Add analysis of bound curve

Block RIP/bound/linefit.m

@@ -0,0 +1,12 @@
+function [k, b] = linefit(x, y)
+    n = length(x);
+    x = reshape(x, n, 1);
+    y = reshape(y, n, 1);
+    A = [x, ones(n, 1)];
+    bb = y;
+    B = A' * A;
+    bb = A' * bb;
+    yy = B \ bb;
+    k = yy(1);
+    b = yy(2);
+end

Block RIP/bound/main.m

@@ -3,23 +3,34 @@ clear;
 
 M = 50;
 eps = 1e-5;
-delta = 0.3;
+delta = 1/3;
 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);
+nums = 20:0.1:50;
+len = length(nums);
+N = zeros(1, len);
+upper_bound_C1 = zeros(1, len);
+upper_bound_C2 = zeros(1, len);
+log_ub_C1 = zeros(1, len);
+log_ub_C2 = zeros(1, len);
 
-for i = 1: length(nums)
+for i = 1: len
     N(i) = 10^nums(i);
     upper_bound_C1(i) = get_our_ub(1, N(i), C, M, eps);
+    log_ub_C1(i) = log(upper_bound_C1(i));
     upper_bound_C2(i) = get_wl_ub(N(i), M, eps);
+    log_ub_C2(i) = log(upper_bound_C2(i));
     N(i) = nums(i);
 end
 
 semilogy(N, upper_bound_C1, 'r-', N, upper_bound_C2, 'b');
+legend("Our result", "Wang's result");
 xlabel("log_{10}(N)");
 ylabel("Upper bound of K");
-title("Prob(\delta_K < 0.3) >= 1 - 10^{-5}")
+title_name = strcat("Prob(\delta_K < ", string(delta), ") >= 1 - ", string(eps));
+title(title_name);
+
+[k1, b1] = linefit(N, log_ub_C1);
+[k2, b2] = linefit(N, log_ub_C2);
+fprintf("Our result gradient: %f\n", k1);
+fprintf("Wang's result gradient: %f\n", k2);