generating matrices/using outer

Question

I'm a new (~1 day old) R user. I'm trying to generate all 216 outcomes of three throws of a six-sided die. The point is to then apply some function to each triplet (say, maximum face value). This is what I've come up with:

mat <- matrix(numeric(0), ncol=3)
for (i in 1:6) {
    for (j in 1:6) {
        for (k in 1:6) {
            mat <- rbind(mat, c(i, j, k))
        }
    }
}

# find maximum of each outcome
apply(mat, 1, max)

Is there a better and more concise way to do this with R? I would've liked to use outer this way:

outer(1:6, outer(1:6, 1:6, max), max)

but it fails with the error

Error in outer(1:6, 1:6, max) : dims [product 36] do not match the length of object [1]

Answer 1

We can use expand.grid to create the combinations in a data.frame, convert to matrix and get the maximum value of each row by rowMaxs from library(matrixStats).

library(matrixStats)
rowMaxs(as.matrix(expand.grid(rep(list(1:6),3))))
#[1] 1 2 3 4 5 6 2 2 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 2
#[38] 2 3 4 5 6 2 2 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 3 3
#[75] 3 4 5 6 3 3 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 4 4 4
#[112] 4 5 6 4 4 4 4 5 6 4 4 4 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 5 5 5 5
#[149] 5 6 5 5 5 5 5 6 5 5 5 5 5 6 5 5 5 5 5 6 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6
#[186] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

Or we can use pmax with expand.grid

do.call(pmax, expand.grid(rep(list(1:6),3)))

Or as suggested by @Ben Bolker, we can also use apply with MARGIN=1

apply(expand.grid(rep(list(1:6),3)),1,max) 

---

Another option is outer with pmax.

c(outer(1:6, outer(1:6, 1:6, FUN=pmax), FUN= pmax))
#[1] 1 2 3 4 5 6 2 2 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 2
#[38] 2 3 4 5 6 2 2 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 3 3
#[75] 3 4 5 6 3 3 3 4 5 6 3 3 3 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 4 4 4
#[112] 4 5 6 4 4 4 4 5 6 4 4 4 4 5 6 4 4 4 4 5 6 5 5 5 5 5 6 6 6 6 6 6 6 5 5 5 5
#[149] 5 6 5 5 5 5 5 6 5 5 5 5 5 6 5 5 5 5 5 6 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6
#[186] 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

Or outer with Vectorized max

f1 <- function(x,y) max(x,y)
c(outer(1:6, outer(1:6, 1:6, Vectorize(f1)), Vectorize(f1)))