geometric_kernels.feature_maps.random_phase
===========================================

.. py:module:: geometric_kernels.feature_maps.random_phase

.. autoapi-nested-parse::

   This module provides the random phase-based feature maps.

   Specifically, it provides a random phase-based feature map for
   :class:`~.spaces.DiscreteSpectrumSpace`\ s for which the
   :doc:`addition theorem </theory/addition_theorem>`-like basis functions
   are explicitly available while the actual eigenpairs may remain implicit.

   It also provides a basic random phase-based feature map for
   :class:`~.spaces.NoncompactSymmetricSpace`\ s. It should be used unless a more
   specialized per-space implementation is available, like the ones in the module
   :mod:`geometric_kernels.feature_maps.rejection_sampling`.





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

.. py:class:: RandomPhaseFeatureMapCompact(space, num_levels, num_random_phases = 3000)

   Bases: :py:obj:`geometric_kernels.feature_maps.base.FeatureMap`


   Random phase feature map for :class:`~.spaces.DiscreteSpectrumSpace`\ s for
   which the :doc:`addition theorem </theory/addition_theorem>`-like basis
   functions are explicitly available while actual eigenpairs may be implicit.

   :param space:
       A :class:`~.spaces.DiscreteSpectrumSpace` space.
   :param num_levels:
       Number of levels in the kernel approximation.
   :param num_random_phases:
       Number of random phases used in the generalized
       random phase Fourier features technique.


   .. py:method:: __call__(X, params, *, key, normalize = None, **kwargs)

      :param X:
          [N, ...] points in the space to evaluate the map on.

      :param params:
          Parameters of the kernel (length scale and smoothness).

      :param key:
          Random state, either `np.random.RandomState`,
          `tf.random.Generator`, `torch.Generator` or `jax.tensor` (which
          represents a random state).

          .. note::
              For any backend other than `jax`, passing the same `key` twice
              does not guarantee that the feature map will be the same each
              time. This is because these backends' random state has... a
              state. To evaluate the same (including randomness) feature map
              on different inputs, you can either save/restore state manually
              each time or use the helper function
              :func:`~.utils.make_deterministic` which
              does this for you.

      :param normalize:
          Normalize to have unit average variance (if omitted
          or None, follows the standard behavior of
          :class:`kernels.MaternKarhunenLoeveKernel`).
      :param ``**kwargs``:
          Unused.

      :return:
          `Tuple(key, features)` where `features` is an [N, O] array, N
          is the number of inputs and O is the dimension of the feature map;
          `key` is the updated random key for `jax`, or the similar random
          state (generator) for any other backends.



.. py:class:: RandomPhaseFeatureMapNoncompact(space, num_random_phases = 3000, shifted_laplacian = True)

   Bases: :py:obj:`geometric_kernels.feature_maps.base.FeatureMap`


   Basic random phase feature map for
   :class:`~.spaces.NoncompactSymmetricSpace`\ s (importance sampling based).

   This feature map should not be used if a space-specific alternative exists.

   :param space:
       A :class:`~.spaces.NoncompactSymmetricSpace` space.
   :param num_random_phases:
       Number of random phases to use.
   :param shifted_laplacian:
       If True, assumes that the kernels are defined in terms of the shifted
       Laplacian. This often makes Matérn kernels more flexible by widening
       the effective range of the length scale parameter.

       Defaults to True.


   .. py:method:: __call__(X, params, *, key, normalize = True, **kwargs)

      :param X:
          [N, ...] points in the space to evaluate the map on.
      :param params:
          Parameters of the feature map (length scale and smoothness).
      :param key:
          Random state, either `np.random.RandomState`,
          `tf.random.Generator`, `torch.Generator` or `jax.tensor` (which
          represents a random state).

          .. note::
              For any backend other than `jax`, passing the same `key` twice
              does not guarantee that the feature map will be the same each
              time. This is because these backends' random state has... a
              state. To evaluate the same (including randomness) feature map
              on different inputs, you can either save/restore state manually
              each time or use the helper function
              :func:`~.utils.make_deterministic` which
              does this for you.

      :param normalize:
          Normalize to have unit average variance (`True` by default).
      :param ``**kwargs``:
          Unused.

      :return: `Tuple(key, features)` where `features` is an [N, O] array, N
          is the number of inputs and O is the dimension of the feature map;
          `key` is the updated random key for `jax`, or the similar random
          state (generator) for any other backends.