On Wed, 5 Jul 2023 at 11:18, <ha...@interia.pl> wrote:
>
>
> Python has the "star" ("*") operator for multiplication. In the context of
> collections it is supposed to mean element-wise multiplication. Its
> associated operator is __mul__. It also has the double star ("**") operator
> for exponentiation, which is repeated multiplication. Its associated operator
> is __exp__.
>
> In addition to that Python has the "at" ("@") operator for multiplication. In
> the context of collections it should mean linear product, like matrix times a
> matrix, or matrix times vector. Its associated method is __matmul__.
>
> For completeness we should now have the exponentiation operator meaning
> repeated application of the "at" operator. Its method could me __matexp__.
This was discussed at the time of the PEP that introduced matmul:
https://peps.python.org/pep-0465/#non-definition-of-matrix-power
Quote:
"""
Earlier versions of this PEP also proposed a matrix power operator,
@@, analogous to **. But on further consideration, it was decided that
the utility of this was sufficiently unclear that it would be better
to leave it out for now, and only revisit the issue if – once we have
more experience with @ – it turns out that @@ is truly missed.
"""
It has been nearly 10 years which I guess is enough time to revisit
but most likely the numpy-discussion mailing list is the place to
start that discussion:
https://mail.python.org/mailman3/lists/numpy-discussion.python.org/
I think that the original authors wanted @@ and also other operators.
At the time there had been previous more ambitious PEPs proposing many
more operators or custom operators but those were rejected at least
partly for being too broad. As I remember it there was a conscious
effort to make PEP 465 as minimal as possible just to make sure that
at least the @ operator got accepted.
Matrix powers are not as widely used as matrix multiplication and
probably the most common use would be M@@-1 as a strange looking
version of M^-1 which would otherwise be spelled as np.linalg.inv(M).
It is usually a bad idea to compute matrix inverses though
(np.linalg.solve(a, b) is both faster and more accurate than
np.linalg.inv(a)*b). Matlab uses left and right division like a\b and
a/b for this but NumPy etc already define a/b to mean elementwise
division and then having a new operator a\b mean something completely
different from a/b might be confusing.
I think that the people who would have wanted to push forward with
things like this have probably reduced the scope of what seems
possible to the extent that the only thing left to do is to possibly
add @@. If that is all that is on the table then it possibly does not
have enough value to be worth the effort of a language change. On the
other hand it is a relatively small change since @ is already added.
--
Oscar
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