function y_pred = get_ypred_gp(x,y,x_test,nvar) 
% This function builds an PRS metamodel and predicts the function value at 
% test points. 
% ---Variable Descriptions--- 
% x = normalized design(training points): in an 
% [num_of_points by num_of_variables] matrix 
% y = vector of function values at each x 
% x_test = test points: in an 
% [num_of_points by num_of_variables] matrix 
% nvar = the number of design variables 
% This function uses the Guassian Process Toolbox: 
% Rasmussen, C., Williams, C. �Gaussian Processes for Machine 
% Learning,� MIT, Cambridge, Massachusetts, 2006. 
% Link to Download the Toolbox 
% http://www.gaussianprocess.org/gpml/code/matlab/doc/index.html 
% Add the path name where the gpml toolbox folder is located addpath('...\gpml') 
offset = mean(y); 
y = y - offset; 
% shift the mean to zero % hyperparameters are stored as 
% logtheta = [ log(ell_1) 
% log(ell_2) 
% ... 
% log(ell_D) 
% log(sigma_f) 
% log(sigma_n) ] 
covfunc = {'covSum', {'covSEard','covNoise'}}; 
logtheta0 = [zeros(nvar,1); 
log(0.7*std(y)); 
log(0.7*std(y))]; 
[logtheta, fvals, iter] = minimize(logtheta0, 'gpr', -100, covfunc, x, y); 
% now make predictions 
Xstar = x_test; 
[fstar S2] = gpr(logtheta, covfunc, x, y, x_test); 
y_pred = fstar + offset; 
% adjust the predictions considering the shift