givens变换qr分解MATLAB程序

以下是一个MATLAB程序，用于实现给定的变换QR分解：

function [Q,R] = givens_qr(A)

%获取矩阵A的大小 [m,n] = size(A);

%初始化Q和R Q = eye(m); R = A;

%对于每一列 for j = 1:n %对于该列下面的每一行 for i = j+1:m %计算Givens旋转矩阵 [c,s] = givens(R(j,j),R(i,j)); G = eye(m); G(j,j) = c; G(i,i) = c; G(i,j) = -s; G(j,i) = s;

    %用Givens旋转矩阵更新R和Q
    R = G*R;
    Q = Q*G';
end

end

%使用Q和R重构A A_reconstructed = Q*R;

%检查重构的A是否等于原始的A if norm(A_reconstructed - A) > 1e-10 warning('A重构失败'); end

%定义Givens旋转函数 function [c,s] = givens(a,b) if b == 0 c = sign(a); s = 0; elseif abs(b) > abs(a) t = a/b; s = sign(b)/sqrt(1+t^2); c = st; else t = b/a; c = sign(a)/sqrt(1+t^2); s = ct; end

end

end