geometric_kernels.utils.product
===============================

.. py:module:: geometric_kernels.utils.product

.. autoapi-nested-parse::

   Utilities for dealing with product spaces and product kernels.  





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

.. py:function:: make_product(xs)

   Embed a list of elements of factor spaces into the product space.
   Assumes that elements are batched along the first dimension.

   :param xs:
       List of the batches of elements, each of the shape [N, <axes(space)>],
       where `<axes(space)>` is the shape of the elements of the respective
       space.

   :return:
       An [N, D]-shaped array, a batch of product space elements, where `D` is
       the sum, over all factor spaces, of `prod(<axes(space)>)`.


.. py:function:: params_to_params_list(params)

   Takes a dictionary of parameters of a product kernel and returns a list of
   dictionaries of parameters for the factor kernels.

   :param params:
       Parameters of the product kernel.


.. py:function:: project_product(x, dimension_indices, element_shapes)

   Project an element of the product space onto each factor.
   Assumes that elements are batched along the first dimension.

   :param x:
       An [N, D]-shaped array, a batch of N product space elements.
   :param dimension_indices:
       Determines how a product space element `x` is to be mapped to inputs
       `xi` of the factor kernels. `xi` are assumed to be equal to
       `x[dimension_indices[i]]`, possibly up to a reshape. Such a reshape
       might be necessary to accommodate the spaces whose elements are matrices
       rather than vectors, as determined by `element_shapes`.
   :param element_shapes:
       Shapes of the elements in each factor.

   :return:
       A list of the batches of elements `xi` in factor spaces, each of the
       shape `[N, *element_shapes[i]]`.