将函数应用于列表中的元素组合

Question

I would like to iterate through pairwise combinations of elements in a list in R, and then execute a function using the combination as an input.

In this minimal example I (1) define three matrices, (2) combine them into a list containing the matrices as elements, and then (3) would like to calculate the dot product of the combinations of the elements in the list (ie. matrix 1 vs. matrix 2 and matrix 2 vs. matrix 3).

set.seed

m1 = as.matrix(replicate(2, rnorm(2)))
m2 = as.matrix(replicate(2, rnorm(2)))
m3 = as.matrix(replicate(2, rnorm(2)))

matrix.list = list(m1, m2, m3)

dot.prod = function(matrix.x, matrix.y){
    return(matrix.x %*% matrix.y)
}

So far I have the following to have all combinations of matrix.list as inputs for dot.prod() using a nested loop.

for (i in 1:length(matrix.list)){

  for (j in 1:length(matrix.list)){

            print(dot.prod(matrix.list[[i]], matrix.list[[j]]))
  }
}

Is it possible to do this by using a combinatorial function in R (like combn())? I would be very grateful for any suggestions.

Edit: the function itself doesn't matter - I want to know how to use combinations of elements from a list as inputs for any R function

Answer 1

Let's just do

oo <- outer(matrix.list, matrix.list, Vectorize(crossprod, SIMPLIFY = FALSE))

which gives you a matrix list. Accessing the result is handy. oo[1,2] (actually get into the list oo[1,2][[1]] ) gives the cross product between matrix 1 and matrix 2.

Note, matrix cross product is not %*% (but if you insist, use Vectorize("%*%", SIMPLIFY = FALSE) ). As the operation is not symmetric, oo[1,2] is different from oo[2,1] .

See How to perform pairwise operation like `%in%` and set operations for a list of vectors for the original idea of this.

---

Thanks for your response. To clarify: I want to calculate the dot product, not the cross product, as I stated in my initial question. However, the function itself doesn't matter - I want to know how to use combinations of elements from a list as inputs for any R function.

No idea of what you want. Give you a few other options and pick up yourself. They are all different.

This?

combn(matrix.list, 2, function (u) u[[1]] %*% u[[2]])

This?

mapply("%*%", matrix.list[-length(matrix.list)], matrix.list[-1], SIMPLIFY = FALSE)