:py:mod:`MomentGauge.Statistic.SymbolicPolynomials`
===================================================

.. py:module:: MomentGauge.Statistic.SymbolicPolynomials


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

Classes
~~~~~~~

.. autoapisummary::

   MomentGauge.Statistic.SymbolicPolynomials.SympyGaugeTransformation




.. py:class:: SympyGaugeTransformation(suff_stats)

   
   The mixin class to generate gauge transformation automatically using sympy symbolic computation.
   :param suff_stats:
                      a list of moment functions [:math:`\phi_i`, i=0,\cdots,N-1] in which each :math:`\phi_i` is a polynomial function :math:`\phi_i` ( **u**, :math:`*` **gauge_paras** ) whose

                          **Parameters**:

                              **u** : float array of shape (3) - The 3D sample vector (:math:`u_x`, :math:`u_y`, :math:`u_z`)

                              :math:`*` **gauge_paras** : - Arbitrary many extra parameters. The :math:`*` refers to the unpacking operator in python.

                          **Returns**:

                              float -- the moment value
   :type suff_stats: list

   .. py:method:: get_gauge_transformation(suff_stats, gauge_symbols_source, gauge_symbols_target, transformation_inputs)

      Compute the gauge transformation matrix between different gauge parameters

      .. math::
          :nowrap:

          \begin{equation}
              \phi_i(\mathbf{u}, \mathbf{g}' )= T_{ij}(\mathbf{g}',\mathbf{g}) \phi_j(\mathbf{u}, \mathbf{g})
          \end{equation}

      :param suff_stats:
                         a list of moment functions [:math:`\phi_i`, i=0,\cdots,N-1] in which each :math:`\phi_i` is a polynomial function :math:`\phi_i` ( **u**, :math:`*` **gauge_paras** ) whose

                             **Parameters**:

                                 **u** : float array of shape (3) - The 3D sample vector (:math:`u_x`, :math:`u_y`, :math:`u_z`)

                                 :math:`*` **gauge_paras** : - Arbitrary many extra parameters. The :math:`*` refers to the unpacking operator in python.

                             **Returns**:

                                 float -- the moment value
      :type suff_stats: list
      :param gauge_symbols_source:
                                   A tuple or list containing sympy symbols of **gauge_paras** before transformation. These symbols must match the input of functions in **suff_stats**.

                                       For example, suppose functions in **suff_stats** takes input ( **u**, (**a**, **b**, **c**) ), the **gauge_symbols_source** should be a
                                       nested tuple ( (**a**, **b**, **c**), ), in which **a**, **b**, and **c** are sympy symbols. Alternatively, suppose functions in **suff_stats** takes input ( **u**, **a**, **b**, **c** ), the **gauge_symbols_source** should be a
                                       tuple (**a**, **b**, **c**), in which **a**, **b**, and **c** are sympy symbols.
      :type gauge_symbols_source: tuple or list
      :param gauge_symbols_target:
                                   A tuple or list containing sympy symbols of **gauge_paras** after transformation. These symbols must match the input of functions in **suff_stats**.

                                       For example, suppose functions in **suff_stats** takes input ( **u**, (**a**, **b**, **c**) ), the **gauge_symbols_source** should be a
                                       nested tuple ( (**a'**, **b'**, **c'**), ), in which **a'**, **b'**, and **c'** are sympy symbols. Alternatively, suppose functions in **suff_stats** takes input ( **u**, **a**, **b**, **c** ), the **gauge_symbols_source** should be a
                                       tuple (**a'**, **b'**, **c'**), in which **a'**, **b'**, and **c'** are sympy symbols.
      :type gauge_symbols_target: tuple or list
      :param transformation_inputs: A tuple or list containing sympy symbols specifying the input of the matrix valued function :math:`T_{ij}`. For example, (**a'**, **b'**, **c'**, **a**, **b**, **c**)
      :type transformation_inputs: tuple or list

      :returns:

                a matrix valued function :math:`T_{ij}` whose

                    **Parameters**:

                        **inputs** : float array of shape (len(**transformation_inputs**)) - The array containing values of symbols specified in **transformation_inputs**.

                    **Returns**:

                        float array of shape (N,N) -- the matrix :math:`T_{ij}`
      :rtype: function


   .. py:method:: get_gauge_paras_s_wx_1D(suff_stats, gauge_symbols, transformation_inputs)


   .. py:method:: get_gauge_paras_sr_sx_wx_1D(suff_stats, gauge_symbols, transformation_inputs)


   .. py:method:: conservation_projection_1D(suff_stats, gauge_symbols, transformation_inputs)