# coding=utf-8
'''
作者：采石工
来源：知乎
'''
import numpy as np
from numpy.linalg import cholesky
import matplotlib.pyplot as plt
sampleNo = 1000;
# 一维正态分布
# 下面三种方式是等效的
mu = 3
sigma = 0.1
np.random.seed(0)
s = np.random.normal(mu, sigma, sampleNo )
plt.subplot(141)
plt.hist(s, 30, normed=True)
np.random.seed(0)
s = sigma * np.random.randn(sampleNo ) + mu
plt.subplot(142)
plt.hist(s, 30, normed=True)
np.random.seed(0)
s = sigma * np.random.standard_normal(sampleNo ) + mu
plt.subplot(143)
plt.hist(s, 30, normed=True)
# 二维正态分布
mu = np.array([[1, 5]])
Sigma = np.array([[1, 0.5], [1.5, 3]])
R = cholesky(Sigma)
s = np.dot(np.random.randn(sampleNo, 2), R) + mu
plt.subplot(144)
# 注意绘制的是散点图，而不是直方图
plt.plot(s[:,0],s[:,1],'+')
plt.show()

#-*- coding:utf-8 -*-
# Python实现正态分布
# 绘制正态分布概率密度函数
import numpy as np
import matplotlib.pyplot as plt
import math
u = 0  # 均值μ
u01 = -2
sig = math.sqrt(0.2) # 标准差δ
x = np.linspace(u - 3*sig, u + 3*sig, 50)
y_sig = np.exp(-(x - u) ** 2 /(2* sig **2))/(math.sqrt(2*math.pi)*sig)
print x
print "="*20
print y_sig
plt.plot(x, y_sig, "r-", linewidth=2)
plt.grid(True)
plt.show()