Applying a function to a specific element of a list of a list

Question

I have a function that returns a list of vectors and matrices. I then create a variable that is a list of several of the resulting lists from calls to the function. So I have a list of lists. My question is how do I apply a function over the elements of these lists (note this is not the same as applying a function over the lists themselves). Here is a simple example that retains all the essential features of what I am doing

numtrials = 5

x = rep(list(NULL),numtrials)

testfunction = function(){return( list( c(1,2,3,4,5), matrix(runif(10), 2,5),
                                    matrix(0,2,2) ) )}

for(index in 1:numtrials){
    x[[index]] = testfunction()
}

I want to now calculate the mean of say the (2,3) element of x[[index]][[2]] across all "index" lists. Or even better get a matrix of means, xbar, such that xbar[i,j] = mean(x[[]][[2]][i,j]). I tried to play around with (and of course read the help file for) lapply, and apply, but couldn't get it to work. One of the reasons is that x[[]][[2]][i,j] appears to be invalid notation

Error in x[[]] : invalid subscript type 'symbol'

I think R doesn't know what to make of the "[[]]". I know some people are going to suggest vectorizing but note that my function returns matrices and vectors of different, unrelated dimensions (although I am not opposed to vectorizing if you have a clever way of doing this).

Answer 1

Using abind you can create a list which contains arrays for the relevent components of the internal lists..

eg

library(abind)

xl <- do.call(mapply, c('abind', x, rev.along = 0))


# the second element from each inner list is now within a 3-d array 
# which is the 2nd element of  xl

# you can now construct your matrix of mean values by using `apply`

means <- apply(xl[[2]], 1:2, mean)
means
##            [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.4576039 0.5185270 0.7099742 0.3812656 0.4529965
## [2,] 0.6528345 0.2304651 0.5534443 0.4404609 0.7361132