Update Block RIP

Block RIP/bound/get_our_ub.m

@@ -0,0 +1,3 @@
+function result = get_our_ub(delta, N, C, M, eps)
+    result = delta^2 * N / (C * M * (log(M) - log(eps)));
+end

Block RIP/bound/get_wl_ub.m

@@ -0,0 +1,13 @@
+function result = get_wl_ub(N, M, eps)
+    k1 = sqrt((M - 1) / N);
+    k2 = log(M * N);
+    k3 = sqrt(k2 - log(eps));
+    k4 = sqrt(log(2 * M) - log(eps));
+    
+    delta_1 = 24 * k1 * k2 * (2 * k3 + 1);
+    delta_2 = 1.5 * k1 * (2 * k4 + 1);
+
+    numerator = N * (1/8 - delta_1 - delta_2) ^ 2;
+    denominator = 81 * M * k2 * (1 + 2 * delta_2 / 3);
+    result = numerator / denominator;
+end

Block RIP/bound/main.m

@@ -0,0 +1,25 @@
+clc;
+clear;
+
+M = 50;
+eps = 1e-5;
+delta = 0.3;
+C = 10.66;
+
+nums = 10:0.1:50;
+num = length(nums);
+N = zeros(1, num);
+upper_bound_C1 = zeros(1, num);
+upper_bound_C2 = zeros(1, num);
+
+for i = 1: length(nums)
+    N(i) = 10^nums(i);
+    upper_bound_C1(i) = get_our_ub(1, N(i), C, M, eps);
+    upper_bound_C2(i) = get_wl_ub(N(i), M, eps);
+    N(i) = nums(i);
+end
+
+semilogy(N, upper_bound_C1, 'r-', N, upper_bound_C2, 'b');
+xlabel("log_{10}(N)");
+ylabel("Upper bound of K");
+title("Prob(\delta_K < 0.3) >= 1 - 10^{-5}")