parallelTest.jl

# parallelTest.jl
# automatic differentiation of a function at n = 100e6 points using dual numbers
# compare parallel to serial implementation
# benchmark timings were observed on a 2.66GHz Quad-Core Xeon after an initial warm up run


# initialize processors
availProcs = 8;
addprocs(availProcs-nprocs());


# require loads DualNumbers on all workers
# using DualNumbers
require("using.jl")
# define functions on all workers:
@everywhere begin
	# automatic differentiation using dual numbers
	function autoDiff(f,x)
		y = f(dual(x,1));
		return epsilon(y);
	end

	f(x) = x.^3;
	n = 100000000;
end


# parallel autoDiff
# note that convert(Array, arg1::DArray)
# consumes most of the processing time due to
# the limitations of memory bandwidth
res1 = dzeros(n,1);
@time begin
	# parallel for loop without reduction assignment
	@parallel for worker = 1:nprocs()-1
		# get a SubArray on local processor
		lRes = localpart(res1);
		# get local indexes (returns tuple of ranges)
		lIdx = myindexes(res1);
		for jj = 1:length(lRes);
			# modify SubArray
			lRes[jj] = autoDiff(f,lIdx[1][jj]);
		end
	end
	# copy all data back to worker 1, i.e. DArray -> Array
	convert(Array, res1);
end
# elapsed time: 14.656142945 seconds (3251017544 bytes allocated)


# serial autoDiff
res2 = zeros(n,1);
@time for jj = 1:n
	res2[jj] = autoDiff(f,jj);
end
# elapsed time: 39.727926118 seconds (9599995484 bytes allocated)

# show some other fun stuff in Julia
# apply a function to preceding argument with |> and -> creates an anonymous function
([1:5],[1:5]) |> a->a[1].^2+a[2].^2 |> sum |> inv
# apply a function to each object in array
map((x) -> x * 2, [1, 2, 3])