Question

The problem with my R script is that it takes too much time and the main solution that I consider is to parallelize it. I don’t know where to start.

My code look like this:

n<- nrow (aa) 
output <- matrix (0, n, n)

akl<- function (dii){
        ddi<- as.matrix (dii)
        m<- rowMeans(ddi)
        M<- mean(ddi)
        r<- sweep (ddi, 1, m)
        b<- sweep (r, 2, m)
        return (b + M)  
        }
for (i in 1:n)
{
A<- akl(dist(aa[i,]))

dVarX <- sqrt(mean (A * A))

for (j in i:n)
{
    B<- akl(dist(aa[j,]))
        V <- sqrt (dVarX * (sqrt(mean(B * B))))

        output[i,j] <- (sqrt(mean(A * B))) / V        
}
}   

I would like to parallelize on different cpus. How can I do that?
I saw the SNOW package, is it suitable for my purpose?
Thank you for suggestions,
Gab

Answer 1

There are two ways in which your code could be made to run faster that I could think of:

First: As @Dwin was saying (with a small twist), you could precompute akl (yes, not necesarily dist, but the whole of akl).

# a random square matrix
aa <- matrix(runif(100), ncol=10)
n <- nrow(aa)
output <- matrix (0, n, n)

akl <- function(dii) {
    ddi <- as.matrix(dii)
    m   <- rowMeans(ddi)
    M   <- mean(m) # mean(ddi) == mean(m)
    r   <- sweep(ddi, 1, m)
    b   <- sweep(r, 2, m)
    return(b + M)
}

# precompute akl here
require(plyr)
akl.list <- llply(1:nrow(aa), function(i) {
    akl(dist(aa[i, ]))
})

# Now, apply your function, but index the list instead of computing everytime
for (i in 1:n) {
    A     <- akl.list[[i]]
    dVarX <- sqrt(mean(A * A))

    for (j in i:n) {
        B <- akl.list[[j]]
        V <- sqrt (dVarX * (sqrt(mean(B * B))))
        output[i,j] <- (sqrt(mean(A * B))) / V        
    }
}

This should already get your code to run faster than before (as you compute akl everytime in the inner loop) on larger matrices.

Second: In addition to that, you can get it faster by parallelising as follows:

# now, the parallelisation you require can be achieved as follows
# with the help of `plyr` and `doMC`.

# First step of parallelisation is to compute akl in parallel
require(plyr)
require(doMC)
registerDoMC(10) # 10 Cores/CPUs
    akl.list <- llply(1:nrow(aa), function(i) {
    akl(dist(aa[i, ]))
}, .parallel = TRUE)

# then, you could write your for-loop using plyr again as follows
output <- laply(1:n, function(i) {
    A     <- akl.list[[i]]
    dVarX <- sqrt(mean(A * A))

    t <- laply(i:n, function(j) {
        B <- akl.list[[j]]
        V <- sqrt(dVarX * (sqrt(mean(B*B))))
        sqrt(mean(A * B))/V
    })
    c(rep(0, n-length(t)), t)
}, .parallel = TRUE)

Note that I have added .parallel = TRUE only on the outer loop. This is because, you assign 10 processors to the outer loop. Now, if you add it to both outer and inner loops, then the total number of processers will be 10 * 10 = 100. Please take care of this.