As far as I can understand the "revise" verb, you don't need the
adjacency matrix a, although it does help to have a 2-column matrix of
index pairs.
I think Raul has overlooked your use of the right argument ys within
that verb, though he's right about selecting with it. Here's a
derivation of arcs without explicit recourse to the adjacency matrix
(I've just noticed that Raul presents a similar idiom):
arcs=. ys (]#~ (e.~ {."1)) ($#: I.@,) *|:A
I. returns a vector of indices to the ravelled boolean; $ #: turns them
into a matrix of pairs of indices to an array of the shape of |:A.
(]#~ (e.~ {."1)) selects those arcs with an element of ys as the
from-node (or perhaps they're the to-nodes?)
This form renders the arcs array already sorted, but note that if you
do need to sort the elements of an array, it's sufficient to use the
idiom /: ~ (rather than ({~ /:) . Presumably sorting "arcs" is
merely a matter of taste.
It's quite nice to be able to input several components of an argument by
(local) name with
'A a C'=.x
'ys D'=. y
rather than
A=. > 0{x
a=. > 1{x
ys=. > 0{y
D=. > 1{y
As A is invariant in "ac", you could of course preset the array of
indices for all arcs in A, aix =: ($#: I.@,) *|:A and use aix as an
input to "revise" instead of a .
I used *|:A or (0<|:A) here and wonder why you need to double its lower
diagonal elements.
I also wonder whether your example will still work if there are binary
constraints involving variables (say z and t) indexed with 2 or 3. And
what happens if there are more than one binary constraints on a pair of
variables? eg, X+Y=4 AND X>Y ?
I'd have been very pleased with myself if I'd come up with code as good
as this when I started J - would be pretty pleased if I managed it now!
Mike
On 04/11/2012 2:40 PM, Raul Miller wrote:
In
A=. 0= ? (2$n)$2 NB. generate random matrix of [0,1]
The 0= is unnecessary, and probably reflects a habit based on the
false idea that boolean algebra is does not have an integer domain.
Boolean rings have (subset of) integer domains, and [even after
redefinition] boolean algebra is a boolean ring.
If you ever want to treat Heyting Algebras or Bayesian Probability you
might also want to consider what happens when you replace the $2 with
$0.
I think I would also be more comfortable with
2 2 $ ''; 'y'; 'x'; A
for the displayed table, but that's a minor quibble.
An alternative definition for adj might be
adj=: <@I.@:*
But somewhere around here, I get lost. Your use pattern for arcsX is:
(i.n) arcsX A
where A has the shape n,n
What is the domain of the left argument of arcsX? I am guessing that
it's either i.n or a single element choosen from i.n but if that is
the case, I think I'd define arcsX to only work for the i.n case --
the name says "arcs" after all. Also, if I wanted to extract the
values from the result of arcsX which correspond to a single value
from i. n, that's simple enough -- I can select on the first column of
the result.
In other words, perhaps something like this:
arcs=: $ #: I.@,
arcs *A
Also, I have not taken the time yet, to read "revise", so I will stop here.
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