## This function will solve the Generalized Power Law (GPL)
 ## and calculate (estimate) the parameters D0,D1 and m 
 ## in the GPL model D(t) = D0 + D1*t^m
 ##    note t = reduced time

## Author: Steph Bredenhann <address@hidden>
## Created: 2020-03-14

function [ GPL_RMSE, GPL_RMSE_derivative ] =...
    fn_BBR_GPL_RMSE( x, D, t );

##  n_max = length(D);  
##  fprintf('fn_GPL: n_max = %7.1f \n',n_max);

  D0 = x(1);
  D1 = x(2);
  m  = x(3);
  
##  Dcalc = fn_GPL_model(D0, D1, m, t);
  Dcalc = D0 + D1*t.^m;
  %fprintf('In fn_BBR_GPL_RMSE, D = %7.1f \n',Dcalc);
  
##  Dmeasured
##  Dcalc

  SRE = (D-Dcalc)./D;
  SRE = SRE.^2;

##  D(1)
##  Dcalc(1)
##  SRE(1)
  
  GPL_SSRE = 0;
  for i = 1:length(SRE)
      GPL_SSRE = GPL_SSRE + SRE(i);
  end

  GPL_RMSE = sqrt(GPL_SSRE/length(GPL_SSRE));
  fprintf('fn_GPL: RMSE = %7.5f \n',GPL_RMSE(1));

  % determine derivative with respect to reduced time
  
  if nargout > 1 % gradient required
      GPL_RMSE_derivative = D1*m*tr.^(m-1);
  end

end