I'm no longer puzzled:
]a=:?>:i.6
0 1 0 2 3 4
]a=:=a
1 0 1 0 0 0
0 1 0 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
]b=:?>:i.6
0 0 1 1 1 2
a #@# b
2 1 1 1 1
a ([:##)"# b
2 1 1 1 1
g=: 13 :'x([:##)"# y'
a g b
2 1 1 1 1
5!:4 <'g'
-- [:
--------+- #
-- " -+ L- #
L- _ 1 _
g
([: # #)"_ 1 _
The comic footnote is what I found with ds from Henry Rich!
+/"1 a
2 1 1 1 1
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Linda Alvord
Sent: Friday, January 04, 2013 9:10 AM
To: [email protected]
Subject: Re: [Jprogramming] atop continues to puzzle me
Wow!
at=: 2 :'([: u v)"v'
3 4 5 < at #"0 i.3
------T-------T---------┐
│0 0 0│1 1 1 1│2 2 2 2 2│
L-----+-------+----------
3 4 5 ([:<"1#"0)">i.3
------T-------T---------┐
│0 0 0│1 1 1 1│2 2 2 2 2│
L-----+-------+----------
f=: 13 :'([:<"1#"0)">y'
3 4 5 f i.3
------T-------T---------┐
│0 0 0│1 1 1 1│2 2 2 2 2│
L-----+-------+----------
f
([: <"1 #"0)"0 0 0
5!:4 <'f'
-- [:
│ -- <
+- " -+- 1
--------+
│ │ -- #
-- " -+ L- " -+- 0
L- 0 0 0
Graham, that is some pretty picture.
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Graham
Parkhouse
Sent: Friday, January 04, 2013 7:14 AM
To: [email protected]
Subject: Re: [Jprogramming] atop continues to puzzle me
> On Wed, Jan 2, 2013 at 10:04 AM, Raul Miller <
<mailto:[email protected]> [email protected]>
> wrote:
> > Here's a definition for at which works exactly like @
> >
> > at=: 2 :'([: u v)"v
at=: 2 :'([: u v)"v'
3 4 5 < at #"0 i.3
+-----+-------+---------+
|0 0 0|1 1 1 1|2 2 2 2 2|
+-----+-------+---------+
Linda - we've done it! We've got rid of @!
But we used a conjunction to do it, so the same reasoning applies; we
avoided making J massage an intermediate result into something rectangular.
> Date: Thu, 3 Jan 2013 14:53:17 -0800
> From: Nollaig MacKenzie < <mailto:[email protected]>
[email protected]>
> To: <mailto:[email protected]> [email protected]
> Subject: Re: [Jprogramming] Atop continues to puzzle me
> Message-ID: < <mailto:[email protected]>
[email protected]>
> Content-Type: text/plain; charset=us-ascii
>
> ...
>
> I thought there might be a way of getting a function without using
> composition by using "L:" . But the best I came up with was:
>
> f=. (# L: 0) & <"0
> 3 4 5 f i.3
>
> +-----+-------+---------+
> |0 0 0|1 1 1 1|2 2 2 2 2|
> +-----+-------+---------+
>
> But the "&" vitiates the attempt.
>
> The general argument about J functions having to produce rectangular
> arrays should have convinced me anyway.
>
> NM
>
> --
> Nollaig MacKenzie
> <http://www.yorku.ca/nollaig> http://www.yorku.ca/nollaig
Linda, I think this 'general argument about J functions having to produce
rectangular arrays' should help you see why there are benefits in embracing
@ and the other conjunctions as your friends, to be used as convenient.
Now in your first examples below, rectangular intermediate results are
inevitable anyway, so @ is not necessary.
I found function composition unnatural. I'm getting used to it and enjoying
mixing implicit and explicit as I am inclined. Sometimes, though, I have
little choice, especially with boxed ragged arrays.
> Date: Fri, 04 Jan 2013 06:18:01 -0500
> From: "Linda Alvord" < <mailto:[email protected]>
[email protected]>
> To: < <mailto:[email protected]> [email protected]>
> Subject: Re: [Jprogramming] Atop continues to puzzle me
> Message-ID: <002f01cdea6d$2936bb40$7ba431c0$@net>
> Content-Type: text/plain; charset=ks_c_5601-1987
>
> Here's my progress so far:
>
> 2 <mailto:|.@(*%221)> |.@(*"1) <mailto:|.@(*> a=:i.2 3
> 4 2 0
> 10 8 6
> (|."1) 2(*"1)a
> 4 2 0
> 10 8 6
> 2 <mailto:|.@:(*%221)> |.@:(*"1) <mailto:|.@:(*> a
> 6 8 10
> 0 2 4
> |. 2*"1 a
> 6 8 10
> 0 2 4
> 3 4 5<@#"0 i.3
> +-----+-------+---------+
> |0 0 0|1 1 1 1|2 2 2 2 2|
> +-----+-------+---------+
> 3 4 5#"0&.> i.3
> +-----+-------+---------+
> |0 0 0|1 1 1 1|2 2 2 2 2|
> +-----+-------+---------+
>
> I am trying to remove &. following these rules:
>
> NB. x u&v y ? (v x) u (v y)
> NB. u &.v is equivalent to the composition u & v
> NB. except that the verb obverse to v is applied
> NB. to the result for each cell
> NB.(subject to the monadic rank of v)
>
> (<"1 3 4 5 ) #"0 (>"0 i.3)
> |length error
> | ( <"1 3 4 5)#"0(>"0 i.3)
>
> The is one of my better tries to follow the directions.
>
> Linda
Regards
Graham
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