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function h=som_cplane(varargin)
%SOM_CPLANE Visualize one 2D component plane, U-matrix or color plane.
%
% h=som_cplane(lattice, msize, color, [s], [pos])
% h=som_cplane(topol, color, [s], [pos])
%
% som_cplane('hexa', [10 5], 'none');
% som_cplane('rect', [10 5], 'r');
% som_cplane(sM.topol, sM.codebook(:,1));
% U = som_umat(sM); som_cplane('hexaU',sM.topol.msize,U(:));
%
% Input and output arguments ([]'s are optional):
% lattice (string) 'hexa', 'rect' (component planes)
% 'hexaU', 'rectU' (corresponding U-matrices)
% (matrix) defines the patch (see function VIS_PATCH).
% msize (vector) 1x2 vector defines grid size (M=prod(msize))
% (matrix) Mx2 matrix gives explicit coordinates for each node
% topol (struct) map or topology struct
% color color for the nodes
% (matrix) Mx1 matrix gives indexed colors for the units
% Mx3 matrix of RGB triples gives explicit
% color for each unit
% (Note: in case of U-matrix, the number of color
% values is 4*prod(msize)-2*sum(msize)+1, not prod(msize))
% (string) ColorSpec gives the same color for each node
% 'none' draws black edges only.
% [s] (matrix) size Mx1, gives individual size scaling for each node
% (scalar) gives the same size for each node, default=1.
% Additional features: see 'type som_cplane'
% This argument is ignored if the lattice is 'rectU' or 'hexaU'.
% [pos] (vector) a 1x2 vector that determines position of origin,
% default is [1 1].
%
% h (scalar) the object handle for the PATCH object
%
% Axis are set to the 'ij' mode with equal spacing and turned off if
% 'pos' is not given. If 'lattice' is 'rect', 'hexa', 'rectU' or
% 'hexaU' the node (a,b) has coordinates (a,b) (+pos), except on the
% even numbered rows on the 'hexa' and 'hexaU' grids where the
% coordinates are (a,b+0.5) (+pos).
%
% For more help, try 'type som_cplane' or check out online documentation.
% See also SOM_PIEPLANE, SOM_PLOTPLANE, SOM_BARPLANE, VIS_PATCH,
% SOM_VIS_COORDS
%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% som_cplane
%
% PURPOSE
%
% Visualizes a 2D component plane or u-matrix
%
% SYNTAX
%
% h = som_cplane(topol, color)
% h = som_cplane(lattice, msize, color)
% h = som_cplane(lattice, msize, color)
% h = som_cplane(..., size)
% h = som_cplane(..., size, pos)
%
% DESCRIPTION
%
% Creates some basic visualizations of the SOM grid: the component plane and
% the unified distance matrix. The routine draws the SOM grid as a patch
% object according to the specifications given in the input arguments and
% returns its object handle.
%
% Each unit of the map is presented by a polygon whose color, size, shape
% and location can be specified in various ways. The usual procedure
% is to choose the lattice and map size used in the map training. Then
% the function creates the standard sheet shaped topological
% representation of the map grid with hexagonal or rectangular units.
% When the values from a map codebook component (or from SOM_UMAT)
% are given to the function it produces an indexed coloring for the
% units (as in SURF command). Another possibility is to give a fixed
% RGB color for each unit explicitly.
%
% Special effects (variable unit size, location or shape) can be produced
% giving different types of input variables.
%
% KNOWN BUGS
%
% Using 1x3 or 3x1 grids causes problem, as the MATLAB will treat the color
% information vector 1x3 or 3x1 as a single RGB triple. So, using indexed
% colors is not possible for this particular map size.
%
% It is not possible to specify explicit coordinates for map
% consistig of just one unit as then the msize is interpreted as
% map size.
%
% REQUIRED INPUT ARGUMENTS
%
% Note: M is the number of map units
%
% lattice The basic shape of the map units
%
% (string) 'hexa' or 'rect' creates standard component plane;
% 'hexaU' or 'rectU' creates standard u-matrix.
% (matrix) Lx2 matrix defines the cornes of an arbitary polygon to be used
% as the unit marker. (L is the number of patch vertex: L=6 for
% 'hexa' and L=4 for 'rect')
%
% msize The size of the map grid
%
% (vector) [n1 n2] vector defines the map size (height n1 units, width
% n2 units, total M=n1 x n2 units). The units will be placed to their
% topological locations to form a uniform hexagonal or rectangular grid.
% (matrix) Mx2 matrix defines arbitrary coordinates for the M units
% In this case the argument 'lattice' defines the unit form only.
%
% topol Topology of the map grid
%
% (struct) map or topology struct from which the topology is taken
%
% color Unit colors
%
% (string) (ColorSpec) gives the same color for each unit, 'none'
% draws black unit edges only.
% (vector) Mx1 column vector gives indexed color for each unit using the
% current colormap (see help colormap).
% (matrix) Mx3 matrix of RGB triples as rows gives each unit a fixed color.
%
% OPTIONAL INPUT ARGUMENTS
%
% Note: M is the number of map units.
% Note: if unspecified or given empty values ('' or []) default
% values are used for optional input arguments.
%
% s The size scaling factors for the units
%
% (scalar) scalar gives each unit the same size scaling:
% 0 unit disappears (edges can be seen as a dot).
% 1 by default unit has its normal size (ie. no scaling)
% >1 unit overlaps others
% (matrix) Mx1 double: each unit gets individual size scaling
%
% pos Position of origin
%
% (vector) This argument exists to be able drawing component planes
% in arbitrary locations in a figure. Note the operation:
% if this argument is given, the axis limits setting
% part in the routine is skipped and the limits setting
% will be left to be done by MATLAB's default
% operation.
%
% OUTPUT ARGUMENTS
%
% h (scalar) handle to the created patch object
%
% OBJECT TAGS
%
% One object handle is returned: field Tag is set to
% 'planeC' for component plane
% 'planeU' for U-matrix
%
% FEATURES
%
% There are some extra features in following arguments
%
% size
% - MxL matrix: radial scaling: the distance between
% the center of node m and its kth vertex is scaled by
% s(m,k).
% - Mx1x2 matrix: the uniform scaling is done separately for
% x- and y-directions
% - MxLx2 matrix: the scaling is done separately to x- and y-
% directions for each vertex.
%
% color
% Each vertex may be given individual color.
% The PATCH object interpolates the colors on the
% face if shading is turned to interp.
% - 1xMxL matrix: colormap index for each vertex
% - LxMx3 matrix: RGB color for each vertex
%
% Note: In both cases (size and color) the ordering of the patch
% vertices in the "built-in" patches is the following
%
% 'rect' 'hexa'
% 1 3 1
% 2 4 5 2
% 6 3
% 4
%
% The color interpolation result seem to depend on the order
% in which the patch vertices are defined. Anyway, it gives
% unfavourable results in our case especially with hexa grid:
% this is a MATLAB feature.
%
% EXAMPLES
%
% m=som_make(rand(100,4),'msize',[6 5]) % make a map
%
% % show the first variable plane using indexed color coding
%
% som_cplane(m.topol.lattice,m.topol.msize,m.codebook(:,1));
% or som_cplane(m.topol,m.codebook(:,1));
% or som_cplane(m,m.codebook(:,1));
%
% % show the first variable using different sized black units
%
% som_cplane(m,'k',m.codebook(:,1));
%
% % Show the u-matrix. First we have to calculate it.
% % Note: som_umat returns a matrix therefore we write u(:) to get
% % a vector which contains the values in the proper order.
%
% u=som_umat(m);
% som_cplane('hexaU', m.topol.msize, u(:));
%
% % Show three first variables coded as RGB colors
% % and turn the unit edges off
%
% h=som_cplane(m, m.codebook(:,1:3),1)
% set(h,'edgecolor','none');
%
% % Try this! (see section FEATURES)
%
% som_cplane('rect',[5 5],'none',rand(25,4));
% som_cplane('rect',[5 5],rand(1,25,4));
%
% SEE ALSO
%
% som_barplane Visualize the map prototype vectors as bar diagrams
% som_plotplane Visualize the map prototype vectors as line graphs
% som_pieplane Visualize the map prototype vectors as pie charts
% som_umat Compute unified distance matrix of self-organizing map
% vis_patch Define the basic patches used in som_cplane
% som_vis_coords The default 'hexa' and 'rect' coordinates in visualizations
% Copyright (c) 1999-2000 by the SOM toolbox programming team.
% http://www.cis.hut.fi/projects/somtoolbox/
% Version 2.0beta Johan 061099 juuso 151199 juuso 070600
%%% Check & Init arguments %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[nargin, lattice, msize, color, s, pos]=vis_planeGetArgs(varargin{:});
error(nargchk(3, 5, nargin)); % check no. of input args is correct
%% Translation?
if nargin < 5 | isempty(pos)
pos=NaN; % "no translation" flag
elseif ~vis_valuetype(pos,{'1x2'}),
error('Position of origin has to be given as an 1x2 vector.');
end
%% Patchform %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch class(lattice)
case 'char' % built-in patchforms
pos=pos-1;
switch lattice
case {'hexa', 'hexaU'}
patchform=vis_patch('hexa');
case {'rect', 'rectU'}
patchform=vis_patch('rect');
otherwise
error([ 'Lattice ' lattice ' not implemented!']);
end
case { 'double', 'sparse'}
if vis_valuetype(lattice,{'nx2'}),
patchform=lattice; % users patchform
lattice='rect';
else
error('Patchform matrix has wrong size');
end
otherwise
error('String or matrix expected for lattice.');
end
l=size(patchform,1); % number of vertices
planeType=lattice(end); % 'U' if umatrix otherwise something else
if ~vis_valuetype(msize,{ '1x2', 'nx2'}),
error('msize has to be given as 1x2 or nx2 vectors.');
end
%% msize or coordinates %%%%%%%%%%%%%%%%%%%%%%%
if size(msize,1)>1
% msize is coordinate matrix Nx2?
if planeType == 'U', % don't accept u-matrix
error('U-matrix visualization doesn''t work with free coordinates.');
end
% set number of map unit and unit coordinates
munits=size(msize,1);
unit_coords=msize; msize=[munits 1];
if isnan(pos), % no translation is done here
pos=[0 0]; % using [0 0] in order to prevent
end % axis tightening in
% vis_PlaneAxisProperties (arbitary coords!)
else
% msize is built-in lattice
unit_coords=som_vis_coords(lattice,msize);
% Calculate matrices x and y which 'moves' nodes
% to the correct positions:
% For U-matrix, the size has to be recalculated
if planeType == 'U',
xdim=2*msize(1)-1;ydim=2*msize(2)-1;
else
xdim=msize(1);ydim=msize(2);
end
munits=xdim*ydim;
% Feature warning
if munits == 3
warning('Problems with 1x3 and 3x1 maps. See documentation.');
end
end
%% Color matrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~isnumeric(color) & ~ischar(color),
error('Color matrix is invalid.');
else
d=size(color);
switch length(d)
case 2 %% Flat colors
if ischar(color) % Check for string 'none'
if strcmp(color,'none'),
color=NaN;
end
else
if ~(d(1)== 1 & d(2) == 3) & ...
~(d(1) == munits & (d(2)==1 | d(2)==3))
error('Color data matrix has wrong size.');
elseif d(1)~=1 & d(2)==3
if any(color>1 | color<0)
error('Color data matrix has invalid RGB values.');
end
color=reshape(color,[1 munits 3]); % RGB colors
elseif d(2)==1
color=color'; % indexed
end
end
case 3 %% Interpolated colors
if d(1) == 1 & d(2) == munits & d(3) == l,
color=reshape(color, l, munits);
elseif ~(d(1) == l & d(2) == munits & d(3) == 3)
error('Color data matrix has wrong size.');
end
otherwise
error('Color data matrix has too many dimensions.');
end
end
%% Size matrix? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargin < 4 | isempty(s),
s=1; % default value for s (no scaling)
elseif ~isnumeric(s)
error('Size matrix is not numeric.');
end
%%Determine the type of size matrix
d=size(s);
switch length(d)
case 2
if (d(1)==1 & d(2)==1),
% Each node gets the same, uniform scaling.
s=s'; sx=s; sy=s;
elseif (d(1)==munits & d(2)==l),
% Each vertex is scaled radially respetc to the
% node center.
s=s'; sx=s; sy=s;
elseif d(1)==munits & d(2)==1
% Each node gets an individual uniform scaling.
sx=repmat(s',l,1); sy=sx;
else
error('Size matrix has wrong size.');
end
case 3
if d(1)==munits & d(2)==1 & d(3)==2,
% Each node is individually and uniformly
% scaled separately to x- and y-directions.
sx=repmat(shiftdim(s(:,:,1))',l,1);
sy=repmat(shiftdim(s(:,:,2))',l,1);
elseif d(1)==munits & d(2)==l & d(3)==2,
% Each vertex is scaled separately to x- and y-directions
% with respect to the node center.
sx=shiftdim(s(:,:,1))';
sy=shiftdim(s(:,:,2))';
else
error('Size matrix has wrong size.');
end
otherwise
error('Size matrix has too many dimensions.');
end
% Size zero would cause division by zero. eps is as good (node disappears)
% I tried first NaN, it works well otherwise, but the node is
% then not on the axis and some commands may the work oddly.
% The edge may be visible, though.
sx(sx==0)=eps;
sy(sy==0)=eps;
% Rescale sizes for u-matrix
if planeType=='U',
sx=sx/2;sy=sy/2;
end
%%%% Action %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Making grid. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Translation for each patch
x=repmat(unit_coords(:,1)',l,1);
y=repmat(unit_coords(:,2)',l,1);
% patch vertex coordiantes
nx=repmat(patchform(:,1),1,munits);
ny=repmat(patchform(:,2),1,munits);
% NB: The hexagons are not uniform in order to get even
% y-coordinates for the nodes. This is handled by setting _axis scaling_
% so that the hexa-nodes look like uniform hexagonals. See
% vis_PlaneAxisProperties
%% Make and scale the final input for PATCH:
% 1: combine translation and scaling of each patch
x=(x./sx+nx).*sx; y=(y./sy+ny).*sy;
%% 2: translation of origin (pos)
if ~isnan(pos)
x=x+pos(1);y=y+pos(2); % move upper left corner
end % to pos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Set axes properties
%% Command view([0 90]) shows the map in 2D properly oriented
ax=newplot; % set new plot
vis_PlaneAxisProperties(ax,lattice,msize,pos);
%% Draw the map!
if ~isnan(color)
h_=patch(x,y,color);
else
h_=patch(x,y,'k'); % empty grid
set(h_,'FaceColor','none');
end
%% Set object tag
if planeType=='U'
set(h_,'Tag','planeU');
else
set(h_,'Tag','planeC');
end
%%% Build output %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargout>0, h=h_; end % Set h only,
% if there really is output