I have an nxp matrix and would like to compute the nxn matrix B defined as
B[i, j] = f(A[i,], A[j,])
where f is a function that accepts arguments of the appropriate dimensionality. Is there a neat trick to compute this in R? f is symmetric and positive-definite (if this can help in the computation).
EDIT: Praneet asked to specify f. That is a good point. Although I think it would be interesting to have an efficient solution for any function, I would get a lot of mileage from efficient computation in the important case where f(x, y) is base::norm(xy, type='F').
You can use outer
with the matrix dimensions.
n <- 10
p <- 5
A <- matrix( rnorm(n*p), n, p )
f <- function(x,y) sqrt(sum((x-y)^2))
B <- outer(
1:n, 1:n,
Vectorize( function(i,j) f(A[i,], A[j,]) )
)
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