# coding=utf-8

import numpy as np

from numpy.linalg import cholesky

import matplotlib.pyplot as plt

sampleNo = 1000;

# 一維正態分佈

# 下面三種方式是等效的

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)

# 二維正態分佈

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)

# 注意繪製的是散點圖，而不是直方圖

plt.plot(s[:,0],s[:,1],"+")

plt.show()