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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