FAR_CS/0 - example/lyh - 非满秩相变/test.m

%function[out1,out2,out3,out4,out5,out6] = test(t,k,~)

%sigma = [0,0.01, 0.5, 1, 1.5, 2];
n = 40;
d = 2;
D = 32;
m = 4;
%t = 1;
k = 13;

err = zeros(20,1);

A = zeros(n,D*m);
contri1 = zeros(n,D);
contri2 = zeros(n,D);
        for i = 0:32-1
        %生成高斯基集
	    set = randn(n,d);            
        %生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
	    theta = rand(1,4)*2*pi;
	    temp = [sin(theta);cos(theta)];
            A(:,m*i+1:m*i+m) = set*temp*(i+1);
        end
        x = zeros(m,D);
        col = randperm(D,k);
        x(:,col) = randn(m,k);
        y = A * x(:);
        
        weight =  diag(rand(D*m,1)*30);
        %A2 = zeros(n,D*m);
        %for i= 0:31
        %    A2(:,m*i+1:m*i+m) = A(:,m*i+1:m*i+m) * weight(i+1);
        %end
        A2 = A*weight;
        
        %凸优化利用特殊l21范数求解恢复问题
        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(A(:,(i-1)*m+1:i*m)*x_e(:,i));
        end
        minimize(norm21)
        subject to
        A*x_e(:) == y;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
            contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out1 = re_err;
        x3 = x_e;


        
        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
        end
        minimize(norm21)
        subject to
        A2*x_e(:) == y;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
            contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out2 = re_err;
%err(iter) =norm(contri1-contri2,'fro');


a1 = 0;
a2 = 0;
for i = 1:32
    a1 = a1 +norm(contri1(:,i));
    a2 = a2 +norm(contri1(:,i));
end


%         cvx_begin
%         variable x_e(m,D) 
%         norm21 = 0;
%         for i = 1:D
%             norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
%         end
%         minimize(norm21)
%         subject to
%         A2*x_e(:) == y;
%         cvx_end
%         re_err = 0;
%         for i = 1:D
%             re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
%             contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
%        	end
% 		out2 = re_err;
%%
n = 40;
d = 2;
D = 32;
m = 4;
%t = 1;
k = 4;
A = zeros(n,D*m);
contri1 = zeros(n,D);
contri2 = zeros(n,D);
        for i = 0:32-1
        %生成高斯基集
	    set = randn(n,d);            
        %生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
	    theta = rand(1,4)*2*pi;
	    temp = [sin(theta);cos(theta)];
            A(:,m*i+1:m*i+m) = set*temp*(i+1);
        end
        x = zeros(m,D);
        col = randperm(D,k);
        x(:,col) = randn(m,k);
        y = A * x(:);

        A2 = A * diag(randn(D*m,1)*30);
        
        %凸优化利用特殊l21范数求解恢复问题
        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(x_e(:,i));
        end
        minimize(norm21)
        subject to
        A*x_e(:) == y;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
            contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out1 = re_err;



        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(x_e(:,i));
        end
        minimize(norm21)
        subject to
        A2*x_e(:) == y;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
            contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out2 = re_err;
%%
n = 40;
d = 2;
D = 32;
m = 4;
%t = 1;
k = 6;
A = zeros(n,D*m);
noise = 0.01;
contri1 = zeros(n,D);
contri2 = zeros(n,D);
        for i = 0:32-1
        %生成高斯基集
	    set = randn(n,d);            
        %生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
	    theta = rand(1,4)*2*pi;
	    temp = [sin(theta);cos(theta)];
            A(:,m*i+1:m*i+m) = set*temp*(i+1);
        end
        x = zeros(m,D);
        col = randperm(D,k);
        x(:,col) = randn(m,k);
        y = A * x(:) + randn(n,1)*noise;
        
        weight =  diag(rand(D*m,1)*30);
        %A2 = zeros(n,D*m);
        %for i= 0:31
        %    A2(:,m*i+1:m*i+m) = A(:,m*i+1:m*i+m) * weight(i+1);
        %end
        A2 = A*weight;
        
        %凸优化利用特殊l21范数求解恢复问题
        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(A(:,(i-1)*m+1:i*m)*x_e(:,i));
        end
        minimize(norm21)
        subject to
        norm(A*x_e(:) - y) <= sqrt(40)*0.01;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
            contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out1 = re_err;


        
        cvx_begin
        variable x_e(m,D) 
        norm21 = 0;
        for i = 1:D
            norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
        end
        minimize(norm21)
        subject to
       norm(A2*x_e(:) - y) <= sqrt(40)*0.01;
        cvx_end
        re_err = 0;
        for i = 1:D
            re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
            contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
       	end
		out2 = re_err;