Householder Reflection QR=A

Question

Ismail Güclü 2020-8-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/584759-householder-reflection-qr-a

评论： VIERI 2023-4-28

function [Q,R] = househ(A)
%QR-Zerlegung mit Householder
[m,n]=size(A);
Q = eye(m);
D = eye(m);
p = min(m-1,n);
for k=1:p
    
    %untermatrix erstellen / define sub-matrix
    x = A(:,k);
    if k == 1
        x = A(:,k);
    elseif k <= p  
        for i = 1:(k-1)
            x(i) = 0;  
            
        end
        
    else 
        continue 
    end
    
    %Formeln aus dem Buch / equation of the book
    a = -sign(A(k,k))*norm(x);
    v = x - a*D(:,k);
    H = D-2*(v*v')/(v'*v);
    
    % ---------------------------------
    if k == 1
        Q=H;
    else
        Q = Q*H;
    end
    A=H*A;
    
end
A(find(A==-0))=0; % unnecessary
R=A;
Q=Q';
end