function pseudotour(x,maxit,classes)

% PSEUDOTOUR    Pseudo Grand Tour
%
% PSEUDOTOUR(X, MAXIT)
% This implements the pseudo grand tour of Wegman and Shen. The
% input is the data matrix X. MAXIT specifies the maximum number
% of iterations.

plot_class_labels = 0; 
if( nargin>2 ) 
  plot_class_labels = 1;
  uniq_classes = unique(classes); 
  n_classes    = length(uniq_classes); 
  
  class_colors  = 'bgrcmykw'; 
  class_symbols = '.ox+*sdv';
  ncc = length(class_colors); 
end

[n,p] = size(x);
if rem(p,2) ~= 0
  % Add zeros to the end.
  x = [x,zeros(n,1)];
  p = p+1;
end
% Set up vector of frequencies.
th = mod(exp(1:p),1);
% This is a small irrational number:
delt = exp(1)^(-5); 
cof = sqrt(2/p);
% Set up storage space for projection vectors.
a = zeros(p,1);
b = zeros(p,1);
z = zeros(n,2);
% Get an initial plot, so the tour can be implemented using Handle Graphics.
% 
if( ~plot_class_labels )      % <- no class labels were provided ... 
  ph = plot(z(:,1),z(:,2),'o','erasemode','normal');
else                          % <- class labels were provided ... plot each class in its own color/symbol 
  ph = []; 
  for ci=1:n_classes, 
    inds = find( uniq_classes(ci)==classes ); 
    ph   = [ph; plot(z(inds,1),z(inds,2),'o','erasemode','normal')]; 
    if( ci==1 ) hold on; end; 
  end
end
axis equal, axis off
set(gcf,'backingstore','off','renderer','painters','DoubleBuffer','on')
H = uicontrol(gcf,'style','text',...
    'units','normalized',...
    'position',[0.01 0.01 0.2 0.1],...
    'string','Iteration: ');
iter = 1;
for t=0:delt:(delt*maxit)
  % Find the transformation vectors.
  for j=1:p/2
    a(2*(j-1)+1)=cof*sin(th(j)*t);
    a(2*j)=cof*cos(th(j)*t);
    b(2*(j-1)+1)=cof*cos(th(j)*t);
    b(2*j)=cof*(-sin(th(j)*t));
  end
  % Project onto the vectors.
  z(:,1)=x*a;
  z(:,2)=x*b;
  if( ~plot_class_labels )
    set(ph,'xdata',z(:,1),'ydata',z(:,2)); 
  else
    for ci=1:n_classes, 
      inds = find( uniq_classes(ci)==classes ); 
      di   = mod(ci-1,ncc)+1; 
      set(ph(ci),'xdata',z(inds,1),'ydata',z(inds,2),'Marker',class_symbols(di),'Color',class_colors(di));
    end
  end
  set(H,'string',['Iteration: ',int2str(iter)])
  drawnow
  iter = iter + 1;
end