dropping the key column:

left = pd.DataFrame({'col1' : ['A', 'B', 'C'], 'col2' : [1, 2, 3]})
right = pd.DataFrame({'col1' : ['X', 'Y', 'Z'], 'col2' : [20, 30, 50]})

def cartesian_product_basic(left, right):
    return (
       left.assign(key=1).merge(right.assign(key=1), on='key').drop('key', 1))

cartesian_product_basic(left, right)

NumPy-Based Implementation

For improved performance on larger datasets, we leverage NumPy's implementation of the Cartesian product:

import numpy as np

def cartesian_product(*arrays):
    la = len(arrays)
    dtype = np.result_type(*arrays)
    arr = np.empty([len(a) for a in arrays] + [la], dtype=dtype)
    for i, a in enumerate(np.ix_(*arrays)):
        arr[...,i] = a
    return arr.reshape(-1, la)  

Generalization to Non-Unique Indexed DataFrames

We can extend this approach to handle DataFrames with non-unique indices:

def cartesian_product_generalized(left, right):
    la, lb = len(left), len(right)
    idx = cartesian_product(np.ogrid[:la], np.ogrid[:lb])
    return pd.DataFrame(
        np.column_stack([left.values[idx[:,0]], right.values[idx[:,1]]]))

Simplified Implementation for Two DataFrames

When dealing with only two DataFrames, a simpler technique utilizing np.broadcast_arrays can achieve comparable performance:

def cartesian_product_simplified(left, right):
    la, lb = len(left), len(right)
    ia2, ib2 = np.broadcast_arrays(*np.ogrid[:la,:lb])

    return pd.DataFrame(
        np.column_stack([left.values[ia2.ravel()], right.values[ib2.ravel()]]))

Performance Comparison

Benchmarking these methods reveals that the NumPy-based implementations provide the fastest performance, particularly for larger datasets:

[Image of performance comparison chart]

Further Reading

For a deeper dive into Pandas merging operations, explore the following topics:

• [Merging basics](https://pbpython.com/pandas-merging-101-cheat-sheet.html)
• [Index-based joins](https://pbpython.com/pandas-merging-101-join-indexes.html)
• [Generalizing to multiple DataFrames](https://pbpython.com/pandas-merging-on-multiple-dataframes.html)

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