euclidean
=========

.. py:module:: topmost.models.hierarchical.HyperMiner.manifolds.euclidean

.. autoapi-nested-parse::

   Euclidean manifold.




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



.. autoapisummary::


   topmost.models.hierarchical.HyperMiner.manifolds.euclidean.Euclidean





.. py:class:: Euclidean(**kwargs)

   Bases: :py:obj:`topmost.models.hierarchical.HyperMiner.manifolds.base.Manifold`


   Euclidean Manifold class. Usually we refer it as R^n.

   .. attribute:: name

      The manifold name, and its value is "Euclidean".

      :type: str

   Initialize an Euclidean manifold.
   :param \*\*kwargs: Description


   .. py:attribute:: name
      :value: 'Euclidean'



   .. py:method:: proj(x, c)

      A projection function that prevents x from leaving the manifold.
      :param x: A point should be on the manifold, but it may not meet the manifold constraints.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: A projected point, meeting the manifold constraints.
      :rtype: tensor



   .. py:method:: proj_tan(v, x, c)

      A projection function that prevents v from leaving the tangent space of point x.
      :param v: A point should be on the tangent space, but it may not meet the manifold constraints.
      :type v: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: A projected point, meeting the tangent space constraints.
      :rtype: tensor



   .. py:method:: proj_tan0(v, c)

      A projection function that prevents v from leaving the tangent space of origin point.
      :param v: A point should be on the tangent space, but it may not meet the manifold constraints.
      :type v: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: A projected point, meeting the tangent space constraints.
      :rtype: tensor



   .. py:method:: expmap(v, x, c)

      Map a point v in the tangent space of point x to the manifold.
      :param v: A point in the tangent space of point x.
      :type v: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of mapping tangent point v to the manifold.
      :rtype: tensor



   .. py:method:: expmap0(v, c)

      Map a point v in the tangent space of origin point to the manifold.
      :param v: A point in the tangent space of origin point.
      :type v: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of mapping tangent point v to the manifold.
      :rtype: tensor



   .. py:method:: logmap(y, x, c)

      Map a point y on the manifold to the tangent space of x.
      :param y: A point on the manifold.
      :type y: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of mapping y to the tangent space of x.
      :rtype: tensor



   .. py:method:: logmap0(y, c)

      Map a point y on the manifold to the tangent space of origin point.
      :param y: A point on the manifold.
      :type y: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of mapping y to the tangent space of origin point.
      :rtype: tensor



   .. py:method:: ptransp(v, x, y, c)

      Parallel transport function, used to move point v in the tangent space of x to the tangent space of y.
      :param v: A point in the tangent space of x.
      :type v: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param y: A point on the manifold.
      :type y: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of transporting v from the tangent space at x to the tangent space at y.
      :rtype: tensor



   .. py:method:: ptransp0(v, x, c)

      Parallel transport function, used to move point v in the tangent space of origin point to the tangent space of y.
      :param v: A point in the tangent space of origin point.
      :type v: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: The result of transporting v from the tangent space at origin point to the tangent space at y.
      :rtype: tensor



   .. py:method:: dist(x, y, c)

      Calculate the squared geodesic/distance between x and y.
      :param x: A point on the manifold.
      :type x: tensor
      :param y: A point on the manifold.
      :type y: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: the geodesic/distance between x and y.
      :rtype: tensor



   .. py:method:: egrad2rgrad(grad, x, c)

      Computes Riemannian gradient from the Euclidean gradient, typically used in Riemannian optimizers.
      :param grad: Euclidean gradient at x.
      :type grad: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor

      :returns: Riemannian gradient at x.
      :rtype: tensor



   .. py:method:: inner(v1, v2, x, c, keep_shape=False)

      Computes the inner product of a pair of tangent vectors v1 and v2 at x.
      :param v1: A tangent point at x.
      :type v1: tensor
      :param v2: A tangent point at x.
      :type v2: tensor
      :param x: A point on the manifold.
      :type x: tensor
      :param c: The manifold curvature.
      :type c: tensor
      :param keep_shape: Whether the output tensor keeps shape or not.
      :type keep_shape: bool, optional

      :returns: The inner product of v1 and v2 at x.
      :rtype: tensor