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Add lyh-非满秩相变

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Ksyer
2024-11-11 16:33:48 +08:00
parent e6a19b477e
commit e0b910b56d
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0 - example/lyh - 非满秩相变/test.m
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%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;