Get all possible combinations by row in matrix

Question

I have an m x n matrix that looks like this:

1 2 3
4 5 6

What is the fastest way to get all possible combinations by row? In this case, that would be c(1,4), c(1,5), c(1,6), c(2,4), c(2,5) ... c(3,5), c(3,6)

How do I solve this using a vectorized approach? In general an m x n matrix would have n^m such combinations.

Answer 1

You can use the expand.grid function to get all combinations of the elements in each row, building a list of rows using split as shown here and passing each element of that list to expand.grid with the do.call function:

(m <- rbind(1:3, 4:6))
#      [,1] [,2] [,3]
# [1,]    1    2    3
# [2,]    4    5    6
do.call(expand.grid, split(m, rep(1:nrow(m), ncol(m))))
#   1 2
# 1 1 4
# 2 2 4
# 3 3 4
# 4 1 5
# 5 2 5
# 6 3 5
# 7 1 6
# 8 2 6
# 9 3 6

Here's an example with a 3 x 2 matrix instead of a 2 x 3 matrix:

(m <- matrix(1:6, nrow=3))
#      [,1] [,2]
# [1,]    1    4
# [2,]    2    5
# [3,]    3    6
do.call(expand.grid, split(m, rep(1:nrow(m), ncol(m))))
#   1 2 3
# 1 1 2 3
# 2 4 2 3
# 3 1 5 3
# 4 4 5 3
# 5 1 2 6
# 6 4 2 6
# 7 1 5 6
# 8 4 5 6