This was me. Very nice to hear that someone found it helpful. Thanks for going out of your way to say thanks!
Jim Russell <jimsruss...@yahoo.com> wrote: > Who do I thank tor this? It is a particularly clear and helpful exclamation. > Thank you! > > > On Mar 13, 2020, at 3:56 AM, ethiejiesa via Programming > > <programm...@jsoftware.com> wrote: > > > > I'll contribute a little prose. Hopefully, it's helpful. > > > > In this particular case, notice that > transforms your list of boxes into a > > 5x6 > > table: > > > >> (6?55);(6?55);(6?55);(6?55);(6?55) > > 13 4 19 43 3 52 > > 10 1 4 46 52 11 > > 38 12 48 50 54 45 > > 36 54 39 35 53 50 > > 44 1 7 54 11 41 > > > > So, we should be able to easily "reverse" the above, meaning that dealing > > with > > a 5x6 array is pretty much the same as dealing with 5 boxes of 6-arrays. > > Let's > > just keep this in mind for now, and first try to generate this 6x5 table. > > > > The key point of ? is that it's monadic and dyadic ranks are all 0, meaning > > that it transforms an array of integers into a corresponding array of random > > numbers: > > > > ? 50 6 $ 55 > > ... > > > > produces a random 50x6 array of integers each in the range i.55. This is not > > quite what we want, but we first note that it can be more idiomatically > > written: > > > > 50 6 ?@$ 55 > > > > The utility of @ (and @:) become a lot more apparent when writing tacit > > expressions. In general, x u@v y is equivalent to u (x v y), applying u > > "atop" > > x v y, hence the mnemonic. (NB. The difference between u@v and u@:v is that > > they produce verbs of different rank.) > > > > The dyad n?m produces n random numbers without replacement. Your posed > > problem > > is to generate 50 such lists, so conceptually we want to *reshape* the > > arguments of ? into 50-lists: > > > > (50$6) ? (50$55) > > > > but, better yet, as lots of verbs to ? will automatically reshape an atomic > > argument to the shape of the other argument, so we can abbreviate the above > > in > > one of two ways: > > > > 6 ? (50$55) NB. or > > (50$6) ? 55 > > > > In the first case, the parentheses are not necessary due to J parsing > > rules, so > > its more compact and idomatic to elide them > > > > 6 ? 50$55 > > > > These three previous options should produce the desired random tables. Now, > > putting things together, we just want to "redo" the boxing we did in the > > beginning example: > > > > <"1 (6 ? 50$55) > > > > Which should give the desired result. We need the > > parenthesis to separate the 1 from the 6, otherwise J would interpret this > > as > > <"1 6. Another way to break up the list lexing is like this: > > > > <"1 [ 6 ? 50 $ 55 > > > > Anyway, Hui's use of &. is even nicer. The key ideas is that u&.v first > > runs v > >> on u's aguments and then *undoes* v on the result. The really neat thing is > >> that > is a no-op on non-boxed atoms: > >> > >>> 42 > >> 42 > >> > >> So the idea is to let > be a no-op on our input array of integers, then > >> let ? > >> do it's thing, and finally *undo* > on *each* result. And since undoing > > >> is > >> simply doing <, we get what we want. > >> > >> 6 ?&.> 50 $ 55 > >> > >> The "each result" part above is exactly why this form is slick. ?&.> has > >> the > >> rank of >, i.e. 0 0 0. This means that it will box each list produced by ? > >> as > >> the integers are fed to it, which is exactly what we want in this case. > >> > >> Very cool stuff. Rank! > >> > >> > >> Skip Cave <s...@caveconsulting.com> wrote: > >> Wow! Two completely different ways to generate multiple sets of random > >> integers. Roger used &. which I haven't really ever used or understood. I > >> will definitely need to understand &. for the future. Devon used @, which I > >> also haven't used very much. I need to find some practice and training > >> examples to work on both concepts. > >> > >> Skip Cave > >> Cave Consulting LLC > >> > >> > >>> On Fri, Mar 13, 2020 at 12:04 AM Devon McCormick <devon...@gmail.com> > >>> wrote: > >>> > >>> 6 5?@$55 > >>> Will give you a 6x5 table that is 6 independent rows of 5?55. > >>> > >>> > >>> On Fri, Mar 13, 2020 at 12:52 AM Roger Hui <rogerhui.can...@gmail.com> > >>> wrote: > >>> > >>>> 6 ?&.> 5 $ 55 > >>>> > >>>> > >>> ┌────────────────┬─────────────────┬───────────────┬─────────────────┬───────────────┐ > >>>> │47 28 45 25 8 36│22 40 23 20 11 49│15 16 42 38 4 5│50 45 38 37 13 28│42 > >>> 4 > >>>> 36 7 23 49│ > >>>> > >>>> > >>> └────────────────┴─────────────────┴───────────────┴─────────────────┴───────────────┘ > >>>> > >>>> 6 ?&.> 50 $ 55 > >>>> ... > >>>> > >>>> > >>>> On Thu, Mar 12, 2020 at 9:49 PM Skip Cave <s...@caveconsulting.com> > >>> wrote: > >>>> > >>>>> How can I generate the following result extended 50 times, without > >>>> explicit > >>>>> looping? > >>>>> > >>>>> (6?55);(6?55);(6?55);(6?55);(6?55) > >>>>> > >>>>> > >>>>> > >>>> > >>> ┌───────────────┬───────────────┬─────────────────┬─────────────────┬───────────────┐ > >>>>> > >>>>> │13 4 19 43 3 52│10 1 4 46 52 11│38 12 48 50 54 45│36 54 39 35 53 50│44 > >>>> 1 7 > >>>>> 54 11 41│ > >>>>> > >>>>> > >>>>> > >>>> > >>> └───────────────┴───────────────┴─────────────────┴─────────────────┴───────────────┘ > >>>>> > >>>>> > >>>>> > >>>>> Skip Cave > >>>>> Cave Consulting LLC > >>>>> ---------------------------------------------------------------------- > >>>>> For information about J forums see http://www.jsoftware.com/forums.htm > >>>>> > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see http://www.jsoftware.com/forums.htm > >>>> > >>> > >>> > >>> -- > >>> > >>> Devon McCormick, CFA > >>> > >>> Quantitative Consultant > >>> ---------------------------------------------------------------------- > >>> 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
