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Python 3

• Matrice de covariance

import numpy as np

A = np.array([ [0.1,2,2.0,1],[0.2,3,3.0,1],[0.1,4,4.1,1] ])

B=np.cov(A)

At=A.transpose()

Bt=np.cov(At)

print("Cov A \n",B)

print("Cov B \n",Bt)

• Coefficient de corrélation

import numpy as np

A = np.array([ [0.1,2,2.0,1],[0.2,3,3.0,1],[0.1,4,4.1,1] ])

B=np.cov(A)

print("Cov A \n",B)

print("Coeff correlation ligne 1 et ligne 2",np.corrcoef(A[:1,:],A[1:2,:]))

• Valeurs et vecteurs propres
  • Instructions fondamentales

Si B est une matrice carrée, LA est l'objet "Linear Algebra"

w, v = LA.eig(B)

trouve le vecteur w des valeurs propres et la liste des vecteurs propres est la matrice v. Chaque colonne est un vecteur propre.

• Exemple de réductions de dimension

reconstruct.py

import numpy as np

from numpy import linalg as LA

A = np.array([ [0.1,2,2.0,1],[0.2,3,3.0,1],[0.1,4,4.1,1] ])

B=np.cov(A)

At=A.transpose()

Bt=np.cov(At)

print("Cov A \n",B)

print("Cov At \n",Bt)

w, v = LA.eig(B)

print("Eigenvalues of B",w)

print("Eigenvectors of B \n",v)

w1, v1 = LA.eig(Bt)

print("Eigenvalues of Bt",w1)

print("Eigenvectors of Bt \n",v1)

 #Reduction to two largest eigenvalues of Bt

v1r=v1[:,:2]

print("2 Eigenvectors of Bt \n",v1r)

Ar=np.dot(A,v1r)

print("Reduced matrix A with 2 columns \n",Ar)

 #Reduction to two largest eigenvalues of B

vr=v[:,:2]

print("2 Eigenvectors of B \n",vr)

Arl=np.dot(vr.transpose(),A)

print("Reduced matrix A with 2 lines \n",Arl)

print("Product of reduced matrices \n",np.dot(Ar,Arl))

print("Original matrix \n",A)