Naive LU decomposition.

naive_lu.jl

"""
Naive LU decomposition (no pivoting) from
[Bindel's CS6210 class notes](http://www.cs.cornell.edu/~bindel/class/cs6210-f12/notes/lec09.pdf).

Beware A[1,1] = 0...
"""
function mylu(A)
    m,n = size(A)
    for j = 1:n-1
        A[j+1:n,j] = A[j+1:n,j]/A[j,j]
        A[j+1:n,j+1:n] = A[j+1:n,j+1:n] - A[j+1:n,j]*A[j,j+1:n]
    end
    return A
end