这里的[Q, R] = qr_givens(H)是什么matlab代码

以下是一个简单的Matlab实现示例：

function [Q, R] = qr_givens(H)
% H: 待分解的矩阵
% Q: 正交矩阵
% R: 上三角矩阵

[m, n] = size(H);
Q = eye(m);
R = H;

for j = 1:n
    for i = m:-1:j+1
        % 计算Givens旋转矩阵
        [c, s] = givens_rotation(R(i-1,j), R(i,j));
        G = eye(m);
        G(i-1:i, i-1:i) = [c, s; -s, c];
        
        % 更新R和Q
        R = G' * R;
        Q = Q * G;
    end
end
end

function [c, s] = givens_rotation(a, b)
% 计算Givens旋转矩阵的参数c和s
if b == 0
    c = 1;
    s = 0;
elseif abs(b) > abs(a)
    t = -a / b;
    s = 1 / sqrt(1 + t^2);
    c = s * t;
else
    t = -b / a;
    c = 1 / sqrt(1 + t^2);
    s = c * t;
end
end

这个实现是基于Givens旋转方法的QR分解算法。输入一个矩阵H，输出正交矩阵Q和上三角矩阵R。

相关问题

matlab givens qr分解代码

The Givens QR factorization is a method for computing the QR decomposition of a matrix using Givens rotations. In Matlab, the `qr` function can be used to compute the QR factorization, but it uses a different algorithm that is more efficient for dense matrices. However, here is an example code for computing the Givens QR factorization using planerot function:

function [Q, R] = givens_qr(A)
% Computes the QR factorization of matrix A using Givens rotations

[m, n] = size(A);
R = A;

% Initialize Q as an identity matrix
Q = eye(m);

% Compute the Givens QR factorization
for j = 1:n
    for i = m:-1:(j+1)
        % Compute the Givens rotation matrix
        [c, s] = planerot(R(i-1,j), R(i,j));
        G = eye(m);
        G(i-1:i, i-1:i) = [c -s; s c];
        
        % Apply the Givens rotation to R and Q
        R = G' * R;
        Q = Q * G;
    end
end

This code computes the Givens QR factorization of a matrix `A` using nested loops to apply Givens rotations to the input matrix `A` to obtain the upper triangular matrix `R`, and accumulate the product of the Givens rotation matrices into an orthogonal matrix `Q`. The `planerot` function is used to compute the Givens rotation matrices. Note that this implementation is not optimized for efficiency and may not be suitable for large matrices.

givens矩阵的qr分解matlab的代码怎么写

以下是givens矩阵的qr分解matlab的代码：

function [Q,R] = givens_qr(A)
[m,n] = size(A);
Q = eye(m);
R = A;
for j = 1:n
for i = m:-1:(j+1)
if R(i,j) ~= 0
[c,s] = givens(R(j,j),R(i,j));
G = eye(m);
G([j,i],[j,i]) = [c -s; s c];
R = G'*R;
Q = Q*G;
end
end
end
end

function [c,s] = givens(a,b)
if b == 0
c = 1;
s = 0;
elseif abs(b) > abs(a)
t = -a/b;
s = 1/sqrt(1+t^2);
c = s*t;
else
t = -b/a;
c = 1/sqrt(1+t^2);
s = c*t;
end
end