from sympy import *
import math
import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.axisartist as axisartist
def f(x):
if x == 0:
x = Symbol('x')
return limit(sin(x)/x, x, 0)
else:
return float(math.sin(x)/x)
def func(a, b, e):
h = b - a
T = list()
T.append((f(a)+f(b))*h/2)
s = 0
x = a + h/2
while x < b:
s = s + f(x)
x = x + h
T.append((T[-1]+h*s)/2)
while abs(T[-1]-T[-2]) >= e:
h = h/2
s = 0
x = a + h/2
s = s + f(x)
x = x + h
while x < b:
s = s + f(x)
x = x + h
T.append((T[-1] + h * s) / 2)
print(h)
return T[-1]
def show(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(10**-10, 6, 10**-4)
y_list = np.sin(x_list)/x_list
plt.plot(x_list, y_list)
# plt.legend()
plt.text(1.8, 1, 'The solution of Step 2 Distribution:', fontsize=12)
plt.text(2.6, 0.8, res, fontsize=12)
for x in np.arange(0.05, 6, 0.05):
plt.vlines(x, 0, sin(x) / x, colors='r', linestyles='dashed')
# for x in np.arange(0.02, 0.25, 0.03):
# plt.vlines(x, 0, sin(x)/x, colors='r', linestyles='dashed')
# for x in np.arange(0.25, 1.9, 0.05):
# plt.vlines(x, 0, sin(x) / x, colors='r', linestyles='dashed')
# for x in np.arange(2.3, 6, 0.05):
# plt.vlines(x, 0, sin(x) / x, colors='r', linestyles='dashed')
plt.vlines(2.05, 0, sin(2.05) / 2.05, colors='r', linestyles='dashed')
plt.show()
if __name__ == '__main__':
res = func(0, 6, 0.0001)
show(res)
