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

Stefan Otte stefan.otte at gmail.com
Tue May 12 09:29:10 EDT 2015

```Hey,

here is an ipython notebook with benchmarks of all implementations (scroll
to the bottom for plots):

https://github.com/sotte/ipynb_snippets/blob/master/2015-05%20gridspace%20-%20cartesian.ipynb

Overall, Jaime's version is the fastest.

On Tue, May 12, 2015 at 2:01 PM Jaime Fernández del Río <
jaime.frio at gmail.com> wrote:

> 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 his for your test cases:
>
> 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
>
> --
> (\__/)
> ( O.o)
> ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes
> de dominación mundial.
>  _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at scipy.org
> http://mail.scipy.org/mailman/listinfo/numpy-discussion
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/numpy-discussion/attachments/20150512/2f5df59d/attachment.html>
```