code: def logistic(x, a=0., b=1.):
          r
          expx = numpy.exp(x)
          return (a + b*expx)/(1. + expx)
docs: 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.