.. index:: pair: namespace; primitive
.. _doxid-namespaceprimitive:

namespace primitive
===================

.. toctree::
	:hidden:

Overview
~~~~~~~~

Functions for generating primitive rings. :ref:`More...<details-namespaceprimitive>`


.. ref-code-block:: cpp
	:class: doxyrest-overview-code-block

	
	namespace primitive {

	// structs

	struct :ref:`Graph<doxid-structprimitive_1_1_graph>`;
	struct :ref:`Vertex<doxid-structprimitive_1_1_vertex>`;

	// classes

	class :ref:`RingUpdater<doxid-classprimitive_1_1_ring_updater>`;

	} // namespace primitive
.. _details-namespaceprimitive:

Detailed Documentation
~~~~~~~~~~~~~~~~~~~~~~

Functions for generating primitive rings.

This namespace contains struct definitions and functions that are used for generating primitive (shortest-path) rings (directed cyclic graphs).

The :ref:`Vertex <doxid-structprimitive_1_1_vertex>` object is a collection of elements for each point, required for graph traversal. The :ref:`Graph <doxid-structprimitive_1_1_graph>` object is an object for the whole frame, containing the information of all vertices, and a row-ordered vector of vector of the rings generated.

The `Franzblau shortest-path criterion <https://journals.aps.org/prb/pdf/10.1103/PhysRevB.44.4925>`__ has been used. The SP (shortest-path) criterion is midway between the least restrictive and most restrictive criteria in the hierarchy.

The following is the procedure for finding primitive rings:

#. All possible rings (including non-SP) rings are found, in the :ref:`primitive::countAllRingsFromIndex <doxid-group__primitive_1gac81b1dd4b67e8200de61e52c498c1b2f>` function, using the `backtracking algorithm <https://www.math.upenn.edu/~wilf/website/CombinatorialAlgorithms.pdf>`__. This is a recursive algorithm.

#. The non-SP rings are then removed from the list of all rings, using the Franzblau shortest path criterion (:ref:`primitive::removeNonSPrings <doxid-group__primitive_1ga592086d3afae4fab5aa5ff6aa5c1d215>`), answered by a hop-bounded breadth-first sweep per vertex.



.. _doxid-namespaceprimitive_1autotoc_md5_1s1:





.. _doxid-namespaceprimitive_1autotoc_md5_1s2:





.. _doxid-namespaceprimitive_1autotoc_md5:

Changelog
+++++++++

* Amrita Goswami [`amrita16thaug646@gmail.com <mailto:amrita16thaug646@gmail.com>`__]; date modified: Nov 14, 2019

* Rohit Goswami [`rog32@hi.is <mailto:rog32@hi.is>`__]; date modified: Mar 20, 2021