Quickly generate the cartesian product of a matrix

Question

Let\'s say I have a matrix x which contains 10 rows and 2 columns. I want to generate a new matrix M that contains each unique pair of rows from

Answer 1

Using Dirk's answer:

idx <- expand.grid(1:nrow(x), 1:nrow(x))
idx<-idx[idx[,1] >= idx[,2],]
N <- cbind(x[idx[,2],], x[idx[,1],])

> all(M == N)
[1] TRUE

Thanks everyone!

Answer 2

Inspired from the other answers, here is a function implementing cartesian product of two matrices, in the case of two matrices, the full cartesian product, for only one argument, omitting one of each pair:

cartesian_prod <- function(M1, M2) {
if(missing(M2)) {  M2 <- M1
     ind  <- expand.grid(1:NROW(M1), 1:NROW(M2))
     ind <- ind[ind[,1] >= ind[,2],] } else {
                                          ind  <- expand.grid(1:NROW(M1), 1:NROW(M2))}
rbind(cbind(M1[ind[,1],], M2[ind[,2],]))

}

Answer 3

I'm not quite grokking what you are doing so I'll just throw out something that may, or may not help.

Here's what I think of as the Cartesian product of the two columns:

expand.grid(x[,1],x[,2])

Answer 4

The expand.grid() function useful for this:

R> GG <- expand.grid(1:10,1:10)
R> GG <- GG[GG[,1]>=GG[,2],]     # trim it to your 55 pairs
R> dim(GG)
[1] 55  2
R> head(GG)
  Var1 Var2
1    1    1
2    2    1
3    3    1
4    4    1
5    5    1
6    6    1
R> 

Now you have the 'n*(n+1)/2' subsets and you can simple index your original matrix.

Answer 5

You can also try the "relations" package. Here is the vignette. It should work like this:

relation_table(x %><% x)