One option is to consider a Kronecker-type expansion.  See code below.
-tgs

perhaps <- function(A,B){
nA <- nrow(A)
nB <- nrow(B)

C <-
kronecker(matrix(1,nrow=nA,ncol=1),B) >=
kronecker(A,matrix(1,nrow=nB,ncol=1))

matrix(rowSums(C) == ncol(A), nA, nB, byrow=TRUE)
}

Marius <- function(A,B) apply(B, 1, function(b) apply(A, 1, function(a)
all(a <= b)))

N <- 1000
M <- 5
P <- 5000
A <- matrix(runif(N,1,1000),nrow=N,ncol=M)
B <- matrix(runif(M,1,1000),nrow=P,ncol=M)


system.time(perhaps(A,B))
system.time(Marius(A,B))


On Sat, Dec 8, 2012 at 6:28 AM, Marius Hofert <marius.hofert@math.ethz.ch>wrote:

> Dear expeRts,
>
> I have two matrices A and B. They have the same number of columns but
> possibly different number of rows. I would like to compare each row of A
> with each row of B and check whether all entries in a row of A are less
> than or equal to all entries in a row of B. Here is a minimal working
> example:
>
> A <- rbind(matrix(1:4, ncol=2, byrow=TRUE), c(6, 2)) # (3, 2) matrix
> B <- matrix(1:10, ncol=2) # (5, 2) matrix
> ( ind <- apply(B, 1, function(b) apply(A, 1, function(a) all(a <= b))) ) #
> (3, 5) = (nrow(A), nrow(B)) matrix
>
> The question is: How can this be implemented more efficiently in R, that
> is, in a faster way?
>
> Thanks & cheers,
>
> Marius
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
>

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