function x=mnhf_newton_system(Fun,Jac,x,tol,trace)
%MNHF_NEWTON_SYSTEM solves a system of nonlin. eqns. using Newton's method.
%
%  Fun   - name of the external function to compute f 
%  Jac   - name of the externan function to compute J
%  x     - vector of initial guesses
%  tol   - error criterion
%  trace - print intermediate results
%
%  Usage  mnhf_newton_system(@cstrF,@cstrJ,[3.0 2.0 1.0 0.75 0.5]',1e-10,1)

%Check inputs
if nargin < 5, trace = 1; end
if nargin < 4, tol = 1e-8; end

fprintf('\nCount\t Norm(f)\n')
fprintf('-------------------------\n')

Nmax = 25;
f = 1.0;   % Can select any arbitrary value with magnitude > tol.
count = 0; % Initialize counter.

while (norm(f)  > tol && count <= Nmax)
 count = count+1;       % Increment counter.
 f = feval(Fun,x);      % Function evaluation.
 J = feval(Jac,x);      % Jacobian evaluation. 
 x = x-J\f;             % Update the guess.
 if trace
  fprintf(1,'%3i %12.5f\n',count,norm(f)); 
 end
end

if count > Nmax
 fprintf('Maximum number of iterations reached.\n\n')
end