Can this random matrix simulation be sped up?

General Usage Performance
12

In my test the allocations are reduced to 250 Mb:

 17.909110 seconds (616.27 k allocations: 256.346 MiB, 1.37% gc time)

This is the code:

using LinearAlgebra

function symplectic(N,G,R)

	for i in 0:N-1
		for j in 0:N-1
			@. R = randn()
			@inbounds G[2*i + 1,2*j + 1] = R[1] + R[2]*im
			@inbounds G[2*i+1 + 1,2*j+1 + 1] = R[1] - R[2]*im
			@inbounds G[2*i+1 + 1,2*j + 1] = -R[3] + R[4]*im
			@inbounds G[2*i + 1,2*j+1+ 1] = R[3] + R[4]*im
		end
	end
      ev = svdvals!(G)
	return ev[2*N]*N
end

function data(n,samples)
	G = Array{Complex{Float64}}(undef, 2n ,2n)
      R = zeros(4)
	for i in 1:samples
	   println(symplectic(n,G,R))
	end
end

n = 100
samples = 1000
data(n,samples)
@time data(n,samples)

And the difference (to 2Gib) is using svdvals! (note the exclamation mark)

Edit: I am not sure if this is doing the same as your code, exactly. But appropriate use of adjoint! and mul! could reduce the allocations even further.

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