The APL Orchard

elliptic00

03:49

 m ← 2 3 4 ⍴ ⍳ 24
      m
 1  2  3  4
 5  6  7  8
 9 10 11 12

13 14 15 16
17 18 19 20
21 22 23 24
      ⌽m
 4  3  2  1
 8  7  6  5
12 11 10  9

16 15 14 13
20 19 18 17
24 23 22 21
      ⊖⍤1⊢m
 4  3  2  1
 8  7  6  5
12 11 10  9

16 15 14 13
20 19 18 17
24 23 22 21

⍝ Why we still need ⌽, it seems to me ⊖ can do eveything ⌽ can do

What ⌽ can do, but ⊖ can not do?

⍝ ⌽ can not specify any rank?

user

04:11

Sugar, I suppose? Specifying the axis when you want the other would be annoying

elliptic00

07:00

Assume we have rank 3 arround, x => row, y = colum and z-axis, which one is leading axis?

x is leading axis?

Itay123

07:46

any way to use ' inside a character vector

RGS

09:16

@Itay123 Just double it: ⋄ 'I''m happy to help'

TryAPL

@RGS I'm happy to help

RGS

@elliptic00 The “columns” are the last axis always, the rows are the axis that precedes it, and what I think you are calling the “z-axis” is actually the first one. Take a look at this 3D array: ⋄ 2 3 4⍴⍳24

TryAPL

@RGS
 1  2  3  4
 5  6  7  8
 9 10 11 12

13 14 15 16
17 18 19 20
21 22 23 24

RGS

Its shape is 2 3 4. It has 2 slices, that we see here as two matrices separated by a blank line. The leading axis contains these slices, so the leading axis here has length 2.

Then each “matrix” or “slice” or “plane” contains 3 rows (the second axis) and 4 columns (the third, and last, axis).

elliptic00

@RGS nice, thanks,

RGS

09:19

Take a look at the diagram in here: https://course.dyalog.com/Array-model/#rank-vs-axis
It should help you out. The diagram uses the 3D array `2 3 4⍴⎕A` instead of the integers.

@elliptic00 You are right, ⌽ and ⊖ do the “same” thing, except they have a different default axis. But you can use axis specification on both.

elliptic00

⍝ ⊖ uses the leading axis by default
      ⍝ ⌽ uses the last axis 'by default' -> not sure about that, I can not specify axis for ⌽

RGS

You could delete one, or the other, from the APL keyboard :P But it's a nice amenity, to have ⌽ to rotate along the last axis. You can always write ⊖ as ⌽[1], but writing ⌽ in terms of ⊖ requires that you take a look at the array: ⌽array ←→ ⊖[≢⍴array] array

@elliptic00 You can specify an axis for ⌽: ⋄ ⌽[1]3 4⍴⎕A

TryAPL

@RGS
IJKL
EFGH
ABCD

RGS

See? I used ⌽ as “rotate first”.

elliptic00

⍝ @RGS , I like the way ⌽[1] to index axis, it is easier to understand,

Thanks,

RGS

09:26

My pleasure. But it is recommended that you use ⊖ when you want to rotate the first axis :)

elliptic00

Yep.... save a few character. APL -> every character count:)

every character matter, APL

Adám

@elliptic00 You're absolutely right, but ⌽ precedes the invention of the rank operator by a long time. In fact, originally, Iverson had 64 functions like ⌽ ⍉ ⊖ but it was found that those three were enough to express most things without it becoming too awkward. Just ⌽ and ⍉ would have worked too, but ⍉⌽⍉M to flip vertically was apparently too verbose.

2

elliptic00

09:47

Iverson try to replace all mathematical symbol with APL :), I love the idea

Adám