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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 | |
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 |
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