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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 values
sTopol = som_set('som_topol','lattice','rect');
% topol
if isstruct(topol),
switch topol.type,
case 'som_map', sTopol = topol.topol;
case 'som_topol', sTopol = topol;
end
elseif 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
end
else
sTopol.msize = topol;
end
if prod(sTopol.msize)==0, error('Map size is 0.'); end
% lattice
if nargin>1 & ~isempty(lattice) & ~isnan(lattice), sTopol.lattice = lattice; end
% shape
if nargin>2 & ~isempty(shape) & ~isnan(shape), sTopol.shape = shape; end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Action
msize = sTopol.msize;
lattice = sTopol.lattice;
shape = sTopol.shape;
munits = prod(msize);
Ud = zeros(munits,munits);
% free topology
if strcmp(lattice,'free'),
N1 = sTopol.connection;
Ud = som_neighborhood(N1,Inf);
end
% coordinates of map units when the grid is spread on a plane
Coords = som_unit_coords(msize,lattice,'sheet');
% width and height of the grid
dx = max(Coords(:,1))-min(Coords(:,1));
if msize(1)>1, dx = dx*msize(1)/(msize(1)-1); else dx = dx+1; end
dy = 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 location
switch 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));
end
case '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);
end
case '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);
end
otherwise,
error (['Unknown shape: ', shape]);
end
Ud = Ud + Ud';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%