随机漫步理论

理论部分:

代码部分:

import random
import matplotlib.pyplot as plt
import numpy as np
position = 0
walk = [position]
steps = 1000
for i in range(steps):
    step = 1 if random.randint(0, 1) else -1
    position += step
    walk.append(position)
#plt.plot(walk[:1000])


nsteps = 1000
draws = np.random.randint(0, 2, size=nsteps)
steps = np.where(draws > 0, 1, -1)
walk = steps.cumsum()  # 一维向量就可以这样来
#plt.plot(walk[:1000])

print( "min:" + str(walk.min()) )
print( "max:" + str(walk.max()) )
# 需要多久才能距离初始0点至少10步远（任一方向均可）
print((np.abs(walk) >= 10).argmax())


nwalks = 5000
nsteps = 1000
#模拟多个随机漫步过程（比如5000个）
draws = np.random.randint(-1, 1, size=(nwalks, nsteps)) # 0 or 1
print(draws)
steps = np.where(draws >= 0, 1, -1)
print(steps)
walks = steps.cumsum(1)
print(walks)
print("max: " + str(walks.max()) )
print("min: " + str(walks.min()))

# 用any方法来对此进行检查 因为不是5000个过程都到达了30的距离
hits30 = (np.abs(walks) >= 30).any(1)  
print("sum: " + str(hits30.sum()) )   # Number that hit 30 or -30
 
plt.plot(walks[0])
plt.plot(walks[1])
plt.plot(walks[2])
plt.plot(walks[3])
plt.plot(walks[4])
plt.plot(walks[5])
plt.plot(walks[6])
plt.plot(walks[7])
plt.plot(walks[8])

　　

　

https://www.jianshu.com/p/numpy_test