function Coords = som_unit_coords(topol,lattice,shape)%SOM_UNIT_COORDS Locations of units on the SOM grid. %% Co = som_unit_coords(topol, [lattice], [shape])% %  Co = som_unit_coords(sMap);%  Co = som_unit_coords(sMap.topol);%  Co = som_unit_coords(msize, 'hexa', 'cyl');%  Co = som_unit_coords([10 4 4], 'rect', 'toroid');%%  Input and output arguments ([]'s are optional): %   topol              topology of the SOM grid%             (struct) topology or map struct%             (vector) the 'msize' field of topology struct%   [lattice] (string) map lattice, 'rect' by default%   [shape]   (string) map shape, 'sheet' by default%%   Co        (matrix, size [munits k]) coordinates for each map unit    %% For more help, try 'type som_unit_coords' or check out online documentation.% See also SOM_UNIT_DISTS, SOM_UNIT_NEIGHS.%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% som_unit_coords%% PURPOSE%% Returns map grid coordinates for the units of a Self-Organizing Map.%% SYNTAX%%  Co = som_unit_coords(sTopol);%  Co = som_unit_coords(sM.topol);%  Co = som_unit_coords(msize);%  Co = som_unit_coords(msize,'hexa');%  Co = som_unit_coords(msize,'rect','toroid');%% DESCRIPTION%% Calculates the map grid coordinates of the units of a SOM based on % the given topology. The coordinates are such that they can be used to% position map units in space. In case of 'sheet' shape they can be % (and are) used to measure interunit distances. %% NOTE: for 'hexa' lattice, the x-coordinates of every other row are shifted % by +0.5, and the y-coordinates are multiplied by sqrt(0.75). This is done % to make distances of a unit to all its six neighbors equal. It is not % possible to use 'hexa' lattice with higher than 2-dimensional map grids.%% 'cyl' and 'toroid' shapes: the coordinates are initially determined as % in case of 'sheet' shape, but are then bended around the x- or the % x- and then y-axes to get the desired shape. % % POSSIBLE BUGS%% I don't know if the bending operation works ok for high-dimensional% map grids. Anyway, if anyone wants to make a 4-dimensional% toroid map, (s)he deserves it.%% REQUIRED INPUT ARGUMENTS% %  topol          Map grid dimensions.%        (struct) topology struct or map struct, the topology %                 (msize, lattice, shape) of the map is taken from %                 the appropriate fields (see e.g. SOM_SET)%        (vector) the vector which gives the size of the map grid%                 (msize-field of the topology struct).%  % OPTIONAL INPUT ARGUMENTS % %  lattice (string) The map lattice, either 'rect' or 'hexa'. Default%                   is 'rect'. 'hexa' can only be used with 1- or %                   2-dimensional map grids.%  shape   (string) The map shape, either 'sheet', 'cyl' or 'toroid'. %                   Default is 'sheet'. %% OUTPUT ARGUMENTS%%  Co   (matrix) coordinates for each map units, size is [munits k] %                where k is 2, or more if the map grid is higher%                dimensional or the shape is 'cyl' or 'toroid'%% EXAMPLES%% Simplest case:%  Co = som_unit_coords(sTopol);%  Co = som_unit_coords(sMap.topol);%  Co = som_unit_coords(msize);%  Co = som_unit_coords([10 10]);%% If topology is given as vector, lattice is 'rect' and shape is 'sheet'% by default. To change these, you can use the optional arguments:%  Co = som_unit_coords(msize, 'hexa', 'toroid');%% The coordinates can also be calculated for high-dimensional grids:%  Co = som_unit_coords([4 4 4 4 4 4]);%% SEE ALSO% %  som_unit_dists    Calculate interunit distance along the map grid.%  som_unit_neighs   Calculate neighborhoods of map units.% Copyright (c) 1997-2000 by the SOM toolbox programming team.% http://www.cis.hut.fi/projects/somtoolbox/% Version 1.0beta juuso 110997% Version 2.0beta juuso 101199 070600%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Check arguments error(nargchk(1, 3, nargin));% default valuessTopol = som_set('som_topol','lattice','rect');% topolif isstruct(topol),   switch topol.type,   case 'som_map', sTopol = topol.topol;  case 'som_topol', sTopol = topol;  endelseif iscell(topol),   for i=1:length(topol),     if isnumeric(topol{i}), sTopol.msize = topol{i};     elseif ischar(topol{i}),        switch topol{i},       case {'rect','hexa'}, sTopol.lattice = topol{i};       case {'sheet','cyl','toroid'}, sTopol.shape = topol{i};       end    end  endelse  sTopol.msize = topol;endif prod(sTopol.msize)==0, error('Map size is 0.'); end% latticeif nargin>1 & ~isempty(lattice) & ~isnan(lattice), sTopol.lattice = lattice; end% shape if nargin>2 & ~isempty(shape) & ~isnan(shape), sTopol.shape = shape; end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Actionmsize = sTopol.msize;lattice = sTopol.lattice;shape = sTopol.shape;% init variablesif length(msize)==1, msize = [msize 1]; endmunits = prod(msize);mdim = length(msize);Coords = zeros(munits,mdim);% initial coordinates for each map unit ('rect' lattice, 'sheet' shape)k = [1 cumprod(msize(1:end-1))]; inds = [0:(munits-1)]';for i = mdim:-1:1,   Coords(:,i) = floor(inds/k(i)); % these are subscripts in matrix-notation  inds = rem(inds,k(i)); end% change subscripts to coordinates (move from (ij)-notation to (xy)-notation)Coords(:,[1 2]) = fliplr(Coords(:,[1 2])); % 'hexa' latticeif strcmp(lattice,'hexa'),   % check  if mdim > 2,     error('You can only use hexa lattice with 1- or 2-dimensional maps.');  end  % offset x-coordinates of every other row   inds_for_row = (cumsum(ones(msize(2),1))-1)*msize(1);   for i=2:2:msize(1),     Coords(i+inds_for_row,1) = Coords(i+inds_for_row,1) + 0.5;   endend% shapesswitch shape, case 'sheet',   if strcmp(lattice,'hexa'),     % this correction is made to make distances to all     % neighboring units equal    Coords(:,2) = Coords(:,2)*sqrt(0.75);   endcase 'cyl',   % to make cylinder the coordinates must lie in 3D space, at least  if mdim<3, Coords = [Coords ones(munits,1)]; mdim = 3; end  % Bend the coordinates to a circle in the plane formed by x- and   % and z-axis. Notice that the angle to which the last coordinates  % are bended is _not_ 360 degrees, because that would be equal to   % the angle of the first coordinates (0 degrees).  Coords(:,1)     = Coords(:,1)/max(Coords(:,1));  Coords(:,1)     = 2*pi * Coords(:,1) * msize(2)/(msize(2)+1);  Coords(:,[1 3]) = [cos(Coords(:,1)) sin(Coords(:,1))];                    case 'toroid',   % NOTE: if lattice is 'hexa', the msize(1) should be even, otherwise   % the bending the upper and lower edges of the map do not match   % to each other  if strcmp(lattice,'hexa') & rem(msize(1),2)==1,     warning('Map size along y-coordinate is not even.');  end  % to make toroid the coordinates must lie in 3D space, at least  if mdim<3, Coords = [Coords ones(munits,1)]; mdim = 3; end  % First bend the coordinates to a circle in the plane formed  % by x- and z-axis. Then bend in the plane formed by y- and  % z-axis. (See also the notes in 'cyl').  Coords(:,1)     = Coords(:,1)/max(Coords(:,1));  Coords(:,1)     = 2*pi * Coords(:,1) * msize(2)/(msize(2)+1);  Coords(:,[1 3]) = [cos(Coords(:,1)) sin(Coords(:,1))];  Coords(:,2)     = Coords(:,2)/max(Coords(:,2));  Coords(:,2)     = 2*pi * Coords(:,2) * msize(1)/(msize(1)+1);  Coords(:,3)     = Coords(:,3) - min(Coords(:,3)) + 1;  Coords(:,[2 3]) = Coords(:,[3 3]) .* [cos(Coords(:,2)) sin(Coords(:,2))];  endreturn;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% subfunctionsfunction C = bend(cx,cy,angle,xishexa)  dx = max(cx) - min(cx);  if dx ~= 0,     % in case of hexagonal lattice it must be taken into account that    % coordinates of every second row are +0.5 off to the right    if xishexa, dx = dx-0.5; end    cx = angle*(cx - min(cx))/dx;   end      C(:,1) = (cy - min(cy)+1) .* cos(cx);  C(:,2) = (cy - min(cy)+1) .* sin(cx);% end of bend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%