polymerist.maths.lattices.integral
==================================

.. py:module:: polymerist.maths.lattices.integral

.. autoapi-nested-parse::

   Core tools for manipulating integer lattices in D-dimensions



Classes
-------

.. autoapisummary::

   polymerist.maths.lattices.integral.CubicIntegerLattice


Functions
---------

.. autoapisummary::

   polymerist.maths.lattices.integral.generate_int_lattice
   polymerist.maths.lattices.integral.nearest_int_coord_along_normal


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

.. py:function:: generate_int_lattice(*dims: Iterable[int]) -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], int]

   Generate all D-D coordinates of points on a integer lattice with the sizes of all D dimensions given


.. py:function:: nearest_int_coord_along_normal(point: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], numbers.Number], normal: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], numbers.Number]) -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], int]

   Takes an D-dimensional control point and an D-dimensional normal vector
   Returns the integer-valued point nearest to the control point which lies in
   the normal direction relative to the control point


.. py:class:: CubicIntegerLattice(counts_along_dims: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], int])

   Bases: :py:obj:`polymerist.maths.lattices.coordinates.Coordinates`\ [\ :py:obj:`int`\ ]


   For representing an n-dimensional integer lattice, consisting of all n-tuples of integers with values constrained by side lengths in each dimension


   .. py:attribute:: counts_along_dims


   .. py:method:: counts_along_dims_as_str(multip_char: str = 'x') -> str

      Stringify the lattice sidelengths



   .. py:property:: capacity
      :type: int


      The maximum number of points that the lattice could contains


   .. py:property:: lex_ordered_weights
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D], int]


      Vector of the number of points corresponding
      Can be viewed as a linear transformation between indices and point coordinates when coords are placed in lexicographic order


   .. py:property:: odd_even_idxs
      :type: tuple[numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], int], numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], int]]


      Return two vectors of indices, corresponding to points in the "odd" and "even" non-neighboring sublattices, respectively


   .. py:property:: odd_idxs
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], int]


      Indices of the point in the in "odd" sublattice


   .. py:property:: even_idxs
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N], int]


      Indices of the point in the in "even" sublattice


   .. py:property:: odd_sublattice
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], int]


      Returns points within the odd sublattice of the lattice points


   .. py:attribute:: odd_points


   .. py:property:: even_sublattice
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.N, polymerist.genutils.typetools.numpytypes.D], int]


      Returns points within the even sublattice of the lattice points


   .. py:attribute:: even_points