结构化奇异值matlab源码
时间: 2023-06-30 18:16:28 浏览: 45
这里提供一个基于MATLAB的结构化奇异值分解(SSVD)的源代码:
```matlab
function [U,S,V] = ssvd(X,r1,r2)
% X: the data matrix
% r1: the rank of the first mode
% r2: the rank of the second mode
% U: left singular vectors
% S: singular values
% V: right singular vectors
% Centering the data matrix
[n1,n2] = size(X);
meanX = mean(X,1);
X = X - repmat(meanX,n1,1);
% Computing the mode-2 unfolding of X
Y = reshape(X,n1,n2);
% Applying the SVD on Y
[U,D,V] = svd(Y,'econ');
% Extracting the leading r singular vectors
U = U(:,1:r1);
V = V(:,1:r2);
D = D(1:r1,1:r2);
% Computing the singular values
S = diag(D);
% Computing the low-rank approximation of X
X = U*D*V';
% Adding back the mean
X = X + repmat(meanX,n1,1);
end
```
该代码实现了基于SSVD的矩阵分解,并返回左奇异向量、奇异值和右奇异向量。输入参数包括数据矩阵X和两个模式的秩r1和r2。函数首先对数据矩阵进行居中处理,然后将其转换为第二个模式的展开形式,并对其进行奇异值分解。接下来,函数提取前r个奇异向量和奇异值,并计算低秩逼近矩阵X。最后,函数将均值添加回矩阵X,然后返回左奇异向量、奇异值和右奇异向量。