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Add analysis of bound curve

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Ksyer
2024-02-22 10:52:46 +08:00
parent f0a14fae0f
commit a6956f3947
4 changed files with 1917 additions and 8 deletions
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Block RIP/bound/main.m
+19 -8
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@@ -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);