:py:mod:`did.kernels`
=====================

.. py:module:: did.kernels

.. autoapi-nested-parse::

   kernels.py

   Implements generic Kernel module as well as Abel and Gaussian kernels.



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

Classes
~~~~~~~

.. autoapisummary::

   did.kernels.Kernel



Functions
~~~~~~~~~

.. autoapisummary::

   did.kernels.sq_dist
   did.kernels.abel_kernel
   did.kernels.gaussian_kernel



.. py:class:: Kernel(kernel_name, kernel_fn, kernel_params)

   Bases: :py:obj:`torch.nn.Module`

   Generic Kernel nn.Module.

   Implements a `validate_input` static method and forward.

   .. py:method:: validate_input(x)
      :staticmethod:

      Validate input, else add dimension in front.

      :Parameters: **x** (*torch.Tensor*) -- Input tensor to validate.

      :returns: Validated input tensor, or unsqueezed at 0 dimension.
      :rtype: torch.Tensor


   .. py:method:: forward(self, x, y)



.. py:function:: sq_dist(X1, X2)

   Wrapper for `torch.cdist` with exponent 2.

   :math:`\Vert X_1 - X_2\Vert^2_2`

   :Parameters: * **X1** (*torch.Tensor with size (n, d)*)
                * **X2** (*torch.Tensor with size (m, d)*)

   :returns:
   :rtype: torch.Tensor with size (n, m)


.. py:function:: abel_kernel(X1, X2, a=1.0)

   Kernel function for Abel kernel defined as:

   :math:`k(x, y) = \exp(-a\Vert x - y\Vert_2)`.

   :Parameters: * **X1** (*torch.Tensor with size (n, d)*)
                * **X2** (*torch.Tensor with size (m, d)*)
                * **a** (*float, parameter*)

   :returns:
   :rtype: torch.Tensor with size (n, m)


.. py:function:: gaussian_kernel(X1, X2, sigma=1.0)

   Kernel function for Gaussian kernel defined as:


   :math:`k(x, y) = \exp\left(-\frac{\Vert x - y\Vert_2 ^2}{2 \sigma^2}\right)`.

   :Parameters: * **X1** (*torch.Tensor with size (n, d)*)
                * **X2** (*torch.Tensor with size (m, d)*)
                * **sigma** (*float, bandwidth parameter*)

   :returns:
   :rtype: torch.Tensor with size (n, m)