基于Jacobi的可以对任意矩阵进行奇异值分解的Matlab代码
时间: 2023-12-06 16:45:26 浏览: 33
以下是基于Jacobi迭代算法的Matlab代码,可以对任意矩阵进行奇异值分解:
```matlab
function [U,S,V] = svd_jacobi(A, niter)
% SVD_JACOBI Singular Value Decomposition via Jacobi iteration.
% [U,S,V] = SVD_JACOBI(A, NITER) computes the singular value
% decomposition of A using the Jacobi iteration method. The input
% matrix A can be of any size. NITER is the number of iterations to
% perform (default = 50).
%
% Example:
% A = rand(5,3);
% [U,S,V] = svd_jacobi(A);
%
% Note:
% This implementation is not optimized for speed or memory usage.
% Use at your own risk.
if nargin < 2
niter = 50;
end
[m, n] = size(A);
U = eye(m);
V = eye(n);
for i = 1:niter
for p = 1:n-1
for q = p+1:n
G = [A(:,p) A(:,q)];
[U1,~,~] = svd(G,0);
Uq = U1(:,2);
Up = U1(:,1);
A(:,p) = A(:,p) - (Up' * A(:,p)) * Up - (Uq' * A(:,p)) * Uq;
A(:,q) = A(:,q) - (Up' * A(:,q)) * Up - (Uq' * A(:,q)) * Uq;
A(:,p) = A(:,p) * cos(atan2(norm(Uq),norm(Up))) - A(:,q) * sin(atan2(norm(Uq),norm(Up)));
A(:,q) = A(:,p) * sin(atan2(norm(Uq),norm(Up))) + A(:,q) * cos(atan2(norm(Uq),norm(Up)));
V(:,[p q]) = V(:,[p q]) * [Up Uq];
end
end
end
S = diag(sqrt(sum(A.^2)));
U = A * pinv(S) * U;
end
```
其中,输入参数`A`为待分解的矩阵,`niter`为迭代次数(默认为50)。输出参数`U`、`S`、`V`分别是SVD分解后的左奇异矩阵、奇异值对角矩阵和右奇异矩阵。