m=: 3 4
(m}~ >:@(m&{)) 1 2 3 4 5 6
1 2 3 5 6 6
Do you see what I mean?
Louis
On 03 Mar 2016, at 06:54, Raul Miller <[email protected]> wrote:
>> With ammend, no transformation of the indices is needed;
>> m&{^:_1 could be equivalent to m&}.
>
> I think you do not mean m&}. but instead meant m&} because } is amend
> and }. is drop.
>
> But m&} is a syntax error.
>
> So maybe you really meant m} instead?
>
> But m} is not an inverse for m&{ for any significant examples I can think of.
>
> But perhaps I am missing something? This would hardly be the first
> occasion where I've overlooked something obvious. (Could you provide a
> working example of what you were suggesting?)
>
> Thanks,
>
> ---
> Raul
>
>
>> On Wed, Mar 2, 2016 at 9:02 PM, Louis de Forcrand <[email protected]> wrote:
>> Of course. I've even used that before... Silly me. However I still can't
>> understand the inverse of 3&{, for example.
>> The inverse to m&{ is equivalent to
>> (/:~ m)&{ (if (i.@# -: /:~) m).
>> With ammend, no transformation of the indices is needed;
>> m&{^:_1 could be equivalent to m&}.
>> This would also render m&{ compatible with boxed m (in order to index into
>> arrays), and more practical with non-permutation m.
>>
>> Louis
>>
>>
>>> On 03 Mar 2016, at 01:58, Raul Miller <[email protected]> wrote:
>>>
>>> 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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>>> ----------------------------------------------------------------------
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