Thanks Marshall, That's indeed very slick, and something I reached for in J on more than one occasion, when handling block matrices.
Best regards, Jan-Pieter On Wed, 15 Jun 2022, 23:06 Marshall Lochbaum, <mwlochb...@gmail.com> wrote: > It's an interesting transpose, but BQN has a much more elegant solution: > with multidimensional Join, the product of arrays is just ∾a×<b, or ∾×⟜< > as a tacit function. > > Code: > https://mlochbaum.github.io/BQN/try.html#code=YSDihpAgMTArMuKAvzPipYrihpU2CmIg4oaQIDPigL804qWK4oaVMTIK4oi+YcOXPGI= > > Docs: https://mlochbaum.github.io/BQN/doc/join.html#join > > J's raze is just like Join for list arguments, but that implicit ravel > means it's stuck doing 1-dimensional joins forever. I said in the > previous podcast that I really didn't like J's implicit ravel and this > is why (and I said I missed its multidimensional i. for example code > only... also relevant). > > Even so, it's nice to know the connection between Join and Transpose. > Thanks for the link—I've seen it but it didn't occur to me in this > context. > > Marshall > > On Wed, Jun 15, 2022 at 09:00:13PM +0200, Jan-Pieter Jacobs wrote: > > Hi, > > > > I'd like to thank the entire Arraycast crew for this excellent podcast, > I'm > > always looking forward to the next episode. I find it super informative, > > with a healthy dose of humour. Great job; please continue ;). > > > > Since you didn't seem to find many applications of dyadic transpose, I'd > > like to point out the Kronecker product page on the J wiki: > > https://code.jsoftware.com/wiki/Essays/Kronecker_Product > > > > Conceptually, it multiplies each element of a left array with the > entirity > > of the right array. > > One of the implementations (kp) uses dyadic transpose to zip together the > > axes of the *"0 _ in alternating order. > > > > A while back, I coded up a generalised version for arbitrarily shaped > > arrays (that is any but not scalar. see the "kpnd" verb, on the same > page), > > using the same approach. I hope this extension makes sense, because I > could > > not find any implementation or description of such generalisation. The > "as" > > verb calculates the required axis shuffle needed, to be later reshaped > into > > the final shape by the "cs" verb. > > > > As an aside (I didn't put it on the Kronecker product page since it's not > > exactly a Kronecker product), in recent J (903 or up), one can define a > > generic Kronecker-dyad forming adverb as the following tacit modifier: > > > > kd =: (("0 _) |:~ as) (]: ($,)~ cs) > > > > such that kpnd is equivalent to * kd. This way one could do Kronecker > sums > > (+kp) or Kronecker versions of whatever rank 0 dyad you'd like. > > > > Now to find an application for these verbs... Always nice to have a > pretty > > solution waiting to meet its corresponding problem :p. > > > > Best regards, > > Jan-Pieter > > > > On Sat, 11 Jun 2022, 18:21 'robert therriault' via Programming, < > > programm...@jsoftware.com> wrote: > > > > > Hi everyone, > > > > > > In this episode we explore monadic and dyadic transpose and the ways > it is > > > interpreted in APL, BQN and J. > > > > > > Host: Conor Hoekstra Panel: Marshall Lochbaum, Adám Brudzewsky, Stephen > > > Taylor and Bob Therriault. > > > > > > > https://www.arraycast.com/episodes/episode28-rank-and-leading-axis-gbbpe > > > > > > Cheers, bob > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
