Update Block RIP

Block RIP/Phase transitions/can_recovery.m

@@ -0,0 +1,25 @@
+function flg = can_recovery(Psi, s, eps)
+    [m, n] = size(Psi);
+
+    x = zeros(n, 1);
+    random_indices = randperm(n, s);
+    x(random_indices) = randn(s, 1);
+    x = sign(x);
+    y = Psi * x;
+
+    cvx_begin
+    variable s1(n)
+    minimize(norm(s1, 1))
+    subject to
+    norm(y - Psi * s1) <= eps
+    cvx_end
+
+    p = norm(x - s1, 2);
+
+    if p < eps
+        flg = 1;
+    else
+        flg = 0;
+    end
+
+end

Block RIP/Phase transitions/get_Psi.m

@@ -0,0 +1,11 @@
+function Psi = get_Psi(N, M, epi)
+    Psi = zeros(N,M*N);
+    for n = 0 : N-1
+        Cn = floor(rand()*M);
+        for q = 0 : N-1
+            for p = 0:M-1
+                Psi(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi)) / sqrt(N);
+            end
+        end
+    end
+end

Block RIP/Phase transitions/main.m

@@ -0,0 +1,34 @@
+clc;
+clear;
+
+N = 32;
+M = 4;
+k = 5;
+epi = 0.02;
+
+Psi_wide = get_Psi(N, M, epi);
+
+max_n = 100;
+max_s = 100;
+trials_time = 50;
+d = 5;
+eps = 1e-5;
+
+prob = zeros(max_n, max_s);
+
+for n = 1:max_n
+    Psi_narrow = get_Psi(n, M, 0);
+    parfor s = 1:max_s
+        if n > s
+            x = 0;
+            for t = 1:trials_time
+                x = x + can_recovery(Psi_narrow, s, eps);
+            end
+            prob(n, s) = x / trials_time;
+        else
+            prob(n, s) = 0;
+        end
+    end
+end
+
+save("Expr1.mat", "prob");