%VANDERMONDEM Fixedd mapping, extend data matrix
%
% Z = VANDERMONDEM(X,N)
% Z = X*VANDERMONDEM([],N)
% Z = X*VANDERMONDEM(N)
%
% INPUT
% X Data matrix
% N Order of the polynomail
%
% OUTPUT
% Z New data matrix containing X upto order N
%
% DESCRIPTION
% Construct the Vandermonde matrix Z from the original data matrix X by
% including all orders upto N. Note that also order 0 is added:
% Z = [ones X X^2 X^3 ... X^N]
% This construction allows for the trivial extension of linear methods
% to obtain polynomail regressions.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% LINEARR
% Copyright: D.M.J. Tax, D.M.J.Tax@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
function z = vandermondem(varargin)
mapname = 'Vandermonde map';
argin = shiftargin(varargin,'scalar');
argin = setdefaults(argin,[],1);
if mapping_task(argin,'definition')
z = define_mapping(argin,'fixed',mapname);
elseif mapping_task(argin,'training') % Execute.
[x,n] = deal(argin{:});
dat = +x;
[m,dim] = size(dat);
I = 1:dim;
z = ones(m,n*dim+1);
for i=0:(n-1)
z(:,(i+1)*dim+I) = dat.*z(:,i*dim+I);
end
% remove the superfluous ones:
z(:,1:dim-1) = [];
z = setdat(x,z);
end
return