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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 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;
% init variables
if length(msize)==1, msize = [msize 1]; end
munits = 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' lattice
if 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;
end
end
% shapes
switch 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);
end
case '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))];
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% subfunctions
function 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%