% Script file to show how to use bisection and Newton's method
%  (all in one script file).  The commands are the next two lines-
% be sure split out and save the functions as their own m-files
% (like bisect.m, NewtonMethod.m and testfunc01.m )

xb=bisect(@testfunc01,0,1,1e-9)
xc=NewtonMethod(@testfunc01,0,20,1e-9)




% Functions defined below:

function [y,dy]=testfunc01(x)
% Test function e^x-3x
y=exp(x)-3*x;  % Output y
dy=exp(x)-3;   % and dy
end


function out=NewtonMethod(F,x0,numits,tol)
%  Inputs to Newton's Method:
%     F- Name of a function that returns BOTH 
%        values of g(x) and g'(x)
%     x0= Initial value of x.
%     numits=  Maximum number of iterations
%     tol   =  Tolerance (like 1e-6) measures
%              change between iterates of x
%
%  Example:
%    function [y,dy]=F(x)
%         y=x^2 - x - 1;
%        dy=2*x-1
%  
%  out=NewtonMethod(F,1,10,1e-8)
%

for k=1:numits
   [g,dg]=feval(F,x0);
   if dg==0
      error('Derivative is zero');
   end
   xnew=x0-g/dg;
   d=abs(xnew-x0);
   if d<tol
      out=xnew;
      break
   end
   x0=xnew;
end    
fprintf('Newton used %d iterations\n',k);
out=xnew;
end