The APL Orchard

      a←40 20⍴⎕A ⋄ b←⎕C 30 50⍴⎕A
      ]runtime -c ↑a∘.,⍥(⊂⍤¯1)b "a,⍤99 ¯1⍤¯1 99⊢b"

  ↑a∘.,⍥(⊂⍤¯1)b    → 9.6E¯5 |   0% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕
  a,⍤99 ¯1⍤¯1 99⊢b → 2.9E¯5 | -70% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕

      ]runtime -c a∘.,⍥(⊂⍤¯1)b "↓a,⍤99 ¯1⍤¯1 99⊢b"

  a∘.,⍥(⊂⍤¯1)b      → 7.9E¯5 |   0% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕
  ↓a,⍤99 ¯1⍤¯1 99⊢b → 4.9E¯5 | -38% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕

So it isn't the final assembly (↑) that kills the native outer product.

Joseph Adams

8:43 AM

@Adám reading that article I'm blown away by the speed comparison of {⊂⍵} vs. ⊢∘⊂ as a left to stencil \_(⍥)_/

Joseph Adams

3:19 PM

@Adám haven't watched the presentation yet (though from the supporting material I'm gathering that it's mostly about @), but as an initial draft... Feedback welcome from all sides!

also note: I've no idea if there even ma be similar primitive in J/K/BQN etc, so I didn't mention those at all

RGS

@JosephAdams haven't read the whole thing, but I'll ~~steal~~ borrow some of it when I write about stencil in the MDAPL book :D

Joseph Adams

@RGS You're welcome to :D though I have to admit that, of course, much of the content is taken from the article by Roger Hui and the Dyalog Language doc :p

Adám

That's fine.

Wong Jia Hau

3:35 PM

Why is verb train invented?

Adám

@WongJiaHau You mean why were trains invented?

rak1507

jsoftware.com/papers/fork.htm

Wong Jia Hau

Yes, more specifically, why were they only invented in J but not APL?

rak1507

@WongJiaHau they are in APL, aplwiki.com/wiki/Tacit_programming

Wong Jia Hau

Oops, sorry my bad

Adám

3:41 PM

@WongJiaHau They were invented as a parallel to the traditional mathematical notation (f+g)(x) and were actually invented in APL, but first implemented in J.

Wong Jia Hau

@Adám in that sense can we say that trains are related to distributions?

Adám

@WongJiaHau You could say that, but it generalises the concept, much like f/ generalises Σ and Π.

Joseph Adams

4:00 PM

@Adám hmm that's something I don't understand (yet) -- could you elaborate how trains (or the like) generalize distributions (of which I recon you're talking about the distributions from stochastics)?

Adám

@JosephAdams Oh no, I'm taking about functions distributing over other functions: (f+g)(x) ≡ f(x)+g(x)

Joseph Adams

Ahh, sorry then I misunderstood -- so it's the distributive property in arithmetic. Thank you for clarifying!

user

@Adám Interesting, I didn't know this was also an instance of the distributive property

Adám

@user13999904 Hi Nils Lüschow. Email access@apl.chat if you want to participate here.

Joseph Adams

side note: in the code example immediately prior to here ⊢ is mentioned (to be used so that a value is printed) but you're assigning to quad instead in the example.

Adám

4:19 PM

@JosephAdams Fixed. Thanks.

Marshall

4:30 PM

@JosephAdams FYI (you don't have to write it up), Stencil is derived from case 3 of J's Cut (more detailed doc), with modifications. Everything I know of in any other language is more like Windowed Reduce than Stencil, although I don't know K very well.

Joseph Adams

@Marshall yes seems very similar besides having to pad the array ones-self if you want the centering that ⌺ does -- thanks for the pointer

Marshall

It's actually much older than that, appearing in Rationalized APL and later A Dictionary of APL (search for "tesselations").

Adám

@JosephAdams Conversely, getting ⌺ to use the top left corner of the input array as the top left corner of the first window is major work.

Joseph Adams

I guess in that regard J's cut is in fact better :P suppose the major work is figuring out how much larger one has to choose the rectangles so you can chop away the padding

oh, though not quite -- the inner rectangles then are too large too...hmmm does seem quite bad after all

Adám

You have to pad the input array.

Joseph Adams

4:40 PM

@Marshall s/first link/for this one/ if anyone's reading along

Marshall

Fortunately, McDonnell discusses it a little here, where he claims Rationalized APL is the first appearance. He would know.

@JosephAdams That's right, thanks (just outside the edit window).

Adám

Luckily, there is plenty of "design space" in ⌺ to allow specification of starting point. E.g. it could be specified as an offset in a third row of the right operand.

mo523

9:32 PM

@Adám I most definitely am. I touched on it briefly in school and have since been planning on spending some time learning it in depth. Finally have the time this summer.
I just ordered the Dyalog APL book which Amazon says is coming Monday.
I'll probably start hanging out around here with questions :)

rak1507

in school?!

mo523

Yes. Took a programming languages class.
Was one of the 'obscure' languages we learned a bit about

rak1507

Ah, cool!

you might be interested in dyalogaplcompetition.com/?goto=welcome

mo523

Actually just saw that and will definitely be trying out the problems, but I've graduated already so not eligible for the prize (not that I think I have a chance this early into my apl education)

Thanks for sending it though

rak1507

ah, shame, still fun to do the problems though

mo523

9:40 PM

Ya, I've done the acm contests a few times so looking forward to these problems

user

Use APL to hack into the government and pretend you're in some fake school :P

rak1507

@mo523 they're quite different to regular competitive programming stuff, much more marked on style than speed or accuracy

well, accuracy probably is the number one thing

mo523

It's the style that drew me to apl
We had a hw to get the avg of a 2d array and that's when it clicked for me. Went from 'what is this "language"' to 'wow'

rak1507

nice

mo523

My solution was 10 characters (I'm sure it can be done even better) which is worlds cooler than using nested for loops with a bunch of variables.

@Adám btw what made you ping me? Did you just notice I was here and reached out? Just curious

hyper-neutrino

9:47 PM

Ooh, I might take a look at this competition. I've written like 3 answers in APL total though :P

rak1507

what was the exact problem? flatten the array and then take the average, or average each row/column?

@mo523 yep

mo523

I'll look up the problem. Should only take a min

M is the matrix representing the body of the average seasonal temperature. (table shown below)

Chicago 47.8 72.3 55.2 25.0
Houston 68.5 82.3 71.2 54.7
San Francisco 55.5 77.8 59.5 34.4

c) Write a function to determine
iv. Over-all average temperature

@rak1507 Cool beans. Very nice of you

rak1507

I'm not Adám, but that's why he pinged you

mo523

Thanks. had a feeling that's what you meant

rak1507

here's something fun, the average of a 1d list is (+/÷≢) aplwiki.com/wiki/Tacit_programming

hyper-neutrino

9:53 PM

eh, kind of a silly question, but how do i write a matrix as a literal? i tried a bunch of ways but all of them either fail or just give a flat list, i'm a bit confused because i don't remember doing this before :P

rak1507

@hyper-neutrino you don't, either use ⍴ or ↑ like ↑(1 2 3)(4 5 6)(7 8 9)

hyper-neutrino

ah. okay

rak1507

proposed new array notation will allow matrix literals (and other cool stuff too)

hyper-neutrino

@mo523 you mentioned you had a 10-byter

i got 10 as well with {(+⌿÷≢),⍵}, is this what you had too? :P

mo523

My solution was this (given my very very limited apl knowledge)
+/+/M÷×/⍴M
Get the sum of the sum of the array (so 2d down to 1d down to a single total)
Divided by the product of the dimensions of the array (so total elements)
ergo: sum/count

@hyper-neutrino lol I don't know what half those symbols do

rak1507

9:57 PM

ooh, this is actually quite interesting given that the array is in a variable

hyper-neutrino

@mo523 ah, lol. well it's just sum / length of the matrix flattened into a vector

rak1507

I think the shortest solution is M⌹⍥,M=M

hyper-neutrino

(is this what we call a dfn?)

rak1507

yes

(+/÷≢), works too as (f g) is an atop

hyper-neutrino

ah

rak1507

9:59 PM

the simplest solution is probably (+/,M)÷≢,M which is basically what you had, just using , to flatten the array

mo523

I'm totally lost :)

user

@rak1507 Might not want to show them trains just yet

rak1507

@user no trains there

user

Oops, wrong message

hyper-neutrino

@rak1507 is the () necessary?

user

10:00 PM

It's right associative

rak1507

@user ah fair enough I was replying to hyper there

hyper-neutrino

{+⌿,⍵÷≢,⍵} seemed to work when i tested on tryapl

rak1507

@hyper-neutrino nice coincidence

hyper-neutrino

lol

rip

mo523

I'll need to come back to this once I actually start learning apl

Adám

10:01 PM

@mo523 Indeed. I do that, as some feel too intimidated to chat.

rak1507

if your array is (a b c), that's +/(a÷3) (b÷3) (c÷3), which is correct, but it's not the same as (+/a b c)÷3

hyper-neutrino

ah wait, this is sum(flat(matrix / len(flat(matrix)))) isn't it?

instead of sum(flat(matrix)) / len(flat(matrix)) like intended?

rak1507

yea

mo523

Very much appreciated. Though it was more just checking out the community that I hope to join soon than intimidation.

As an aside, is there any way I can pm you?

Adám

@mo523 On Stack Exchange, all messages are public, but you can email me: adam@ with the domain of www.dyalog.com

mo523

10:06 PM

Cool thanks will do

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