R parallel code for two arrays - arrays

Question

I'm trying to process two 3d arrays using parallel computing in R. I have a function that takes two vectors as input, so I need to loop through the rows and columns of my arrays. Doing this in serial code is simply too slow and R gets stuck as the arrays are large.
I've not found a solution for doing this with parallel functions and would appreciate any suggestions. I've tried parApply but do not know how to incorporate a second input, and mcmapply but it is hard to use over rows/cols. Ideally the output should also be an array of the same dimension.
Below is a reproducible example of what I'm trying to do in serial code. Any help on how this could be written in parallel code would be much appreciated!
fun <- function(a,b)
{
a*b
}
input1 <- array(data=1:1000, dim=c(10,10,10))
input2 <- array(data=2:1001, dim=c(10,10,10))
result <- array(data=NA, dim=c(10,10,10))
for(i in 1:nrow(mat1))
{ for(j in 1:ncol(mat1)) {
result[,i,j] <- fun(input1[,i,j], input2[,i,j])
}}

Answer 1

Here's one way to do it with the foreach package:
library(doSNOW)
library(abind)
cl <- makeSOCKcluster(parallel::detectCores())
registerDoSNOW(cl)
fun <- function(a,b) a*b
input1 <- array(rnorm(60), dim=c(4,5,3))
input2 <- array(rnorm(60), dim=c(4,5,3))
rdim <- dim(input1)[1:2]
comb <- function(...) abind(..., along=3)
result <-
foreach(i1=iapply(input1, 3), i2=iapply(input2, 3),
.multicombine=TRUE, .combine='comb') %dopar% {
r <- array(data=NA, dim=rdim)
for (i in 1:ncol(i1)) {
r[,i] <- fun(i1[,i], i2[,i])
}
r
}
The "iapply" function from the iterators package is used to split the 3D input arrays into 2D matrices. The result matrices are combined into a 3D array using the "abind" function from the abind package.
Note that I'm specifically using the "doSNOW" parallel backend because it sends data from the two "iapply" iterators to the workers and processes the results on-the-fly. This reduces the memory needed by the master process. The "doParallel" backend can't work on-the-fly because the "parallel" package doesn't export the necessary functions.