function [W,Omega]=MTERL(data,label,lambda,gamma,nu)

%the Omega sloved in the demo can  refer to: 

%Yu Zhang and Dit-Yan Yeung. A Convex Formulation for Learning Task Relationships in Multi-Task Learning. 

%In: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI), 2010.

m=length(label); 

d=size(data{1,1},2);

W=zeros(d,m); 

V=zeros(d,m);

[W,Omega]=myAPG(W,V,data,label,lambda,gamma,nu);

end

function [W,Omega]=myAPG(W_initial,V,data,label,lambda,gamma,nu)

m=length(label);

d=size(data{1,1},2);

epsilon=10^(-8);

max_iteration=1000;

t=0;  alpha = 1; W=W_initial;

Omega=eye(m)/m;

[data_O,label_O,task_index,ins_num]=PreprocessMTData(data,label);

n=size(data_O,1);

insIndex=cell(1,m);

ins_indicator=zeros(m,n);

for i=1:m

    insIndex{i}=sort(find(task_index==i));

    ins_indicator(i,insIndex{i})=1;

end

threshold=10^(-12);

model.alpha=zeros(1,n);

model.b=zeros(1,m);kertype='linear';kerpar=0;

Km=CalculateKernelMatrix(data_O,kertype,kerpar);

m_Cor=real(Omega/(lambda*Omega+gamma*eye(m)));

for iter=1:max_iteration

    old_model=model;

    old_Omega=Omega;

    MTKm=Km.*m_Cor(task_index,task_index);

    model=MTRL_RR(MTKm,label_O,task_index,insIndex,ins_num);

    clear MTKm;

    temp=m_Cor(:,task_index)*diag(model.alpha);

    temp=temp*Km*temp';

    [eigVector,eigValue]=eig(temp+epsilon*eye(m));

    clear temp;

    eigValue=sqrt(abs(diag(eigValue)));

    eigValue=eigValue/sum(eigValue);

    Omega=eigVector*diag(eigValue)*eigVector';

    m_Cor=eigVector*diag(eigValue./(lambda*eigValue+gamma))*eigVector';

    clear eigVector eigValue;

    if norm(model.alpha-old_model.alpha,2)<=threshold*n&&norm(model.b-old_model.b,2)<=threshold*m&&norm(Omega-old_Omega,'fro')<=threshold*m*m

        clear old_model old_Omega;

        break;

    end

    clear old_model old_Omega; 

    U=(1-alpha)*W+alpha*V;

    Lu=100000;%should be set

    G=[];

    for i=1:d

        Vi=min(1,max(-1,U(i,:)/nu));

        G=[G;sum(abs(U(i,:)))*Vi];       

    end

    tmp_o = U*Omega^(-1);

    for i=1:m

        V(:,i)=V(:,i)-1/(alpha*Lu)*( data{1,i}'* (data{1,i}* U(:,i)-label{1,i}') + lambda*G(:,i) +gamma* tmp_o(:,i));

    end  

    W=(1-alpha)*W+alpha*V;

    alpha=2/(t+1);

    t=t+1;    

    F_wh=0;  

    for i=1:m

        F_wh = F_wh+norm(label{1,i}-W(:,i)'*data{1,i}',2)^2/(2*m);

    end

    for i=1:d      

        F_wh =F_wh+lambda*sum( abs(W(i,:)) )^2/2;

    end

    F_wh = F_wh + gamma * trace(W*Omega^(-1)*W')/2;

    fValue(iter,1)=F_wh;    

    if (iter>10 && (abs(fValue(iter,1)-fValue(iter-1,1))/abs(fValue(iter-1,1))<epsilon))   

        break;

    end   

end

end