I found an interesting (apparently untitled) article by Richard L. W. Brown
of York University in which he uses J to illustrate functional programming
by writing a short program to implement a version of George Danzig's Simplex
algorithm for solving linear programming problems. The article says it is
an update in 2001 from versions that appeared in Gimme Arrays in November of
1994 and in Vector, vol 11, #4, in April 1995, so that the code would have
been from an earlier version of J, which may partially explain the problem
I've encountered, which is described below.
In the article, Brown creates a conjunction by:
at =: 2 : '([EMAIL PROTECTED])y.]'
This conjunction works fine.
However, Brown also suggests making a tacit version of 'at' by:
at =: 12 : 'x.@:y.)y.)'
but this produces an error:
at =: 12 : 'x.@:y.)y.)'
|domain error
| at=: 12 :'x.@:y.)y.)'
Brown then actually writes out the tacit definition he says the 12 : command
produces as:
at =: ((@:`].)`])(`:6)
which, when run, also produces an error:
at =: ((@:`].)`])(`:6)
|spelling error
| at =: ((@:`].)`])(`:6)
| ^
The ]. is not a typo--the dot is there in the text, so I am assuming that
there was once a definition for ]. that is now withdrawn (I'd love to know
what it was). More perplexing to me is that I can't see why the tacit
version doesn't work. Is there a tacit version, or did the loss of ].
prevent the possibility of a tacit version?
I'm not second-guessing dropping ]. (if that's what the issue is)--I'm sure
there are good reasons for the choice made; I just want to know if there is
a way to work around this to produce a tacit version of the conjunction.
Using
at =: 2 : '([EMAIL PROTECTED])y.]'
works fine, but I'm just trying to understand more about tacit programming.
For those who want to tinker with Brown's program, it is (with some changes
in notation I made for unrelated reasons):
pc =: ml@(0&,)@}:@{. NB. Second way, accounting for 0
if =: @.
else =: `
inf =: _:@[
unb =: 1&[EMAIL PROTECTED]@]
opt =: 0&= @ ]
frX =: [EMAIL PROTECTED]
lrX =: }.-(({."1 @}.)*/{.)
pivX =: ({.,lrX)@(frX,}.)
rowX =: ((|[EMAIL PROTECTED]),}.)~
colX =: rowX"1
atX =: 2 : '(u.@:v.)v.]'
prX =: >:@ml@:(({:"1)dp({."1))
pinX =: (pivX atX rowX else inf if unb prX) atX colX
simplexX =: (simplexX @ pinX else [ if opt) pc
A typical linear programming problem formatted for input is:
MBrown =: 3 6 $ 1 _2 _3 0 0 0 0 4 1 1 0 12 0 2 5 0 1 15
MBrown
1 _2 _3 0 0 0
0 4 1 1 0 12
0 2 5 0 1 15
And simplexX MBrown produces the solution correctly as:
simplexX MBrown
1 0 0 0.22222 0.55556 11
0 1 0 0.27778 _0.055556 2.5
0 0 1 _0.11111 0.22222 2
(For those who want to go look up the paper, I've found another problem in
an earlier part of it: Brown gives two other versions of a J program to
solve the same problem, but these, although they work on his example, do not
work on other more general linear programming problems; the version above
does, which is why I've concentrated on studying this one.)
Carl
Carl S Ledbetter
346 Madison Street
Denver, CO 80206-4437
303-888-1227 (Cell)
303-377-5914 (Home)
303-366-5921 (Fax)
[EMAIL PROTECTED]
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
