Your expectation of easy extension is unfounded.
If you want this function, I think you should write your own conjunction
for it and get some experience.
In my code, I have sometimes needed to transpose before an operation but
very seldom have I needed to transpose before and then transpose back.
Henry Rich
On 1/24/2022 12:06 AM, Elijah Stone wrote:
On Mon, 24 Jan 2022, Hauke Rehr wrote:
How many operations can be optimized
to not actually bring it to the front?
(special combinations wrt the t. family)
I expect that most verbs which currently have IRS (integrated rank
support) could be easily extended with integrated transpose support.
When I said 'harder to implement performantly', I was thinking of
virtual nouns for verbs _without_ IRS/ITS. But it occurs to me that
it is not actually significantly more work, though you do need a new
array representation. You need shape to be completely virtual, so |:
does not do any work. This approach is used in ngn/apl and described
at http://archive.vector.org.uk/art10501160.
(Though I think maintaining verbs with virtual shape over long periods
of time is probably a bad idea, because it makes it difficult to
reason about locality.)
-E
Not that many, I think. So it’s better
to actually
1. prepare your data layout and =: the result
2. apply an easily understood algorithm to it
… but I agree with your “advantages” section
Am 24.01.22 um 05:30 schrieb Elijah Stone:
Suppose I would like to normalise a vector. Easy: %+/&.:*:. Nice
and pretty, gotta love under.
What if I've got an array of vectors, and I want to normalise all of
them? There are two ways, corresponding to two different
representations: %+/&.:*:"1 and %"_1 _ +/&.:*:. The former
corresponds to an array where the last axis is the axis axis, and
the latter to an array where the leading axis is the axis axis
(which may seem odd, but I've found it useful).
There are two operations involved: a division and a reduction.
Neither of these _needs_ to be applied at rank, but we cannot avoid
ranking _both_ of them. Now suppose the axis axis is neither
leading nor trailing. Then we need: (%"_1 _ +/&.:*:)"n.
" is inherently eachy. That is not a bad thing--sometimes there are
eaches to be eached--but it does mean it is somewhat heavy-handed.
|: is an interesting alternative. %"_1 1 can be written as
%&.(0&|:`a:). And the sum can be performed moving the axis in
question to the front rather than to the back.
I therefore propose a 'transpose-ish' family of conjunctions. Say:
t. t: t.. t:: (RIP Taylor series). u t. n brings axis n to the
front (brings it near) before applying u; u t.. n brings axis n to
the rear (brings it far, hence the longer suffix); u t: n brings
axis n to the front before applying u, but returns it afterwards
(hence two dots); t:: should be obvious.
Advantages: encourages holistic, array-oriented thinking over eachy
thinking. Distinguishes rank's role as a vehicle for repetition
from its role as a general alternative to the axis operator. A
single application under transpose can replace nested applications
at rank.
Disadvantages: harder to teach. Maybe harder to understand (though
operations on high-dimensional arrays may be difficult to understand
regardless). Probably harder to implement performantly. I propose
too many primitives, and if The Powers That Be are not wise enough
to reject them all, they will turn the language into C++.
Thoughts?
-E
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