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
