The APL Orchard

RikedyP

15:01

Welcome to APL Quest 2019-6! Today's quest is Area Code à la Gauss:

> Given a nested list of pairs of numbers describing the points of a polygon in two dimensions, compute the area of the polygon using Gauss' area formula, also known as the shoelace formula.

      (your_function) (2 4)(3 ¯8)(1 2)
7
      (your_function) (1 1)   ⍝ a point has no area
0
      (your_function) (1 1)(2 2)   ⍝ neither does a line
0

Richard

Just a fast one. And a lot of duplicate code wich probably can be removed

{|2÷⍨(+/¯1↓×/(0 1)⊖⍵)-+/¯1↓×/(1 0)⊖⍵}{↑⍵,⊂⊃⍵}⊆

RikedyP

yeah feels like an over perhaps, but I see you're concatenating the first value (like in the description on the problem page) in a similar way to @RubenVerg

Richard

yes

p.s. try apl freezes so didn't test it

RikedyP

huh that's odd - it's working for me

Richard

than it's just my browser, np.

@RubenVerg used ,⍤⊆. is just ⊆ not sufficient?

RikedyP

15:07

so you're taking the products of the two rotations separately and then subtracting them

I've got one that does the steps as 3 reductions: -/+/×/

before I show that code, any guess how I did it?

Richard

@RikedyP yes. Just followed litteraly the description.

@RikedyP No. I saw Ruben also use ×, but didn't grap it.

RikedyP

how can you get a single array (3D) with the contents of (0 1⊖⍵) and (1 0⊖⍵), without simply joining those two

@RubenVerg imho the only obscure part is the 2+.÷⍨ instead of 0.5×+/ or 2÷⍨+/

it also took me a minute to grok, but otherwise it's a decent algorithm - note that it's a pair-wise reduction 2F/which is not immediately obvious with all the tacit going on

2-/⍤×∘⌽/⍵ ⍝ difference of product of each point (xy) with reversed right-neighbour

So I've got:
Gauss←{0.5×|-/+/×/(2 2⍴0 1 0 ¯1)⊖⍤1 99↑,⊆⍵}

Richard

@RikedyP no idea, sorry

RikedyP

@Richard np, see above

So if I were to summarise it, I'd say:

@Richard has broken things apart in the code itself, and expressed each part of the algorithm as a piece of code

@RubenVerg took a more functional approach and devised a pair-wise reduction

I manipulated the shape of the data to get the algorithm expressed as reductions

Richard

yes that's nice

RikedyP

15:16

I think we all have some version of ,⊂ to deal with the simple vector (one point, 0 area) case

Richard

but the , is not necessary, is it?

using ⊆

RikedyP

for us who mixed, it is

↑,⊆

otherwise ↑ gives back the same vector and I get a RANK ERROR. I'm not sure for yours

and @RubenVerg kept everything nested anyway

because you're catenating the first point you get a matrix after ↑⍵ regardless

Richard

yes, just tried it. Always find that difficult

RikedyP

any questions about these 3? I'll have a brief think if we can put an over in yours

Richard

@RikedyP Yes please, was thinking about that

RikedyP

15:21

which bits of code are repeated exactly?

Richard

+/¯1↓×

RikedyP

almost

Richard

inlcuding the / of course

RikedyP

there we are :P

Richard

copy paste error

RikedyP

15:22

so in ⍺(F⍥G)⍵ what's the F and what's the G?

and what are ⍺ and ⍵ for that matter :P

Richard

G is the preprocess part. So +/¯1↓× is F

RikedyP

ah well it was 50/50

Richard

G is the rotate

:(

RikedyP

other way around. The repeated part is the pre-process

what are you doing with the two things? Hint: it's dyadic

well that hint was useless...

what are you doing between the two values after pre-processing them?

Richard

But we are first doing the rotate, and then the reduce etc.

RikedyP

15:26

yeah that's all pre-processing

in this instance

and unfortunately we can't factor out the rotations because of the different arguments (unless we use Rank operator like I did)

Richard

so for F⍥G, G is first applied

On ⍺ and ⍵

RikedyP

maybe it would help if you guess the ⍺ and ⍵ first

actually I'll just say

they are the rotated ⍵s

⍺←0 1⊖⍵ ⋄ ⍵←1 0⊖⍵

Richard

⍺ and ⍵ are the ⊖

RikedyP

So we've done the rotations before we get to the F⍥G

(0 1⊖⍵)F⍥G(1 0⊖⍵)

Apply G to both arguments, and apply F between the results of those applications

Richard

ah, and F is then |2÷⍨

RikedyP

15:30

no you've gone too far into the future there

Richard

-+/

RikedyP

well you could tie them in as an atop, but not worth

just the -

G already has +/

Richard

ah yes, we are substracting them after rotating them both

RikedyP

*after summing the products of both

summing the products of the rotations - but we didn't factor out the rotations, so those are still explicitly applied to our argument

Richard

yes, ...

RikedyP

15:33

wanna have a stab at putting it together? Or shall I paste it?

Richard

working on it :)

(0 1⊖⍵)-⍥/¯1↓×/ (1 0⊖⍵)
but probably needs a ∘ somewhere

RikedyP

you're really quite close, although have forgotten the sum

is TryAPL still playing up for you? Can I ask your web browser and operating system?

and perhaps also recommend you download Dyalog APL :P

RubenVerg

@RikedyP can't remember why I did that

Richard

firefox, but I am using the interpreter

RubenVerg

I suppose I accidentally assumed it was shorter

golf brain kicked in :)

Richard

15:37

NP is just my computer

RikedyP

@RubenVerg yeah I figured

@Richard
|2÷⍨((0 1)⊖⍵)-⍥(+/¯1↓×/)(1 0)⊖⍵

@RubenVerg is shorter than mine

Richard

Not my best week...

RubenVerg

@RikedyP I still don't fully get the rules for when a tacit chain stops, but I noticed that I didn't need any parens around the reduction for it to work, it's definitely much clearer with

RikedyP

@Richard not bad at all

@RubenVerg well you've really only got a 2-train in the overall function

the left tine is just a dfn, with a tacit function made using function composition operators

A train is always just a function isolated from its arguments

You can isolate functions by either using parentheses ⍺(FGHIJKL)⍵ or by assigning a name Train←FGHIJKL

RubenVerg

why does it not parse as a fork ((2)(-/ after × composed with reverse)(/))?

sorry don't have an APL keymap on hand

RikedyP

15:42

@RubenVerg because function composition operators already bind those symbols into a single function

so it would be a 1-train

Richard

the / operator probably goes first

RikedyP

which is just function application

RubenVerg

oh right because here / is an operator

the thing with / being both operator and function is confusing

RikedyP

so you could do
2(-/×∘⌽)/ ⍝ perhaps

@RubenVerg indeed it is, although you can get used to it with time, but if we started over definitely wouldn't have that

but that's not the thing preventing a train from forming here, it's your use of atop ⍤ and beside ∘

RubenVerg

@RikedyP that's longer is it? I think the extra composition is clear enough

RikedyP

15:44

@RubenVerg yeah longer by 1. Note that a 2-train is an atop

RubenVerg

right

RikedyP

I only brought it up because you asked why what you had wasn't a train

and having thought for a second, it is indeed both due to / being an operator and your use of compositions

RubenVerg

also do I actually need such a long expression for x,x[1]?

seems weird it isn't shorter

RikedyP

x,1⌷x

same length

Yeah I mean there's no primitive for "concatenate the first bit"

(⊂∘⊃,⊢)⍵

RubenVerg

@RikedyP used that in the last one, decided to go with enclose disclose just for variatio

idk how to say in english

RikedyP

15:50

variety

yeah fair enough

RubenVerg

you call it variety also in poetry?

RikedyP

not sure I understand the question

you mean is there a fancier word for variety?

Richard

@RikedyP (⊣,⊂∘⊃)⍵

RikedyP

@Richard indeed

RubenVerg

in Italian "variatio" is specifically using two language constructs to mean the same thing

RikedyP

15:51

right any last Qs before I dip out?

@RubenVerg oh probably synonyms then?

but how broad is "constructs" in that definition?

RubenVerg

wait I'll look for an example

Richard

variation v.s. variety

RikedyP

you'd say "a variation" as the thing that is different, whereas variety is just the quality of having differences

RubenVerg

@RikedyP like complements

RikedyP

@RubenVerg yeah that's also a term with a few meanings in English, but I think I get the gist

I think "variation" as @Richard said is maybe closest

RubenVerg

15:54

okay this seems to not exist in english so nevermind

Richard

thanks all, CY next week

RubenVerg

anyways it's like a rhetorical figure

RikedyP

like in music too? if you have a theme

RubenVerg

okay here is a translation of a dictionary definition

RikedyP

@Richard Thanks as always @Richard

@RubenVerg yes please let's see before I go

RubenVerg

15:57

variatio: Rhetorical principle opposed to repetition, to which many [rhetorical] figures are connected, like polyptoton and synonimy, and many more. These can be used to get a variation in speech and therefore avoiding monotony.

the roman poet Sallust is known for using variatio very often

RikedyP

Oh so it includes several rhetorical concepts in the one word "variatio"

RubenVerg

it's like a family of figures

RikedyP

yeah not sure we have that in English as a single word

RubenVerg

and a style of writing

RikedyP

it says "opposed to repetition", but I'm guessing the idea is you want to say the same thing again (for effect) but not literally use the same phrase again

RubenVerg

16:00

repetition here refers to specifically using the same words/construct next to each other

RikedyP

Yeah it's just called "variation" in English I think

RubenVerg

iteratio in latin/specific lexicon for poetry in italian

RikedyP

maybe our poetry is not as good ;)

anyway thanks for your contributions today - see you around !

Next week will be 2019-10: Odds & Evens

Silas

17:32

@RikedyP and probably slower too, especially as 2F/ with comparisons and simple mathematic fns (think just +×÷-) optimised.

RubenVerg

likely

RubenVerg

19:15

is there a way to add a line break without ending an expression?

like \ in python or c

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