% This is rough Mfile for secant method and of course needs to be changed
% to a function and tested appropriately.

% clear all clears all variables, etc in the memory
clear all
clc

% Defining the inputs
% function f(x) of the equation f(x)=0 (use functional notation for function)
% maximum number of iterations, nmax
%	prespecified tolerance, tol
%	initial guess, older_guess
%	initial guess, old_guess


f=inline('x^3-27')
older_guess=236.7
old_guess=1233.4
nmax=10
tol=0.005

% Using a loop to conduct the recursion
for i=1:1:nmax
    fprimenum=f(old_guess)-f(older_guess)
    fprimeden=old_guess-older_guess
    fprime=fprimenum/fprimeden
    % using the formula to calculate new guess
    new_guess=old_guess-f(old_guess)/fprime
    % calculating the absolute relative approximate error
    absea=abs((new_guess-old_guess)/new_guess)*100
    % Checking if the absolute relative approximate error is less than the
    % tolerance
    if (absea<tol) 
        nused=i
        flag=22
        break;
    end
    % renewing the two guesses.  The sequence in which they are renewed is
    % very important
    older_guess=old_guess
    old_guess=new_guess
    % flag=11 will be assigned if the tolerance is never met
    flag=11
end