(This article was first published on

In the previous post on **A second megabyte of memory**, and kindly contributed to R-bloggers)*RcppEigen*I described an example of sampling from collection of multinomial distributions represented by a matrix of probabilities. In the timing example the matrix was 100000 by 5 with each of the 100000 rows summing to 1. The objective is to create a vector of 100000 1-based indices representing a sample from the probabilities in each row.

For each row we take the cumulative sums and, for safety, normalize by dividing by the last element then compare these values to a random draw from a standard uniform distribution. The number of elements in the cumulative sums that are less than the uniform draw is the 0-based index of the result. We add 1 to convert to a 1-based index.

I have been experimenting a bit with a very interesting new language called Julia and decided to write a similar function in it. The version shown here has been updated according to suggestions from Jeff Bezanson, Stefan Karpinski and Viral Shah on the

*julia-dev*list at Google Groups

function samp1(x::Array{Float64, 2},)

cs = cumsum(reshape(x, length(x)))

sum(cs/cs[end] < rand()) + 1

end

function samp(X::Array{Float64, 2},)

if any(X < 0)

error("Negative probabilities not allowed")

end

[samp1(X[i,:]) | i = 1:size(X,1)]

end

This version is about 10 times as fast as the pure R version but about 9 times slower than the RcppEigenversion.**Update:**

In the thread on the julia-dev list about this example Stefan Karpinski showed that in Julia you can enhance performance by de-vectorizing your code and came up with the following version which is much faster than the RcppEigenversion

To a longtime R/S programmer the concept of de-vectorizing your code seems heretical but I can understand that code created by a JITwill be happier with the looping and break style.

function SKsamp(X::Matrix{Float64})

if any(X < 0)

error("Negative probabilities not allowed")

end

s = Array(Int, size(X,1))

for i = 1:size(X,1)

r = rand()

for j = 1:size(X,2)

r -= X[i,j]

if r <= 0.0

s[i] = j

break

end

end

end

return s

end

In any case, I think this example shows that R programmers should take a look at Julia. Two immediate applications I can imagine are McMC methods and large scale iterative fits such as Generalized linear models

To

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