牛顿切线法求根

Posted 2020-10-17

 1 #coding=utf-8
 2 from sympy import *
 3 import numpy as np
 4 from sympy import *
 5 import math
 6 import matplotlib.pyplot as plt
 7 
 8 plt.close()
 9 fig = plt.figure()
10 #网格可见
11 plt.grid(True)
12 plt.axis([0, 5, -2, 25])
13 #开启交互
14 plt.ion()
15 #plt.title("牛顿法")
16 #设置xy轴的名称
17 plt.xlabel("X")
18 plt.ylabel("Y")
19 x = np.linspace(0, 10, 100)
20 y = x**2-2
21 plt.plot(x, y, label="$y$", color="red", linewidth=1)
22 plt.show()
23 
24 
25 #定义变量x
26 x = Symbol(‘x‘)
27 #定义函数f
28 f = x**2-2
29 x0=5.0
30 while(1):
31     y0=x0**2-2
32     g = diff(f,x,1)
33     k = g.subs(x,x0)
34     # y1 = f.sub(x,x0)
35     b = y0-k*x0
36     x1=-b/k
37     plt.plot([x0,x0],[0,y0])
38     plt.plot([x1,x0],[0,y0])
39     print(x1)
40     if (abs(x1 - x0) < 0.00001):
41         x0=x1
42         break
43     x0=x1
44     plt.pause(0.5)
45 show_res = ‘[x=‘ + str(x0) +  ‘]‘
46 plt.text(1,1, show_res)
47 while True:
48     plt.pause(0.05)