QR分解matlab程序

以下是QR分解的Matlab程序：

function [Q,R] = QR_decomposition(A)
% QR Decomposition using Householder reflections
% A: matrix to be decomposed
% Q: orthogonal matrix
% R: upper triangular matrix
[m,n] = size(A);
Q = eye(m);
for k = 1:n
    % Compute the Householder reflection that zeros out below the diagonal
    x = A(k:m,k);
    e1 = zeros(length(x),1);
    e1(1) = 1;
    v = sign(x(1))*norm(x)*e1 + x;
    v = v/norm(v);
    % Apply the reflection to A and Q
    A(k:m,k:n) = A(k:m,k:n) - 2*v*(v'*A(k:m,k:n));
    Q(k:m,:) = Q(k:m,:) - 2*v*(v'*Q(k:m,:));
end
R = triu(A);
end

这个程序使用Householder反射来进行QR分解。输入矩阵A，输出正交矩阵Q和上三角矩阵R。