As discussed offline, I do not think that the strategy should be to put this function private, but rather to augment this function with the parameter `normalized`. If `normalized`==`True`, then you could run the code you have now. When `False`, you'd call `orthonormalize_matrix` on both vars1 and vars2, and then call your function with `normalized`=`True`. Setting the default value to `True` should not change your code much.