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 <[email protected]> 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 <[email protected]> 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 <[email protected]>
> > 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 <[email protected]>
> > 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
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