function xx = degexpand(x,deg,addbias)
% X = degexpand(x,m)
% Takes matrix x in which each column is an example.
% Produces matrix X such that x(i,:)=[1 x_1 x_1^2 ... x_1^m x_2 ... x_d^m]
% Also normalizes each column of X to the range [-1 1]
% X = degexpand(x,m,0) skips adding the ones as the first column in X
% (c) Greg Shakhnarovich MIT 2002

if (nargin < 3)
  addbias=1;
end

% and also scales down each feature.
[m,n] = size(x) ;
xx = reshape(  repmat(x',[1,1,deg]) .^ ...
	       repmat(reshape(1:deg,[1,1,deg]),[n,m]) ...
	       ,[n,m*deg]) ;
% Scale down to numbers in [-1,1]
xx = xx / diag(max(abs(xx))) ;
  
if (addbias)
  xx = [ones(size(xx,1),1) xx];
end