How to unroll a nested for-loop in R so that it can be run in parallel

parallel-loop-unroll.R

library(parallel)

# Create matrix to store result -------------------------------------------
M <- 4
N <- 6
A <- matrix(0, nrow = M, ncol = N)

list <- list(3, 4, 6)

# Serial version ----------------------------------------------------------
for (i in 1:M) {
  for (j in 1:N) {
    A[i, j] <- ifelse(i < j, 
                      i - j, 
                      i + j) +
      sum(unlist(list))
  }
}

A


# Parallel version --------------------------------------------------------

cl <- makeCluster(getOption("cl.cores", detectCores()))

# 1. Identify the "cases" - basically all the combinations of i and j
cases <- expand.grid(i = 1:M, j = 1:N)
cases


# 2. Write a function to apply to each row
my_sum <- function(x, list) {
  # x is a row from a data frame
  # extract objects from data frame:
  i <- x["i"]
  j <- x["j"]
  
  # do your computations:
  ifelse(i < j, i - j, i + j) + sum(unlist(list))
}

clusterExport(cl, "list")

# 3. apply your function in parallel over the rows of the data frame
result <- parApply(cl = cl,      # our cluster object
                   X = cases,    # the array to iterate over
                   FUN = my_sum, # the function to apply
                   MARGIN = 1, 
                   list = list)   # iterate over the rows, not the columns

# 4. If you need a matrix as output, create one from the result
# (R fills in the columns first)
A_parallel <- matrix(result, nrow = M, ncol = N)
A_parallel

# confirm that the two are equal
all(A_parallel == A)

stopCluster(cl)