单边jacobi的奇异值分解matlab伪代码

以下是单边Jacobi奇异值分解的MATLAB伪代码：

function [U,S,V] = jacobi_svd(A)
% A: m x n matrix
% U: m x r matrix (orthogonal columns)
% S: r x r diagonal matrix (singular values)
% V: n x r matrix (orthogonal columns)

[m,n] = size(A);
U = eye(m);
V = eye(n);
eps = 1e-10; % convergence threshold
max_iter = 1000; % maximum number of iterations
iter = 0;
converged = false;

while ~converged && iter < max_iter
    converged = true;
    for i = 1:n-1
        for j = i+1:n
            G = [A(:,i) A(:,j)];
            [Q,R] = qr(G,0);
            A(:,i) = Q(:,1);
            A(:,j) = Q(:,2);
            V(:,i) = V(:,i)*R(1,1) + V(:,j)*R(1,2);
            V(:,j) = V(:,i)*R(2,1) + V(:,j)*R(2,2);
            if abs(A(m,i)) > eps || abs(A(m,j)) > eps
                converged = false;
            end
        end
    end
    iter = iter + 1;
end

S = diag(A(1:n,1:n));
U = A(:,1:n);

该代码以A作为输入，返回U、S和V，这些矩阵是奇异值分解A的结果。其中U和V是正交矩阵，S是对角矩阵，对角线上的元素是奇异值。该算法使用Jacobi迭代来计算奇异值和奇异向量。