--- a
+++ b/Demo/MTFL.m
@@ -0,0 +1,83 @@
+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
\ No newline at end of file