Your ($#: I.@,) can be replaced: ((4$. $.) -: $#: I.@,) 4 5$ 0 1 0 1
R.E. Boss > -----Oorspronkelijk bericht----- > Van: programming-boun...@forums.jsoftware.com > [mailto:programming-boun...@forums.jsoftware.com] Namens Mike Day > Verzonden: zondag 4 november 2012 18:53 > Aan: programm...@jsoftware.com > Onderwerp: Re: [Jprogramming] Arc consistency in J > > 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. > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
