Add "FAR vs PD"

2024-05-11 15:43:25 +08:00
parent 17386d80c1
commit b48ab07dd0
21 changed files with 412 additions and 0 deletions
@@ -0,0 +1,72 @@
+function P_fa = FAR_simu(threshold)
+    global N M epi trail_times
+
+    % Define measurement matrix
+    A = get_Psi(N, M, epi);
+
+    % Define sparse vector x
+    [Lambda, x] = get_sparse_vector(N * M, 1);
+    Lambda_C = setdiff(1:N*M, Lambda);
+
+    % Try "trail_times" times
+    NN = N;
+    results = zeros(trail_times, N * M);
+
+    if exist("FAR_recovery_1_LASSO_5.mat")
+        load("FAR_recovery_0_debiasedLASSO_500.mat", "results");
+    else
+        for T = 1: trail_times
+            % y = Ax + n
+            n = randn(NN, 1) * 0.1;
+            y_noise = A * x + n;
+            
+            % x_hat = CS(A, y)
+            x_hat = recovery(A, y_noise);
+            results(T, :) = x_hat;
+        end
+    end
+
+    % Distribute of H_0 and H_1
+    H_0_distribute = zeros(1, length(Lambda_C));
+    H_1_distribute = zeros(1, length(Lambda));
+
+    i1 = 1;
+    i2 = 1;
+    Ts = [];
+    
+    for t = 1: trail_times
+        x_hat = results(t, :);
+        T = 0;
+        for i = 1: length(x)
+            if ismember(i, Lambda_C)
+                H_0_distribute(i1) = x_hat(i);
+                i1 = i1 + 1;
+            elseif ismember(i, Lambda)
+                T = T + abs(x_hat(i));
+                H_1_distribute(i2) = x_hat(i);
+                i2 = i2 + 1;
+            end
+        end
+        Ts = [Ts T];
+    end
+
+
+    % Draw
+    figure(1)
+    subplot(2, 1, 1);
+    title("Freq histogram of H_0");
+    histfit(real(H_0_distribute));
+    
+    subplot(2, 1, 2);
+    title("Freq histogram of H_1");
+    histfit(real(H_1_distribute));
+    
+    H_0_mean = mean(H_0_distribute);
+    H_0_std = std(H_0_distribute);
+    H_1_mean = mean(H_1_distribute);
+    H_1_std = std(H_1_distribute);
+
+    fprintf("H_0: mu = %f, std = %f\n", H_0_mean, H_0_std);
+    fprintf("H_1: mu = %f, std = %f\n", H_1_mean, H_1_std);
+    % P_fa = normcdf(threshold, H_0_mean, H_0_std);
+end