import numba
import numpy as np


@numba.njit
def identity(x):
    """A no-op link function."""
    return x


@numba.njit
def _identity_inverse(x):
    return x


identity.inverse = _identity_inverse


@numba.njit
def logit(x):
    """A logit link function useful for going from probability units to log-odds units."""
    return np.log(x / (1 - x))


@numba.njit
def _logit_inverse(x):
    return 1 / (1 + np.exp(-x))


logit.inverse = _logit_inverse