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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