[Numpy-discussion] It looks like Py 3.5 will include a dedicated infix matrix multiply operator

[Anthony Scopatz]

This is awesome!  Congrats!


On Sun, Mar 16, 2014 at 9:39 AM, Eelco Hoogendoorn <
hoogendoorn.eelco at gmail.com> wrote:

> Note that I am not opposed to extra operators in python, and only mildly
> opposed to a matrix multiplication operator in numpy; but let me lay out
> the case against, for your consideration.
>
> First of all, the use of matrix semantics relative to arrays semantics is
> extremely rare; even in linear algebra heavy code, arrays semantics often
> dominate. As such, the default of array semantics for numpy has been a
> great choice. Ive never looked back at MATLAB semantics.
>
> Secondly, I feel the urge to conform to a historical mathematical notation
> is misguided, especially for the problem domain of linear algebra. Perhaps
> in the world of mathematics your operation is associative or commutes, but
> on your computer, the order of operations will influence both outcomes and
> performance. Even for products, we usually care not only about the outcome,
> but also how that outcome is arrived at. And along the same lines, I don't
> suppose I need to explain how I feel about A@@-1 and the likes. Sure, it
> isn't to hard to learn or infer this implies a matrix inverse, but why on
> earth would I want to pretend the rich complexity of numerical matrix
> inversion can be mangled into one symbol? Id much rather write inv or pinv,
> or whatever particular algorithm happens to be called for given the
> situation. Considering this isn't the num-lisp discussion group, I suppose
> I am hardly the only one who feels so.
>
> On the whole, I feel the @ operator is mostly superfluous. I prefer to be
> explicit about where I place my brackets. I prefer to be explicit about the
> data layout and axes that go into a (multi)linear product, rather than rely
> on obtuse row/column conventions which are not transparent across function
> calls. When I do linear algebra, it is almost always vectorized over
> additional axes; how does a special operator which is only well defined for
> a few special cases of 2d and 1d tensors help me with that? On the
> whole, the linear algebra conventions inspired by the particular
> constraints of people working with blackboards, are a rather ugly and hacky
> beast in my opinion, which I feel no inclination to emulate. As a sidenote
> to the contrary; I love using broadcasting semantics when writing papers.
> Sure, your reviewers will balk at it, but it wouldn't do to give the
> dinosaurs the last word on what any given formal language ought to be like.
> We get to define the future, and im not sure the set of conventions that
> goes under the name of 'matrix multiplication' is one of particular
> importance to the future of numerical linear algebra.
>
> Note that I don't think there is much harm in an @ operator; but I don't
> see myself using it either. Aside from making textbook examples like a
> gram-schmidt orthogonalization more compact to write, I don't see it having
> much of an impact in the real world.
>
>
> On Sat, Mar 15, 2014 at 3:52 PM, Charles R Harris <
> charlesr.harris at gmail.com> wrote:
>
>>
>>
>>
>> On Fri, Mar 14, 2014 at 6:51 PM, Nathaniel Smith <njs at pobox.com> wrote:
>>
>>> Well, that was fast. Guido says he'll accept the addition of '@' as an
>>> infix operator for matrix multiplication, once some details are ironed
>>> out:
>>>   https://mail.python.org/pipermail/python-ideas/2014-March/027109.html
>>>   http://legacy.python.org/dev/peps/pep-0465/
>>>
>>> Specifically, we need to figure out whether we want to make an
>>> argument for a matrix power operator ("@@"), and what
>>> precedence/associativity we want '@' to have. I'll post two separate
>>> threads to get feedback on those in an organized way -- this is just a
>>> heads-up.
>>>
>>>
>> Surprisingly little discussion on python-ideas, or so it seemed to me.
>> Guido came out in favor less than halfway through. Congratulations on
>> putting together a successful proposal, many of us had given up on ever
>> seeing a matrix multiplication operator.
>>
>> Chuck
>>
>>
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>
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