[R] Vectorizing a function: what does it mean?

[Duncan Murdoch]

On 09/05/2011 1:31 PM, David Winsemius wrote:
> On May 9, 2011, at 11:57 AM, Ron Michael wrote:
>
> >  Dear all, I would really appreciate if somebody can help me to
> >  understand what does the phrase "Vectorize your function" mean? And
> >  what is the job of Vectorize() function in doing that? I have read
> >  many threads where experts suggest to Vectorize the function, which
> >  will speed up entire calculation (and more elegant ofcourse.)
> >
> >  I used to think that vectorizing function means, to create a
> >  function such a way so that if input(s) are vector then this
> >  function will also return a vector output (without having any extra
> >  effort like use of 'for' loop etc.) Is this understanding correct?
> >
> >  Here I have tried 2 essentially similar functions:
> >
> >>  fn1<- function(x,y,z) return(x+y+z)
> >>  fn2<- Vectorize(function(x,y,z) return(x+y+z), SIMPLIFY=TRUE)
> >>  fn1(1:3, 4:6,5)
> >  [1] 10 12 14
> >>  fn2(1:3, 4:6,5)
> >  [1] 10 12 14
> >
> >
> >  You see that, fn1() and fn2() is giving same answer (vectorized?)
> >  despite of the fact that fn1() is not wrapped within Vectorize()
> >  function. Therefore I want to know: what additional thing this
> >  Vectorize() function brings on the table?
>
> That is because you used "+"  which is "vectorized" to start with. Try
> is with "sum" and you will not be as "happy"
>   >  sum(a=1:3, b=4:6, cc=7:9)
> [1] 45
>
> It removed all your structure.
>
>   >  Vsum<-function(...) {what<- list(...); lenlist<- length(what);
> y<-matrix(unlist(what), ncol=lenlist); apply(y,1,sum)}
>   >  Vsum(a=1:3, b=4:6, cc=7:9)
> [1] 12 15 18
> # Does not recycle as I might have expected, although it does recycle
>   >  (Vsum( a=1:3, b=4:6, cc=7))
> [1] 12  8 11
>
>
>   >  (mapply(sum, a=1:3, b=4:6, cc=7:9))
>    # also works and recycles as expected:
> [1] 12 15 18
>
>   >  (mapply(sum, a=1:3, b=4:6, cc=7))
> [1] 12 14 16
>
> # but _not_ VSum<- Vectorize(sum) for reasons not clear to me behaves
> the same as sum()

The problem with Vectorize(sum) is that Vectorize doesn`t see any 
parameters to vectorize in sum().  It needs simple functions with 
parameters like fn1, and it rewrites them to loop over the values of the 
parameters.

Duncan Murdoch