% Exampmle 9.3a (Physics 330)

clear;close all;

%*********************************************************
% Define the function as an in line function (See Chapter 12
% for more details.)
%*********************************************************

func=inline('exp(-x)-x','x');

% First plot the function

x=0:.01:2;
f=func(x);
plot(x,f,'r-',x,0*x,'b-')

%*********************************************************
% (Note that the second plot is just a blue x-axis (y=0)
% 0*x is just a quick way to load an array of zeros the
% same size as x)

% From the plot it looks like the solution is near x=.6

% Secant method to solve the equation exp(-x)-x = 0

% Use an initial guess of x1=0.6
%*********************************************************

x1=0.6;

% find f(x1)

f1=func(x1);

% find a nearby second guess

x2=0.99*x1;

% set chk, the error, to 1 so it won't trigger the while
% before the loop gets started

chk=1;

% start the loop

while chk>1e-8

% find f(x2)

   f2=func(x2);

% find the new x from the straight line approximation and print it

   xnew = x2 - f2*(x2-x1)/(f2-f1)

% find chk the error by seeing how closely f(x)=0 is approximated

   chk=abs(f2);

% load the old x2 and f2 into x1 and f1; then put the new x into x2

   x1=x2;f1=f2;x2=xnew;

% end of loop
end