% NewtwonForRosenbrock.m
%
%------------------------------------------------------------------------
% Newton's Mehod for Minimization of the Rozebrock function
% f:[x1; x2] |---> 100(x2-x1^2)^2 + (1-x1)^2. 
%------------------------------------------------------------------------
%clear all, close all
% Choose initial guess and evaluate function and gradient. Store results. 
xvec = [0:1:11]';
yvec = [260 992 2717 5341 8224 13195 21355 32196 35230 43352 45524 47572]';
cost_fn = @logistic;
x = [yvec(1) yvec(12) 1]'; %near to optimal value computed by nlinfit

[f, g, GN]=feval(cost_fn,x,xvec,yvec);
x_hist = x;
num_hist = [f; norm(g); 0];
% Set stopping tolerances than implement Newton Iteration
iter_flag = 1;
iter = 1;
iter_max = 10;
grad_tol = 1e-10;
while iter_flag
  iter = iter+1;
  p = -GN\g;
  x = x + p;
  [f, g, GN]=feval(cost_fn,x,xvec,yvec);
  % Record iterates and numerical performance values
  x_hist = [x_hist x];
  num_hist = [num_hist [f; norm(g); norm(p)]];
  fprintf('iter=%d f=%5.5e |g|=%5.5e\tx=[%f %f]\n',iter,f,norm(g),x(1),x(2));
  % Check stopping criteria
  if norm(g) < grad_tol
      disp('Grandient tolerance met. Stop iterations')
      iter_flag = 0;
  elseif iter == iter_max
      disp('Maximum number of iterations reached.')
      iter_flag = 0;
  end
end