% integ_test calculates a numerical approximation to the integral
%  of a function and plots the error as a function of Delta x.

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   10-Apr-2005 -- original version for Physics 263
%
% To do:
%   * Calculate the "exact" answer using MATLAB's built-in functions
%

% clear the memory
clear;

% set the limits of the integral and put in the exact result
%  (which depends on the test integrand, of course!)
a = 0;
b = 1;
test_integral1_exact = exp(b) - exp(a);

% parameters defining the range of the calculation 
N_min = 10;               % starting number of integration subintervals
N_max = 200;              % final number of integration subintervals
Delta_N = 5;              % increment in number of intervals

% Now we step through each value of N (e.g., N=10 then 15 then 20 up
%  to N_max) using a "loop".  The loop extends from the
%  "for" statement until the "end" (i.e., the indented part).
counter = 0;   % start a counter at 0
for N = N_min : Delta_N : N_max
    counter = counter + 1;   % increment the counter
    
    % set the current element of Delta_x
    Delta_x(counter) = (b-a) / N;  % figure out Delta x from the total
                                   %  number of subintervals

    % evaluate an approximation to the test integral 
    integral_naive = integ_naive('test_integrand1', a, b, N);

    % evaluate the <<relative>> error by comparing to the exact result
    %  (note the use of the absolute value function "abs" so 
    %    error > 0 always)
    %  (... means continued to the next line)
    error_naive(counter) = abs( (integral_naive - test_integral1_exact) ...
                                       / test_integral1_exact );    
end
                    
% plot the error vs. Delta_x on a log-log plot
%  To plot two curves, use loglog(Delta_x,error1,Delta_x,error2)
loglog(Delta_x,error_naive)
xlabel('Delta x');  ylabel('|relative error|');   % add labels for axes