[Jprogramming] forward differences

[R.E. Boss]

   diffx=: 4 :'(}. - }:)^:x y'
   5 diffx (i.10)^5
120 120 120 120 120


R.E. Boss


> -----Oorspronkelijk bericht-----
> Van: programming-bounces at jsoftware.com [mailto:programming-
> bounces at jsoftware.com] Namens Tracy Harms
> Verzonden: woensdag 12 december 2007 23:13
> Aan: programming at jsoftware.com
> Onderwerp: [Jprogramming] forward differences
> 
> Awhile back Rob Hodgkinson brought my attention to the
> forward difference function.
> 
>    ] a=:(i.10)^3
> 0 1 8 27 64 125 216 343 512 729
>    diff=:  }. - }:
>    diff a
> 1 7 19 37 61 91 127 169 217
>    diff^:3 a
> 6 6 6 6 6 6 6
> 
> I want to write a verb that uses the left parameter to
> identify the order of forward difference, and the
> right for the data.
> 
> The problem I encounter seems to turn on my need to
> process a monadic verb within a dyadic context. Here
> are some failed incremental efforts:
> 
>    diff1=:  }. - }:^:1
>    diff1 a
> 1 7 19 37 61 91 127 169 217
>    NB. Success to that small degree. But:
>    diffx=:  }. - }:^:[
>    1 diffx a
> |domain error: diffx
> |   1     diffx a
>    NB. Explicit definition also fails:
>    diffxe=: 3 : '}. - }:^:x y'
>    1 diffxe a
> |domain error: diffxe
> |   1     diffxe a
> 
> How do I keep the left parameter from forcing a dyadic
> interpretation of (}. - }:)?  Or, is that not the
> problem?
> 
> 
> --
> Tracy B. Harms
> 
>      The advantages of executability and universality
>      found in programming languages can be effectively
>      combined, in a single coherent language, with the
>      advantages offered by mathematical notation.
> 				Kenneth E. Iverson
> 
> 
> 
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