--- a
+++ b/Demo_RR/maLRR.m
@@ -0,0 +1,128 @@
+function [Z,Ez,Ew,W,Wi] = maLRR(T,S,Dim,Maxiter,alaph,beta)
+% maLRR--Multi-Center Adaptation Framework with Low-Rank Representation
+% Input:
+%       T: Target domain data
+%       S: Source domain data
+% Output:
+%       Z: Low rank representation of the source domain in target domain
+%       Ez: error matrix of representation
+%       Ew: error matrix of project
+%       W: the project matrix of different source data
+%       Ws: the shared project matrix
+%  The code requires a GPU to run
+
+%The parameters need to be tuned
+mu = 1e-5;tol = 1e-8;max_mu = 1e6;rho =1.2;iter = 0;
+[d,m] = size(T);M = length(S);Z = cell(1,M);Wi = cell(1,M);
+W = eye(Dim,d);Ew = cell(1,M);Ez = cell(1,M);F = cell(1,M);Y1 = cell(1,M);
+Y2 = cell(1,M);Y3 = zeros(Dim,d);Y4 = cell(1,M);Y1_tmp = cell(1,M);
+Y2_tmp = cell(1,M);Y3_tmp =  zeros(Dim,d);Y4_tmp = cell(1,M);stopC = zeros(1,M);J = zeros(d);
+for i=1:M
+    Z{1,i} = zeros(m,size(S{1,i},2));
+    Wi{1,i} = zeros(Dim,d);Ew{1,i} = zeros(Dim,d);
+    Ez{1,i} = zeros(Dim,size(S{1,i},2));
+    F{1,i} = zeros(m,size(S{1,i},2));
+    Y1{1,i} = zeros(Dim,size(S{1,i},2));
+    Y2{1,i} = zeros(Dim,d);
+    Y4{1,i} = zeros(m,size(S{1,i},2));
+    Y1_tmp{1,i} =zeros(Dim,size(S{1,i},2));
+    Y2_tmp{1,i} = zeros(Dim,d);
+    Y4_tmp{1,i} = zeros(m,size(S{1,i},2));
+end
+while iter < Maxiter
+    iter
+    iter = iter+1;
+    for i=1:M
+        temp = Z{1,i} + Y4{1,i}/mu;
+        gpu_tmp = gpuArray(temp);
+        [U_Temp,sigma_Temp,V_Temp] = svd(gpu_tmp,'econ');
+        gpu_U_Temp = gather(U_Temp);
+        gpu_sigma = gather(sigma_Temp);
+        gpu_V_Temp = gather(V_Temp);
+        sigma = diag(gpu_sigma);
+        svp = length(find(sigma>1/mu));
+        if svp>=1
+            sigma = sigma(1:svp)-1/mu;
+        else
+            svp = 1;
+            sigma = 0;
+        end
+        F{1,i} = gpu_U_Temp(:,1:svp)*diag(sigma)*gpu_V_Temp(:,1:svp)';
+    end
+    for i=1:M
+        Wpt1 = S{1,i}*S{1,i}'+eye(d);
+        Wpt2 = (W*T*Z{1,i}+Ez{1,i})*S{1,i}'+W+Ew{1,i}-(Y1{1,i}*S{1,i}'+Y2{1,i})/mu;
+        temp = Wpt2/ Wpt1;
+        Wi{1,i} = temp;
+    end
+    for i=1:M
+        Zpt1 = T'*(W'*W)*T+eye(m);
+        Zpt2 = (T'*W'*Y1{1,i}-Y4{1,i})/mu + F{1,i}+T'*W'*(Wi{1,i}*S{1,i}-Ez{1,i});
+        temp = Zpt1\Zpt2;
+        Z{1,i} = temp;
+    end
+    temp = W + Y3/mu;
+    gpu_tmp = gpuArray(temp);
+    [U_Temp,sigma_Temp,V_Temp] = svd(gpu_tmp,'econ');
+    gpu_U_Temp = gather(U_Temp);
+    gpu_sigma = gather(sigma_Temp);
+    gpu_V_Temp = gather(V_Temp);
+    sigma = diag(gpu_sigma);
+    svp = length(find(sigma>1/mu));
+    if svp>=1
+        sigma = sigma(1:svp)-1/mu;
+    else
+        svp = 1;
+        sigma = 0;
+    end
+    J = gpu_U_Temp(:,1:svp)*diag(sigma)*gpu_V_Temp(:,1:svp)';
+    for i=1:M
+        temp = Wi{1,i}*S{1,i}-W*T*Z{1,i}+ Y1{1,i}/mu;
+        Ez{1,i} = max(0,temp - alaph/mu)+min(0,temp + alaph/mu);
+    end
+    for i=1:M
+        temp = Wi{1,i}-W+Y2{1,i}/mu;
+        Ew{1,i} = max(0,temp - beta/mu)+min(0,temp + beta/mu);
+    end
+    temp = zeros(d);
+    for i=1:M
+        temp = temp + T*Z{1,i}*Z{1,i}'*T'+eye(d);
+    end
+    Wpt1 = temp + eye(d);
+    temp = zeros(Dim,d);
+    for i=1:M
+        temp = temp + Y1{1,i}*Z{1,i}'*T'+Y2{1,i};
+    end
+    Wpt2 = (temp+ mu*J-Y3)/mu;
+    temp = zeros(Dim,d);
+    for i=1:M
+        temp = temp + (Wi{1,i}*S{1,i}-Ez{1,i})*Z{1,i}'*T'+Wi{1,i}-Ew{1,i};
+    end
+    Wpt2 = Wpt2 + temp;
+    W = Wpt2/Wpt1;
+    W = orth(W);
+    Y3_tmp = W-J;
+    for i=1:M
+        Y1_tmp{1,i} = Wi{1,i}*S{1,i}-W*T*Z{1,i}-Ez{1,i};
+        Y2_tmp{1,i} = Wi{1,i}-W-Ew{1,i};
+        Y4_tmp{1,i} = Z{1,i}-F{1,i};
+        stopC(1,i) = max(max(max(abs(Y1_tmp{1,i}))),max(max(abs(Y2_tmp{1,i}))));
+        stopC(1,i) = max(max(max(abs(Y3_tmp))),stopC(1,i));
+        stopC(1,i) = max(max(max(abs(Y4_tmp{1,i}))),stopC(1,i));
+    end
+    if iter==1 || mod(iter,50)==0 || max(stopC)<tol
+        disp(['iter ' num2str(iter) ',mu=' num2str(mu,'%2.1e') ...
+            ',stopALM=' num2str(max(stopC),'%2.3e')]);
+    end
+    if max(stopC)<tol
+        break;
+    else
+        Y3 = Y3 + mu*Y3_tmp;
+        for i=1:M
+            Y1{1,i} = Y1{1,i} + mu*Y1_tmp{1,i};
+            Y2{1,i} = Y2{1,i} + mu*Y2_tmp{1,i};
+            Y4{1,i} = Y4{1,i} + mu*Y4_tmp{1,i};
+        end
+        mu = min(max_mu,mu*rho);
+    end
+end
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