function [y_pred,dmodel] = get_ypred_krig(x,y,x_test,nvar,b,c,cor,reg) 
% 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 
% b = the lower bound on theta 
% c = the upper bound on theta 
% cor = the correlation functions 
% --Currently Supported Correlation Functions-- 
% cor = 1 -> Cubic; 
% cor = 2 -> Exponential; 
% cor = 3 -> Gaussian; 
% cor = 4 -> Linear; 
% cor = 5 -> Spherical; 
% cor = 6 -> Spline; 
% reg = regression polynomial 
% --Currently Supported Regression Polynomials-- 
% reg = 1 -> 0 degree; 
% reg = 2 -> 1st degree; 
% reg = 3 -> 2nd degree; 
% This function uses the Guassian Process Toolbox: 
% Lophaven SN, Nielsen HB, S�ndergaard J �DACE � A MATLAB Kriging 
% Toolbox,� Informatics and mathematical modeling, 
% Technical University of Denmark, Lyngby, 2002. 
% Linke to download Toolbox 
% http://www2.imm.dtu.dk/~hbn/dace/ 
% Add the path name where the dace toolbox folder is located addpath('...\dace') 
a = (b+c)/2; 
if cor == 1 
  correlation = @corrcubic; 
elseif cor == 2 
  correlation = @correxp; 
elseif cor == 3 
  correlation = @corrgauss; 
elseif cor == 4 
  correlation = @corrlin; 
elseif cor == 5 
  correlation = @corrspherical; 
elseif cor == 6 
  correlation = @corrspline; 
end 
if reg == 1 
  regression = @regpoly0; 
elseif reg == 2 
  regression = @regpoly1; 
elseif reg == 3 
  regression = @regpoly2; 
end 
% MODEL IDENTIFICATION 
% Identifying the Kriging Model Parameters (Correlation Structure) 
% Initial values for the correlation parameters and lower and upper bounds 
theta0 = a*ones(1,nvar); 
lob = b*ones(1,nvar); 
upb = c*ones(1,nvar); 
% Specification of the input and output data, and the regression 
% and correlation model [dmodel, perf] = dacefit(x, y, regression, correlation, theta0, lob, upb); 
% dmodel: a data structure with all the necessary information to feed the 
% predictor function 
% perf: a data structure with details of the optimization process leading 
% to the correlation structure parameters 
% PREDICTION at test points [y_pred, mse] = predictor(x_test, dmodel); 
% y_pred: values of the prediction at the x locations 
% mse: mse for each predicted point