I think you need to change your definition of Fdot for the v=. [: case
to use > u&.>
Consider, for example, this cheesy example:
, Fdot [: <^:4"0 'abcdef'
(In real life, though, you might actually be working with moderately
deeply nested data, even with folds.)
That's all I can think of, at the moment.
Thanks,
--
Raul
On Wed, Aug 3, 2016 at 9:11 AM, Henry Rich <henryhr...@gmail.com> wrote:
> Thanks for the ideas, guys. New proposal below.
>
> Let's keep the definition in explicit form, so that we can have more readers
> involved.
>
> u/\ has no place here: it requires u to be associative.
>
> Definition:
>
> [x] u F. v y
>
> where
>
> u is a verb to be applied repeatedly
> v is a verb to apply to the result of each execution of u, to
> produce the part saved in the final result, or [: to get the full result of
> only the final execution of u
> x is the (optional) initial value (if omitted, u is applied first
> between the last 2 items of y)
> y is the argument array
> F. applies between items of y starting at the end, F: starts at the front.
> In either case the x argument to u is the next item of y, and the y argument
> to u is the initial value/state from previous execution.
>
> Formal definition:
> Fdot =: 2 : 0
> cap =. [:
> if. 'v' -:&(5!:1)&< 'cap' do.
> u&:>/ (<"_1 y)
> else.
> v@> u&.>/\. (<"_1 y)
> end.
> :
> cap =. [:
> if. 'v' -:&(5!:1)&< 'cap' do.
> u&:>/ (<"_1 y) , <x
> else.
> v@> u&.>/\. (<"_1 y) , <x
> end.
> )
>
> Fcolon =: 2 : 0
> cap =. [:
> if. 'v' -:&(5!:1)&< 'cap' do.
> u&:>/@|. (<"_1 y)
> else.
> v@> u&.>/\.&.|. (<"_1 y)
> end.
> :
> cap =. [:
> if. 'v' -:&(5!:1)&< 'cap' do.
> u&:>/ (|. <"_1 y) , <x
> else.
> v@> u&.>/\.&.|. (<"_1 y) ,~ <x
> end.
> )
>
>
>
> Example:
>
> f =. ((i. , ]) >./)@:(({:@])`({.@])`[})
>
> this takes x=list and y=index,value. It stores value into x at location
> index, and returns the index and value of the largest atom in the resulting
> list. (Yeah, it's a punk function.)
>
> 0 0 f Fdot (1&{) a =: 20 20 ?@$ 10099 99 99 99 99 99 99 99 99 99 99 99
> 99 99 99 99 99 99 99 96 0
>
>
> The result is the list of the indexes that were encountered.
>
> 0 0 f Fdot [: a =: 20 20 ?@$ 100
>
> 2 99
>
>
> The result is the result of the last execution only.
>
>
> Henry Rich
>
>
> On 8/3/2016 4:11 AM, 'Pascal Jasmin' via Source wrote:
>>
>> posting code before words,
>>
>> reduce2 =: (((&.>)/)(>@:))(@:(<"_1@:[ , <@:]))
>> reduce3 =: ((((&.>)/)\.)(>@:))(@:(<"_1@:[ , <@:]))
>>
>> Rdot =: 2 : '>@:(u&.>(n aar 5!:0))@:(<"_1@:[ , <@:])'
>> Rdot1 =: 2 : '>@:(u&.>(n aar 5!:0))@:(<"_1@:[ ,~ <@:])'
>>
>> + reduce2
>>>
>>> @:(+&.>/)@:(<"_1@:[ , <@:])
>>
>> + Rdot '/'
>>>
>>> @:(+&.>/)@:(<"_1@:[ , <@:])
>>
>> + reduce2
>>>
>>> @:(+&.>/)@:(<"_1@:[ , <@:])
>>
>>
>> + reduce3
>>>
>>> @:(+&.>/\.)@:(<"_1@:[ , <@:])
>>
>> + Rdot '/\.'
>>>
>>> @:(+&.>/\.)@:(<"_1@:[ , <@:])
>>
>> They are grouped by equivalent use. Rdot1 reverses the order, but the
>> only point of that seems to use (Rdot1 '/\') instead of Rdot '/\.' Rdot1
>> '/\' could easily have a reduce4 adverb "predefinition".
>>
>>
>> The first thing you seem to be missing is using just / instead of /\. Its
>> a much more common use. The next point is that Ndot1 probably should use /\
>> instead of /\.
>>
>>
>>
>> 1 2 + Rdot'/'~ 1 2 3 4
>> 11 12
>> 1 2 + Rdot'/\.'~ 1 2 3 4
>> 11 12
>> 10 11
>> 8 9
>> 5 6
>> 1 2
>> 1 2 + Rdot1'/\'~ 1 2 3 4
>> 1 2
>> 2 3
>> 4 5
>> 7 8
>> 11 12
>>
>> Rdot1 isn't absolutely necessary because (u Rdot'/\.'~ |.) will produce
>> all of the same items in reverse order.
>>
>>
>>
>> I don't think any other use case makes sense. And I don't see a monadic
>> application making sense either. A monad would just use / or /\. or /\
>> instead. The other model is:
>>
>>
>> reducE =: 1 : (':'; 'o=. x for_i. y do. o =. o u i end.')
>>
>> which is the same as u~ reduce2~
>>
>>
>> The next point to notice is that the pattern (adverb) (>@:)(@:(<"_1@:[ ,
>> <@:])) imposes a guarantee on its u argument to produce a consistent shape.
>> In terms of looking for special code, there's just 2 necessary patterns on
>> the left: (&.>/) or (&.>/\.)
>>
>> bit 1: if / and /\. are the only practical uses of this, then the result
>> can always be unboxed at the end. because u&.>/ started with 2 boxes on.
>> If u wants to add "extra" box layers, then u can do so, and it is up to u to
>> figure out a consistent interpretation. Usually pretty straightforward, but
>> I'd need to see a use case for bit1 "auto-boxing" that is diffucult to do in
>> u.
>>
>> imo bit0 is not needed, but bit 2 is / or /\. . A 3rd conceivable use
>> that may be too esoteric is instead of (<"_1@:[ , <@]) :
>> <@(<\@:[ ,. <@]) or
>> <@(<\.@:[ ,. <@])
>>
>>
>> this builds boxes of lists of boxes, and is different from the "core
>> pattern" I described above. What seems to actually be the core pattern is
>> the 2:
>>
>> ((&.>)/)(>@:)(list of boxings adverb)
>>
>> ((&.>)/\.)(>@:)(list of boxings adverb)
>>
>> where the "list of boxings adverb" could be limited to:
>>
>> @:(u(<"_1@:) , v(<@:)) and maybe
>> @:(u(<"_1@:) ,~ v(<@:))
>>
>> u and v can maybe even be limited to [ ]
>>
>> there's a similar pattern in ,&< ... We know that both sides (and that
>> count = 2) were homogeneous prior to their boxings. In the case of
>>
>>
>> (>@:)(list of boxings adverb)
>>
>> we know that u (to left of this adverb) must create a homogeneous result
>> (or error). In addition to fold/scan operations, u can also be something
>> like x&{ leaf.
>>
>> in the context of fold/scan,
>>
>> fold(initialstate, array, function) the u and v in the above pattern are
>> initialstate and array. As you know, the optimization potential is that
>> they never have to be boxed. The point of the rambling, is that there is a
>> more general pattern in (>@:)(@:(boxing of 2 variables verb))
>>
>> I'd recommend against putting an extra function parameter for twiddling
>> (reversing) x or y. I think its better for user to pretweak them, or they
>> can write/use a modifier that adds the functionality.
>>
>>
>> about v,
>>
>> your implementation I think means that it can only be a noun, and so I
>> think the result would always have a compatible shape, and so no need to box
>> it. An alternative to a v parameter to function is special code for
>>
>> (v {"_1 (bound N.)), and then consider {. {: # without the "_1
>> restriction.
>> (v {"1 _1 L:0 _ (bound N.)) might also solve the box/no box bit.
>>
>>
>> A problem with having a v embedded parameter in the modifier is that it
>> may be a function of the data. 90%+ of the time, you will want all of it.
>> A selection formula might be (<@i.@#"_1 {"1 _1 leaf ]) even though the same
>> (selection vector) value would most likely be generated for all items.
>> Basically having a v parameter embedded in the modifier would mean instead
>> of
>>
>> v&{&.> u&.>/\. (<"_1 y) , <x
>>
>> have
>>
>> v&.> u&.>/\. (<"_1 y) , <x
>>
>> This would let ] be a simple v parameter to get the full results. In
>> terms of optimization, you may not need to care whether # or {. is used.
>> The shape is not guaranteed linear either, so v may be much more complex
>> than a noun argument to { .
>>
>> The v parameter is obviously not needed for / version. Seperate functions
>> are good if you accept that both are useful. But you can also look at it as
>> 3 function patterns
>>
>> u (((&.>)/)(>@:))(@:(boxing of 2 variables)) (reduce2)
>> u reduce3(v&>@:) NB. /\. version
>>
>> u reduce3(v&.>@:)
>>
>> But for the latter 2, it may be better and simpler to do it through
>> special code detection? If you call either
>>
>> (u reduce3)(v&.>@:)
>> or
>>
>> v&.>@:(u reduce3)
>>
>> then v can get "optimized within the main loop"
>>
>>
>> ----- Original Message -----
>> From: Henry Rich <henryhr...@gmail.com>
>> To: Source forum <sou...@jsoftware.com>
>> Sent: Tuesday, August 2, 2016 8:43 PM
>> Subject: [Jsource] Proposal for new looping primitive x N.
>>
>> As Marshall once noted, the biggest deficiency in J is looping over an
>> array when you need a result from each iteration, and the calculation
>> requires an initial value and some internal state. Your code looks like
>>
>> result {"_1 f/\. array , initialstate
>>
>> where each execution of f produces a result value plus the internal
>> state to feed into the next iteration. The problems are:
>> * the result is the entire array of internal state, which is more, maybe
>> MUCH more than you need, since the final result needs only a portion of
>> the state
>> * The state is probably not commensurate with a item of the array, so
>> you end up boxing the initial state and the array items, which is very
>> wasteful.
>>
>> I propose a new primitive, call it N. (for insert). N. is an adverb
>> that produces a conjunction. In (x N.), x specifies options for the
>> processing, much as the right operand of u;.n does.
>>
>> Definition:
>>
>> [x] u (n N.) v y
>>
>> where
>>
>> u is the function to be applied
>> v is the selector to apply to the result of each execution of u, to
>> produce the part saved in the final result
>> x is the (optional) initial value (if omitted, f is applied first
>> between the last 2 items of y)
>> y is the argument array
>> n selects from several variants:
>> bit 0=0 operation goes back to front
>> bit 0=1 operation goes front to back, as if using &.|.
>> bit 1=0 selected result from each iteration becomes one item of result
>> bit 1=1 selected result from each iteration is boxed before becoming
>> an item of result
>>
>> Formal definition:
>> Ndot0 =: 2 : 0
>> v&{@> u&.>/\. (<"_1 y)
>> :
>> v&{@> u&.>/\. (<"_1 y) , <x
>> )
>> Ndot1 =: 2 : 0
>> v&{@> u&.>/\.&.|. (<"_1 y)
>> :
>> v&{@> u&.>/\.&.|. (<"_1 y) ,~ <x
>> )
>> Ndot2 =: 2 : 0
>> v&{&.> u&.>/\. (<"_1 y)
>> :
>> v&{&.> u&.>/\. (<"_1 y) , <x
>> )
>> Ndot3 =: 2 : 0
>> v&{&.> u&.>/\.&.|. (<"_1 y)
>> :
>> v&{&.> u&.>/\.&.|. (<"_1 y) ,~ <x
>> )
>>
>> Ndot =: 1 : 0
>> assert. m e. i. 4
>> select. m
>> case. 0 do. Ndot0
>> case. 1 do. Ndot1
>> case. 2 do. Ndot2
>> case. 3 do. Ndot3
>> end.
>> )
>>
>>
>> I look forward to criticism of this proposal.
>>
>> Henry Rich
>>
>> ----------------------------------------------------------------------
>> 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
