Hi,
I have just sent a PR (
https://github.com/numpy/numpy/pull/5015), adding the possibility of having frozen dimensions in gufunc signatures. As a proof of concept, I have added a `cross1d` gufunc to `numpy.core.umath_tests`:
In [1]: import numpy as np
In [2]: from numpy.core.umath_tests import cross1d
In [3]: cross1d.signature
Out[3]: '(3),(3)->(3)'
In [4]: a = np.random.rand(1000, 3)
In [5]: b = np.random.rand(1000, 3)
In [6]: np.allclose(np.cross(a, b), cross1d(a, b))
Out[6]: True
In [7]: %timeit np.cross(a, b)
10000 loops, best of 3: 76.1 us per loop
In [8]: %timeit cross1d(a, b)
100000 loops, best of 3: 13.1 us per loop
In [9]: c = np.random.rand(1000, 2)
In [10]: d = np.random.rand(1000, 2)
In [11]: cross1d(c, d)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-11-72c66212e40c> in <module>()
----> 1 cross1d(c, d)
ValueError: cross1d: Operand 0 has a mismatch in its core dimension 0, with gufunc signature (3),(3)->(3) (size 2 is different from 3)
The speed up over `np.cross` is nice, and while `np.cross` is not the best of examples, as it needs to handle more sizes, in many cases this will allow producing gufuncs that work without a Python wrapper redoing checks that are best left to the iterator, such as dimension sizes.
It still needs tests, but before embarking on fully developing those, I wanted to make sure that there is an interest on this.
I would also like to further enhance gufuncs providing computed dimensions, e.g. making it possible to e.g. define `pairwise_cross` with signature '(n, 3)->($m, 3)', where the $ indicates that m is a computed dimension, that would have to be calculated by a function passed to the gufunc constructor and stored in the gufunc object, based on the other core dimensions. In this case it would make $m be n*(n-1), so that all pairwise cross products between 3D vectors could be computed.
The syntax with '$' is kind of crappy, so any suggestions on how to better express this in the signature are more than welcome, as well as any feedback on the merits (or lack of them) of implementing this.
Jaime
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