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Bayesian_group_paper.m
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Bayesian_group_paper.m
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function [Z,H]=Bayesian_group_paper(Y_all,X_all,N_point,etc,G)
Pm=[];
H=[];
rho=0.001;
[T,S,K]=size(Y_all);
N=size(X_all,2);
gap_d=1.085;
search_area=[-1:2/N_point:1]'/gap_d;
reslu=2/N_point/gap_d;
N_grid=length(search_area);
for kk=1:K
search_area(:,kk)=[-1:2/N_point:1]';
Fm(:,:,kk)=exp(-1i*pi*gap_d*(0:N-1)'*search_area(:,kk)');
end
a=0.0001;b=0.0001;
maxiter=500;
tol=1e-4;
%%%%%%%%%%%%%%%
delta_last=100;
converged = false;
iter = 0;
Aw=zeros(T,N_grid,K);
for kk=1:K
Aw(:,:,kk)=X_all(:,:,kk)*Fm(:,:,kk);
end
Z=rand(K,G);
Z= diag( 1./sum(Z,2) ) * Z;
Aw=[Aw,Aw];
%initialization
alpha0=1;
alpha_all=ones(N_grid*2, K);
alpha_all(N_grid+1:end,:)= alpha_all(N_grid+1:end,:)*rho;
mu=zeros(N_grid*2,S,K);
for kk=1:K
Phi_delta = Aw(:,:,kk) * diag(1./alpha_all(:,kk));
V_temp= 1/alpha0*eye(T) + Phi_delta * Aw(:,:,kk)';
Sigma(:,:,kk) = diag(1./alpha_all(:,kk)) -Phi_delta' * (V_temp \Phi_delta);
mu(:,:,kk) = alpha0 * Sigma(:,:,kk) * Aw(:,:,kk)' * Y_all(:,:,kk);
end
alpha_star=rand(N_grid,G);
alpha_remain=ones(N_grid,K);
while ~converged
Phi=Aw;
switch iter-floor(iter/5)*5
case 0 %update alpha0
term0=zeros(T,S,K);
term2=0;
for kk=1:K
term0(:,:,kk)=Phi(:,:,kk)*mu(:,:,kk);
temp1=sum(diag(Phi(:,:,kk)* Sigma(:,:,kk)*Phi(:,:,kk)'));
term2=term2+temp1;
end
resid=Y_all-term0;
alpha0=( S*K*T + a )/( b + norm(resid(:), 'fro')^2 + S* real(term2) );
case 1 %update x
for kk=1:K
diag_inv= diag( 1./ ( [alpha_star * ( Z(kk,:).' ) ; rho^(-1)* alpha_remain(:,kk) ]) );
Phi_delta = Phi(:,:,kk) * diag_inv;
V_temp= 1/alpha0*eye(T) + Phi_delta * Phi(:,:,kk)';
Sigma(:,:,kk) = diag_inv-Phi_delta' * (V_temp \Phi_delta);
mu(:,:,kk) = alpha0 * Sigma(:,:,kk) * Phi(:,:,kk)' * Y_all(:,:,kk);
end
case 2 %update alpha^* and remained
mu2=abs(mu).^2;
xx=mu2;
for kk=1:K
sigma2_kk= real( diag( Sigma(:,:,kk)) );
xx(:,:,kk)=mu2(:,:,kk) + sigma2_kk*ones(1,S);
end
c_k= a + sum(Z)*S;
xx_temp=zeros(2*N_grid, K);
for kk=1:K
xx_temp(:,kk)= sum( xx(:,:,kk), 2);
end
d_ik= b + xx_temp(1:N_grid,:)* Z;
for gg=1:G
alpha_star(:,gg)= c_k(gg)./d_ik(:,gg);
ln_alpha_star(:,gg)= psi( c_k(gg) ) -log(d_ik(:,gg));
end
if iter<100
ln_alpha_star=log(alpha_star);
end
%%%%%%%%%%%%%%% update alpha_remain
alpha_remain = (a+1) ./ ( b+xx_temp(N_grid+1:end,:) *(rho^(-1)) );
case 3
for kk=1:K
for gg=1:G
t1= S* sum( ln_alpha_star(:,gg)) ;
t2= sum(xx_temp(1:N_grid,kk).* alpha_star(:,gg) ) ;
et(kk,gg)= t1-t2;
end
end
Z1=[];
for kk=1:K
temp(kk,:)= exp(et(kk,:)-max(max(et(kk,:))));
end
Z= diag( 1./sum(temp,2) ) * temp;
case 4
%%%%%%%%%%%%%%%%%%%%%%%%%%%% grid refine
for kk=1:K
term0(:,:,kk)=Phi(:,:,kk)*mu(:,:,kk);
end
resid=Y_all-term0;
m1=mu(1:N_grid,:,:); m2=mu(N_grid+1:end,:,:);
mu12=m1+m2;
mu222= abs(mu12).^2;
for kk=1:K
sum_mu=sum( mu222(:,:,kk) , 2);
Pm=sum_mu;
[~,sort_ind]=sort(Pm, 'descend');
index_amp = sort_ind(1:etc);
Sigma12= Sigma(1:N_grid,1:N_grid,kk)+Sigma(N_grid+1:end,N_grid+1:end,kk)+ Sigma(1:N_grid,N_grid+1:end,kk) + Sigma(N_grid+1:end,1:N_grid,kk);
tempPS=Phi(:,1:N_grid,kk)* Sigma12(:,index_amp) ;
df=zeros(length(index_amp),1);
for j=1:length(index_amp)
ii=index_amp(j);
ai=Fm(:,ii,kk);
mut=mu12(ii,:,kk);
Sigmat=Sigma12(:,ii);
c1=mut*mut' + S*Sigmat(ii);
c1=abs(c1)*(-alpha0);
Yti=resid(:,:,kk) + Phi(:, ii,kk)*mu12(ii,:,kk);
c2= S*( tempPS(:,j) - Phi(:,ii,kk)*Sigmat(ii) ) -Yti*(mut');
c2= c2*(-alpha0);
phii=Phi(:,ii,kk);
sinta= search_area(ii,kk); costa=cos(asin(sinta));
c3=(-1i*pi*gap_d* costa)*[0:N-1]'; % c3=(-1i*2*pi*gap_d/sqrt(N))*[0:N-1]';
tt1= X_all(:,:,kk)*(c3.*ai);
f1= tt1'*phii*c1 + tt1'*c2;
f1= 2*real(f1);
df(j)=f1;
% angle_cand= sign(f1)*reslu/100 ;
% sin_add = search_area(ii,kk) + angle_cand;
% search_area(ii,kk)=sin_add;
% ro1=exp(-sin_add*pi*gap_d*1i);
% Fm(:,ii,kk)=ro1.^((0:N-1)')/sqrt(N);
% Aw(:,ii,kk)=X_all(:,:,kk)* Fm(:,ii,kk);
% Aw(:,N_grid+ii,kk)= Aw(:,ii,kk);
end
ddff=sign(df)*reslu/100;
search_area(index_amp,kk) = search_area(index_amp,kk) + ddff;
Fm(:,index_amp,kk)=exp(-1i*pi*gap_d*(0:N-1)'* (search_area(index_amp,kk))');
Aw(:,index_amp,kk)=X_all(:,:,kk)* Fm(:,index_amp,kk);
Aw(:,N_grid+index_amp,kk)=Aw(:,index_amp,kk);
end
end
% stopping criteria
erro=norm(alpha_all - delta_last)/norm(delta_last);
if erro < tol || iter >= maxiter
converged = true;
end
iter = iter + 1;
end
% figure;hold on;
% for kk=1:K
% subplot(4,5,kk);plot(sum(mu2(:,:,kk),2)); title(kk);
% end
for kk=1:K
Pm=sum(mu222(:,:,kk),2);
[~,sort_ind]=sort(Pm, 'descend');
ther1=mean(Pm(sort_ind(1:etc)))*0.01;
index_amp=find(Pm>ther1);
Tn= X_all(:,:,kk)*Fm(:,index_amp,kk);
Ss= Tn \ Y_all(:,:,kk);
H(:,:,kk)= Fm(:,index_amp,kk)*Ss;
end
% figure(5);plot(1./alpha_star)
% figure(6);plot(1./alpha_remain)
%