Using numpy to build an array of all combinations of two arrays

In newer version of numpy (>1.8.x), numpy.meshgrid() provides a much faster implementation:

@pv's solution

In [113]:

%timeit cartesian(([1, 2, 3], [4, 5], [6, 7]))
10000 loops, best of 3: 135 µs per loop
In [114]:

cartesian(([1, 2, 3], [4, 5], [6, 7]))

Out[114]:
array([[1, 4, 6],
       [1, 4, 7],
       [1, 5, 6],
       [1, 5, 7],
       [2, 4, 6],
       [2, 4, 7],
       [2, 5, 6],
       [2, 5, 7],
       [3, 4, 6],
       [3, 4, 7],
       [3, 5, 6],
       [3, 5, 7]])

numpy.meshgrid() use to be 2D only, now it is capable of ND. In this case, 3D:

In [115]:

%timeit np.array(np.meshgrid([1, 2, 3], [4, 5], [6, 7])).T.reshape(-1,3)
10000 loops, best of 3: 74.1 µs per loop
In [116]:

np.array(np.meshgrid([1, 2, 3], [4, 5], [6, 7])).T.reshape(-1,3)

Out[116]:
array([[1, 4, 6],
       [1, 5, 6],
       [2, 4, 6],
       [2, 5, 6],
       [3, 4, 6],
       [3, 5, 6],
       [1, 4, 7],
       [1, 5, 7],
       [2, 4, 7],
       [2, 5, 7],
       [3, 4, 7],
       [3, 5, 7]])

Note that the order of the final resultant is slightly different.

Here's a pure-numpy implementation. It's about 5× faster than using itertools.

Python 3:

import numpy as np

def cartesian(arrays, out=None):
    """
    Generate a cartesian product of input arrays.

    Parameters
    ----------
    arrays : list of array-like
        1-D arrays to form the cartesian product of.
    out : ndarray
        Array to place the cartesian product in.

    Returns
    -------
    out : ndarray
        2-D array of shape (M, len(arrays)) containing cartesian products
        formed of input arrays.

    Examples
    --------
    >>> cartesian(([1, 2, 3], [4, 5], [6, 7]))
    array([[1, 4, 6],
           [1, 4, 7],
           [1, 5, 6],
           [1, 5, 7],
           [2, 4, 6],
           [2, 4, 7],
           [2, 5, 6],
           [2, 5, 7],
           [3, 4, 6],
           [3, 4, 7],
           [3, 5, 6],
           [3, 5, 7]])

    """

    arrays = [np.asarray(x) for x in arrays]
    dtype = arrays[0].dtype

    n = np.prod([x.size for x in arrays])
    if out is None:
        out = np.zeros([n, len(arrays)], dtype=dtype)

    #m = n / arrays[0].size
    m = int(n / arrays[0].size) 
    out[:,0] = np.repeat(arrays[0], m)
    if arrays[1:]:
        cartesian(arrays[1:], out=out[0:m, 1:])
        for j in range(1, arrays[0].size):
        #for j in xrange(1, arrays[0].size):
            out[j*m:(j+1)*m, 1:] = out[0:m, 1:]
    return out

Python 2:

import numpy as np

def cartesian(arrays, out=None):
    arrays = [np.asarray(x) for x in arrays]
    dtype = arrays[0].dtype

    n = np.prod([x.size for x in arrays])
    if out is None:
        out = np.zeros([n, len(arrays)], dtype=dtype)

    m = n / arrays[0].size
    out[:,0] = np.repeat(arrays[0], m)
    if arrays[1:]:
        cartesian(arrays[1:], out=out[0:m, 1:])
        for j in xrange(1, arrays[0].size):
            out[j*m:(j+1)*m, 1:] = out[0:m, 1:]
    return out