Computational time of qr, svd and eig?

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Duc Anh Le
Duc Anh Le 2019-5-2
编辑： Duc Anh Le 2019-5-3
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))?
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KSSV
KSSV 2019-5-3
why not...show us your code....let us check....
Duc Anh Le
Duc Anh Le 2019-5-3
编辑：Duc Anh Le 2019-5-3
%% 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])

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回答（1 个）

KSSV
KSSV 2019-5-3
%% 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])
  1 个评论
Duc Anh Le
Duc Anh Le 2019-5-3
编辑：Duc Anh Le 2019-5-3
Thanks for the correction, is there an explanation to why the elapsed time for m < n is less than for m > n?

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