apply function to elements over a list

Question

Sorry for the simple question but I can't think of a good way to take functions elements of a list of data frames. I am sure there is something within the plyr/reshape2 packages but I just can't think of it.

For example I have a list A as follows:

>A
[[1]]
        [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
   [1,]    1    1    1    1    1    1    1    1    1     1
   [2,]    1    1    1    1    1    1    1    1    1     1
   [3,]    1    1    1    1    1    1    1    1    1     1
   [4,]    1    1    1    1    1    1    1    1    1     1
   [5,]    1    1    1    1    1    1    1    1    1     1

[[2]]
       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
 [1,]    2    2    2    2    2    2    2    2    2     2
 [2,]    2    2    2    2    2    2    2    2    2     2
 [3,]    2    2    2    2    2    2    2    2    2     2
 [4,]    2    2    2    2    2    2    2    2    2     2
 [5,]    2    2    2    2    2    2    2    2    2     2

Say I want to take the mean across the corresponding elements of the matrices in the list. One way to do this would be

Reduce("+",A)/length(A)

I can't seem to feed Reduce() more complex functions and assume there is a better way in general.

Answer 1

In this case, maybe you're better off with your data in an array rather than a list?

#Recreate data
A <- list(a=matrix(1,5,10),b=matrix(2,5,10))

#Convert to array
A1 <- array(do.call(cbind,A),dim = c(5,10,2))

#Better way to convert to array
require(abind)
A1 <- abind(A,along = 3)

#Now we can simply use apply
apply(A1,c(1,2),mean)

Answer 2

Maybe do.call?

do.call(`+`, A)/length(A)

Or if you really don't want to abind it into a larger matrix,

array(sapply(seq_along(A[[1]]), function(i) mean(sapply(A,`[`,i))), 
      dim=dim(A[[1]]))