function Ud = som_unit_dists(topol,lattice,shape)%SOM_UNIT_DISTS Distances between unit-locations on the map grid.%% Ud = som_unit_dists(topol,[lattice],[shape])% %  Ud = som_unit_dists(sMap);%  Ud = som_unit_dists(sMap.topol);%  Ud = som_unit_dists(msize, 'hexa', 'cyl');%  Ud = som_unit_dists([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%%   Ud        (matrix, size [munits munits]) distance from each map unit %                      to each map unit%% For more help, try 'type som_unit_dists' or check out online documentation.% See also SOM_UNIT_COORDS, SOM_UNIT_NEIGHS.%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% som_unit_dists%% PURPOSE%% Returns interunit distances between the units of a Self-Organizing Map% along the map grid.%% SYNTAX%%  Ud = som_unit_dists(sTopol);%  Ud = som_unit_dists(sM.topol);%  Ud = som_unit_dists(msize);%  Ud = som_unit_dists(msize,'hexa');%  Ud = som_unit_dists(msize,'rect','toroid');%% DESCRIPTION%% Calculates the distances between the units of a SOM based on the % given topology. The distance are euclidian and they are measured% along the map grid (in the output space). %% In case of 'sheet' shape, the distances can be measured directly% from the unit coordinates given by SOM_UNIT_COORDS. %% In case of 'cyl' and 'toroid' shapes this is not so. In these cases% the coordinates are calculated as in the case of 'sheet' shape and% the shape is then taken into account by shifting the map grid into% different positions. %% Consider, for example, a 4x3 map. The basic position of map units % is shown on the left (with '1' - 'C' each denoting one map unit). % In case of a 'cyl' shape, units on the left and right edges are% neighbors, so for this purpose the map is copied on the left and% right sides of the map, as on right. %%    basic               left     basic    right%    -------             -------  -------  -------%    1  5  9             1  5  9  1  5  9  1  5  9%    2  6  a             2  6  a  2  6  a  2  6  a  %    3  7  b             3  7  b  3  7  b  3  7  b %    4  8  c             4  8  c  4  8  c  4  8  c % % For the 'toroid' shape a similar trick is done, except that the % copies are placed all around the basic position:%%             1  5  9  1  5  9  1  5  9%             2  6  a  2  6  a  2  6  a  %             3  7  b  3  7  b  3  7  b %             4  8  c  4  8  c  4  8  c %             1  5  9  1  5  9  1  5  9%             2  6  a  2  6  a  2  6  a  %             3  7  b  3  7  b  3  7  b %             4  8  c  4  8  c  4  8  c %             1  5  9  1  5  9  1  5  9%             2  6  a  2  6  a  2  6  a  %             3  7  b  3  7  b  3  7  b %             4  8  c  4  8  c  4  8  c %% From this we can see that the distance from unit '1' is 1 to units% '9','2','4' and '5', and sqrt(2) to units 'C','A','8' and '6'. Notice % that in the case of a 'hexa' lattice and 'toroid' shape, the size% of the map in y-direction should be even. The reason can be clearly% seen from the two figures below. On the left the basic positions for% a 3x3 map. If the map is copied above itself, it can be seen that the% lattice is broken (on the right):%%     basic positions                 example of broken lattice%     ---------------                 -------------------------%                                     1  4  7 %                                      2  5  8%                                     3  6  9%     1  4  7                         1  4  7 %      2  5  8                         2  5  8%     3  6  9                         3  6  9%% % 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%%  Ud   (matrix) distances from each map unit to each other map unit,%                size is [munits munits]%% EXAMPLES%% Simplest case:%  Ud = som_unit_dists(sTopol);%  Ud = som_unit_dists(sMap.topol);%  Ud = som_unit_dists(msize);%  Ud = som_unit_dists([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:%  Ud = som_unit_dists(msize, 'hexa', 'toroid');%% The distances can also be calculated for high-dimensional grids:%  Ud = som_unit_dists([4 4 4 4 4 4]);%% SEE ALSO% %  som_unit_coords   Calculate grid coordinates.%  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 170400 070600 130600%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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;munits = prod(msize);Ud = zeros(munits,munits);% free topologyif strcmp(lattice,'free'),  N1 = sTopol.connection;   Ud = som_neighborhood(N1,Inf);end% coordinates of map units when the grid is spread on a planeCoords = som_unit_coords(msize,lattice,'sheet');% width and height of the griddx = max(Coords(:,1))-min(Coords(:,1));if msize(1)>1, dx = dx*msize(1)/(msize(1)-1); else dx = dx+1; enddy = max(Coords(:,2))-min(Coords(:,2));if msize(2)>1, dy = dy*msize(2)/(msize(2)-1); else dy = dy+1; end% calculate distance from each location to each other locationswitch shape, case 'sheet',  for i=1:(munits-1),     inds = [(i+1):munits];     Dco = (Coords(inds,:) - Coords(ones(munits-i,1)*i,:))';     Ud(i,inds) = sqrt(sum(Dco.^2));  endcase 'cyl',   for i=1:(munits-1),     inds = [(i+1):munits];     Dco  = (Coords(inds,:) - Coords(ones(munits-i,1)*i,:))';     dist = sum(Dco.^2);    % The cylinder shape is taken into account by adding and substracting    % the width of the map (dx) from the x-coordinate (ie. shifting the    % map right and left).    DcoS = Dco; DcoS(1,:) = DcoS(1,:) + dx;  %East (x+dx)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) - dx;  %West (x-dx)    dist = min(dist,sum(DcoS.^2));    Ud(i,inds) = sqrt(dist);  endcase 'toroid',   for i=1:(munits-1),     inds = [(i+1):munits];     Dco  = (Coords(inds,:) - Coords(ones(munits-i,1)*i,:))';     dist = sum(Dco.^2);     % The toroid shape is taken into account as the cylinder shape was     % (see above), except that the map is shifted also vertically.    DcoS = Dco; DcoS(1,:) = DcoS(1,:) + dx;  %East (x+dx)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) - dx;  %West (x+dx)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(2,:) = DcoS(2,:) + dy;  %South (y+dy)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(2,:) = DcoS(2,:) - dy;  %North (y-dy)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) + dx; DcoS(2,:) = DcoS(2,:) - dy; %NorthEast (x+dx, y-dy)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) + dx; DcoS(2,:) = DcoS(2,:) + dy; %SouthEast (x+dx, y+dy)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) - dx; DcoS(2,:) = DcoS(2,:) + dy; %SouthWest (x-dx, y+dy)    dist = min(dist,sum(DcoS.^2));    DcoS = Dco; DcoS(1,:) = DcoS(1,:) - dx; DcoS(2,:) = DcoS(2,:) - dy; %NorthWest (x-dx, y-dy)    dist = min(dist,sum(DcoS.^2));    Ud(i,inds) = sqrt(dist);  endotherwise,   error (['Unknown shape: ', shape]);endUd = Ud + Ud';%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%