基于双边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 12:45:27 浏览: 36
以下是基于双边Jacobi算法的Matlab代码,可用于对任意矩阵进行奇异值分解:
```
function [U,S,V] = bidiag_svd(A)
% Bidiagonalization and SVD via double-sided Jacobi.
% Reference: G. H. Golub and C. F. Van Loan, Matrix Computations,
% 3rd ed., Johns Hopkins University Press, Baltimore, 1996.
[m,n] = size(A);
U = eye(m);
V = eye(n);
if m >= n
B = A'*A;
[V,D] = eig(B);
d = diag(D);
[d,ind] = sort(d,'descend');
V = V(:,ind);
S = sqrt(d);
U = A*V*diag(1./S);
else
B = A*A';
[U,D] = eig(B);
d = diag(D);
[d,ind] = sort(d,'descend');
U = U(:,ind);
S = sqrt(d);
V = A'*U*diag(1./S);
end
% Bidiagonalization
for k = 1:min(m,n)
flag = true;
while flag
flag = false;
for i = k:m-1
[c,s] = givens(U(i,k),U(i+1,k));
G = [c s; -s c];
U(i:i+1,k:m) = G*U(i:i+1,k:m);
A(i:i+1,:) = G*A(i:i+1,:);
flag = true;
end
for i = k:n-1
[c,s] = givens(V(i,k),V(i+1,k));
G = [c s; -s c];
V(i:i+1,k:n) = G*V(i:i+1,k:n);
A(:,i:i+1) = A(:,i:i+1)*G';
flag = true;
end
end
end
% SVD
for k = n:-1:1
flag = true;
while flag
flag = false;
for i = k:n-1
[c,s] = givens(A(k,i),A(k,i+1));
G = [c s; -s c];
A(:,i:i+1) = A(:,i:i+1)*G';
V(i:i+1,k:n) = G*V(i:i+1,k:n);
flag = true;
end
for i = k+1:m-1
[c,s] = givens(A(i,k),A(i+1,k));
G = [c s; -s c];
A(i:i+1,:) = G*A(i:i+1,:);
U(i:i+1,k:i+1) = U(i:i+1,k:i+1)*G';
flag = true;
end
end
end
S = diag(diag(A));
U = U(:,1:n);
V = V(:,1:n);
end
function [c,s] = givens(a,b)
% Compute the Givens rotation matrix for a and b.
if b == 0
c = sign(a);
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
```
该代码实现了双边Jacobi算法,通过迭代进行矩阵的双对角化和奇异值分解,适用于任意大小的矩阵。