How Can I Efficiently Perform a Cartesian Product (CROSS JOIN) in Pandas?

Efficient Cartesian Product (CROSS JOIN) in Pandas

Introduction:

Cartesian product, also known as CROSS JOIN, is a fundamental operation in data analysis. In pandas, it involves combining every row of one DataFrame with every row of another. While simple to understand, calculating the Cartesian product directly can be computationally expensive, especially for large datasets.

Best Practices:

1. The 'key' Column Method:

This approach works well for small to medium-sized datasets:

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

2. NumPy-Based Solutions:

For larger datasets, NumPy-based solutions offer better performance:

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)  

3. Generalized CROSS JOIN for Unique and Non-Unique Indices:

This method can handle DataFrames with any type of index:

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]]]))

4. Multi-DataFrame CROSS JOIN:

This extends the previous approach to handle multiple DataFrames:

def cartesian_product_multi(*dfs):
    idx = cartesian_product(*[np.ogrid[:len(df)] for df in dfs])
    return pd.DataFrame(
        np.column_stack([df.values[idx[:,i]] for i,df in enumerate(dfs)]))

5. Simplified CROSS JOIN for Two DataFrames:

This method, which is almost as fast as @senderle's cartesian_product, is particularly effective for two DataFrames:

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 on varying dataset sizes reveals that the NumPy-based solutions consistently outperform the others for large datasets.

Conclusion:

Choosing the right method for computing the Cartesian product in pandas depends on the size and characteristics of your datasets. If performance is a priority, opt for one of the NumPy-based solutions. For convenience and flexibility, consider the 'key' column method or the generalized CROSS JOIN.

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