% numdiff.m
% This code is a script that performs numerical
% differentiation.  It is currently implementing
% a centered difference algorithm.  

% NOTE:  The step size is currently decreased 
%        by a factor of 10 each time through the 
%        following loop.

% NOTE:  This driver requires you to define the 
%        name of the function that you want to evaluate  
%        for the difference approximation. (string format)

% Initialize variables
clear;
nam='ex2';  %Name of the function to be evaluated.
            % Notice that it is entered as a string--
            % that is, it is in apostrophes.

x0 = 0.8;   %x value where we are approximating 
            % the derivative

h  = 0.1;   %Step size
M  = 4;     %Number of iterations

tru= cos(0.8);  %True value of the derivative
                % necessary for error output.

% Making a table for output
fprintf(1,' It#    Step    Diff Approx.         Error   \n');
fprintf(1,'-----------------------------------------------\n');

for i = 1:M
    d(i) = (feval(nam,x0+h)-feval(nam,x0-h))/2/h;
    
    %output results
    fprintf(1,' %2d   %5.4f  %10.9e   %10.9e\n',i,h,d(i),abs(tru-d(i)));
    
    % Calculate the new value of h for the next iteration.
    h = h/10;
end; %end-i-loop