import math
import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.axisartist as axisartist
def f(x):
return x-2*math.sin(x)
def f1(x):
return 1-2*math.cos(x)
def dichotomy(e):
a = 1
b = 3
while abs(a-b) > e:
if f(a) * f(b) > 0:
print('根不在输入区间内')
break
c = (a + b) / 2
if f(a)*f(c) > 0:
a = c
else:
b = c
print((a+b)/2)
show1((a+b)/2)
def Newton(i, e):
x_list = list()
x_list.append(i)
x_list.append(x_list[-1] - f(x_list[-1]) / f1(x_list[-1]))
while (x_list[-1]-x_list[-2]) > e:
x_list.append(x_list[-1]-f(x_list[-1])/f1(x_list[-1]))
print(x_list[-1])
show2(x_list[-1])
def Chord_cut(x0, x1, e):
x_list = list()
x_list.append(x0)
x_list.append(x1)
while (x_list[-1] - x_list[-2]) > e:
x_list.append(x_list[-1] - f(x_list[-1]) * (x_list[-1] - x_list[0]) / (f(x_list[-1]) - f(x_list[0])))
print(x_list[-1])
show3(x_list[-1])
def show1(res):
# 创建画布
fig = plt.figure()
# 使用axisartist.Subplot方法创建一个绘图区对象ax
ax = axisartist.Subplot(fig, 111)
# 将绘图区对象添加到画布中
fig.add_axes(ax)
ax.axis[:].set_visible(False)
ax.axis["x"] = ax.new_floating_axis(0, 0)
ax.axis["x"].set_axisline_style("->", size=1.0)
ax.axis["y"] = ax.new_floating_axis(1, 0)
ax.axis["y"].set_axisline_style("-|>", size=1.0)
ax.axis["x"].set_axis_direction("top")
ax.axis["y"].set_axis_direction("right")
x_list = np.arange(0, 4, 0.1)
x_list = list(x_list)
y_list = list()
for x in x_list:
y_list.append(f(x))
plt.plot(x_list, y_list, 'b')
plt.vlines(1, 0, 1-2*math.sin(1), colors='r', linestyles='dashed')
plt.vlines(3, 0, 3-2*math.sin(3), colors='r', linestyles='dashed')
plt.text(0.2, 4, 'The solution of dichotomy', fontsize=15)
plt.text(0.2, 3.5, res, fontsize=15)
plt.show()
def show2(res):
# 创建画布
fig = plt.figure()
# 使用axisartist.Subplot方法创建一个绘图区对象ax
ax = axisartist.Subplot(fig, 111)
# 将绘图区对象添加到画布中
fig.add_axes(ax)
ax.axis[:].set_visible(False)
ax.axis["x"] = ax.new_floating_axis(0, 0)
ax.axis["x"].set_axisline_style("->", size=1.0)
ax.axis["y"] = ax.new_floating_axis(1, 0)
ax.axis["y"].set_axisline_style("-|>", size=1.0)
ax.axis["x"].set_axis_direction("top")
ax.axis["y"].set_axis_direction("right")
x_list = np.arange(0, 4, 0.1)
x_list = list(x_list)
y_list = list()
for x in x_list:
y_list.append(f(x))
plt.plot(x_list, y_list, 'b')
plt.vlines(1, 0, 1-2*math.sin(1), colors='r', linestyles='dashed')
plt.vlines(3, 0, 3-2*math.sin(3), colors='r', linestyles='dashed')
plt.text(0.2, 4, 'The solution of Newton', fontsize=15)
plt.text(0.2, 3.5, res, fontsize=15)
plt.show()
def show3(res):
# 创建画布
fig = plt.figure()
# 使用axisartist.Subplot方法创建一个绘图区对象ax
ax = axisartist.Subplot(fig, 111)
# 将绘图区对象添加到画布中
fig.add_axes(ax)
ax.axis[:].set_visible(False)
ax.axis["x"] = ax.new_floating_axis(0, 0)
ax.axis["x"].set_axisline_style("->", size=1.0)
ax.axis["y"] = ax.new_floating_axis(1, 0)
ax.axis["y"].set_axisline_style("-|>", size=1.0)
ax.axis["x"].set_axis_direction("top")
ax.axis["y"].set_axis_direction("right")
x_list = np.arange(0, 4, 0.1)
x_list = list(x_list)
y_list = list()
for x in x_list:
y_list.append(f(x))
plt.plot(x_list, y_list, 'b')
plt.vlines(1, 0, 1-2*math.sin(1), colors='r', linestyles='dashed')
plt.vlines(3, 0, 3-2*math.sin(3), colors='r', linestyles='dashed')
plt.text(0.2, 4, 'The solution of Chord_cut', fontsize=15)
plt.text(0.2, 3.5, res, fontsize=15)
plt.show()
if __name__ == '__main__':
dichotomy(0.001)
Newton(1.9, 0.0001)
Chord_cut(1.8, 1.9, 0.0001)
