QR Factorization Using Householder Transformations
60 visualizzazioni (ultimi 30 giorni)
Mostra commenti meno recenti
Hüseyin
il 12 Gen 2015
Risposto: Davide Poggiali
il 20 Apr 2020
function [Q,R]=QRfactor(A)
[m,n]=size(A);
R=A; %Start with R=A
Q=eye(m); %Set Q as the identity matrix
for k=1:m-1
x=zeros(m,1);
x(k:m,1)=R(k:m,k);
g=norm(x);
v=x; v(k)=x(k)+g;
%Orthogonal transformation matrix that eliminates one element
%below the diagonal of the matrix it is post-multiplying:
s=norm(v);
if s~=0, w=v/s; u=2*R'*w;
R=R-w*u'; %Product HR
Q=Q-2*Q*w*w'; %Product QR
end
end
for A=[-2 2 3; 1 3 5; -3 -1 2]
I got the answers Q and R different from when I use [Q,R]=qr(A). Where am I wrong with code.
1 Commento
John D'Errico
il 12 Gen 2015
Please learn to use the code button when you post code. It takes only one click of the mouse to do so.
Risposta accettata
Titus Edelhofer
il 12 Gen 2015
Hi Hüseyin,
I don't think something is wrong. Q*R gives A (at least for your matrix A). Having different Q and R from MATLAB's implementation does not necessarily mean something is wrong (as long as Q*R=A and Q is orthogonal, i.e. Q'*Q = identity).
Titus
3 Commenti
John D'Errico
il 12 Gen 2015
Modificato: John D'Errico
il 12 Gen 2015
You are not listening. Q and R are not unique. Your code is fine. That it produces elements with sign differences in some cases merely means that an arbitrary choice was made about sign in the MATLAB code that differs from your choice. And since the MATLAB code for QR is proprietary, you can NEVER know exactly what they did.
Più risposte (2)
Francesco Onorati
il 9 Giu 2016
The reason why there are differencies in the sign is that for numerical stability the 2-norm of each vector is taken with the opposite sign of the pivotal element of the vector itself. As you take always the norm as positive, sometimes it is in agreement with MATLAB code, sometimes it is not (here I'm supposing MATLAB uses Housolder transformation to do QR decomposition).
0 Commenti
Davide Poggiali
il 20 Apr 2020
You just have to change two lines
g=-sign(x(k))*norm(x);
v=x; v(k)=x(k)-g;
to get what you're looking for. source: wiki
0 Commenti
Vedere anche
Categorie
Scopri di più su Logical in Help Center e File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!