#-*- coding:utf-8 -*-

from numpy import *

import matplotlib.pyplot as plt
def pca(data):
    # 減去均值
    m = mean(data,axis=0)
    data -= m
    print m
    # 協方差矩陣
    C = cov(transpose(data))
    # 計算特徵值特徵向量，按降序排序
    evals,evecs = linalg.eig(C)
    print evals,evecs
    indices = argsort(evals) #得到的是索引值
 

    indices = indices[::-1]#降序
    print 'indices',indices
    evecs = evecs[:,indices]
    print evecs
    evals = evals[indices]
    print evals
    # 產生新的資料矩陣
    x = dot(transpose(evecs),transpose(data))
    print x
    # 重新計算原資料
    y=transpose(dot(evecs,x))+m
    return x,y,evals,evecs

x = random.normal(5
 
,.5,1000)
y = random.normal(3,1,1000)

a = x*cos(pi/4) + y*sin(pi/4)
b = -x*sin(pi/4) + y*cos(pi/4)
print a

plt.plot(a,b,'r.')
plt.xlabel('x')
plt.ylabel('y')

plt.title('raw dataset')

data = zeros((1000,2))
data[:,0] = a
data[:,1] = b
x,y,evals,evecs = pca(data)
print evecs

plt.figure()
plt.plot(y[:,0],y[:,1],'.'
 
)
plt.xlabel('x')
plt.ylabel('y')
plt.title('new dataset')
plt.show()