# [R] How to do it without for loops?

Gabor Grothendieck ggrothendieck at gmail.com
Wed Mar 8 18:30:30 CET 2006

```Yes, its horribly inefficient but as I stated
the reason I mentioned it was because it could be translated
more easily from mathematical notation and I did mention I

Actually one problem with both of the solutions is determining
that they are correct.  From that viewpoint, although not as
elegant or fun, a more straightforward
translation of the original question might actually be preferable
(Thomas also already mentioned the computation in f):

f <- function(x) crossprod(crossprod(x[[3]], as.matrix(x[,1:2])))
mm <-by(dat, dat\$id, f)
mm[[1]] + mm[[2]] + mm[[3]]

or the last line could be replaced with these two if you don't know
that there are necessarily three components:

result <- mm[[1]]
result[] <- do.call("mapply", c(sum, mm))

One thing that this bought out for me is that R does not have
a parallel to pmax for sum.  If one had psum of if "+" allowed
more than 2 arguments one could have done this instead of the
two lines involving result above:

do.call("psum", mm)  # if psum analog to pmax were available
do.call("+", mm)  # if + allowed > 2 arguments

On 3/8/06, Thomas Lumley <tlumley at u.washington.edu> wrote:
> On Wed, 8 Mar 2006, Gabor Grothendieck wrote:
>
> > Thomas' solution is better but thought this might be of interest
> > anyways since it can be written closer to mathematical notation.
> > That is, the required expression can be written in the
> > following equivalent way for a suitable matrix A:
> >
> > X' diag(u) A' A diag(u) X
>
> Um. n x n matrix? O(n^2) storage? O(n^3) execution time? Yes, it's fine
> when n=20, or even 200,  but still...
>
>        -thomas
>
>
>
> > where diag(u) is a diagonal matrix with u along the diagonal
> > as in the R diag function, spaces refer to matrix multiplication
> > and ' means transpose.
> >
> > Thus we have:
> >
> > A <- outer(unique(dat\$id), dat\$id, "==")
> > crossprod(A %*% diag(dat\$u) %*% as.matrix(dat[1:2]))
> >
> >
> > On 3/8/06, Thomas Lumley <tlumley at u.washington.edu> wrote:
> >> On Wed, 8 Mar 2006, ronggui wrote:
> >>
> >>> Thank you for all .
> >>>
> >>> One more question.How can I calculate these efficiently?
> >>>
> >>> set.seed(100)
> >>> dat<-data.frame(x1=rnorm(20),x2=rnorm(20),u=rnorm(20),id=round(2*runif(20)))
> >>> # In this example,id's elements are  0,1,2.
> >>> y<-list()
> >>> for (i in 0:2){
> >>> X<-as.matrix(subset(dat,id==i,c("x1","x2")))
> >>> u<-as.matrix(subset(dat,id==i,c("u")))
> >>> y[[i+1]]<-t(X)%*%u%*%t(u)%*%X
> >>> }
> >>> y[[1]]+y[[2]]+y[[3]]
> >>>
> >>
> >> would seem an obvious improvement over the matrix multiplications.
> >>
> >> There is a better solution, though.
> >>
> >> Xu<-dat[,c("x1","x2")]*dat[,"u"]
> >> crossprod( rowsum(Xu, dat\$id))
> >>
> >>        -thomas
> >>
> >>
> >>> the above code is not elegant.And my second solution to this problem
> >>> is using by to get a list.
> >>>
> >>> matlis<-by(dat, dat\$id, function(x){
> >>> a<-as.matrix(x[,c("x1","x2")])
> >>> b<-as.matrix(x[, "u"])
> >>> t(a) %*% b  %*% t(b) %*% a
> >>> })
> >>>
> >>> S <- matrix(unlist(matlis), 4, length(matlis))
> >>> S1 <- matrix(rowSums(S), 2, 2)
> >>>
> >>> The code works ,but I want to ask if there is any other more better
> >>> ways to do it? It seems that this kind of computation is quite common.
> >>>
> >>>
> >>>
> >>>
> >>>
> >>> 2006/2/28, Gabor Grothendieck <ggrothendieck at gmail.com>:
> >>>> Try:
> >>>>
> >>>> crossprod(x)
> >>>>
> >>>> or
> >>>>
> >>>> t(x) %*% x
> >>>>
> >>>> On 2/28/06, ronggui <ronggui.huang at gmail.com> wrote:
> >>>>> This is the code:
> >>>>>
> >>>>> x<-matrix(rnorm(20),5)
> >>>>> y<-list()
> >>>>> for (i in seq(nrow(x))) y[[i]]<-t(x[i,,drop=F])%*%x[i,,drop=F]
> >>>>> y[[1]]+y[[2]]+y[[3]]+y[[4]]+y[[5]]
> >>>>>
> >>>>> How can I do it without using for loops?
> >>>>> Thank you in advance!
> >>>>> --
> >>>>> ronggui
> >>>>> Deparment of Sociology
> >>>>> Fudan University
> >>>>>
> >>>>> ______________________________________________
> >>>>> R-help at stat.math.ethz.ch mailing list
> >>>>> https://stat.ethz.ch/mailman/listinfo/r-help
> >>>>>
> >>>>
> >>>
> >>>
> >>> --
> >>> »ÆÈÙ¹ó
> >>> Deparment of Sociology
> >>> Fudan University
> >>>
> >>>
> >>
> >> Thomas Lumley                   Assoc. Professor, Biostatistics
> >> tlumley at u.washington.edu        University of Washington, Seattle
> >>
> >> ______________________________________________
> >> R-help at stat.math.ethz.ch mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >>
> >>
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help