[Numpy-discussion] matmul as a ufunc

[Eric Wieser]

which ensure that it is still well defined (as the identity) on 1d arrays.

This strikes me as a bad idea. There’s already enough confusion from
beginners that array_1d.T is a no-op. If we introduce a matrix-transpose,
it should either error on <1d inputs with a useful message, or insert the
extra dimension. I’d favor the former.

Eric

On Mon, 28 May 2018 at 16:27 Stephan Hoyer shoyer at gmail.com
<http://mailto:shoyer@gmail.com> wrote:

On Mon, May 21, 2018 at 5:42 PM Matti Picus <matti.picus at gmail.com> wrote:
>
>> - create a wrapper that can convince the ufunc mechanism to call
>> __array_ufunc__ even on functions that are not true ufuncs
>>
>
> I am somewhat opposed to this approach, because __array_ufunc__ is about
> overloading ufuncs, and as soon as we relax this guarantee the set of
> invariants __array_ufunc__ implementors rely on becomes much more limited.
>
> We really should have another mechanism for arbitrary function overloading
> in NumPy (NEP to follow shortly!).
>
>
>> - expand the semantics of core signatures so that a single matmul ufunc
>> can implement matrix-matrix, vector-matrix, matrix-vector, and
>> vector-vector multiplication.
>
>
> I was initially concerned that adding optional dimensions for gufuncs
> would introduce additional complexity for only the benefit of a single
> function (matmul), but I'm now convinced that it makes sense:
> 1. All other arithmetic overloads use __array_ufunc__, and it would be
> nice to keep @/matmul in the same place.
> 2. There's a common family of gufuncs for which optional dimensions like
> np.matmul make sense: matrix functions where 1D arrays should be treated as
> 2D row- or column-vectors.
>
> One example of this class of behavior would be np.linalg.solve, which
> could support vectors like Ax=b and matrices like Ax=B with the signature
> (m,m),(m,n?)->(m,n?). We couldn't immediately make np.linalg.solve a gufunc
> since it uses a subtly different dispatching rule, but it's the same
> use-case.
>
> Another example would be the "matrix transpose" function that has been
> occasionally proposed, to swap the last two dimensions of an array. It
> could have the signature (m?,n)->(n,m?), which ensure that it is still well
> defined (as the identity) on 1d arrays.
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