% script:  lu_time_ex.m
% time different ways to do lu factorization

n = [25 50 100 200]';
repeat = 4;  % number of times at each n
luscalar_t = [];  lurowvect_t = []; lumatlevel_t = [];
lubuiltin_t = []; 

for k = 1:length(n)
    A = diag(ones(n(k)-1,1),-1)+diag(3*ones(n(k),1),0)+...
           diag(ones(n(k)-1,1),-1);
    
    tic;
    for j = 1:repeat
        [L,U] = luscalar(A);
    end
    luscalar_t = [luscalar_t toc/repeat]
    clear L; clear U;
    
    tic;
    for j = 1:repeat
        [L,U] = lu(A);
    end
    lubuiltin_t = [lubuiltin_t toc/repeat]
    
end

loglog(n,2e-8*n.^3,n,luscalar_t,n,lubuiltin_t,'o-')
xlabel('n'); ylabel('time'); 
title('Timings for different methods');
legend('n^3','Scalar','Built-in','Location','Northwest');
legend('boxoff');