import numpy as np
import matplotlib.pyplot as plt
# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)
plt.show()
print(x_data.shape)
# 数据中心化
def zeroMean(dataMat):
    # 按列求平均，即各个特征的平均
    meanVal = np.mean(dataMat, axis=0) 
    newData = dataMat - meanVal
    return newData, meanVal
newData,meanVal=zeroMean(data)
# np.cov用于求协方差矩阵，参数rowvar=0说明数据一行代表一个样本
covMat = np.cov(newData, rowvar=0)
# 协方差矩阵
print(covMat)
# np.linalg.eig求矩阵的特征值和特征向量
eigVals, eigVects = np.linalg.eig(np.mat(covMat))
# 特征值
print(eigVals)
# 特征向量
print(eigVects)
# 对特征值从小到大排序
eigValIndice = np.argsort(eigVals)
print(eigValIndice)
top = 1
# 最大的top个特征值的下标
n_eigValIndice = eigValIndice[-1:-(top+1):-1]
print(n_eigValIndice)
# 最大的n个特征值对应的特征向量
n_eigVect = eigVects[:,n_eigValIndice]
print(n_eigVect)
# 低维特征空间的数据
lowDDataMat = newData*n_eigVect
print(lowDDataMat)
# 利用低纬度数据来重构数据
reconMat = (lowDDataMat*n_eigVect.T) + meanVal
print(reconMat)
# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)
# 重构的数据
x_data = np.array(reconMat)[:,0]
y_data = np.array(reconMat)[:,1]
plt.scatter(x_data,y_data,c='r')
plt.show()