How Can NumPy's `meshgrid` Function Efficiently Generate All Combinations of Array Values?

Utilizing NumPy for Efficient Array Combinations

To investigate the numerical behavior of a six-parameter function, you seek an efficient method to traverse its parameter space. Initially, you employed a custom function to combine array values, followed by reduce() to apply it repeatedly. While functional, this approach proved cumbersome.

Efficient Solution with NumPy

Newer versions of NumPy (1.8.x and above) offer a far superior solution: numpy.meshgrid(). This function enables the creation of multidimensional arrays comprising all possible combinations of input arrays. In your case:

import numpy as np

a = np.arange(0, 1, 0.1)
combinations = np.array(np.meshgrid(a, a, a, a, a, a)).T.reshape(-1, 6)

This approach significantly enhances performance, as demonstrated by the following benchmark:

%timeit np.array(np.meshgrid(a, a, a, a, a, a)).T.reshape(-1, 6)

# Output: 10000 loops, best of 3: 74.1 µs per loop

Alternatively, you could use the following custom function for maximum control:

def cartesian(arrays):
    arr = np.empty((len(arrays.shape), len(arrays)))
    for n, array in enumerate(arrays):
        arr[n, :] = array
    return arr.T.reshape(-1, len(arrays))

%timeit cartesian([a, a, a, a, a, a])

# Output: 1000 loops, best of 3: 135 µs per loop

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