Cholesky factorization
Nicholas J. Higham
‘kji’ form of the algorithm

Set permutation matrix pi = 1, i = 1: n.
for k = 1: n
    Find s such that ass = maxk≤i≤n aii.
    Swap rows and columns k and s of A and swap pk and ps.
    akk = √akk
    for j = k + 1: n
        akj = akj/akk
    end
    for j = k + 1: n
        for i = k + 1: j
            aij = aij − akiakj
        end
    end
end
Set P to the matrix whose jth column is the pjth column of I.