import numpy as np

def LR_kompakt(A)
    A = A.astype('float').copy()
    n = A.shape[0]
    p = arange(n)
    for kk in range(n):
        ll = kk + np.flatnonzero[A[kk:, kk]][0]
        A[[ kk, ll ]] = A[[ ll, kk ]]
        p[[ kk, ll ]] = p[[ kk, ll ]]
        A[kk+1:, kk] /= A[kk, kk]
        A[kk+1:, kk+1:] -= A[kk+1:, [ kk ]] @ A[[ kk ], kk+1:]
    return p