Yes it's more instructive, so just replace my version with yours (it's a
wiki: open for improvements). nextY (among other issues) is is indeed a
more instructive name (in the meantime I changed mine locally to yn1:
still a bit cryptic).
On 14-05-12 10:19, Ric Sherlock wrote:
> I really appreciate this illustration of how to reformulate an
> accumulating loop using a running suffix. I think having both versions
> on RC is a great way of helping those interested understand how the J
> approach differs.
>
> I've had another look at the problem and this is how I'd suggest
> formating the solution for the audience at Rosetta Code.
>
> nextY=: adverb define
> :
> tableau=. 1 0.5 0.5, x * u y
> ks=. (x * [: u y + (* x&,))/\. tableau
> ({:y) + 6 %~ +/ 1 2 2 1 * ks
> )
>
> rk4M2=: adverb define
> 'Y0 a b h'=. 4{. y
> T=. a + i.@>:&.(%&h) b-a
> (,. [: h&(u nextY)@,/\. Y0 ,~ }.)&.|. T
> )
>
> All versions produce the same result:
>
> (fyp rk4 -: fyp rk42) 1 0 10 0.001
> 1
> (fyp rk4 -: fyp rk4M) 1 0 10 0.001
> 1
> (fyp rk4 -: fyp rk4M2) 1 0 10 0.001
> 1
>
> In my opinion there aren't any worthwhile differences in performance
> for any of the versions and I think that clarity is more important for
> RC anyway, however for the purposes of completeness ...
> (Note that the verb timespacex is defined in stdlib.ijs in J7)
> 10 timespacex 'fyp rk4 1 0 10 0.001'
> 0.1677 531584
> 10 timespacex 'fyp rk42 1 0 10 0.001'
> 0.13001 531584
> 10 timespacex 'fyp rk4M 1 0 10 0.001'
> 0.131611 798336
> 10 timespacex 'fyp rk4M2 1 0 10 0.001'
> 0.146232 665344
>
>
> On Sat, May 12, 2012 at 5:32 AM, Aai<agroeneveld...@gmail.com> wrote:
>> Observation: the following variant of Ric's contribution gains in speed
>> by using a one-line 'pseudo fold' for the loop calculations.
>>
>> Here are the timings:
>>
>> ts@(,&' args')&> 'fyp rk4';'fyp rk42' [args=. 1 0 10 0.001
>> 0.551397 527936
>> 0.449719 527936
>>
>> rk42 is almost as fast (?) as my rk4M.
>>
>> mind line wrapping
>>
>> rk42=: 1 :0
>> Y=.Yt=.{. 'Y0 a b h'=. 4{. y
>> T=. a + i.@>:&.(%&h) b - a
>> for_t. }: T do.
>> Y=.Y,Yt=.Yt+6%~+/1 2 2 1*k1,k2,k3,k4=.h*u ty+h,k3=.h*u ty+-:h,k2=.h*u
>> ty+-:h,k1=.h*u ty=.t,Yt
>> end.
>> T ,. Y
>> )
>>
>>
>>
>> On 10-05-12 22:52, Ric Sherlock wrote:
>>> Yes thanks for this. I wasn't especially happy with the existing
>>> solution. I agree with Raul that it would be nicer to be consistent
>>> with the definition style.
>>> I'll try to have a go over the weekend but if it is possible to break
>>> either of those long lines up into more recognizable (to non tacit J
>>> users) chunks. I think that would be worthwhile.
>>>
>>> On Fri, May 11, 2012 at 8:12 AM, Raul Miller<rauldmil...@gmail.com>
>>> wrote:
>>>> On Thu, May 10, 2012 at 1:46 PM, Aai<agroeneveld...@gmail.com> wrote:
>>>>> The J contribution on Rosetta Code
>>>>> http://rosettacode.org/wiki/Runge-Kutta_method#J for subject is a loopy
>>>>> one. My goal is to change that into a more functional and J-ish one.
>>>>>
>>>>> Here's my attempt for that particular task:
>>>>>
>>>>> p4=: 1 :(':';'({:y)+6%~+/1 2 2 1*(x*[: u y+(*x&,@{:))/\.1 0.5 0.5,x*u y')
>>>>>
>>>>> rk4M=: 1 :0
>>>>> 'Y0 a b h'=. 4{. y
>>>>> (,.[:h&(u p4)@(,{:)/\.Y0,~}.)&.|. a+i.@>:&.(%&h) b-a
>>>>> )
>>>>>
>>>>> (fyp rk4 -: fyp rk4M) 1 0 10 0.001
>>>>> 1
>>>> As a minor point, I think I would change the definition of p4
>>>> to use the same definition format as rk4M
>>>>
>>>> p4=: 1 :0
>>>> :
>>>> ({:y)+6%~+/1 2 2 1*(x*[: u y+(*x&,@{:))/\.1 0.5 0.5,x*u y
>>>> )
>>>>
>>>> But I do not have the time to focus on this one.
>>>>
>>>> I hope I'm not overlooking anything important.
>>>> (I wonder if the parenthesized expressions deserve names?)
>>>>
>>>> Thanks for tackling this!
>>>>
>>>> --
>>>> Raul
>>>> ----------------------------------------------------------------------
>>>> For information about J forums seehttp://www.jsoftware.com/forums.htm
>>> ----------------------------------------------------------------------
>>> For information about J forums seehttp://www.jsoftware.com/forums.htm
>> --
>> Met vriendelijke groet,
>> @@i = Arie Groeneveld
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
--
Met vriendelijke groet,
@@i = Arie Groeneveld
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