I meant that +/"1 in our fantasy language would be the equivalent of +/&.> in J.
Cheers, Mike On Tue, Sep 9, 2014 at 8:15 AM, Linda Alvord <lindaalv...@verizon.net> wrote: > I thought Michal was indicating at the end of his message that these were > the same. > > >Something like +/"1 x instead of +/&.> x (obviously there's not much > >difference here). > > Linda > > -----Original Message----- > From: programming-boun...@forums.jsoftware.com [mailto: > programming-boun...@forums.jsoftware.com] On Behalf Of Michal D. > Sent: Tuesday, September 09, 2014 1:14 AM > To: programm...@jsoftware.com > Subject: Re: [Jprogramming] Ragged Array Shapes are Trees > > One can imagine that it's possible for > > ] x =. (<@i."0) 1+i.3 > +-+---+-----+ > |0|0 1|0 1 2| > +-+---+-----+ > > to be laid out in memory as [0 0 1 0 1 2] with an additional vector > representing the starting point of each rank-1 array [0 1 3 6]. I would be > willing to wager a large sum that this is much more computationally > efficient than having a representation where each rank-1 array is floating > off somewhere in memory [0] [0 1] [0 1 2] with an array of pointers to > them. > > Of course this representation is possible, but somewhat verbose, to do > manually in J (http://dl.acm.org/citation.cfm?id=804488). That's why I'm > fantasizing about a language where such a representation would be closer to > the core of the language. > > Something like +/"1 x instead of +/&.> x (obviously there's not much > difference here). > > Like we've both suggested, it may be that boxing with a sufficiently > optimized interpreter is the solution. > > Cheers, > > Mike > > On Mon, Sep 8, 2014 at 8:10 AM, Raul Miller <rauldmil...@gmail.com> wrote: > > > What does this mean "shapes extended to support ragged arrays without > > boxing"? > > > > K has ragged arrays without boxing, but K's concept of shape only > > applies to the non-ragged prefix dimensions. > > > > Meanwhile, it seems to me that the guarantee you suggest would be > > computationally expensive. > > > > (Not saying the ideas shouldn't be explored, but I suspect what you > > are really after is a more efficient boxing implementation and that > > will lead in an entirely different direction.) > > > > Thanks, > > > > -- > > Raul > > > > > > On Mon, Sep 8, 2014 at 11:01 AM, Michal D. <michal.dobrog...@gmail.com> > > wrote: > > > Thanks Pascal, that's a nice formulation for the 2-level deep case. It > > > breaks down of course for deeper nesting but could serve as a base. > > > > > > ([:|. $ ;~ $ each) ((i.2 3);(,0)) ; (i. 2 3) > > > +-+-------+ > > > |2|+-+---+| > > > | ||2|2 3|| > > > | |+-+---+| > > > +-+-------+ > > > > > > There's no specific problem I'm trying to solve directly in J at the > > > moment. It's more of a language design problem. My interest in this > is > > a > > > J like language, but with shapes extended to support ragged arrays > > without > > > boxing. Failing that, we could have some optimization guarantees like > > 'an > > > array of boxes containing equal rank values are allocated > contiguously'. > > > > > > Cheers, > > > > > > Mike > > > > > > > > > > > > On Sat, Sep 6, 2014 at 9:28 AM, 'Pascal Jasmin' via Programming < > > > programm...@jsoftware.com> wrote: > > > > > >> Hi Michal, > > >> > > >> maybe this is an interesting representation for what you want? > > >> > > >> ([:|. $ ;~ $ each) (i. 2 3) ; (,0) ; 0 1 > > >> ┌─┬─────────┐ > > >> │3│┌───┬─┬─┐│ > > >> │ ││2 3│1│2││ > > >> │ │└───┴─┴─┘│ > > >> └─┴─────────┘ > > >> > > >> > > >> > > >> ----- Original Message ----- > > >> From: Michal D. <michal.dobrog...@gmail.com> > > >> To: programm...@jsoftware.com > > >> Cc: > > >> Sent: Saturday, September 6, 2014 12:06 PM > > >> Subject: [Jprogramming] Ragged Array Shapes are Trees > > >> > > >> I just came to the realization that ragged array shapes, regardless of > > how > > >> you want to represent them, are trees. I would be interested in any > > >> references to prior exploration of this idea. > > >> > > >> Some example data (boxes are used to display ragged arrays, but > > otherwise > > >> have no semantic meaning): > > >> > > >> ] A =. i. 2 3 > > >> 0 1 2 > > >> 3 4 5 > > >> ] B =. (< @ i."0) 1+i.2 > > >> +-+---+ > > >> |0|0 1| > > >> +-+---+ > > >> ] C =. A ; B > > >> +-----+-+---+ > > >> |0 1 2|0|0 1| > > >> |3 4 5| | | > > >> +-----+-+---+ > > >> ] D =. A ; < B > > >> +-----+-------+ > > >> |0 1 2|+-+---+| > > >> |3 4 5||0|0 1|| > > >> | |+-+---+| > > >> +-----+-------+ > > >> > > >> The corresponding shape trees (monospace font required, root node is > on > > the > > >> left): > > >> > > >> A: 2 - 3 > > >> > > >> 1 > > >> / > > >> B: 2 > > >> \ > > >> 2 > > >> > > >> 2 - 3 > > >> / > > >> C: 3 - 1 > > >> \ > > >> 2 > > >> > > >> 2 - 3 > > >> / > > >> D: 2 1 > > >> \ / > > >> 2 > > >> \ > > >> 2 > > >> > > >> In some sense the shape tree for A is compressed, the verbose > > alternative > > >> being: > > >> > > >> 3 > > >> / > > >> A: 2 > > >> \ > > >> 3 > > >> > > >> Compressing D in a similar manner leaves the full shape of the tree > > >> ambiguous - there is no way to distinguish the duplicate structure of > > leaf > > >> 3 from the structure of leaves 1, 2. > > >> > > >> 3 > > >> / > > >> D: 2 - 2 - 1 > > >> \ > > >> 2 > > >> > > >> We could resolving this ambiguity by listing the shapes of all the > items > > >> explicitly. The problem here is that 'compression' could very easily > > lead > > >> to an increase in representation size, although it is nice and uniform > > for > > >> ragged arrays of uniform rank. > > >> > > >> 3 > > >> / > > >> | 3 > > >> | / > > >> D: 2 - 2 + > > >> | \ > > >> | 1 > > >> \ > > >> 2 > > >> > > >> Regardless of compression, I would be interested in prior work in > > >> representing shapes of ragged arrays as trees. > > >> > > >> Cheers, > > >> > > >> Mike > > >> ---------------------------------------------------------------------- > > >> 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 > > > ---------------------------------------------------------------------- > 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
