function [y_pred,lambda] = get_ypred_rbf(x,y,x_test,c,choice) 
% This function builds an RBF metamodel and predicts the function value at 
% test points. 
% This function can also be used to calculate lambda based on the given 
% design points to use for analytic functions. A value for x_test must 
% be defined since 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 points: in an 
% [num_of_points by num_of_variables] matrix 
% c = user chosen RBF constant (good general value is c = 1) 
% choice = user chosen RBF radial basis function choice 
% (good general value is choice = 3) 
% --Currently Supported Basis Funcitons-- 
% choice = 1 -> Thin Plate; 
phi = r^2*ln(c*r) 
% choice = 2 -> Gaussian; 
phi = exp(-c*r^2) 
% choice = 3 -> Multiguadric; 
phi = sqrt(r^2+c^2) 
% choice = 4 -> Inverse Multiquadric; 
phi = 1/sqrt(r^2+c^2) 
n = size(x,1); 
% number of training points 
n_test = size(x_test,1); 
% number of test points 
% Define matrix A 
for i=1:n 
  for j=1:n 
    xj=x(j,:); 
    xi=x(i,:); 
    r=norm(xj-xi); 
    phi = get_phi(r,c,choice); 
    A(i,j) = phi; 
  end 
end 
% Solve for lambda 
lambda = A\y; 
% Calculate the RBF prediction at test points 
for j = 1:n_test 
  y_pred(j,1) = 0; 
  xj = x_test(j,:); 
  for i = 1:n 
    xi = x(i,:); 
    r = norm(xj-xi); 
    phi = get_phi(r,c,choice); 
    y_pred(j,1)=y_pred(j,1)+lambda(i)*phi; 
  end 
end 
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function phi = get_phi(r,c,choice) 
% choice: 1=thin-plate, 2=gaussian, 3=multiquadric, 4=inverse multiquadric 
if choice == 1 
  if r==0 
    phi = 0; 
  else 
    phi = r^2*log(c*r); 
end 
elseif choice == 2 
  phi = exp(-c*r^2); 
elseif choice == 3 
  phi = sqrt(r^2+c^2); 
elseif choice == 4 
  phi = 1/sqrt(r^2+c^2); 
end 
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