[Numpy-discussion] Create a n-D grid; meshgrid alternative

Jaime Fernández del Río jaime.frio at gmail.com
Tue May 12 08:01:26 EDT 2015

```On Tue, May 12, 2015 at 1:17 AM, Stefan Otte <stefan.otte at gmail.com> wrote:

> Hello,
>
> indeed I was looking for the cartesian product.
>
> I timed the two stackoverflow answers and the winner is not quite as clear:
>
> n_elements:    10  cartesian  0.00427 cartesian2  0.00172
> n_elements:   100  cartesian  0.02758 cartesian2  0.01044
> n_elements:  1000  cartesian  0.97628 cartesian2  1.12145
> n_elements:  5000  cartesian 17.14133 cartesian2 31.12241
>
> (This is for two arrays as parameters: np.linspace(0, 1, n_elements))
> cartesian2 seems to be slower for bigger.
>

On my system, the following variation on Pauli's answer is 2-4x faster than

def cartesian4(arrays, out=None):
arrays = [np.asarray(x).ravel() for x in arrays]
dtype = np.result_type(*arrays)

n = np.prod([arr.size for arr in arrays])
if out is None:
out = np.empty((len(arrays), n), dtype=dtype)
else:
out = out.T

for j, arr in enumerate(arrays):
n /= arr.size
out.shape = (len(arrays), -1, arr.size, n)
out[j] = arr[np.newaxis, :, np.newaxis]
out.shape = (len(arrays), -1)

return out.T

> I'd really appreciate if this was be part of numpy. Should I create a pull
> request?
>

There hasn't been any opposition, quite the contrary, so yes, I would go
ahead an create that PR. I somehow feel this belongs with the set
operations, rather than with the indexing ones. Other thoughts?

Also for consideration: should it work on flattened arrays? or should we
give it an axis argument, and then "broadcast on the rest", a la
generalized ufunc?

Jaime

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