Matlab code used in  "M. Torda, J. Y. Goulermas, R. Pucek, V. Kurlin, Entropic trust region for densest crystallographic symmetry group packings".

Requirements: 
	MATLAB r2021b + Parallel Computing Toolbox
	NVIDIA CUDA Enabled GPU with compute capability 3.5 and higher

P2 packing of convex polygons:

	'packingP2nGon.m' - performs densest P2 packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of .txt file containing polygon vertices coordinates
				nRuns - number of packing refinement runs
				nWorkers - number of workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a,b'     - lengths of primitive cell edges
				'alpha'   - primitive cell angle

		Example: packingP2nGon('octagon.txt', 100, 10)
	
	'drawP2nGon.m' - draws a visualization of a P2 configuration for a given convex polygon
	
		Input arguments:
			solution -  name of the text file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
				'b'     - length of primitive cell edge
				'alpha' - primitive cell angle
			polygon - name of text file containing polygon vertices coordinates

		Example: drawP2nGon('octagonP2solution.txt', 'octagon.txt')

	'packingP2nGonCon.m' - overlap constraint computation for 'n' P2 configurations of a given convex polygon.

	'packingObliqueObj.m' - computes volume of the primitive cell for oblique crystal system configuration of a given convex polygon.

PG packing of convex polygons:

	'packingPGnGon.m' - performs densest PG packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of .txt file containing polygon vertices coordinates
				nRuns - number of packing refinement runs
				nWorkers - number of workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a,b'     - lengths of primitive cell edges

		Example: packingPGnGon('pentagon.txt', 100, 10)
	
	'drawPGnGon.m' - draws a visualization of a PG configuration for a given convex polygon
	
		Input arguments:
			solution -  name of the text file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
				'b'     - length of primitive cell edge

			polygon - name of text file containing polygon vertices coordinates

		Example: drawPGnGon('pentagonPGsolution.txt', 'pentagon.txt')

	'packingPGnGonCon.m' - overlap constraint computation for 'n' PG configurations of a given convex polygon.

	'packingRectangularObj.m' - computes volume of the primitive cell for rectangular crystal system configuration of a given convex polygon.

P2GG packing of convex polygons:

	'packingP2GGnGon.m' - performs densest P2GG packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of .txt file containing polygon vertices coordinates
				nRuns - number of packing refinement runs
				nWorkers - number of workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a,b'     - lengths of primitive cell edges

		Example: packingPGnGon('heptagon.txt', 100, 10)
	
	'drawP2GGnGon.m' - draws a visualization of a PG configuration for a given convex polygon
	
		Input arguments:
			solution -  name of the text file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
				'b'     - length of primitive cell edge

			polygon - name of text file containing polygon vertices coordinates

		Example: drawP2GGnGon('heptagonP2GGsolution.txt', 'heptagon.txt')

	'packingP2GGnGonCon.m' - overlap constraint computation for 'n' PG configurations of a given convex polygon.

	'packingRectangularObj.m' - computes volume of the primitive cell for rectangular crystal system configuration of a given convex polygon.

P3 packing of convex polygons:

	'packingP3nGon.m' - performs densest P3 packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of .txt file containing polygon vertices coordinates
				nRuns - number of packing refinement runs
				nWorkers - number of CPU workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a,b'     - lengths of primitive cell edges

		Example: packingP3nGon('hexagon.txt', 100, 10)
	
	'drawP3nGon.m' - draws a visualization of a P3 configuration for a given convex polygon
	
		Input arguments:
			solution -  name of the .txt file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
				'b'     - length of primitive cell edge
			polygon - name of .txt file containing polygon vertices coordinates

		Example: drawP3nGon('hexagonP3solution.txt', 'hexagon.txt')

	'packingP3nGonCon.m' - overlap constraint computation for 'n' P3 configurations of a given convex polygon.

	'packingHexagonalObj.m' - computes volume of the primitive cell for hexagonal crystal system configuration of a given convex polygon.

P4 packing of convex polygons:

	'packingP4nGon.m' - performs densest P4 packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of text file containing polygon vertices coordinates
				nRuns - number packing refinement runs
				nWorkers - number of workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a'       - length of primitive cell edge

		Example: packingP4nGon('iregPentagon.txt', 100, 10)
	
	'drawP4nGon.m' - draws a visualization of a P4 configuration for a given convex polygon
		
		Input arguments:
			solution -  name of the text file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
			polygon - name of text file containing polygon vertices coordinates

		Example: drawP4nGon('iregPentagonP4solution.txt', 'iregPentagon.txt')

	'packingP4nGonCon.m' - overlap constraint computation for 'n' P4 configurations of a given convex polygon.

	'packingSquareObj.m' - computes volume of the primitive cell for square crystal system configuration of a given convex polygon.

P6M packing of convex polygons:

	'packingP6NGon.m' - performs densest P6M packing for a given convex polygon. 
	
		Input arguments:
				polygon - name of .txt file containing polygon vertices coordinates
				nRuns - number packing refinement runs
				nWorkers - number of workers to use in computations


		Output: highest packing configuration achieved with the following structure properties
				'density' - packing density
				'x,y'     - fractional coordinates of the centroid of  given polygon
				'omega'   - angle of rotation of give polygon
				'a'       - length of primitive cell edge

		Example: packingP6MnGon('iregTriangle.txt', 100, 10)
	
	'drawP6MnGon.m' - draws a visualization of a P6M configuration for a given convex polygon
		
		Input arguments:
			solution -  name of the .txt file containing:
				'x'     - fractional coordinate of the centroid of given polygon
				'y'     - fractional coordinate of the centroid of given polygon
				'omega' - angle of rotation of give polygon
				'a'     - length of primitive cell edge
			polygon - name of .txt file containing polygon vertices coordinates

		Example: drawP6MnGon('iregTriangleP6Msolution.txt', 'iregTriangle.txt')

	'packingP6MnGonCon.m' - overlap constraint computation for 'n' P6M configurations of a given convex polygon.

	'packingHexagonalObj.m' - computes volume of the primitive cell for hexagonal crystal system configuration of a given convex polygon.

Entropic trust region optimization:
	'entropicPacking.m' - initial run of the entropic trust region

	'entropicPackingRef.m' - refining run of the entropic trust region

Extended multivariate von Mises Gibbs sampler:
	'emvmRand.m' - simulates n realizations of the exponential family reparametrisation of extended multivariate von Mises distribution.
	'gvmRand.m' - rejection sampling generating n realizations from the generalized von Mises distribution. "R. Gatto, Some computational aspects of the generalized von mises distribution, Statistics and computing, (2008)."