aaa

按方法整理/非线性方程-牛顿下山法.py

@@ -0,0 +1,50 @@
+import math
+
+def NewtonDownHillSolve(fx, dfx, x0, err1,err2, N0,min_t):
+    count = 0
+    print(f"k={count}, x0={x0}")
+    x1 = x0 + 1 + err1
+    while abs(x1 - x0) > err1 or abs(fx(x1)) > err2:
+        t = 1
+        if abs(dfx(x1)) < 1e-10:
+            print("导数为0，无法下山")
+            return None, 0
+        print(f"当前点: x0={x0}")
+        while t >= min_t:
+            x1 = x0 - t * fx(x0) / dfx(x0)
+            print(f"下山: t={t}, x1={x1}, abs(fx(x1))={abs(fx(x1))}, abs(fx(x0))={abs(fx(x0))}")
+            if abs(fx(x1)) < abs(fx(x0)):
+                break
+            t *= 0.5
+        if t < min_t:
+            print("达到最小t，下山失败")
+            return None, -2
+        # x1 = x0 - fx(x0) / dfx(x0)
+        count += 1
+        print(f"k={count}, x{count}={x1},x1-x0={abs(x1-x0)}")
+        if count > N0:
+            return None, -1
+        x0 = x1
+    print(f"收敛: x1={x1}, fx(x1)={fx(x1)}")
+    return x1, 1
+
+
+if __name__ == "__main__":
+    ##############################################################################################################
+    err1 = 1e-5      # 根的误差限   见P147
+    err2 = 1e-5      # 残量精度     见P147
+    N0 = 100         # 最大迭代次数
+    min_t = 1e-10    # 最小t值
+    x0 = 0.6         # 初始值
+    fx = lambda x: x**3 - x - 1       # 原函数
+    dfx = lambda x: 3*x**2 - 1        # 导函数
+
+    result, status = NewtonDownHillSolve(fx, dfx, x0, err1, err2, N0, min_t)
+    if status == 1:
+        print(f"收敛 解为: {result}")
+    elif status == -1:
+        print("不收敛")
+    elif status == -2:
+        print("下山失败")
+    else:
+        print("导数为0，无法收敛")