Dealing with multidimensional output in parallel programming - r

Question

I am currently working on a program to evaluate the out-of-sample performance of several forecasting models on simulated data. For those who are familiar with finance, it works exactly like backtesting a trading strategy, except that I would evaluate forecasts and not transactions.
Some of the objects I currently manipulate using for loops for this type of task are 7 dimensional arrays (dimensions stand for Monte Carlo replications, data generating processes, forecast horizons, 3 dimensions for model parameter selection, and one dimension for all the periods covered in the out-of-sample analysis). Obviously, it is painfully slow, so parallel computing has became a must for me.
My problem is: how do I keep track of more than 2 dimensions in R? Let's just show you using 'for loops' and only 3 dimensions what I mean:
x <- array(dim=c(2,2,2))
for (i in 1:2){
for (j in 1:2){
for (k in 1:2){
x[i,j,k] <- i+j+k
}
}
}
If I use something like 'foreach', I am very annoyed by the fact that, to my knowledge, available combining functionalities will return lists, matrices or vectors -- but not arbitrarily large multidimensional arrays. For instance:
library(doParallel)
library(foreach)
# Get the number of cores to use
no_cores <- max(1, detectCores()-1)
# Make cluster object using no_cores
cl <- makeCluster(no_cores)
# Initialize cluster for parallel computing
registerDoParallel(cl)
x <- foreach(i=1:2, .combine=rbind)%:%
foreach(j=1:2, .combine=cbind)%:%
foreach(k=1:2, .combine=c)%dopar%{
i+j+k
}
Here, I basically combine results into vectors, then matrices and, finally, I pile up matrices by rows. Another option would be to use lists, or pile matrices through columns, but you can imagine the mess when you have 7 dimensions and millions of iterations to track.
I suppose I could also write my own 'combine' function and get the kind of output I want, but I suspect that I am not the first person to encounter this problem. Either there is a way to do exactly what I want, or someone here can point out a way to think differently about storing my results. It wouldn't be surprising that I am taking an absurdly inefficient path toward solving this problem -- I am an economist, not a data scientist, after all!
Any help would be greatly appreciated. Thanks in advance.

Answer 1

There is one available solution that I finally stumbled upon tonight. I can create an appropriate combination function along the dimension of my choice using the 'abind' function of the 'abind' package:
library(abind)
# Get the number of cores to use
no_cores <- max(1, detectCores()-1)
# Make cluster object using no_cores
cl <- makeCluster(no_cores)
# Initialize cluster for parallel computing
registerDoParallel(cl)
mbind <- function(...) abind(..., along=3)
x <- foreach(i=1:2, .combine=mbind)%:%
foreach(j=1:2, .combine=cbind)%:%
foreach(k=1:2, .combine=c)%dopar%{
i+j+k
}
I would still like to see if someone has other means of doing what I want to do, however. There might be many ways to do it and I am new to R, yet this solution is a distinct possibility.

Answer 2

What I would do and I already use in one of my packages, bigstatsr.
Take only one dimension and cut it in no_cores blocks. It should have sufficient iterations (e.g. 20 for 4 cores). For each iteration, construct part of the array you want and store it in a temporary file. The, use the content of these files to fill the whole array. By doing so, you fill only preallocated objects, which should be faster and easier.
Example:
x.all <- array(dim=c(20,2,2))
no_cores <- 3
tmpfile <- tempfile()
range.parts <- bigstatsr:::CutBySize(nrow(x.all), nb = no_cores)
library(foreach)
cl <- parallel::makeCluster(no_cores)
doParallel::registerDoParallel(cl)
foreach(ic = 1:no_cores) %dopar% {
ind <- bigstatsr:::seq2(range.parts[ic, ])
x <- array(dim = c(length(ind), 2, 2))
for (i in seq_along(ind)){
for (j in 1:2){
for (k in 1:2){
x[i,j,k] <- ind[i]+j+k
}
}
}
saveRDS(x, file = paste0(tmpfile, "_", ic, ".rds"))
}
parallel::stopCluster(cl)
for (ic in 1:no_cores) {
ind <- bigstatsr:::seq2(range.parts[ic, ])
x.all[ind, , ] <- readRDS(paste0(tmpfile, "_", ic, ".rds"))
}
print(x.all)
Instead of writing files, you could also directly return the no_cores parts of the array in foreach and combine them with the right abind.