chenmh_fapi.m

Frequently used algorithms for numerical analysis and signal processing

function [V, err, orth] = Chenmh_FAPI(x,r,beta);

[p,T] = size(x);
if (r > p) disp(['Subspace dimension error!']); end
V = eye(p); V = V(:,1:r);
Ei = eye(r);
err = zeros(1,T);
orth = zeros(1,T); 
for t = 1:T
    x_in = x(:,t);
    z = V'*x_in; h = Ei*z;
    g = h/(beta+z'*h);
    e = x_in-V*z;
        
    tau = e'*e/(1+(e'*e)*(g'*g)+(1+(e'*e)*(g'*g))^0.5);
    const = 1-tau*(g'*g);
    h_hat = Ei'*(const*z+tau*g);
    epn = tau/const*(Ei*g-(h_hat'*g)*g);
    Ei = 1/beta*(Ei-g*h_hat'+epn*g');
    e_hat = const*e-tau*V*g;
    
    V = V + e_hat*g';
    err(t) = norm(e);
    orth(t) = norm(V'*V-eye(r),'fro');
end

%% Rubbish
%     temp = eye(r)+e'*e*g*g';
%     [U,S] = svd(temp);
%     Thi = U*S^-0.5*U';
%     Ei = 1/beta*Thi'*(eye(r)-g*z')*Ei*(Thi')^-1;