%% Loops and Vectorization I

%% 
% Note: *Avoid loops whenever possible* (even though the latest versions of
% MATLAB now optimize loops and are much more efficient than they used to be) 
%
% As a first example we compute the square of the length (or 2-norm) of a
% random vector:
%
% Define the length of vector
n = 50000;

%%
% Define a random vector
x = rand(n,1);

%%
% 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)

%% 
% 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)

%%
% 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)