How to Efficiently Create a Cartesian Product of Pandas DataFrames?

Cartesian Product in Pandas: Best Practices and Solutions

When working with Pandas dataframes, it is often necessary to create the Cartesian product of two or more dataframes. This can be a useful operation for combining data from multiple sources or exploring the relationships between different variables.

The Cross Merge Method

In recent versions of Pandas (>= 1.2), the cross merge method provides a convenient way to compute the Cartesian product of two dataframes. To use this method, simply call the merge function with the how='cross' argument:

import pandas as pd

df1 = pd.DataFrame({'col1': [1, 2], 'col2': [3, 4]})
df2 = pd.DataFrame({'col3': [5, 6]})

df_cartesian = pd.merge(df1, df2, how='cross')

The resulting dataframe, df_cartesian, will contain all combinations of rows from df1 and df2, resulting in a Cartesian product.

Using Repeated Keys in Merge

For versions of Pandas prior to 1.2, it was necessary to use a slightly different approach to create the Cartesian product. This approach involved using repeated keys in one of the dataframes and then merging on those keys:

df1 = pd.DataFrame({'key': [1, 1], 'col1': [1, 2], 'col2': [3, 4]})
df2 = pd.DataFrame({'key': [1, 1], 'col3': [5, 6]})

df_cartesian = pd.merge(df1, df2, on='key')[['col1', 'col2', 'col3']]

By creating a key that is repeated for each row in both dataframes, we can effectively perform a Cartesian product by merging on that key.

Conclusion

Whether you are using Pandas >= 1.2 or an earlier version, the methods described above provide efficient ways to create the Cartesian product of two or more dataframes. Depending on the specific version of Pandas you are using, one approach may be more convenient or efficient than the other.

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