#!/usr/bin/env python# coding: utf-8#copyRight by heibankeimport numpy as np import matplotlib.pyplot as plt from solutions_3 import *# 产生一个方波(x,y)x = np.linspace(-10,10,300) y=[]for i in np.cos(x): if i>0: y.append(0) else: y.append(2)y=np.array(y)# write Your code, Fourier function plt.plot(x,y,color='g',label='origin') plt.plot(x,fourier(x,y,3),color='r',label='3')plt.plot(x,fourier(x,y,8),color='b',label='8')plt.plot(x,fourier(x,y,23),color='k',label='23')plt.legend()plt.axis('equal')plt.show()
#!/usr/bin/env python# coding: utf-8#copyRight by heibankeimport numpy as np import matplotlib.pyplot as plt from solutions_3 import *A=np.array([[3,1],[2,4]])/4.0# write Your code# def eigshow(A):eigshow(A)
PCA
#!/usr/bin/env python# coding: utf-8#copyRight by heibankeimport numpy as npimport matplotlib.pyplot as plt def pca(dataMat, topNfeat=5): meanVals = np.mean(dataMat, axis=0) meanRemoved = dataMat - meanVals #减去均值 covMat = meanRemoved.T.dot(meanRemoved) #求协方差方阵 eigVals, eigVects = np.linalg.eig(covMat) #求特征值和特征向量 eigValInd = np.argsort(eigVals) #对特征值进行排序 eigValInd = eigValInd[:-(topNfeat + 1):-1] redEigVects = eigVects[:, eigValInd] #除去不需要的特征向量 lowDDataMat = meanRemoved.dot(redEigVects) #求新的数据矩阵 reconMat = (lowDDataMat.dot(redEigVects.T)) + meanVals reduceData = lowDDataMat + np.mean(dataMat) return reduceData,reconMat N=100x=np.linspace(2,4,N)y=x*2-4x1=x+(np.random.rand(N)-0.5)*1.5y1=y+(np.random.rand(N)-0.5)*1.5data = np.array([x1,y1])a,b=pca(data.T,1)plt.plot(x,y,color='g',linestyle='-',marker='',label='ideal') plt.plot(x1,y1,color='b',linestyle='',marker='o',label='noise')plt.plot(b[:,0],b[:,1],color='r',linestyle='',marker='>',label='recon')plt.plot(a[:,0],np.zeros(N),color='k',linestyle='',marker='*',label='lowD')plt.legend()plt.axis('equal')plt.show()
SVD
#!/usr/bin/python# -*- coding: utf-8 -*# Copy Right by heibankeimport numpy as npfrom matplotlib import pyplot as pltA=np.array([[-0.2,-1],[1.1,0.5]])U,s,V=np.linalg.svd(A)# S=np.array([[s[0],0],[0,s[1]]])# modified by conkangS=np.diag(s)fig = plt.figure()ax0 = fig.add_subplot(221)ax1 = fig.add_subplot(222)ax2 = fig.add_subplot(223)ax3 = fig.add_subplot(224)def plot_2D_mat(M,ax,text=""): ax.plot([0,M[0,0]],[0,M[1,0]],'b-o') ax.plot([0,M[0,1]],[0,M[1,1]],'r-o') ax.set_title(text) ax.axis('equal') ax.set_xlim([-1.5,1.5]) ax.set_ylim([-1.5,1.5]) ax.grid(True) plot_2D_mat(np.eye(2),ax0,"origin")plot_2D_mat(A,ax1,"A (USV) Matrix")plot_2D_mat(V.T,ax2,"V Matrix")plot_2D_mat(S.dot(V.T),ax3,"SV Matrix")plt.show() https://pan.baidu.com/s/1gfMX6h1