Julia is column major

[ChrisRackauckas]

This code is row major:

https://github.com/JulesKouatchou/basic_language_comparison/blob/master/Julia/test_laplace_jacobi_4.jl#L40-L55

function optimized_time_step(u::Matrix{T})  where {T}
    n, m = size(u)
    error = T(0.0) # not an optimization, but makes it work for all element types
    @inbounds for j = 2:m-1
        for i = 2:n-1 # @simd ivdep, but why is it writing into u[j,i]? That's not the time step.
            temp = u[j, i];
            u[j, i] = ( T(4) *(u[j-1, i] + u[j+1, i] +
                        u[j, i-1] + u[j, i+1]) +
                        u[j-1, i-1] + u[j+1, i+1] +
                        u[j+1, i-1] + u[j-1, i+1]) / T(20)
            difference = u[j, i] - temp
            error += difference*difference;
        end
    end
    return sqrt(error)
end

is probably a better code, though this is a case where most people would do:

using LoopVectorization
function optimized_time_step(u::Matrix{T})  where {T}
    n, m = size(u)
    error = T(0.0) # not an optimization, but makes it work for all element types
    @turbo for j = 2:m-1 # @tturbo for threading
        for i = 2:n-1
            temp = u[j, i];
            u[j, i] = ( T(4) *(u[j-1, i] + u[j+1, i] +
                        u[j, i-1] + u[j, i+1]) +
                        u[j-1, i-1] + u[j+1, i+1] +
                        u[j+1, i-1] + u[j-1, i+1]) / T(20)
            difference = u[j, i] - temp
            error += difference*difference;
        end
    end
    return sqrt(error)
end

[JulesKouatchou]

Thank you for the suggestion. I will include it in the code.