It has of course no effect on a (first) call:
it's an iteration, not a recursion. :-\
For successive calls with the same argument
I presume the result is still in memory?
-------....-----------------
In trying to understand what's going on:
bellN0 120
5.1263e145
bellN0 120x
5.1263e145
???
bellN17=: [:{.([:+/\{:,])^:(]`1:)
timer 'bellN17 120'
0.000223
timer 'bellN0 120'
0.000244
bellN0X=:[:{."1 (([:+/\{:,])^:(]`(x:@1:)))
timer 'bellN0X 120'
0.582729
That's why bellN0 has a major speed advantage??
So I think the imperative bellN1 is still the winner
for big values (ext. prec.).
timer 'bellN1 120'
0.126827
Hints:
- think arraywise
- avoid loops
- avoid low ranks
But, here's what I still have to work on :-(
Thanks
FWIW:
I was inspired by an amazing approach in Haskell
nextRow :: [Integer] -> [Integer]
nextRow r = next
where next = last r : zipWith (+) r next
...and I've not enough experience to emulate
(translate) that in J.
R.E. Boss schreef:
> Notice the difference between bellN and (the improved version) bellN0:
>
> bellN=: [:{.([:+/\{:,x:&])^:(]`1:) M.
> bellN0=:[:{."1 (([:+/\{:,])^:(]`1:))
>
> (bellN0 -: bellN"0)i.120x
> 1
>
> 5 ts'bellN"0 i.120x'
> 0.23613405 22528
>
> 5 ts'bellN0 i.120x'
> 0.00025226441 244864
>
> which is 86 times as efficient.
>
>
> BTW, what does M. do?
>
>
> R.E. Boss
>
>
>
>> -----Oorspronkelijk bericht-----
>> Van: [EMAIL PROTECTED] [mailto:programming-
>> [EMAIL PROTECTED] Namens Arie Groeneveld
>> Verzonden: zaterdag 15 december 2007 17:01
>> Aan: Programming forum
>> Onderwerp: [Jprogramming] Bell numbers
>>
>> J4F
>>
>> Generating Bell numbers based on using
>> the pierce Triangle.
>>
>> bell numbers: 1,1,2,5,15,52,203,877,4140,21147,115975
>>
>> I can come up with these two verbs
>>
>> NB. for n>21 I need to add ext. precision -- x:&]
>> bellN=: [:{.([:+/\{:,x:&])^:(]`1:) M.
>>
>> NB. next pierce triangle row
>> vp3hr=: 3 : 0
>> v=.{:y
>> for_i. i.#y do.
>> v=. v,(i{v)+i{y
>> end.
>> )
>>
>> bellN1=: [:{.vp3hr^:(]`(x:@1:))
>>
>>
>> bellN"0 i.10
>> 1 1 2 5 15 52 203 877 4140 21147
>>
>> bellN1"0 i.10
>> 1 1 2 5 15 52 203 877 4140 21147
>>
>> (bellN -: bellN1) 100
>> 1
>>
>> timer 'bellN1 100'
>> 0.086825
>>
>> timer 'bellN 100' NB. first call
>> 0.305226
>>
>>
>>
>> Other possibilities?
>>
>>
>> Regards
>>
>> =@@i
>>
>>
>>
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>>
>
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>
>
>
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