In my exploration of the Bell numbers I hit on something strange.
ptr=: [:+/\ {:, ]
PTR=: [:+/\. ], {.
are two verbs which produce the Pierce numbers
http://www.research.att.com/~njas/sequences/A011971
ptr^:(i.`(x:@1:))5
1 0 0 0 0
1 2 0 0 0
2 3 5 0 0
5 7 10 15 0
15 20 27 37 52
PTR^:(i.`(x:@1:))5
1 0 0 0 0
2 1 0 0 0
5 3 2 0 0
15 10 7 5 0
52 37 27 20 15
Notice the row wise relation between the two:
(ptr^:(i.`(x:@1:)) (-:|.)&{: PTR^:(i.`(x:@1:)))120
1
But look at the amazing difference in performance:
5 ts'ptr^:(i.`(x:@1:))120'
0.40665763 1604992
5 ts'PTR^:(i.`(x:@1:))120'
0.014059384 1604992
Same amount of space, but almost 30 times as fast!!
Any explanation ???
BTW, this leads to a (1.6 times) faster verb for Bell numbers:
5 ts'Bn2 120'
0.014777791 1594880
(Bn1-:1,Bn2) 120
1
although 10 times more space is used
R.E. Boss
> -----Oorspronkelijk bericht-----
> Van: [EMAIL PROTECTED] [mailto:programming-
> [EMAIL PROTECTED] Namens R.E. Boss
> Verzonden: dinsdag 18 december 2007 20:51
> Aan: 'Programming forum'
> Onderwerp: RE: [Jprogramming] Bell numbers
>
> If Pascals triangle is used for (i.! <:) , a considerable improvement can
> be
> achieved:
>
> Bn1=:[:{. (({.,[:+/ */),:(0&,+ ,&0)@{:)^:(]`(,:[EMAIL PROTECTED]:@1:))
>
> (Bn-:Bn1 )120
> 1
> 5 ts'Bn 120'
> 0.32217713 140928
> 5 ts'Bn1 120'
> 0.02378813 167424
>
> more than 10 times as efficient.
>
>
> R.E. Boss
>
>
> > -----Oorspronkelijk bericht-----
> > Van: R.E. Boss [mailto:[EMAIL PROTECTED]
> > Verzonden: maandag 17 december 2007 22:20
> > Aan: 'Programming forum'
> > Onderwerp: RE: [Jprogramming] Bell numbers
> >
> > Better performance gives the recursive formula from
> > http://en.wikipedia.org/wiki/Bell_number
> >
> > Bn=: (, [:+/ (i.! <:)@# *])^:(]`(x:@1:))
> >
> > 5 ts 'bellN0X i.120'
> > 0.47826126 3212288
> >
> > 5 ts'Bn<: 120'
> > 0.30759069 140800
> >
> > ([EMAIL PROTECTED] -:Bn@<:) 120
> > 1
> >
> >
> > R.E. Boss
> >
> >
>
>
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