Well... of course, you can express matrix multiplication *using* rank: (1+i.4 3) +/@:*"1 _(1+i.3 4) 38 44 50 56 83 98 113 128 128 152 176 200 173 206 239 272
And, conceptually, all verbs in J have rank, so that always gets used. But, I guess you are asking how to avoid the rank conjunction -- which would be: how can you use just the implicit ranks (and, presumably, other adverbs and conjunctions). And, that can be done, but I don't think it's elegant. For example: +/(1 2;0;3)|:(1+i.4 3) */ (1+i.3 4) 38 44 50 56 83 98 113 128 128 152 176 200 173 206 239 272 Basically, you probably want a rank 1 operation in there, somewhere, to merge the rightmost dimension of the left argument with the leftmost dimension of the right argument... But there aren't that many operations in J which are rank 1, and getting them to do multiply is not likely to be straightforward (though I might be overlooking something). You might be able to use #. for example, but the approach would be convoluted. Does any of this help? -- Raul On Tue, Jul 12, 2022 at 11:09 PM Thomas McGuire <tmcguir...@gmail.com> wrote: > > Devon had shared a kx example of performing matrix multiplication backing out > the loops from a wikipedia pseudocode. Providing an elegant solution in K. > > You can see it in the NYCJUG notes here: > https://code.jsoftware.com/wiki/NYCJUG/2022-07-12 > <https://code.jsoftware.com/wiki/NYCJUG/2022-07-12> > > The Kx solution is as follows: > > matmul: {x{+/x*y}/:\:+y} > > The each right (/:) and each left operators (\:) in sequence appear to > perform in a similar way to J’s table operator ‘/‘. > > After some messing around with rank I came up with the following J equivalent: > > matmul =: {{x {{+/x*y}}”1 1/ |:y}} > > (1+i. 4 3) matmul 1+i. 3 4 > 38 44 50 56 > 83 98 113 128 > 128 152 176 200 > 173 206 239 272 > (1+i. 4 3) +/ . * 1+i. 3 4 > 38 44 50 56 > 83 98 113 128 > 128 152 176 200 > 173 206 239 272 > > By transposing the y operand I deliver columns of y to rows of x which gets > operated on by the inner anonymous dfns. Wondering if there is a more elegant > way that does not play around with rank? > > Tom McGuire > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
