:py:mod:`pemtk.sym._directProduct`
==================================

.. py:module:: pemtk.sym._directProduct

.. autoapi-nested-parse::

   Direct product functions for libmsym and symmetrized harmonics routines.

   17/04/23 v1

   Developed/adapted from libmsym demo code, see https://github.com/mcodev31/libmsym/issues/29
   Special thanks to mcodev31 for the help.

   For quick reference tables, see also http://www.gernot-katzers-spice-pages.com/character_tables/index.html

   Formulas should follow those on p29 in Atkins, B.P.W., Child, M.S. and Phillips, C.S.G. (2006) Tables for Group Theory. Oxford University Press.



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


Functions
~~~~~~~~~

.. autoapisummary::

   pemtk.sym._directProduct.prod
   pemtk.sym._directProduct.prodList
   pemtk.sym._directProduct.dotArray
   pemtk.sym._directProduct.symDecomposition
   pemtk.sym._directProduct.diretProductFromList
   pemtk.sym._directProduct.directProductTable



.. py:function:: prod(character_table, s1, s2)

   Array product of two irrep characters.

   :param character_table:
   :type character_table: libmsym character table.
   :param s1: Index for irrep/symmetry species 1.
   :type s1: int
   :param s2: Index for irrep/symmetry species 2.
   :type s2: int

   :returns: **np.array**
   :rtype: array product.


.. py:function:: prodList(character_table, symList)

   Array product of (any number of) irrep characters from a list.

   :param character_table:
   :type character_table: libmsym character table.
   :param symList: List of species to use.
                   E.g. symList = ['A1g','A1u','B1u', 'B1u'] defines resultant as direct product of these terms.
   :type symList: list

   :returns: **np.array**
   :rtype: array product.

   .. rubric:: Examples

   >>> PG = 'D2h'
   >>> ctx = msym.Context(elements=[msym.Element(name = "H", coordinates = [.0,.0,.0])], basis_functions=[], point_group=PG)
   >>> r = prodMulti(ctx.character_table, ['A1g','A1u','B1u', 'B1u'])
   >>> r
   array([ 1.,  1., -1., -1., -1., -1.,  1.,  1.])


.. py:function:: dotArray(character_table, s, p)

   Irrep representation dot products.


.. py:function:: symDecomposition(character_table, p)

   Decompose basis vector to irreps

   :param character_table:
   :type character_table: libmsym character table.
   :param p: Vecotor for analysis.
             Must contain len(character_table.symmetry_species) elements.
   :type p: np.array


.. py:function:: diretProductFromList(PG='Cs', terms=[])

   Compute direct products from a list of irreps/species with [libmsym](https://github.com/mcodev31/libmsym).

   Developed from https://github.com/mcodev31/libmsym/issues/29.

   :param PG: Supported point groups from libmsym: Ci, Cs, Cnv, Dn, Dnh, Dnd, Td, O, Oh, I and Ih
   :type PG: point group string.
   :param terms: List of species to use.
                 E.g. symList = ['A1g','A1u','B1u', 'B1u'] defines resultant as direct product of these terms.
   :type terms: list

   :returns: * **list** (*resultant as list of specices.*)
             * **dict** (*contains various other forms of the output (as labelled).*)

   .. rubric:: Examples

   >>> dDict, _ = diretProductFromList(PG = 'D2h', terms = ['A1g','A1u','B1u', 'B1u'])
   >>> dDict
   {'A1g': 0,
    'B1g': 0,
    'A1u': 1,
    'B1u': 0,
    'B3g': 0,
    'B3u': 0,
    'B2g': 0,
    'B2u': 0}


.. py:function:: directProductTable(PG='Cs')

   Generate direct product tables with [libmsym](https://github.com/mcodev31/libmsym).

   Developed from https://github.com/mcodev31/libmsym/issues/29


   :param PG: Supported point groups from libmsym: Ci, Cs, Cnv, Dn, Dnh, Dnd, Td, O, Oh, I and Ih
   :type PG: point group string.

   :returns: * **pd.DataFrame** (*direct product table.*)
             * **dict** (*contains various other forms of the output (as labelled).*)