Getting a grand sum of a 3d array quickly in R

3darr.R

### This generates an array which takes up around 600 Mb in memory
input_sizes <- c(100, .1e6, 8)
names(input_sizes) <- c("draws", "nobs", "categories")
my_arr <- array(rnorm(prod(input_sizes)),
                dim = input_sizes)

## Returns a 2D matrix of dimensions draws by nobs
## i.e., sums over categories

### This version takes around 17-18s on my laptop
system.time(grand_total_a <- apply(my_arr[,,], c(1, 2), sum))

### This version takes about 2-3 seconds
system.time({
    grand_total_b <- matrix(NA, nrow = 100, ncol = .1e6)
    for (i in 1:100) {
        grand_total_b[i, ] <- rowSums(my_arr[i, , ])
    }
})

all(grand_total_a == grand_total_b)