There the "naive" Julia code, simply implementing the code like I would in Fortran is a factor of 10 or 15 slower than the optimised cython version (which would be the same as a regular C version), the optimised Julia version is still a factor of 5 slower than the cython and pythran version. Can you show me how to optimise it so that Julia performs on par with pythran or cython?

    apply_filter(x, y) = vec(y)' \* vec(x)

    function cma!(wxy, E, mu, R, os, ntaps)
        L, pols = size(E)
        N = (L ÷ os ÷ ntaps - 1) \* ntaps  # ÷ or div are integer division
        err = similar(E)  # allocate array without initializing its values
        @inbounds for k in axes(E, 2)  # avoid assuming 1-based arrays. Just need a single inbounds macro call
            @views for i in 1:N   # everything in this block is a view
                X = E[i*os-1:i*os+ntaps-2, :]
                Xest = apply_filter(X, wxy[:,:, k])
                err[i,k] = (R - abs2(Xest)) \* Xest  # abs2 avoids needless extra work
                wxy[:,:,k] .+= (mu \* conj(err[i,k])) .\* X  # remember the dots!
            end  
        end
        return wxy, err  # note order of returns, seems more idiomatic
    end