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.