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

[josef.pktd at gmail.com]

On Sun, Mar 16, 2014 at 10:54 AM, Nathaniel Smith <njs at pobox.com> wrote:

> On Sun, Mar 16, 2014 at 2:39 PM, 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.
>
> Different people work on different code and have different experiences
> here -- yours may or may be typical yours. Pauli did some quick checks
> on scikit-learn & nipy & scipy, and found that in their test suites,
> uses of np.dot and uses of elementwise-multiplication are ~equally
> common: https://github.com/numpy/numpy/pull/4351#issuecomment-37717330h
>
> > 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.
> >
>
> My impression from the other thread is that @@ probably won't end up
> existing, so you're safe here ;-).
>
> > 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?
>
> Einstein notation is coming up on its 100th birthday and is just as
> blackboard-friendly as matrix product notation. Yet there's still a
> huge number of domains where the matrix notation dominates. It's cool
> if you aren't one of the people who find it useful, but I don't think
> it's going anywhere soon.
>
> > 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.
>
> The analysis in the PEP found ~780 calls to np.dot, just in the two
> projects I happened to look at. @ will get tons of use in the real
> world. Maybe all those people who will be using it would be happier if
> they were using einsum instead, I dunno, but it's an argument you'll
> have to convince them of, not me :-).
>

Just as example

I just read for the first time two journal articles in econometrics that
use einsum notation.
I have no idea what their formulas are supposed to mean, no sum signs and
no matrix algebra.
I need to have a strong incentive to stare at those formulas again.

(statsmodels search finds 1520 "dot", including sandbox and examples)

Josef
<TODO: learn how to use einsums>


>
> -n
>
> --
> Nathaniel J. Smith
> Postdoctoral researcher - Informatics - University of Edinburgh
> http://vorpus.org
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