Yes, those are not precise terms. I personally think of &. as embodying
conjugation (from group theory). For monads, the analogy is often precise:
u&.v y <-> v^:_1 u v y
But you are right, the idea of conjugation is abstract enough that it is
embodied by a dizzingly wide variety of applications: vector space base
transformation, measure of operator non-commutivity, localization of the
effects Rubik's cube turns, even complex conjugation etc.
Anyway, specifically in th case of u&.>, since < is "box" and > is pretty much
"unbox", I figured "do" and "undo" are reasonable approximations for a gentle
explatation in the case at hand. Hopefully, it's helpful to Skip.
Hauke Rehr <hauke.r...@uni-jena.de> wrote:
> In my opinion, “do” and “undo” is not the idea/concept of &.
> and doesn’t get across what it actually does.
>
> &. is very helpful in a plethora of use cases
> it is like transform, work in transformed space, transform back
> (like working with conjugate matrices or in fourier space, e.g.)
>
> From my personal experience (which is not much),
> I’ve had most use of &. with v ∈ { >, |., |: }
> but being aware of what it does for you will make
> you find it’s useful in many more cases.
>
> hope this helps
>
>
> Am 13.03.20 um 08:55 schrieb ethiejiesa via Programming:
> > 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
