netgraph_find_x.m

％The Metabolic Networks Toolbox contains functions to create, ％modify, display, and simulate bioche

function x = netgraph_find_x(graphics_object,gridsize,k1,k2,k3,k4,db);
  % inital guess from PCA

  db  = graphics_object.db.^0.2;
  dum = repmat(mean(db.^2),size(db,1),1);
  [xeig,a,s] = pca( -0.5*(db.^2-dum-dum')); 
  x          = s(1:2,:); 
  x          = diag([-1 1]'.*sign(x(:,1)-mean(x,2)))*x;
  
  [Ni,Nj]=ind2sub(size(graphics_object.N),find((graphics_object.N~=0)));
  
  gridsize = 0.01; % distance between discrete x values
  k1 = 0.01;  % overall repulsion strength
  k2 = 0.5*sqrt(1/length(graphics_object.metnames));  % overall repulsion scale
  k3 = 0.2;  % neighbour attraction strength
  
% move points around -> similar distances
  x=x+0.001*randn(size(x));
  for it=1:10
    edgecenters = 0.5*(x(:,Ni)+x(:,Nj));
    for i=1:size(x,2);
      distances = repmat(x(:,i),1,size(x,2)+length(Ni)) - [x, edgecenters]; %
      f1 = sum(distances.^2)+10^-10;
      f1 = exp(-f1/(2*k2^2))./sqrt(f1);
      dummy = x(:,find(db(i,:)==1));
      if length(dummy),	       xdum = mean(dummy,2);
      else,                     xdum = x(:,i);	       end
      xnew(:,i)= x(:,i) + k1 * sum(distances.*repmat(f1,2,1),2) ...
	  + k3 * ( xdum - x(:,i) );
    end
    x = xnew;
    x = x-repmat(min(x')',1,size(x,2));
    x = diag(1./(max(x')'))*x;
    x = gridsize * round(x/gridsize);
  end
  
  x = x-repmat(min(x')',1,size(x,2));
  x = diag(min(1,1./(max(x')')))*x;
  x = gridsize * round(x/gridsize);