gwkokab.utils.kernel
====================

.. py:module:: gwkokab.utils.kernel


Functions
---------

.. autoapisummary::

   gwkokab.utils.kernel.log_planck_taper_window


Module Contents
---------------

.. py:function:: log_planck_taper_window(x: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   If :math:`x` is the point at which to evaluate the window, then the Planck taper
   window is defined as,

   .. math::

       S(x)=\begin{cases}
           0                                                                   & \text{if } x < 0,           \\
           \displaystyle\frac{1}{1+e^{\left(\frac{1}{x}+\frac{1}{x-1}\right)}} & \text{if } 0 \leq x \leq 1, \\
           1                                                                   & \text{if } x > 1,           \\
       \end{cases}

   This function evaluates the log of the Planck taper window :math:`\ln{S(x)}`.

   :param x: point at which to evaluate the window
   :type x: ArrayLike

   :returns: window value
   :rtype: ArrayLike