% This is a script file to illustrate loops and 
% MATLAB's built-in vectorization
%
clc
disp('                         Loops and Vectorization')
disp(' ')
disp('Note: AVOID LOOPS WHENEVER POSSIBLE (perhaps not so much in MATLAB 7)')
disp('As a first example we compute the square of the length (or 2-norm) of a random vector:')
n = input('Enter length of vector [enter=50000]: ');
if isempty(n)
    n = 50000;
end
x = rand(n,1);
disp('How long does a for-loop take?')
tic;
s = 0;
for i=1:n
    s = s + x(i)^2;
end
t1 = toc;
fprintf('norm(x) = %f \n', s)
fprintf('Time with for-loop: %f seconds\n\n', t1)

disp('Now vectorized using MATLAB''s sum function:')
tic;
s = sum(x.^2);
t2 = toc;
fprintf('norm(x) = %f \n', s)
fprintf('Time vectorized with sum: %f seconds\n\n', t2)

disp('And using MATLAB''s norm function:')
tic;
s = norm(x)^2;
t3 = toc;
fprintf('norm(x) = %f \n', s)
fprintf('Time vectorized with norm: %f seconds\n\n', t3)