def logistic(x, a=0., b=1.):
        r"""Computes the logistic function with range :math:`\in (a, b)`.

        This is given by:

        .. math::

            \mathrm{logistic}(x; a, b) = \frac{a + b e^x}{1 + e^x}.

        Note that this is also the inverse of the logit function with domain
        :math:`(a, b)`.

        Parameters
        ----------
        x : float
            The value to evaluate.
        a : float, optional
            The minimum bound of the range of the logistic function. Default
            is 0.
        b : float, optional
            The maximum bound of the range of the logistic function. Default
            is 1.

        Returns
        -------
        float
            The logistic of x.
        """
        expx = numpy.exp(x)
        return (a + b*expx)/(1. + expx)