Update wide vs narrow code

2024-07-22 21:17:57 +08:00
parent 13f660826d
commit 9cbe8e31ea
14 changed files with 1642 additions and 0 deletions
@@ -0,0 +1,95 @@
+function [recovery_results, sigma_w2, thresholds] = All_Recovery2(A, x, P_fa, noise_sigma, trail_times, LASSO_lambda, tau)
+
+    sz = size(A);
+    M = sz(1);
+    N = sz(2);
+
+    recovery_results = zeros(2, trail_times, N);
+    sigma_w2 = zeros(2, trail_times, 1);
+    thresholds = zeros(2, trail_times, 1);
+    
+    for hypo = 2: -1: 1
+        % hypo-假设
+        hypo = 3 - hypo;
+        h = waitbar(0, '正在仿真' + string(hypo-1) + '假设情况');
+        for T = 1:trail_times
+            waitbar(T / trail_times, h);
+    
+            noise = get_noise(noise_sigma, M, 1);
+
+            % y = Ax + n
+            if hypo == 1
+                y_noise = noise;
+            else
+                y_noise = A * x + noise;
+            end
+
+            [x_LASSO, x_hat_d] = cVAMPro(y_noise, A, LASSO_lambda, tau, 100);
+            % x_LASSO = FISTA(y_noise, A, LASSO_lambda, 1e-5);
+
+
+            sz = size(A);
+            n = sz(2);
+            gamma = sz(1) / sz(2);
+            lambda = LASSO_lambda;
+
+            % CROD求去偏
+            rho_active = sum(abs(x_LASSO) > 1e-3)/n;
+            Q_hat = (gamma - rho_active)/(1 - rho_active);
+            Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
+            diff = 1;
+            while(diff > 1e-4)
+                Rho_pre = Rho;
+                Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
+                diff = abs(Rho - Rho_pre);
+            end
+            Q_hat = (gamma-Rho)/(1-Rho);
+            x_d_CROD = x_LASSO + A'*(y_noise - A*x_LASSO)/Q_hat; % x_d_CROD == x_hat_d
+            sigma_n = noise_sigma;
+        
+            % CROD求门限和检验统计量
+            RSS = sum(abs(y_noise - A * x_LASSO).^2)/length(y_noise);
+            chi = Rho*(1 - Rho)/(gamma - Rho);
+            if chi ~= 0
+                chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
+                z = -(1 - chi + chi_temp) / (2*chi);
+                z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
+                G_prime = (z + 1/chi);
+                G_wprime = (z_prime + 1/chi/chi);
+                chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+                    + (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
+            else
+                G_prime = gamma;
+                G_wprime = gamma*(1-gamma);
+                chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+                    + (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
+            end
+            sigma_CROD = sqrt(2*chi_hat) / Q_hat;
+
+            if sigma_CROD > 1
+                sigma_CROD = sigma_CROD;
+            end
+            sigma_w2(hypo, T) = sigma_CROD^2;
+            thresholds(hypo, T) = -sigma_CROD^2 * log(P_fa);
+            % figure; subplot(221); plot(real(x)); subplot(222); plot(real(x_LASSO)); subplot(223); plot(real(x_hat_d)); subplot(224); plot(real(x_d_CROD));
+
+            % % data4 folder
+            % if hypo == 2
+            %     x_hat = x_d_CROD;
+            %     % x_hat = x_hat_d;
+            % else
+            %     x_hat = x_d_CROD;
+            % end
+
+            % data5 folder
+            if hypo == 2
+                x_hat = x_hat_d;
+            else
+                x_hat = x_d_CROD;
+            end
+
+            recovery_results(hypo, T, :) = x_hat;
+        end
+        close(h);
+    end
+end