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

[David Winsemius]

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()

>
> Thanks for your time.
>
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David Winsemius, MD
West Hartford, CT