From 82a0353f74b13eaffbd894c251089cade27941e4 Mon Sep 17 00:00:00 2001
From: Ksyer <>
Date: Tue, 19 Dec 2023 17:12:43 +0800
Subject: [PATCH] Add Analysis of FAR via CS folder

---
 Analysis of FAR via CS/I.mat      | Bin 0 -> 2778 bytes
 Analysis of FAR via CS/Main.m     |  43 ++++++++++++++++++++++++++++++
 Analysis of FAR via CS/calc_int.m |  11 ++++++++
 3 files changed, 54 insertions(+)
 create mode 100644 Analysis of FAR via CS/I.mat
 create mode 100644 Analysis of FAR via CS/Main.m
 create mode 100644 Analysis of FAR via CS/calc_int.m

diff --git a/Analysis of FAR via CS/I.mat b/Analysis of FAR via CS/I.mat
new file mode 100644
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diff --git a/Analysis of FAR via CS/Main.m b/Analysis of FAR via CS/Main.m
new file mode 100644
index 0000000..1f3bc9e
--- /dev/null
+++ b/Analysis of FAR via CS/Main.m	
@@ -0,0 +1,43 @@
+cache = true;
+
+if cache
+    load("I.mat");
+else
+    tau_min = 0;
+    tau_max = 10;
+    tau_interval = 0.1;
+    tau_range = tau_min:tau_interval:tau_max;
+
+    s_b_min = 1;
+    s_b_max = 32;
+    s_b_range = s_b_min:s_b_max;
+
+    result = zeros(1, 32);
+
+    m = 4;
+
+    I = zeros(length(tau_range), 0);
+
+    for tau_idx = 1:length(tau_range)
+        tau = tau_range(tau_idx);
+        I(tau_idx) = calc_int(tau, m);
+    end
+
+end
+
+%%
+
+for s_b_idx = 1:length(s_b_range)
+    s_b = s_b_range(s_b_idx);
+    f_set = zeros(length(tau_range), 1);
+
+    for tau_idx = 1:length(tau_range)
+        tau = tau_range(tau_idx);
+        f_set(tau_idx) = s_b * (1 + tau ^ 2) + (100 - s_b) * I(tau_idx);
+    end
+
+    t = min(f_set);
+    result(s_b_idx) = t;
+end
+
+plot(s_b_range, result);
diff --git a/Analysis of FAR via CS/calc_int.m b/Analysis of FAR via CS/calc_int.m
new file mode 100644
index 0000000..e667f94
--- /dev/null
+++ b/Analysis of FAR via CS/calc_int.m	
@@ -0,0 +1,11 @@
+function I = calc_int(tau, m)
+
+    if tau < 0
+        I = 0;
+    else
+        syms x f;
+        f = (x - tau) ^ 2 * x ^ (m - 1) * exp(-x ^ 2/2) / (2 ^ (m / 2 - 1) * gamma(m / 2));
+        I = double(int(f, [tau, +inf]));
+    end
+
+end