function [y_pred,p1,beta,bias,ker] = get_ypred_svr(x,y,x_test,nvar,c,p1,kr,C) 
% This function builds an PRS metamodel and predicts the function value at 
% test points. 
% This function can also be used to determine and output the SVR parameters 
% ("p1", "beta", "bias", "ker") needed to create an analytic function. A value 
% for x_test must be input with the appropriate number of design variables because 
% the function expects it. 
% ---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 point(s): in an 
% [num_of_points by num_of_variables] matrix 
% nvar = the number of design variables 
% c = user chosen insensitive zone paramter 
% p1 = user chosen kernel parameter 
% kr = user chosen kernel function 
% y_pred = SVR metamodel prediction at the test point(s) 
% beta = SVR parameter("Difference of Lagrange Multipliers" - Gunn Toolbox) 
% bias = SVR bias 
% ker = Kernel name associated with user chosen "kr" 
% --Currently Supported Kernel Functions-- 
% kr = 1 -> linear; 
% kr = 2 -> sigmoid; 
% kr = 3 -> Spline; 
% kr = 4 -> bSpline; 
% kr = 5 -> fourier; 
% kr = 6 -> erfb; 
% kr = 7 -> anova; 
% kr = 8 -> rbf; 
% C = user Chosen Penalty Parameter 
% This function uses the Guassian Process Toolbox: 
% Gunn, SR. �Support vector machines for classification and 
% regression,� Technical Report, University of Southampton, 1997. 
% Link to download Toolbox 
% http://www.isis.ecs.soton.ac.uk/resources/svminfo/ 
% Add the path name where the svmgunn toolbox folder is located addpath('...\svmgunn') global beta bias ker xt yt b global p1 
n = size(x,1); 
% number of experiments 
n_test = size(x_test,1); 
% number of test points 
yn = (y-ones(n,1)*mean(y))./(ones(n,1)*max(abs(y-ones(n,1)*mean(y)),[],1)); 
%================================ 
% 3) Support Vector Regression 
%================================ 
% 3.1) SVR parameters 
% [C] = C_estimation(xt,yt,zt); 
% Parameter that controls the amount of penalization for %
% points outside the e-tube 
% C = mean(y) + 3*std(y); 
% e = 3; 
% Insensitive zone 
range = abs(max(yn)-min(yn)); 
e = c/100*range; 
%-------------------------------- 
% 3.2) Kernel & loss function specification 
% ker = 'poly'; 
% Kernel function [spline] 
% p1 = 3; 
% Polynomial degree 
% loss = 'eInsensitive'; 
% Loss function [eInsensitive, quadratic] 
%-------------------------------- 
% Kernel function 
if kr == 1 
  ker = 'linear'; 
elseif kr == 2 
  ker = 'sigmoid'; 
elseif kr == 3 
  ker = 'spline'; 
elseif kr == 4 
  ker = 'bspline'; 
elseif kr == 5 
  ker = 'fourier'; 
elseif kr == 6 
  ker = 'erfb'; 
elseif kr == 7 
  ker = 'anova'; 
elseif kr == 8 
  ker = 'rbf'; 
end 
% p1 = std(y); 
% Polynomial degree 
% p1 = pp*p1; 
loss = 'eInsensitive'; 
% Loss function [eInsensitive, quadratic] 
% 3.3) SVR solution 
% [nsv,beta,bias] = svr([xt,yt],zt,ker,C,loss,e); 
% From Steve R. Gunn (Matlab Toolbox) 
[nsv,beta,bias] = svr(x,yn,ker,C,loss,e); 
% From Steve R. Gunn (Matlab Toolbox) 
% 3.4) Prediction 
y_pred = svroutput(x,x_test,ker,beta,bias); 
y_pred = y_pred.*max(abs(y-ones(n,1)*mean(y)))+mean(y);