function R = LeveMarq(F,GF,HF,x0,tol,kmax)
%
% Levenberg-Marquardt Algorihtm for computing a
% local minimum of a function of several variables: 
%
% input data :
%       
%       F  :    handle to the function implementing the
%               objective function
%       GF  :   handle to the function implementing 
%               the gradient of the objective function
%       HF  :   handle to the function implementing 
%               the Hessian matrix of the objective 
%       x0  :   column vector – initial approximation
%       tol:    relative tolerance 
%       kmax:   max number of iterations
%
% output data :
%
%       R   :    Solution
%

xcurr = x0;
% inizialize xprev
 xprev = 10*x0*tol; k=1;
 B = -GF(xprev);
while(norm(xprev-xcurr)/norm(xprev)>=tol+eps && norm(B)>=tol+eps && k<kmax)
    k = k+1;
    xprev = xcurr;
    H = HF(xprev);
    B = -GF(xprev);
    lambda=fminbnd(@(x) lambdamin(x,xprev,F,H,-B),-10,10);
    c = (H-lambda*diag(diag(H)))\B;
    xcurr = xprev + c;   
end
if nargout==0
   w=sprintf('Number of iterations : %d\n ',k);
   disp(w)
   w=sprintf('Estimated Error :%f\n',norm(c));disp(w)
   w=sprintf('Solution : [%f , %f]',xcurr); disp(w)
  else 
    R = xcurr; 
 end
end