randmatstat_optimized.jl

using LinearAlgebra, Statistics

function randmatstat(t)
    n = 5
    v = zeros(t)
    w = zeros(t)
    a = zeros(n, n)
    b = zeros(n, n)
    c = zeros(n, n)
    d = zeros(n, n)
    P = zeros(n, 4n)
    Q = zeros(2n, 2n)
    PtP1 = zeros(4n, 4n)
    PtP2 = zeros(4n, 4n)
    QtQ1 = zeros(2n, 2n)
    QtQ2 = zeros(2n, 2n)
    for i = 1:t
        a .= randn()
        b .= randn()
        c .= randn()
        d .= randn()
        P[:, 0n .+ (1:n)] .= a
        P[:, 1n .+ (1:n)] .= b
        P[:, 2n .+ (1:n)] .= c
        P[:, 3n .+ (1:n)] .= d
        Q[0n .+ (1:n), 0n .+ (1:n)] .= a
        Q[0n .+ (1:n), 1n .+ (1:n)] .= b
        Q[1n .+ (1:n), 0n .+ (1:n)] .= c
        Q[1n .+ (1:n), 1n .+ (1:n)] .= d
        mul!(PtP1, P', P)
        mul!(PtP2, PtP1, PtP1)
        mul!(PtP1, PtP2, PtP2)
        mul!(QtQ1, Q', Q)
        mul!(QtQ2, QtQ1, QtQ1)
        mul!(QtQ1, QtQ2, QtQ2)
        v[i] = tr(PtP2)
        w[i] = tr(QtQ2)
    end
    return std(v)/mean(v), std(w)/mean(w)
end