function [varargout] = getlatt(latt,element,varargin)%GETLATT Count for a lattice parameters.%   VOL = GETLATT(L,P)%   [VOL,D2] = GETLATT(L,P)%   [VOL,D2,ERR] = GETLATT(L,P)%   [VOL,D2,ERR,HERMITE] = GETLATT(L,P)%   [VOL,D2,ERR,HERMITE,TAU] = GETLATT(L,P)% %   [...] = GETLATT(L,P) computes fundamental volume, minimum squared%   distance, hermite's parameter and kissing number of the Voronoi cell%   the element P belongs to. To obtain parameters of all lattice%   elements use the tracelatt function. %%   [...] = GETLATT(L,P,'PropertyName',PropertyValue,...)%%   Getlatt Property List%%   Echo           'on' | {'off'}%%   NOTE: GETLATT function gives sensible results only for geometrically%         uniform lattices. %%   Example:%       pts1 = 4 ^ 4;%       pts2 = 2 ^ 4;%       [D4,G1] = makelatt('D',pts1,4);%       [Hex,G2] = makelatt('Hex',pts2,2);%       [vol1,dist1,hermite1,tau1] = getlatt(D4,87)%       [vol2,dist2,hermite2,tau2] = getlatt(Hex,5)% %       vol_D4 = sqrt(det(G1));%       vol_Hex = sqrt(det(G2));%%  See also TRACELATT.%   Copyright 2001-2003 Kamil Anis, anisk@feld.cvut.cz%   Dept. of Radioelectronics, %   Faculty of Electrical Engineering%   Czech Technical University in Prague%   $Revision: 0.2 $  $Date: 2003/09/28 14:08:22 $%   --%   <additional stuff goes here>global ECHOname = 'GETLATT';[idt,tag] = iecho(name);nopts = length(varargin) / 2;opts = reshape(varargin,[2 nopts])';ord1 = strmatch('Echo',opts(:,1));% Echoif ~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;  endelse  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  endend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% BODY BEGIN %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%[m,n] = size(latt);if (element <= 0) | (element > m)  if ech    disp(' ');    disp([tag,'There is no such element in the lattice.']);    disp([idt,'Returning an empty output.']);    disp(' ');  end  varargout = {[],[],[],[],[]};  returnendcoord = latt(element,:);empty_latt = 0; i = 1;% kissing numbers etc.[tau,sh] = kiss(latt,element);% sh = sshell(latt,element);% the splitter algorithmwhile (i <= n) & (empty_latt == 0)  % determining the cutt-off lanes  dist = abs(latt(:,i) - coord(:,i));    % removing zero component and finding the shortest distance  if sum(dist ~= 0) == 0    edges(i) = 1;    empty_latt = 1;    empty_dim = i;            if ech      str1 = num2str(element); str2 = num2str(i);      disp(' ');      disp([tag,'Unable to compute lattice parameters.']);      disp([idt,'Splitter failed at dimension ',str2,'.']);      disp([idt,'Voronoi cell of element #',...        str1,' is used for the computation.']);      disp([idt,...        'This might be caused by the edge effects of the finite lattice.']);      disp([idt,...        'Try another element or use TRACELATT to trace for all cells.']);      disp([idt,'Returning an empty output.']);      disp(' ');    end            % if the splitter fails leave the function    varargout = {[],[],[],[],empty_dim};    return        else    edges(i) = min(dist(find(dist)));    empty_dim = [];  end    % splitting lattice...  [pos,num] = find(abs(latt(:,i) - coord(:,i)) < edges(i));  latt = latt(pos,:);  i = i + 1;end% counting minimum squared distance to the neighbours% [na,foo] = size(sh);% [na,foo] = size(tau);if tau > 0  coords = repmat(coord,tau,1);  d2 = sum(abs(sh - coords) .^ 2,2); % ||x-y||^2 = sum(abs(x-y)^2)   volume = prod(edges);  d2(find(d2 == 0)) = NaN;   d2_min = min(d2); % minimum nonzero distance  hermite = d2_min / (volume ^ (2 / n));  varargout = {volume,d2_min,hermite,tau,empty_dim};else  varargout = {[],[],[],[],empty_dim};end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% BODY END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%