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annotate toolboxes/MIRtoolbox1.3.2/somtoolbox/som_unit_coords.m @ 0:e9a9cd732c1e tip

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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 function Coords = som_unit_coords(topol,lattice,shape)
wolffd@0 2
wolffd@0 3 %SOM_UNIT_COORDS Locations of units on the SOM grid.
wolffd@0 4 %
wolffd@0 5 % Co = som_unit_coords(topol, [lattice], [shape])
wolffd@0 6 %
wolffd@0 7 % Co = som_unit_coords(sMap);
wolffd@0 8 % Co = som_unit_coords(sMap.topol);
wolffd@0 9 % Co = som_unit_coords(msize, 'hexa', 'cyl');
wolffd@0 10 % Co = som_unit_coords([10 4 4], 'rect', 'toroid');
wolffd@0 11 %
wolffd@0 12 % Input and output arguments ([]'s are optional):
wolffd@0 13 % topol topology of the SOM grid
wolffd@0 14 % (struct) topology or map struct
wolffd@0 15 % (vector) the 'msize' field of topology struct
wolffd@0 16 % [lattice] (string) map lattice, 'rect' by default
wolffd@0 17 % [shape] (string) map shape, 'sheet' by default
wolffd@0 18 %
wolffd@0 19 % Co (matrix, size [munits k]) coordinates for each map unit
wolffd@0 20 %
wolffd@0 21 % For more help, try 'type som_unit_coords' or check out online documentation.
wolffd@0 22 % See also SOM_UNIT_DISTS, SOM_UNIT_NEIGHS.
wolffd@0 23
wolffd@0 24 %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0 25 %
wolffd@0 26 % som_unit_coords
wolffd@0 27 %
wolffd@0 28 % PURPOSE
wolffd@0 29 %
wolffd@0 30 % Returns map grid coordinates for the units of a Self-Organizing Map.
wolffd@0 31 %
wolffd@0 32 % SYNTAX
wolffd@0 33 %
wolffd@0 34 % Co = som_unit_coords(sTopol);
wolffd@0 35 % Co = som_unit_coords(sM.topol);
wolffd@0 36 % Co = som_unit_coords(msize);
wolffd@0 37 % Co = som_unit_coords(msize,'hexa');
wolffd@0 38 % Co = som_unit_coords(msize,'rect','toroid');
wolffd@0 39 %
wolffd@0 40 % DESCRIPTION
wolffd@0 41 %
wolffd@0 42 % Calculates the map grid coordinates of the units of a SOM based on
wolffd@0 43 % the given topology. The coordinates are such that they can be used to
wolffd@0 44 % position map units in space. In case of 'sheet' shape they can be
wolffd@0 45 % (and are) used to measure interunit distances.
wolffd@0 46 %
wolffd@0 47 % NOTE: for 'hexa' lattice, the x-coordinates of every other row are shifted
wolffd@0 48 % by +0.5, and the y-coordinates are multiplied by sqrt(0.75). This is done
wolffd@0 49 % to make distances of a unit to all its six neighbors equal. It is not
wolffd@0 50 % possible to use 'hexa' lattice with higher than 2-dimensional map grids.
wolffd@0 51 %
wolffd@0 52 % 'cyl' and 'toroid' shapes: the coordinates are initially determined as
wolffd@0 53 % in case of 'sheet' shape, but are then bended around the x- or the
wolffd@0 54 % x- and then y-axes to get the desired shape.
wolffd@0 55 %
wolffd@0 56 % POSSIBLE BUGS
wolffd@0 57 %
wolffd@0 58 % I don't know if the bending operation works ok for high-dimensional
wolffd@0 59 % map grids. Anyway, if anyone wants to make a 4-dimensional
wolffd@0 60 % toroid map, (s)he deserves it.
wolffd@0 61 %
wolffd@0 62 % REQUIRED INPUT ARGUMENTS
wolffd@0 63 %
wolffd@0 64 % topol Map grid dimensions.
wolffd@0 65 % (struct) topology struct or map struct, the topology
wolffd@0 66 % (msize, lattice, shape) of the map is taken from
wolffd@0 67 % the appropriate fields (see e.g. SOM_SET)
wolffd@0 68 % (vector) the vector which gives the size of the map grid
wolffd@0 69 % (msize-field of the topology struct).
wolffd@0 70 %
wolffd@0 71 % OPTIONAL INPUT ARGUMENTS
wolffd@0 72 %
wolffd@0 73 % lattice (string) The map lattice, either 'rect' or 'hexa'. Default
wolffd@0 74 % is 'rect'. 'hexa' can only be used with 1- or
wolffd@0 75 % 2-dimensional map grids.
wolffd@0 76 % shape (string) The map shape, either 'sheet', 'cyl' or 'toroid'.
wolffd@0 77 % Default is 'sheet'.
wolffd@0 78 %
wolffd@0 79 % OUTPUT ARGUMENTS
wolffd@0 80 %
wolffd@0 81 % Co (matrix) coordinates for each map units, size is [munits k]
wolffd@0 82 % where k is 2, or more if the map grid is higher
wolffd@0 83 % dimensional or the shape is 'cyl' or 'toroid'
wolffd@0 84 %
wolffd@0 85 % EXAMPLES
wolffd@0 86 %
wolffd@0 87 % Simplest case:
wolffd@0 88 % Co = som_unit_coords(sTopol);
wolffd@0 89 % Co = som_unit_coords(sMap.topol);
wolffd@0 90 % Co = som_unit_coords(msize);
wolffd@0 91 % Co = som_unit_coords([10 10]);
wolffd@0 92 %
wolffd@0 93 % If topology is given as vector, lattice is 'rect' and shape is 'sheet'
wolffd@0 94 % by default. To change these, you can use the optional arguments:
wolffd@0 95 % Co = som_unit_coords(msize, 'hexa', 'toroid');
wolffd@0 96 %
wolffd@0 97 % The coordinates can also be calculated for high-dimensional grids:
wolffd@0 98 % Co = som_unit_coords([4 4 4 4 4 4]);
wolffd@0 99 %
wolffd@0 100 % SEE ALSO
wolffd@0 101 %
wolffd@0 102 % som_unit_dists Calculate interunit distance along the map grid.
wolffd@0 103 % som_unit_neighs Calculate neighborhoods of map units.
wolffd@0 104
wolffd@0 105 % Copyright (c) 1997-2000 by the SOM toolbox programming team.
wolffd@0 106 % http://www.cis.hut.fi/projects/somtoolbox/
wolffd@0 107
wolffd@0 108 % Version 1.0beta juuso 110997
wolffd@0 109 % Version 2.0beta juuso 101199 070600
wolffd@0 110
wolffd@0 111 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0 112 %% Check arguments
wolffd@0 113
wolffd@0 114 error(nargchk(1, 3, nargin));
wolffd@0 115
wolffd@0 116 % default values
wolffd@0 117 sTopol = som_set('som_topol','lattice','rect');
wolffd@0 118
wolffd@0 119 % topol
wolffd@0 120 if isstruct(topol),
wolffd@0 121 switch topol.type,
wolffd@0 122 case 'som_map', sTopol = topol.topol;
wolffd@0 123 case 'som_topol', sTopol = topol;
wolffd@0 124 end
wolffd@0 125 elseif iscell(topol),
wolffd@0 126 for i=1:length(topol),
wolffd@0 127 if isnumeric(topol{i}), sTopol.msize = topol{i};
wolffd@0 128 elseif ischar(topol{i}),
wolffd@0 129 switch topol{i},
wolffd@0 130 case {'rect','hexa'}, sTopol.lattice = topol{i};
wolffd@0 131 case {'sheet','cyl','toroid'}, sTopol.shape = topol{i};
wolffd@0 132 end
wolffd@0 133 end
wolffd@0 134 end
wolffd@0 135 else
wolffd@0 136 sTopol.msize = topol;
wolffd@0 137 end
wolffd@0 138 if prod(sTopol.msize)==0, error('Map size is 0.'); end
wolffd@0 139
wolffd@0 140 % lattice
wolffd@0 141 if nargin>1 & ~isempty(lattice) & ~isnan(lattice), sTopol.lattice = lattice; end
wolffd@0 142
wolffd@0 143 % shape
wolffd@0 144 if nargin>2 & ~isempty(shape) & ~isnan(shape), sTopol.shape = shape; end
wolffd@0 145
wolffd@0 146 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0 147 %% Action
wolffd@0 148
wolffd@0 149 msize = sTopol.msize;
wolffd@0 150 lattice = sTopol.lattice;
wolffd@0 151 shape = sTopol.shape;
wolffd@0 152
wolffd@0 153 % init variables
wolffd@0 154
wolffd@0 155 if length(msize)==1, msize = [msize 1]; end
wolffd@0 156 munits = prod(msize);
wolffd@0 157 mdim = length(msize);
wolffd@0 158 Coords = zeros(munits,mdim);
wolffd@0 159
wolffd@0 160 % initial coordinates for each map unit ('rect' lattice, 'sheet' shape)
wolffd@0 161 k = [1 cumprod(msize(1:end-1))];
wolffd@0 162 inds = [0:(munits-1)]';
wolffd@0 163 for i = mdim:-1:1,
wolffd@0 164 Coords(:,i) = floor(inds/k(i)); % these are subscripts in matrix-notation
wolffd@0 165 inds = rem(inds,k(i));
wolffd@0 166 end
wolffd@0 167 % change subscripts to coordinates (move from (ij)-notation to (xy)-notation)
wolffd@0 168 Coords(:,[1 2]) = fliplr(Coords(:,[1 2]));
wolffd@0 169
wolffd@0 170 % 'hexa' lattice
wolffd@0 171 if strcmp(lattice,'hexa'),
wolffd@0 172 % check
wolffd@0 173 if mdim > 2,
wolffd@0 174 error('You can only use hexa lattice with 1- or 2-dimensional maps.');
wolffd@0 175 end
wolffd@0 176 % offset x-coordinates of every other row
wolffd@0 177 inds_for_row = (cumsum(ones(msize(2),1))-1)*msize(1);
wolffd@0 178 for i=2:2:msize(1),
wolffd@0 179 Coords(i+inds_for_row,1) = Coords(i+inds_for_row,1) + 0.5;
wolffd@0 180 end
wolffd@0 181 end
wolffd@0 182
wolffd@0 183 % shapes
wolffd@0 184 switch shape,
wolffd@0 185 case 'sheet',
wolffd@0 186 if strcmp(lattice,'hexa'),
wolffd@0 187 % this correction is made to make distances to all
wolffd@0 188 % neighboring units equal
wolffd@0 189 Coords(:,2) = Coords(:,2)*sqrt(0.75);
wolffd@0 190 end
wolffd@0 191
wolffd@0 192 case 'cyl',
wolffd@0 193 % to make cylinder the coordinates must lie in 3D space, at least
wolffd@0 194 if mdim<3, Coords = [Coords ones(munits,1)]; mdim = 3; end
wolffd@0 195
wolffd@0 196 % Bend the coordinates to a circle in the plane formed by x- and
wolffd@0 197 % and z-axis. Notice that the angle to which the last coordinates
wolffd@0 198 % are bended is _not_ 360 degrees, because that would be equal to
wolffd@0 199 % the angle of the first coordinates (0 degrees).
wolffd@0 200
wolffd@0 201 Coords(:,1) = Coords(:,1)/max(Coords(:,1));
wolffd@0 202 Coords(:,1) = 2*pi * Coords(:,1) * msize(2)/(msize(2)+1);
wolffd@0 203 Coords(:,[1 3]) = [cos(Coords(:,1)) sin(Coords(:,1))];
wolffd@0 204
wolffd@0 205 case 'toroid',
wolffd@0 206
wolffd@0 207 % NOTE: if lattice is 'hexa', the msize(1) should be even, otherwise
wolffd@0 208 % the bending the upper and lower edges of the map do not match
wolffd@0 209 % to each other
wolffd@0 210 if strcmp(lattice,'hexa') & rem(msize(1),2)==1,
wolffd@0 211 warning('Map size along y-coordinate is not even.');
wolffd@0 212 end
wolffd@0 213
wolffd@0 214 % to make toroid the coordinates must lie in 3D space, at least
wolffd@0 215 if mdim<3, Coords = [Coords ones(munits,1)]; mdim = 3; end
wolffd@0 216
wolffd@0 217 % First bend the coordinates to a circle in the plane formed
wolffd@0 218 % by x- and z-axis. Then bend in the plane formed by y- and
wolffd@0 219 % z-axis. (See also the notes in 'cyl').
wolffd@0 220
wolffd@0 221 Coords(:,1) = Coords(:,1)/max(Coords(:,1));
wolffd@0 222 Coords(:,1) = 2*pi * Coords(:,1) * msize(2)/(msize(2)+1);
wolffd@0 223 Coords(:,[1 3]) = [cos(Coords(:,1)) sin(Coords(:,1))];
wolffd@0 224
wolffd@0 225 Coords(:,2) = Coords(:,2)/max(Coords(:,2));
wolffd@0 226 Coords(:,2) = 2*pi * Coords(:,2) * msize(1)/(msize(1)+1);
wolffd@0 227 Coords(:,3) = Coords(:,3) - min(Coords(:,3)) + 1;
wolffd@0 228 Coords(:,[2 3]) = Coords(:,[3 3]) .* [cos(Coords(:,2)) sin(Coords(:,2))];
wolffd@0 229
wolffd@0 230 end
wolffd@0 231
wolffd@0 232 return;
wolffd@0 233
wolffd@0 234 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0 235 %% subfunctions
wolffd@0 236
wolffd@0 237 function C = bend(cx,cy,angle,xishexa)
wolffd@0 238
wolffd@0 239 dx = max(cx) - min(cx);
wolffd@0 240 if dx ~= 0,
wolffd@0 241 % in case of hexagonal lattice it must be taken into account that
wolffd@0 242 % coordinates of every second row are +0.5 off to the right
wolffd@0 243 if xishexa, dx = dx-0.5; end
wolffd@0 244 cx = angle*(cx - min(cx))/dx;
wolffd@0 245 end
wolffd@0 246 C(:,1) = (cy - min(cy)+1) .* cos(cx);
wolffd@0 247 C(:,2) = (cy - min(cy)+1) .* sin(cx);
wolffd@0 248
wolffd@0 249 % end of bend
wolffd@0 250
wolffd@0 251 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0 252