Question

I have a function of two scalar values x_i, y_j. I have a vector of n x_i values, X and n y_j values, e.g.

myfunction <- function(x,y) min(x,y)
X <- 1:3
Y <- 2:4

I want to fill out the $n$ by $n$ matrix whose elements (i,j) are given by myfunction(x_i, y_j). There’s a lot of ways to do this in R, and I’m curious about their relative performance.

For instance, this seems like a task for outer, but it seems to get confused whether it is passing a vector or scalar to myfunction. First consider:

r
outer(X, Y, paste)


gives me each of the pairs

     [,1]  [,2]  [,3] 
[1,] "1 2" "1 3" "1 4"
[2,] "2 2" "2 3" "2 4"
[3,] "3 2" "3 3" "3 4"

Looks good. But

outer(X, Y, myfunction)

throws the error:

Error: dims [product 9] do not match the length of object [1]

Meanwhile other possible functions seem to behave as I expected with scalars, such as:

myfunction <- function(x,y) exp((x-y)^2)

which works fine

outer(X, Y, myfunction)


         [,1]      [,2]        [,3]
[1,] 2.718282 54.598150 8103.083928
[2,] 1.000000  2.718282   54.598150
[3,] 2.718282  1.000000    2.718282

In a few quick numerical experiments, it seems this is slightly faster than expand.grid, and the function call more compact, but I don’t seem to understand why some functions appear to work as I anticipate and others do not.

The classic expand.grid solution also requires the function to work with vector arguments, which means a very different thing for my example with min; a different version of the same problem. Is there a way to enforce the fact that the arguments to my function must be scalars rather than vectors?

Answer 1

The function passed to outer must be vectorized,

From the source code

   FUN <- match.fun(FUN)
        Y <- rep(Y, rep.int(length(X), length(Y)))
        if (length(X)) 
            X <- rep(X, times = ceiling(length(Y)/length(X)))
        robj <- FUN(X, Y, ...)
        dim(robj) <- c(dX, dY)

min will return a single number, you would want pmin.

More generally you could use Vectorize.