An invitation to a sparse Cholesky factorisation. Left-looking Cholesky factorization in two lines:
for j in range(0,n):
L[j,j] = sqrt(A[j,j] - L[j, 1:(j-1)] * L[j, 1:(j-1)]')
L[(j+1):n, j] = (A[(j+1):n, j] - L[(j+1):n, 1:(j-1)] * L[j, 1:(j-1)]') / L[j,j]