From 6f3e7b4560e4d0fb139e77620e543e60928f5fed Mon Sep 17 00:00:00 2001
From: Yuki <lzy001@sjtu.edu.cn>
Date: Fri, 6 Sep 2024 20:22:46 +0800
Subject: [PATCH] A/4

---
 .gitignore    |  3 +-
 A/4/linear.py | 80 +++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 82 insertions(+), 1 deletion(-)
 create mode 100644 A/4/linear.py

diff --git a/.gitignore b/.gitignore
index e8ed50b..df99b7a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,4 +4,5 @@
 *.dat
 *.log
 *.gif
-__pycache__/
\ No newline at end of file
+__pycache__/
+.idea/
\ No newline at end of file
diff --git a/A/4/linear.py b/A/4/linear.py
new file mode 100644
index 0000000..9c08091
--- /dev/null
+++ b/A/4/linear.py
@@ -0,0 +1,80 @@
+import numpy as np
+from scipy.optimize import minimize
+
+
+# 目标函数
+def objective(x):
+    return 2 * (x[2] + x[4]) * x[5] + (x[3] + x[4]) * x[5]
+
+
+# 非线性约束函数
+def nonlin_constraints(x):
+    R = x[5]
+    theta1, theta2, k1, k2, phi = x[:5]
+
+    r1 = (1.7 / (2 * np.pi)) * theta1
+    r2 = -(1.7 / (2 * np.pi)) * theta2
+
+    tan_phi_left = np.tan(phi)
+    tan_phi_right = (r1 * np.sin(theta1) - 2 * R * np.sin(k1) - r2 * np.sin(theta2) - R * np.sin(k2)) / \
+                    (r1 * np.cos(theta1) - 2 * R * np.cos(k1) - r2 * np.cos(theta2) - R * np.cos(k2))
+
+    ceq1 = (theta1 * np.sin(theta1) - np.cos(theta1)) / (np.sin(theta1) + theta1 * np.cos(theta1)) - np.tan(k1)
+    ceq3 = (theta2 * np.sin(theta2) - np.cos(theta2)) / (np.sin(theta2) + theta2 * np.cos(theta2)) - np.tan(k2)
+
+    d = np.sqrt((r1 * np.cos(theta1) - 2 * R * np.cos(k1) - r2 * np.cos(theta2) - R * np.cos(k2)) ** 2 +
+                (r1 * np.sin(theta1) - 2 * R * np.sin(k1) - r2 * np.sin(theta2) - R * np.sin(k2)) ** 2)
+
+    ceq5 = d - 3 * R
+    ceq6 = tan_phi_right - tan_phi_left
+
+    ceq = [ceq1, ceq3, ceq5, ceq6]
+
+    c = [
+        k1 + phi - 2 * np.pi,
+        k2 + phi - 2 * np.pi,
+        r1 - 4.5,
+        -r2 - 4.5,
+        r1,
+        -r2
+    ]
+
+    return np.array(c), np.array(ceq)
+
+
+# 参数定义和初始猜测
+x0 = [np.pi, 2 * np.pi, np.pi / 2, np.pi / 2, np.pi / 2, 1]
+
+# 上下界定义
+theta1_range = [2 * np.pi, 9 * np.pi]
+theta2_range = [2 * np.pi, 9 * np.pi]
+k_range = [0, 2 * np.pi]
+phi_range = [0, 2 * np.pi]
+R_range = [0, 3]
+
+bounds = [
+    theta1_range,
+    theta2_range,
+    k_range,
+    k_range,
+    phi_range,
+    R_range
+]
+
+# 使用 scipy.optimize.minimize 进行非线性优化
+cons = [
+    {'type': 'eq', 'fun': lambda x: nonlin_constraints(x)[1]},
+    {'type': 'ineq', 'fun': lambda x: -nonlin_constraints(x)[0]}
+]
+
+result = minimize(objective, x0, method='SLSQP', bounds=bounds, constraints=cons, options={'disp': True})
+
+# 打印结果
+print('Optimal Solution:')
+print(f'theta1: {result.x[0]}')
+print(f'theta2: {result.x[1]}')
+print(f'k1: {result.x[2]}')
+print(f'k2: {result.x[3]}')
+print(f'phi: {result.x[4]}')
+print(f'R: {result.x[5]}')
+print(f'Minimum Objective Value: {result.fun}')
\ No newline at end of file