Update Lyh experiment

Phase Transitions in FAR using CS/Expr1.m

@@ -1,4 +1,4 @@
-% Expr1.m to draw Fig 2(a)
+
 
 max_n = 125;
 max_s = 35;

Phase Transitions in FAR using CS/Lyh/捷变频相变/FAR_block_sparsity_phase1.m

@@ -5,10 +5,10 @@ M = 4;
 N = 128;
 %block_sparsity = 1;
 tol = 1e-5;
-trial = 50;
+trial = 20;
 epi = 0.02;
 result = zeros(N,25);
-for col = 4:4:128
+for col = 4:N
     for block_sparsity = 10:18
         success_count = 0;
         for loop = 1:trial

Phase Transitions in FAR using CS/Lyh/捷变频相变_ksy/FAR_block_sparsity_phase1.m

@@ -0,0 +1,45 @@
+close all;
+clear all;
+clc;
+M = 4;
+N = 128;
+%block_sparsity = 1;
+tol = 1e-4;
+trial = 20;
+max_sparsity = 25;
+epi = 0.02;
+result = zeros(N,max_sparsity);
+FAR_model = get_far_model(N, M, epi);
+
+for n = 60:N
+    for s = 10:max_sparsity
+        success_count = 0;
+        for loop = 1:trial
+            col_choose = randperm(N,n);
+            FAR_model_partial = FAR_model(col_choose,:);
+
+            sparse_signal = zeros(M,N);
+            block = randperm(N,s);
+            sparse_signal(:,block) = exp(1i*2*pi*rand(M,s));
+
+            y = FAR_model_partial * sparse_signal(:);
+
+            cvx_begin
+            variable x(M,N) complex
+            norm21 = 0;
+            for i = 1:N
+                norm21 = norm21 + norm(x(:,i));
+            end
+            minimize(norm21)
+            subject to
+            FAR_model_partial * x(:) == y
+            cvx_end
+
+            if norm(x(:)-sparse_signal(:))<tol
+                success_count = success_count+1;
+            end
+        end
+        result(n,s) = success_count/trial;
+    end
+end
+save('FARblockepsilon4.mat');

Phase Transitions in FAR using CS/Lyh/捷变频相变_ksy/FAR_sparsity_phase.m

@@ -0,0 +1,47 @@
+close all;
+clear all;
+clc;
+M = 4;
+N = 128;
+%block_sparsity = 1;
+tol = 1e-5;
+trial = 50;
+epi = 0.02;
+result = zeros(N,25);
+for col = 4:4:128
+    for block_sparsity = 1:25
+        success_count = 0;
+        for loop = 1:trial
+            FAR_model = zeros(N,M*N);
+            %Cn = randperm(M)-1
+            for n = 0 : N-1
+                Cn = floor(rand()*M);
+                for q = 0 : N-1
+                    for p = 0:M-1
+                        FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
+                    end
+                end
+            end
+            
+            col_choose = randperm(N,col);
+            FAR_model = FAR_model(col_choose,:);
+            sparse_signal = zeros(M,N);
+
+            block = randperm(N,block_sparsity);
+            sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
+            
+            y = FAR_model * sparse_signal(:);
+            cvx_begin
+            variable x(M*N) complex
+            minimize(norm(x,1))
+            subject to
+            FAR_model * x == y
+            cvx_end
+            if norm(x-sparse_signal(:))<tol
+                success_count = success_count+1;
+            end
+        end
+        result(col,block_sparsity) = success_count/trial;
+    end
+end
+save('FARepsilon.mat');

Phase Transitions in FAR using CS/Lyh/捷变频相变_ksy/get_far_model.m

@@ -0,0 +1,13 @@
+function FAR_model = get_far_model(N, M, epi)
+    FAR_model = zeros(N,M*N);
+    %Cn = randperm(M)-1
+    for n = 0 : N-1
+        Cn = floor(rand()*M);
+        for q = 0 : N-1
+            for p = 0:M-1
+                FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
+            end
+        end
+    end
+end
+

Phase Transitions in FAR using CS/Lyh/捷变频相变_ksy/theoretic.m

@@ -0,0 +1,7 @@
+function n = theoretic(m,s,d)
+    syms t;
+    syms u;
+    f = s*(m+t^2)+(d-s)*int((u-t)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t,inf);
+    g = diff(f,t);
+    t1 = solve(g);
+    n = s*(m+t1^2)+(d-s)*int((u-t1)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t1,inf);