Ok, I think this qualifies:
G=: [: */ [: > [: ({ <: ])&.>/ <"0@i.@# , <
--
Raul
On Fri, May 3, 2013 at 4:49 PM, Christopher Rosin <[email protected]> wrote:
> Thanks. I would be interested in any one maximal clique; it doesn't
> necessarily matter which one.
> -Chris
>
>
>
>
>
> On Fri, May 3, 2013 at 1:43 PM, Raul Miller <[email protected]> wrote:
>
>> I am finding this hard to reason about.
>>
>> One issue is the sheer arbitrariness of the result. It's "a maximal
>> clique". It's not "all maximal cliques". It's not a maximal clique
>> which is in some way notable except that it's a particular maximal
>> clique which just happens to be convenient to express using a
>> particular notation.
>>
>> So I'm having a hard time reasoning about what makes this particular
>> maximal clique notable, and why I should expect it to be convenient to
>> express using different notation.
>>
>> For reference, though, here's another explicit verb which I believe
>> finds a different maximal clique:
>>
>> g=: 3 :0
>> */>({ <: ])&.>/(]&.>@i.@#,<) y
>> )
>>
>> The ({ <: ]) part corresponds to the inside of the loop.
>>
>> If you wanted a tacit verb, use 13 :0 instead of 3 :0 in the definition of
>> g.
>>
>> I do not know if this helps.
>>
>> --
>> Raul
>>
>> On Fri, May 3, 2013 at 3:22 PM, Christopher Rosin <[email protected]>
>> wrote:
>> > Hi all. Reading this list has been very useful as I've been learning J.
>> >
>> > I'd like to ask for help in finding a simple tacit way to express f
>> below,
>> > or at least an appropriate commonly-used tacit J idiom.
>> >
>> > Say s is a symmetric boolean matrix with 1's on the diagonal, and define:
>> > f =: 3 : 0
>> > for_k. i.#y do. y =. (<:~ k&{) y end.
>> > */ y
>> > )
>> >
>> > e.g.
>> > ] s =: ((= |:) (?. 10 10 $ 2))
>> > 1 0 0 0 1 1 0 1 0 0
>> > 0 1 0 0 0 1 1 1 1 1
>> > 0 0 1 0 1 1 0 0 0 0
>> > 0 0 0 1 1 1 1 1 1 0
>> > 1 0 1 1 1 0 0 1 1 1
>> > 1 1 1 1 0 1 1 0 1 0
>> > 0 1 0 1 0 1 1 0 1 0
>> > 1 1 0 1 1 0 0 1 0 1
>> > 0 1 0 1 1 1 1 0 1 1
>> > 0 1 0 0 1 0 0 1 1 1
>> > f s
>> > 1 0 0 0 1 0 0 1 0 0
>> >
>> > One way to describe f is: given undirected graph s it finds a maximal
>> > clique:
>> > http://mathworld.wolfram.com/MaximalClique.html
>> > (maximal clique, not maximum clique... which would be NP-hard)
>> > The 1's in (f s) mark a clique of nodes linked by edges (marked by 1's
>> in s)
>> > and this clique is maximal in that nothing can be added to it.
>> >
>> > One tacit approach is to translate the for loop using a boxed list of
>> > indices:
>> > g =: [: */@>@((]<:~{)&.>/) <"0@|.@i.@# , <
>> > g s
>> > 1 0 0 0 1 0 0 1 0 0
>> >
>> > Another is to rotate repeatedly so the head is always next to be
>> processed:
>> > h =: */@(([:(1 1)&|.]<:~{.)^:#)
>> > h s
>> > 1 0 0 0 1 0 0 1 0 0
>> >
>> > But these seem somewhat awkward to me.
>> > The explicit function f has just two verbs inside the body of the for
>> loop,
>> > so I was hoping to find a tacit solution that also needed at most two
>> verbs
>> > inside the / or ^: or whatever else is used to replace the loop.
>> >
>> > Any ideas?
>> > Or maybe there is an entirely different approach, more suited to tacit J?
>> >
>> > Thanks.
>> > -Chris
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>> ----------------------------------------------------------------------
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