function [w,b,Yt] = ridgeregress(X,Y,gam, Xt)% Linear ridge regression% % >> [w, b]     = ridgeregress(X, Y, gam)% >> [w, b, Yt] = ridgeregress(X, Y, gam, Xt)% % Ordinary Least squares with a regularization parameter (gam).% % Full syntax% % >> [w, b, Yt] = ridgeregress(X, Y, gam, Xt)% % Outputs    %   w     : d x 1 vector with the regression coefficients%   b     : bias term%   Yt(*) : Nt x 1 vector with predicted outputs of test data% Inputs    %   X     : N x d matrix with the inputs of the training data%   Y     : N x 1 vector with the outputs of the training data%   gam   : Regularization parameter%   Xt(*) : Nt x d matrix with the inputs of the test data% % See also:% bay_rr,bay_lssvm% Copyright (c) 2002,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlab  if size(X,1)~=size(Y,1),  error('X and Y need to have the same number of data points');endif size(Y,2)~=1,  error('Only handling one-dimensional output');endif nargin==4 & size(Xt,2)~=size(X,2),  error('Training input and test inputs need to have the same dimension');end  [nD,nx] = size(X);if nx>nD, warning('dim datapoints larger than number of datapoints...');endXe = [X ones(nD,1)];%H = [ Xe'*Xe + gam^-1*[eye(nx) zeros(nx,1); zeros(1,nx+1)]];H = Xe'*Xe + inv(gam).*eye(nx+1);sol = pinv(H)*Xe'*Y;w = sol(1:end-1);b = sol(end);if nargin<4, return; endYt = Xt*w+b;