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

n = [25 50 100 200 300 400 600 800 1000]';
repeat = 4;  % number of times at each n
asym = 1.5;  % one if symmetric
luscalar_t = [];  lurowvect_t = []; lumatlevel_t = [];
lubuiltin_t = []; qr_t = [];

feature accel off;

for k = 1:length(n)
    v = ones(n(k),1);
    A = diag(ones(n(k)-1,1),-1)+diag(3*ones(n(k),1),0)+...
           diag(asym*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] = lurowvect(A);
    end
    lurowvect_t = [lurowvect_t toc/repeat]
    clear L; clear U;
    
    tic;
    for j = 1:repeat
        [L,U] = lumatlevel(A);
    end
    lumatlevel_t = [lumatlevel_t toc/repeat]
    clear L; clear U;
    
    tic;
    for j = 1:repeat
        [L,U] = lu(A);
    end
    lubuiltin_t = [lubuiltin_t toc/repeat]
    clear L; clear U;
    
    tic;
    for j = 1:repeat
        [Q,R] = qr(A);
    end
    qr_t = [qr_t toc/repeat]
      
end

loglog(n,2e-8*n.^3,n,luscalar_t,'--',n,lurowvect_t,'-.',...
    n,lumatlevel_t,'s-',n,lubuiltin_t,'o-',n,qr_t,'*-',n,1e-9*n.^3,'-')
xlabel('n'); ylabel('time'); 
title('Timings for different methods');
legend('n^3','Scalar','Row Vector','Matrix Level','Built-in','QR',...
    'Location','Northwest');
legend('boxoff');

feature accel on;