makelatt.m

Lattice coding and decoding

function varargout = makelatt(kind,num,dim,varargin)

%MAKELATT Create lattice
%   L = MAKELATT(KIND,PTS,DIM) makes desired kind of dim-dimensional
%   finite lattice that consists of pts elements. Available designs are
%   listed in the table below. All the generated lattices are 
%   geometrically uniform. The lattice points are chosen from the origin
%   to higher shells. Sometimes its usefull to generate lattices from the
%   number of one dimensional pattern side i.e. PTS = DIM ^ SIDE.
%
%   Table of available designs
%
%      Design  | Dimension |   KIND
%   -----------+-----------+----------
%        Zn    |    n>=1   |   'Z'
%        An    |    n>=1   |   'A'
%        Dn    |    n>=3   |   'D'
%    Hexagonal |    n=2    |  'Hex'
%       fcc    |    n=3    |  'fcc'
%
%   [...] = MAKELATT(KIND,PTS,DIM,'PropertyName',PropertyValue,...)
%
%   Makelatt Property List
%
%   Echo           'on' | {'off'}
%
%   See also TRACELATT, TRANSLATT, ROTLATT, GRAB, SHOWLATT.

%   Copyright 2001-2003 Kamil Anis, [e-mail]
%   Dept. of Radioelectronics, 
%   Faculty of Electrical Engineering
%   Czech Technical University in Prague
%   $Revision: 0.1 $  $Date: 2003/1/16 17:33:28 $
%   --
%   <additional stuff goes here>

global ECHO

name = 'MAKELATT';
[idt,tag] = iecho(name);

nopts = length(varargin) / 2;
opts = reshape(varargin,[2 nopts])';

ord1 = strmatch('Echo',opts(:,1));

% Echo
if ~isempty(ord1) % first check whether local option exists
	value1 = opts{ord1,2};
	switch value1
	case 'on'
		ech = 1;
	case 'off'
		ech = 0;
	otherwise
		disp(' ');
		disp([tag,'Invalid option for Echo property.']);
		disp([idt,'Possible values are ''on''|{''off''}.']);
		disp(' ');
		ech = 0;
	end
else
	if ~isempty(ECHO) % than check whether global option exists
		switch ECHO
		case 'on'
			ech = 1;
		case 'off'
			ech = 0;
		otherwise
			disp(' ');
			disp([tag,'Invalid option for Echo property.']);
			disp([idt,'Possible values are ''on''|{''off''}.']);
			disp(' ');
			ech = 0;
		end
	else % if there are no settings use the defaults
		ech = 0; % default value
	end
end

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k = num ^ (1 / dim) - 1;
a = span([0:k],dim);

switch kind
case 'Z'
	G = eye(dim);
	
case 'A'
	if (dim == 2) & ech
		disp(' ');
		disp([tag,'A2 lattice is equivalent or similar to the hexagonal lattice.']);
		disp([idt,'For 2D computations is better to use ''Hex'' lattice.']);
		disp(' ');
	end
	diag_main = -1 * eye(dim);
	diag_lateral = ones(dim - 1,1);
	G = diag_main + diag(diag_lateral,1);
	G(end,end:end + 1) = [-1 1];
  
case 'D'
	if (dim < 3) & ech
		disp(' ');
		disp([tag,'Invalid dimension! DIM must be greater or equal to 3.']);
		disp([idt,'Returning an empty output.']);
		disp(' ');
		G = []; a = [];
	else
		diag_main = -1 * eye(dim);
		diag_lateral = ones(dim - 1,1);
		G = diag_main + diag(diag_lateral,-1);
		G(1,2) = -1;
	end
	
case 'Hex'
	if (dim ~= 2) & ech
		disp(' ');
		disp([tag,'Invalid dimension! DIM must be equal to 2.']);
		disp([idt,'Returning an empty output.']);
		disp(' ');
		G = []; a = [];
	else
		G = 1/2 * [2 0;-1 sqrt(3)];
	end
		
case 'fcc'
	if ech
		disp(' ');
		disp([tag,'''fcc'' latice is equivalent to the D3 lattice.']);
		disp(' ');
	end
	
	G = [-1 -1 0;1 -1 0;0 1 -1];

case 'diff'
   %G = [1 9];
		
   G = [4 4;3 -5];
   %G = [1 9;0 32];
% case 'Leech24'
% 	
% 	G = 
		
end

latt = a(1:end,:) * G;
varargout = {latt,G};

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