merge a vector and 2, 3 matrix to form 3 3 matrix?

@elliptic00 1 2 3⍪2 3⍴?⍨10

I mean I'm given a vector and a matrix, I'm looking for something like merge(vector, matrix) => 3, 3 matrix

I think one way to do is to flatten the matrix to a vector and concatenate two vector and take rank 3 3 to recreate the 3 3 matrix.. is there a way to without any flattening?

@elliptic00 That is exactly what the expression I gave you does. You simply use the primitive function "laminate" which is represented by the symbol "comma-bar"

@PaulMansour That's actually "concatenate [along the] first [axis]". Laminate adds new axes, and is spelled ,[ax] or ⍪[ax]

Thanks, it works, I just did not realize the symbol is "comma-bar", I though ","

it is hard to see the different "," and "comma-bar" from the screen :)

The next obvious question how to merge a column vector with a matrix?

It seems the "comma-bar" only for row vector?

I mean If you don't want to transpose them and transpose them back,

@elliptic00 , comma would just that

m←2 3⍴1 2 3 4 5 6

c←⍪1 2

    m,c
6 1 7 1
3 4 2 2

I think there're some old books such as APL An Interactive Approach covers these array basics

@elliptic00 you might also want to take a look at mastering.dyalog.com/Some-Primitive-Functions.html#concatenate

youtube.com/watch?v=6NvNtYChIo8 this'll be interesting

can't wait for when it premieres at 2AM

haha rip

it's at 10 pm for me which is reasonable

It premieres at 4 am for me

@rak1507 Same here, but that doesn't mean I'll be available to watch it live :(

Wait, is that a video that will premiere or is it a stream?

I can use ⎕ED to open the editor

How can I close it right away?

I found the following in APLCart for finding the most frequent major cell: {⍵⌷⍨⊂0~⍨⊢/0,⊢⌸⍵} -- took me a few minutes of staring at it to understand, but that's very clever I thought.

@RGS What are you doing?

@xpqz It is to avoid computing the unique cells twice. The obvious approach, using ⌸ to select from ∪, does that.

@Adám I want to open the editor, close it, and then open it again :P

Because?

@Adám I want to fight the issue with Link that ignores my whitespace for the first time I Fix a function

:P

@RGS Just update Link!

Why would I do that when I can just fight the system?

Yeah, heading over to GH would do it, right?

Yup, or use 18.1.

18.1 is a hero release in my book.

By me too. So many quality-of-life improvements.

Current QoL favourite: ]repr

@xpqz Do you have the newest version that handles functions too?

How do you mean?

Tied first place: ]APLCart :)

@xpqz Like:

      avg←{
       +⌿⍵
       }÷1⌈≢
      ]repr avg -f=apl
 avg←{
     +⌿⍵
 }÷(1⌈≢)

      avg←{+⌿⍵}÷1⌈≢
      ]repr avg -f=apl
┌→───────────────────────────────────────┐
↓* Command Execution Failed: SYNTAX ERROR│
└────────────────────────────────────────┘

Looks like a no.

@xpqz That even works without -f=apl:

      avg←{+⌿⍵}÷1⌈≢
      ]repr avg
 avg←{+⌿⍵}÷(1⌈≢)

@Adám It looks like the bug only happens if I open a blank editor. If I open the editor but provide the lines '∇ fnName' '∇' to it, it will always respect my whitespace :') So I didn't have to open the editor twice nor update link :P

@Adám speaking of {⍵⌷⍨⊂0~⍨⊢/0,⊢⌸⍵}, why is the 0, there? For the examples I've tried it seems to work without.

@xpqz Did you try an empty argument?

Is this a leading question :)

(I assumed the 0 took care of some empty edge-cases, hence the Q)

DOMAIN ERROR

@xpqz ?

You're right, basically.

Without the 0, it DOMAIN ERRORs on empties.

I thought your DOMAIN ERROR was APL erroring when you tried the whole dfn on empty args

I also had a quick go at it right now and it does seem to me that the 0 is taking care of empty things.

Yes, so it seems.

Otherwise you'll get ∞

Why do I get

      {⍵⌷⍨⊂0~⍨⊢/0,⊢⌸⍵}1 2 3
1 2 3

Aren't the major cells of 1 2 3 the scalars?

@RGS not sure, I think it's a stream

Also interesting to note that, somehow, the code acts in a funky way if ⎕IO←0 and the input arg is a vector with only unique scalars

      ⎕IO ← 0 ⋄ {⍵⌷⍨⊂0~⍨⊢/0,⊢⌸⍵}1 2 3
2 3

@RGS it returns all distinct elements with the highest frequency

@RGS APLcart is ⎕IO←1-only

@dzaima yeah but I find it funny that it works well for all other cases

At the expense of two extra bytes the function could be ⎕IO-independent

      ⎕IO ← 0 ⋄ {⍵⌷⍨⊂¯1~⍨⊢/¯1,⊢⌸⍵}1 2 3
1 2 3

@RGS that fails for pretty much everything else (e.g. 1 1 2)

@dzaima wait really?

the idea is that it relies on the implicit ↑ in ⌸ padding with 0s at the end

What have I done :P

Ok, I should have said "At the expense of two extra bytes, we can screw up the function", but that's not an impressive feat...

@dzaima thanks for the explanation

Oh wow so I only fully understood what the dfn does now

it is really clever!

@RGS yes, that's what I thought. No sorting.

@xpqz in the back of my mind I knew ⌸ was collecting the indices where each major cell appears and I thought we were looking for the major cells where those collections of indices were larger... but the way we determine the collections which are larger is amazing :D

@xpqz unfortunately, it comes at the cost of being worst-case O(n^2)

Hats off to Adám or whoever wrote this wonder.

@dzaima why is it quadratic?

@xpqz worst case is when all major cells are different and because there was no sorting, major cell i is compared with all the i-1 major cells that precede it

Over a vector of size n, this gives 2÷⍨n×n-1 comparisons, which is quadratic.

(I might be off by one)

@xpqz it needs to build a matrix with as many rows as unique elements, and as many columns as the count of the most frequent element

@RGS all distinct is still O(nlogn)

@dzaima is there implicit sorting, then?

@dzaima (e.g. {⍵⌷⍨⊂0~⍨⊢/0,⊢⌸⍵} (⍳,⍴∘1)20000 WS FULLs on the default 256MB heap)

So what is the fastest possible way of doing this?

@RGS ⌸ does whatever it needs to to be fast

(with key)

@dzaima but the shape of that matrix is such that +/⍴matrix≤≢input_vector, right?

Or what am I missing.

(i.e. the number of rows + the number of columns is ≤ the length of the input vector)

@RGS you need ×/⍴ not +/⍴ to know how large a matrix is

I know, I was not counting the number of elements inside the matrix

I was stating a constraint on its shape

@dzaima APLCart also has this:

((⊣/⊢⍤/⍨∘(⌈/=⊢)⊢/){⍺(≢⍵)}⌸)Y

Whilst I haven't had a chance to fully decode that, it looks as if it should not be quadratic.

as it counts the occurrences and finds the max

@RGS more like +/⍴matrix≤1+≢input_vector probably. But that constraint doesn't constrain it much

@xpqz yeah, that should be better

@dzaima Right, off by one.

Ok, so if the sum of the rows and columns is constrained, then the worst-case (as far as memory goes) should occur when all elements are unique, except one of them that occurs in half of the vector, as that should give a matrix with size approximately 4÷⍨n*2

(And that's because when you want to maximise the product a×b with a+b capped at S, you pick a←b←S÷2, cf. mathspp.com/blog/twitter-proofs/maximising-product-fixed-sum)

@RGS right. that's exactly what my example does

@dzaima Yeah, it all makes sense now

You just have to give time to the commoners to catch up

(i didn't intentionally make my example to be maximally bad, but a non-optimally bad example would be harder to come up with)

How is it that I downloaded the Dyalog IDE all of 7 days ago and it gave me 18.0

Mostly rhetorical, just means I get to change versions

because 18.1 isn't released yet

... Oh that'll do it

I thought I missed a release