chenmh_bisvd3.m

Frequently used algorithms for numerical analysis and signal processing

function [V, err, orth] = Chenmh_BiSVD3(x,r,alpha);
%  Chen minhua, 2006.02.10.
%  Bi-Iteration SVD subspace tracking. 
%  "Bi-Iteration SVD Subspace Tracking algorithms," 
%  IEEE Trans. Signal Processing.

%% Chen minhua, 2006.02.11.
%% Result of BiSVD3 is wrong. To be improved.
[p,T] = size(x);
if (r > p) disp(['Subspace dimension error!']); end
V = eye(p); V = V(:,1:r);
err = zeros(1,T);
Tria = zeros(r,r);   % Upper Triangular.
Trib = ones(r,r);   % Distance of consecutive subspaces.
for t = 1:T
    x_in = x(:,t);
    z = V'*x_in; 
    e = x_in-V*z;
    err(t) = norm(e,'fro');
    e_unit = e/err(t);
    Augb = [(1-alpha)^0.5*z'; alpha^0.5*Trib];
    [Gb,Trib] = qr(Augb,0);
    zr = Trib'\z;
    Auga = [alpha*Tria+(1-alpha)*z*zr'; (1-alpha)*err(t)*zr'];
    [Ga,Tria] = qr(Auga,0);
    V = [V, e_unit]*Ga;
    
    orth(t) = norm(V'*V-eye(r),'fro');
end