When I read the preface to The Blue Book (The New S Language, Becker,
Chambers & Wilks) I see comments along the lines of "high-level
language", "primary goal of the S environment is to enable and encourage
good data analysis", etc. While vectorization is a great feature of S
(and R), I don't see it, or programming efficiency, mentioned there at all.
Nonetheless, Peter's suggestion of a general Vectorize() function is
intriguing, and could be useful with other functions that trip users up
in the same way. (Also, I do apprecicate Peter pointing out that not
all functions vectorize naturally, as in his example density
calculations over grids of parameters).
So, here's a first pass at a general Vectorize() function:
Vectorize <- function(FUN, vectorize.args) {
if (!all(is.element(vectorize.args, names(formals(FUN)))))
stop("some args to vectorize are not args of FUN")
FUNV <- eval(substitute(function(x, ...) mapply(FUN, x,
MoreArgs=list(...)), list(FUN=FUN)))
formals(FUNV) <- formals(FUNV)[c(rep(1, length(vectorize.args)), 2)]
names(formals(FUNV))[seq(along=vectorize.args)] <- vectorize.args
body(FUNV) <- body(FUNV)[c(1, 2, rep(3, length(vectorize.args)), 4)]
body(FUNV)[seq(3,len=length(vectorize.args))] <-
lapply(vectorize.args, as.name)
FUNV
}
ssd <- function(A,alpha,Y,t) sum((Y - A*exp(-alpha*t))2)
# SSD is a vectorized version of ssd
SSD <- function(Avec, alphavec, ...) mapply(ssd, Avec, alphavec,
MoreArgs=list(...))
# Vectorize(ssd, c("A", "alpha")) should produce
# function(A, alpha, ...) mapply(ssd, A, alpha, MoreArgs=list(...))
Y <- 1:5; t <- 3
outer(1:3, 1:2, SSD, Y, t)
outer(1:3, 1:2, Vectorize(ssd, c("A", "alpha")), Y, t)
> # transcript of running the above commands
> Vectorize(ssd, c("A", "alpha"))
function (A, alpha, ...)
mapply(function (A, alpha, Y, t)
sum((Y - A * exp(-alpha * t))^2), A, alpha, MoreArgs = list(...))
<environment: 0x1361f40>
> Y <- 1:5; t <- 3
> outer(1:3, 1:2, SSD, Y, t)
[,1] [,2]
[1,] 53.51878 54.92567
[2,] 52.06235 54.85140
[3,] 50.63071 54.77719
> outer(1:3, 1:2, Vectorize(ssd, c("A", "alpha")), Y, t)
[,1] [,2]
[1,] 53.51878 54.92567
[2,] 52.06235 54.85140
[3,] 50.63071 54.77719
>
[There are a couple of minor design issues around syntax -- what is the
best way of specifying the arguments to vectorize? (e.g., what about an
interface that allowed Vectorize(ssd ~ A * alpha)?), and should the
function name rather than the definition appear in the result of
Vectorize()? But those are issues of secondary importance.]
I have to confess I don't really understand how environments work with
functions, so I don't know if this Vectorize() function will work in
general. What is the appropriate environment for returned value of
Vectorize()? Is this approach to creating a Vectorize() function on the
right tack at all? Any other improvements or fixes?
-- Tony Plate
Peter Dalgaard wrote:
> Thomas Lumley <[EMAIL PROTECTED]> writes:
>
>
>>On Sun, 30 Oct 2005, Jonathan Rougier wrote:
>>
>>
>>>I'm not sure about this. Perhaps I am a dinosaur, but my feeling is
>>>that if people are writing functions in R that might be subject to
>>>simple operations like outer products, then they ought to be writing
>>>vectorised functions!
>>
>>I would agree. How about an oapply() function that does multiway (rather
>>than just two-way) outer products. Basing the name on "apply" would
>>emphasize the similarity to other flexible, not particularly optimized
>>second-order functions.
>
>
> In fairness, it should probably be said that not all problems
> vectorize naturally. One example is
>
> ssd <- function(A,alpha) sum((Y - A*exp(-alpha*t))^2)
>
> However, it should be worth noting that with the mapply() function at
> hand, it is pretty easy to turn a non-vectorized function into a
> vectorized one.
>
> SSD <- function(A,alpha) mapply(ssd, A, alpha)
>
> (Anybody want to try their hand on writing a general Vectorize()
> function? I.e. one that allowed
>
> outer(Avec, alphavec, Vectorize(ssd))
>
> to work.)
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