diff --git a/Block RIP/bound/linefit.m b/Block RIP/bound/linefit.m new file mode 100644 index 0000000..a7879f8 --- /dev/null +++ b/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 \ No newline at end of file diff --git a/Block RIP/bound/main.m b/Block RIP/bound/main.m index 6de5259..c163df2 100644 --- a/Block RIP/bound/main.m +++ b/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}") \ No newline at end of file +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); diff --git a/Block RIP/bound/result.eps b/Block RIP/bound/result.eps new file mode 100644 index 0000000..78953af --- /dev/null +++ b/Block RIP/bound/result.eps @@ -0,0 +1,1886 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: (MATLAB, The Mathworks, Inc. 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