math_util
=========

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

.. autoapi-nested-parse::

   Math utils functions.




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




.. autoapisummary::


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Tan


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Tanh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.TanC


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArTan


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArTanh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArTanC


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Cos


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Cosh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArCos


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArCosh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Sin


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.Sinh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.SinC


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArSin


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArSinh


   topmost.models.hierarchical.HyperMiner.manifolds.math_util.ArSinC



.. py:function:: Tan(x)

   Computes tangent of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: A tensor. Has the same type as x.


.. py:function:: Tanh(x)

   Computes hyperbolic tangent of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type as x.
   :rtype: A tensor


.. py:function:: TanC(x, c)

   A unified tangent and inverse tangent function for different signs of curvatures.

   This function is used in k-Stereographic model, a unification of constant curvature manifolds.
   Please refer to https://arxiv.org/abs/2007.07698 for more details.

   First-order expansion is used in order to calculate gradients correctly when c is zero.

   :param x: A tensor.
   :type x: tensor
   :param c: Manifold curvature.
   :type c: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArTan(x)

   Computes inverse tangent of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type as x.
   :rtype: A tensor


.. py:function:: ArTanh(x)

   Computes inverse hyperbolic tangent of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type as x.
   :rtype: A tensor


.. py:function:: ArTanC(x, c)

   A unified hyperbolic tangent and inverse hyperbolic tangent function for different signs of curvatures.

   This function is used in k-Stereographic model, a unification of constant curvature manifolds.
   Please refer to https://arxiv.org/abs/2007.07698 for more details.

   First-order expansion is used in order to calculate gradients correctly when c is zero.

   :param x: A tensor.
   :type x: tensor
   :param c: Manifold curvature.
   :type c: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: Cos(x)

   Computes cosine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: Cosh(x)

   Computes hyperbolic cosine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArCos(x)

   Computes inverse cosine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArCosh(x)

   Computes inverse hyperbolic cosine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: Sin(x)

   Computes sine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: Sinh(x)

   Computes hyperbolic sine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: SinC(x, c)

   A unified sine and inverse sine function for different signs of curvatures.

   This function is used in k-Stereographic model, a unification of constant curvature manifolds.
   Please refer to https://arxiv.org/abs/2007.07698 for more details.

   First-order expansion is used in order to calculate gradients correctly when c is zero.

   :param x: A tensor.
   :type x: tensor
   :param c: Manifold curvature.
   :type c: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArSin(x)

   Computes inverse sine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArSinh(x)

   Computes inverse hyperbolic sine of x element-wise.

   :param x: A tensor.
   :type x: tensor

   :returns: Has the same type of x.
   :rtype: A tensor


.. py:function:: ArSinC(x, c)

   A unified hyperbolic sine and inverse hyperbolic sine function for different signs of curvatures.

   This function is used in k-Stereographic model, a unification of constant curvature manifolds.
   Please refer to https://arxiv.org/abs/2007.07698 for more details.

   First-order expansion is used in order to calculate gradients correctly when c is zero.

   :param x: A tensor.
   :type x: tensor
   :param c: Manifold curvature.
   :type c: tensor

   :returns: Has the same type of x.
   :rtype: A tensor