def inv_logistic(y: Union[float, np.ndarray],
                 k: float,
                 theta: float) -> Optional[float]:
    r"""
    Inverse standard logistic function:

    .. math::

        x = ( log( \frac {1} {y} - 1) / -k ) + \theta

    Args:
        y: :math:`y`
        k: :math:`k`
        theta: :math:`\theta`

    Returns:
        :math:`x`

    """
    if y is None or k is None or theta is None:
        return None
    # noinspection PyUnresolvedReferences
    return (np.log((1 / y) - 1) / -k) + theta
def inv_logistic ( y : Union [ float , np . ndarray ] , k : float , theta : float ) -> Optional [ float ] : if y is None or k is None or theta is None : return None return ( np . log ( ( 1 / y ) - 1 ) / - k ) + theta
r"""
    Inverse standard logistic function:

    .. math::

        x = ( log( \frac {1} {y} - 1) / -k ) + \theta

    Args:
        y: :math:`y`
        k: :math:`k`
        theta: :math:`\theta`

    Returns:
        :math:`x`