Numpy pandas matplot 笔记 for 随机漫步

NumpyPandasMatplot

这个例子让我了解一个在实际任务中如何利用数组操作，首先是一个最简单的随机漫步，从零开始，纯python方法 1000

import random 
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])

import matplotlib.pyplot as plt
%matplotlib inline

walk[:10]

[0, [-1], [-2], [-1], [-2], [-1], [-2], [-1], [-2], [-1]]

随机漫步其实就是一个简单的累加。而用np.random能更快：

import numpy as np

nsteps = 1000
draws = np.random.randint(0,2,size=nsteps)
steps = np.where(draws>0, 1, -1)
print(steps)

[-1 -1 -1  1 -1  1 -1  1  1  1 -1  1 -1  1  1 -1 -1  1 -1 -1 -1  1 -1  1 -1
 -1 -1  1  1  1  1  1 -1  1 -1 -1  1 -1 -1 -1  1 -1  1  1 -1  1 -1 -1 -1  1
  1 -1  1  1  1  1 -1  1 -1  1  1  1 -1 -1  1  1 -1  1  1  1  1 -1  1  1 -1
  1 -1 -1 -1 -1  1  1 -1  1 -1 -1  1  1 -1 -1  1 -1 -1  1 -1  1  1 -1 -1  1
  1 -1  1 -1  1  1 -1  1  1  1 -1 -1  1  1 -1 -1  1  1  1  1 -1  1 -1 -1 -1
  1  1  1 -1  1 -1 -1 -1  1 -1  1  1  1 -1 -1  1  1 -1  1 -1 -1  1  1  1  1
  1  1 -1 -1  1  1  1  1  1 -1 -1  1  1 -1 -1  1 -1 -1  1  1 -1  1  1 -1  1
  1  1 -1 -1 -1  1 -1 -1 -1  1  1 -1  1 -1  1 -1 -1 -1 -1  1  1  1  1  1 -1
 -1 -1  1  1  1  1 -1  1  1  1 -1  1  1  1 -1 -1  1  1  1 -1  1 -1  1  1  1
 -1  1 -1 -1  1  1  1  1  1 -1  1  1  1 -1  1  1  1 -1  1 -1 -1  1  1  1 -1
 -1 -1  1  1  1 -1 -1  1  1  1 -1 -1  1 -1 -1  1 -1  1  1 -1 -1 -1 -1 -1  1
  1  1 -1  1 -1  1  1  1  1  1  1 -1 -1  1  1  1 -1 -1  1 -1 -1  1  1  1 -1
 -1  1  1  1  1  1  1 -1 -1 -1  1 -1 -1 -1 -1  1 -1 -1  1 -1  1 -1  1  1  1
 -1  1 -1  1  1  1  1 -1 -1  1  1 -1 -1  1 -1 -1  1  1  1  1 -1  1 -1 -1  1
  1  1  1 -1 -1  1 -1  1 -1 -1 -1 -1  1 -1  1  1 -1 -1  1  1 -1 -1 -1 -1 -1
  1  1  1 -1 -1 -1 -1 -1 -1 -1  1  1  1  1 -1 -1  1  1 -1  1  1  1 -1 -1  1
  1  1  1 -1 -1 -1 -1 -1 -1 -1 -1  1  1  1  1  1  1  1  1 -1  1 -1 -1  1  1
 -1 -1 -1 -1 -1  1 -1 -1 -1  1  1  1  1  1 -1  1 -1  1 -1  1 -1 -1  1  1  1
 -1  1 -1 -1 -1  1 -1 -1  1  1 -1 -1 -1  1 -1  1 -1  1  1 -1 -1  1 -1  1  1
 -1  1  1 -1  1 -1  1  1  1  1  1  1  1  1 -1 -1 -1  1 -1  1 -1 -1  1 -1 -1
  1  1  1 -1 -1  1  1 -1 -1 -1 -1  1  1 -1  1 -1 -1 -1  1 -1 -1  1 -1  1  1
 -1  1 -1 -1  1  1  1 -1 -1 -1 -1 -1  1  1 -1 -1  1  1  1 -1  1 -1  1 -1  1
  1 -1 -1 -1 -1 -1 -1  1  1 -1  1 -1 -1  1  1  1 -1 -1 -1 -1 -1 -1  1  1 -1
 -1 -1 -1 -1  1 -1 -1 -1  1 -1  1  1  1  1 -1 -1 -1  1  1  1  1 -1  1 -1  1
 -1  1 -1 -1 -1 -1  1 -1  1  1 -1 -1  1 -1 -1 -1  1 -1 -1  1  1 -1  1 -1 -1
  1 -1 -1  1  1  1 -1 -1  1  1  1 -1  1  1  1  1  1 -1  1 -1 -1  1 -1 -1 -1
  1 -1 -1  1 -1  1  1 -1 -1  1  1  1  1 -1 -1  1  1 -1 -1 -1  1 -1  1  1  1
  1  1  1 -1  1  1 -1  1  1 -1 -1 -1 -1 -1 -1  1 -1 -1 -1  1  1  1  1  1  1
  1 -1 -1  1 -1  1  1  1 -1 -1 -1  1 -1 -1 -1  1  1 -1 -1  1 -1  1 -1 -1  1
  1 -1 -1 -1  1 -1 -1 -1  1 -1 -1  1 -1 -1 -1  1  1 -1 -1  1 -1 -1 -1 -1  1
  1 -1  1  1 -1  1 -1  1 -1  1  1  1 -1  1  1  1 -1  1  1 -1 -1  1 -1 -1  1
  1  1 -1  1  1  1  1 -1  1 -1  1 -1  1 -1 -1 -1  1 -1  1  1  1 -1 -1  1  1
  1  1 -1  1  1 -1  1  1 -1 -1 -1  1  1  1 -1  1  1 -1 -1  1  1 -1  1  1  1
 -1  1 -1  1  1  1 -1  1 -1 -1  1 -1 -1 -1  1 -1 -1  1  1 -1 -1 -1 -1  1 -1
  1  1 -1 -1 -1 -1  1 -1  1 -1 -1 -1  1  1 -1  1 -1 -1  1  1  1 -1  1  1 -1
  1  1 -1  1 -1 -1 -1 -1  1 -1  1  1 -1 -1  1 -1 -1 -1  1  1  1  1 -1  1  1
  1 -1  1 -1 -1 -1 -1 -1  1  1  1 -1 -1  1  1 -1  1 -1  1 -1 -1  1 -1  1  1
  1  1  1  1  1 -1 -1 -1 -1 -1  1  1  1 -1 -1  1  1  1 -1  1  1 -1 -1 -1  1
 -1 -1  1 -1 -1 -1  1  1  1 -1  1 -1  1  1 -1  1 -1 -1 -1 -1 -1  1  1 -1  1
  1  1 -1  1 -1  1 -1 -1  1  1 -1  1 -1  1  1  1  1  1  1  1 -1 -1 -1 -1 -1]

walk = steps.cumsum()

walk.min()

-5

walk.max()

41

一次模拟多个随机漫步

nwalks = 5000
nsteps = 1000
draws = np.random.randint(0,2, size=(nwalks, nsteps))
steps = np.where(draws>0, 1,-1)
walks = steps.cumsum(1)

walks

array([[  1,   0,  -1, ...,  -6,  -7,  -8],
       [  1,   0,   1, ...,   6,   7,   6],
       [ -1,  -2,  -3, ...,   2,   3,   2],
       ..., 
       [  1,   0,   1, ...,  54,  53,  54],
       [  1,   0,   1, ..., -28, -29, -30],
       [  1,   2,   3, ..., -32, -31, -30]], dtype=int32)

walks.max()

116

walks.min()

-124

上面的step只是像翻硬币一样二选一，我们也可以用一个概率函数来生成：

steps = np.random.normal(loc=0, scale=0.25, size=(nwalks, nsteps))

steps

array([[-0.16399234, -0.0267885 ,  0.05142689, ..., -0.37457757,
         0.03966075,  0.39067126],
       [ 0.12018613, -0.08792517, -0.05285084, ...,  0.26438388,
        -0.21433596,  0.33423605],
       [-0.06996542, -0.17732628, -0.41869773, ..., -0.00390321,
        -0.12775795,  0.16524036],
       ..., 
       [-0.18181599, -0.37014665, -0.01165527, ..., -0.11092812,
         0.05949846,  0.09946047],
       [-0.36011367, -0.12865467, -0.31651241, ..., -0.02512507,
        -0.00548912,  0.30151192],
       [ 0.32561003,  0.28333045, -0.28733556, ...,  0.14309592,
        -0.31387699,  0.16887155]])