function write_rbf(x_train,lambda,c,choice,filename) 
% This function creates an analytic RBF equation for a given set of 
% training points and RBF parameters. This does not build the metamodel, 
% RBF parameters from a pre-built model are input. These paramters can be 
% taken from get_ypred_rbf.m or by solving the RBF problem. 
% This function is set up to use MATLAB syntax for the output equation 
% ---Variable Descriptions--- 
% x_train = normalized design(training points): in an 
% [num_of_points by num_of_variables] matrix 
% lambda = array of RBF interpolation coefficients 
% c = user chosen RBF constant 
% choice = user chosen RBF radial basis function choice 
% --Currently Supported Basis Functions-- 
% 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) 
% filename = string containing the filname to save the equation as, 
% must be "filename.txt" 
% number of design variables and number of training points. 
ndv = size(x_train,2); 
ntrn = size(x_train,1); 
% open output file with specified filename 
fout = fopen(filename,'w'); 
for k = 1:ntrn 
% define first characters of the line 
if k == 1 
  op = 'y_rbf='; 
else 
  op = '+'; 
end 
% create appropriate lambda string 
lam = ['(' num2str(lambda(k,:)) ')']; 
% define Euclidean norm distance rsqrd and r 
rsqrd = []; 
r = []; 
for kk = 1:ndv 
  if kk == 1 
    rsqrd = [rsqrd '(x' num2str(kk) '-' num2str(x_train(k,kk)) ').^2']; 
  else 
    rsqrd = [rsqrd '+(x' num2str(kk) '-' num2str(x_train(k,kk)) ').^2']; 
  end 
end 
% write the equation based on which basis function was chosen 
if choice == 1 
  phi = ['(' rsqrd ')' '*log(' num2str(c) '*(sqrt(' rsqrd ')))...']; 
% "log" in MATLAB is ln not log10 
  print = [op lam '*' phi]; 
  fprintf(fout,'%s\n',print); 
elseif choice == 2 
  phi = ['exp(-' num2str(c) '*(' rsqrd '))...']; 
  print = [op lam '*' phi]; 
  fprintf(fout,'%s\n',print); 
elseif choice == 3 
  phi = ['sqrt(' rsqrd '+(' num2str(c) ').^2)...']; 
  print = [op lam '*' phi]; 
  fprintf(fout,'%s\n',print); 
elseif choice == 4 
  phi = ['1/(sqrt(' rsqrd '+(' num2str(c) ').^2)...']; 
  print = [op lam '*' phi]; 
  fprintf(fout,'%s\n',print); 
end 
end 
fclose(fout);