Computational time of qr, svd and eig?

How does the time for qr depend on the dimensions of the matrix m and n (does it depend on on the type of linear systems: overdetermined and underdetermined?) How about svd and eig? Does the time depend on whether you ask only for the eigenvalues (as in E=eig(A)) or also for the eigenvectors (as in [V,E]=eig(A))?

[KSSV]

You can check it on your own using tic and toc

[Duc Anh Le]

I tried to do that, but couldnt find any relationship between the computational time and m,n...

[KSSV]

why not...show us your code....let us check....

[Duc Anh Le]

%% Computational time for qr.
clear all; clc; close all;
m = 700;
n = 500;
for k = 1:100
    B1 = randn(m,n); % m>n
    B2 = randn(n,m); % m<n
    tic;
    [Q1,R1] = qr(B1);
    toc;
    t1(k) = toc;
    tic;
    [Q2,R2] = qr(B2);
    toc;
    t2(k) = toc;
end

mean(t1)
mean(t2)

j = 1:100;
figure(1);
plot(j,(t1))
xlabel('# of trial')
ylabel('Elapsed time')
title('Elapsed time for the qr operator (m<n)')
axis([0 100 0 0.05])

figure(2)
plot(j,(t2))
xlabel('# of trial')
ylabel('Elapsed time')
title('Elapsed time for the qr operator (m>n)')
axis([0 100 0 0.05])

Answer 1

[KSSV]

%% Computational time for qr.
clear all; clc; close all;
m = 700;
n = 500;
N = 100 ; 
t11 = zeros(N,1) ; 
t21 = zeros(N,1) ; 
for k = 1:N
    B1 = randn(m,n); % m>n
    B2 = randn(n,m); % m<n
    t10 = tic;
    [Q1,R1] = qr(B1);    
    t11(k) = toc(t10);
    t20 = tic;
    [Q2,R2] = qr(B2);    
    t21(k) = toc(t20);
end
mean(t11)
mean(t21)
j = 1:N;
figure(1);
plot(j,t11,'r',j,t21,'b')
xlabel('# of trial')
ylabel('Elapsed time')
legend('qr for m<n','qr for m>n')
axis([0 100 0 0.05])

[Duc Anh Le]

Thanks for the correction, is there an explanation to why the elapsed time for m < n is less than for m > n?