Thursday, March 1, 2012

Parallelizing Voting simulation

Last week I have compared synchronous and asynchronous implementation of NetLogo Voting model. An interesting afterthought is that synchronous model implementation can be easily made much faster using vectorization.
The two versions of the Voting synchronous code are given here:

step.syn.slow <- function(space) {
    base.x <- c(-1, -1, -10, 01, 1, 1)
    base.y <- c(-101, -1, 1, -1, 0, 1)
    size <- nrow(space)
    new.space <- space
    for (x in 1:size) {
        for (y in 1:size) {
            nei8 <- 1 + ((cbind(x + base.x, y + base.y) - 1) %% size)
            nei.pref <- sum(space[nei8])
            if (nei.pref > 0) { new.space[x, y] <- 1 }
            if (nei.pref < 0) { new.space[x, y] <- -1 }
        }
    }
    return(new.space)
}

step.syn.fast <- function(space) {
    size <- nrow(space)
    shift.back    <- c(2:size, 1)
    shift.forward <- c(size, 1:(size-1))
   
    shift.space <- space[, shift.back] +
                   space[shift.back, shift.back] +
                   space[shift.forward, shift.back] +
                   space[, shift.forward] +
                   space[shift.back, shift.forward] +
                   space[shift.forward, shift.forward] +
                   space[shift.back,] +
                   space[shift.forward,]
    space[shift.space > 0] <- 1
    space[shift.space < 0] <- -1
    return(space)
}

To compare their execution speed I run the following test:

run <- function(size, reps) {
    space <- 2 * matrix(rbinom(size^2, 1, 0.5), nrow = size) - 1
    slow <- system.time(replicate(reps, step.syn.slow(space)))
    fast <- system.time(replicate(reps, step.syn.fast(space)))
    cbind("slow" = slow[3], "fast" = fast[3])
}

run(32, 512)
# Result
#         slow fast
# elapsed 6.02 0.06

run(512, 32)
# Result
#          slow fast
# elapsed 95.77 1.98

As it could be predicted vectorized version of the code is much faster for small and large problem sizes.

Unfortunately such a vectorization is probably impossible to implement in R for asynchronous model.

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