The inverse for m&{ mostly only makes sense when m&{ permutes the argument.
1 2 3 0&{ 'ABCD'
BCDA
1 2 3 0&{inv 'ABCD'
DABC
Then, the inverse reverses the permutation.
Does that help?
Thanks,
--
Raul
On Wed, Mar 2, 2016 at 7:39 PM, Louis de Forcrand <[email protected]> wrote:
> The way J handles inverses to functions is quite unique and, while not
> always very useful, can lead to compact but very descriptive code:
>
> +/&.:*: NB. distance
> +&.^. NB. multiplication
> u&.(a.&i.) NB. u applied to y’s indices in a., then indexed out of a.
> etc.
>
> However, some less easily invertible functions, such as , (ravel), {: and
> related,
> A., m&{ , and others, don’t have a monadic inverse because they are “lossy”
> functions,
> in that there is no function u such that
> y -: u@v y NB. where v is a lossy function
> for an arbitrary y.
>
> However, while there are other lossy functions which I have not cited, the
> ones I
> did are particular in that they are invertible with trains of related dyadic
> functions:
>
> u&., y <—> ($ $ u@,) y
> u&.(m&{.) y <—> (m&}. , u@(m&{.)) y NB. extends to others like }.
> etc.
> NB.
> although {. already has an inverse
> u&.A. y <—> (A.~ u@A.) y
>
> These are all simply “cosmetic”, in that you can obviously write them out
> by hand, but then again, &. is basically cosmetic too. Nevertheless, it leads
> to more elegant and concise code (and sometimes leads to new ways of
> thinking about a problem). However, one inverse that could possibly
> lead to (possibly big?) gains in speed with special code would be:
>
> u&.(m&{) y <—> (m&}~ u@(m&{)) y
>
> This might already be implemented for the fork case.
> I’ve checked, and m&{ already has an inverse, although I don’t see what it’s
> useful for.
>
> On a side note, I’ve noticed that <;.1 has an inverse according to b._1, but
> using it yields a nonce error (which means it hasn’t been implemented yet,
> right?). <;._1@(m&,) could be recognised as a whole as well, so that
> u&.(<;._1@(m&,)) y <—> ({. ;@, m ,&.> }.)@u@(<;._1@(m&,))
> Or it could be added as an obverse to the cut standard library verb.
>
> Again, this can all be done by hand, of course.
>
> Louis
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