geometric_kernels.kernels.matern_kernel_hamming_graph
=====================================================

.. py:module:: geometric_kernels.kernels.matern_kernel_hamming_graph

.. autoapi-nested-parse::

   This module provides the :class:`MaternKernelHammingGraph` kernel, a subclass of
   :class:`MaternKarhunenLoeveKernel` for :class:`HammingGraph` and
   :class:`HypercubeGraph` spaces implementing the closed-form formula for the
   heat kernel when $\nu = \infty$.





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

.. py:class:: MaternKernelHammingGraph(space, num_levels, normalize = True, eigenvalues_laplacian = None, eigenfunctions = None)

   Bases: :py:obj:`geometric_kernels.kernels.karhunen_loeve.MaternKarhunenLoeveKernel`


   For $\nu = \infty$, there exists a closed-form formula for the heat kernel
   on hamming graphs :class:`HammingGraph` (including the binary hypercube case
   :class:`HypercubeGraph`). This class extends :class:`MaternKarhunenLoeveKernel`
   to implement this formula in the case of $\nu = \infty$ for efficiency.

   .. note::
       We only use the closed form expression if `num_levels` is `d + 1` which
       corresponds to exact computation. When truncated to fewer levels, we
       must use the parent class implementation to ensure consistency with
       feature map approximations.


   .. py:method:: K(params, X, X2 = None, **kwargs)

      Compute the cross-covariance matrix between two batches of vectors of
      inputs, or batches of matrices of inputs, depending on the space.

      :param params:
          A dict of kernel parameters, typically containing two keys:
          `"lengthscale"` for length scale and `"nu"` for smoothness.

          The types of values in the params dict determine the output type
          and the backend used for the internal computations, see the
          warning below for more details.

          .. note::
              The values `params["lengthscale"]` and `params["nu"]` are
              typically (1,)-shaped arrays of the suitable backend. This
              serves to point at the backend to be used for internal
              computations.

              In some cases, for example, when the kernel is
              :class:`~.kernels.ProductGeometricKernel`, the values of
              `params` may be (s,)-shaped arrays instead, where `s` is the
              number of factors.

          .. note::
              Finite values of `params["nu"]` typically correspond to the
              generalized (geometric) Matérn kernels.

              Infinite `params["nu"]` typically corresponds to the heat
              kernel (a.k.a. diffusion kernel, generalized squared
              exponential kernel, generalized Gaussian kernel,
              generalized RBF kernel). Although it is often considered to be
              a separate entity, we treat the heat kernel as a member of
              the Matérn family, with smoothness parameter equal to infinity.

      :param X:
          A batch of N inputs, each of which is a vector or a matrix,
          depending on how the elements of the `self.space` are represented.
      :param X2:
          A batch of M inputs, each of which is a vector or a matrix,
          depending on how the elements of the `self.space` are represented.

          `X2=None` sets `X2=X1`.

          Defaults to None.

      :return:
          The N x M cross-covariance matrix.

      .. warning::
         The types of values in the `params` dict determine the backend
         used for internal computations and the output type.

         Even if, say, `geometric_kernels.jax` is imported but the values in
         the `params` dict are NumPy arrays, the output type will be a NumPy
         array, and NumPy will be used for internal computations. To get a
         JAX array as an output and use JAX for internal computations, all
         the values in the `params` dict must be JAX arrays.



   .. py:method:: K_diag(params, X, **kwargs)

      Returns the diagonal of the covariance matrix `self.K(params, X, X)`,
      typically in a more efficient way than actually computing the full
      covariance matrix with `self.K(params, X, X)` and then extracting its
      diagonal.

      :param params:
          Same as for :meth:`~.K`.

      :param X:
          A batch of N inputs, each of which is a vector or a matrix,
          depending on how the elements of the `self.space` are represented.

      :return:
          The N-dimensional vector representing the diagonal of the
          covariance matrix `self.K(params, X, X)`.