mhjensen
35 lines
876 B
Python
35 lines
876 B
Python
#The covariance matrix and its eigenvalues the hard way
|
|
from random import random, seed
|
|
import numpy as np
|
|
|
|
def covariance(x, y, n):
|
|
sum = 0.0
|
|
mean_x = np.mean(x)
|
|
mean_y = np.mean(y)
|
|
for i in range(0, n):
|
|
sum += (x[(i)]-mean_x)*(y[i]-mean_y)
|
|
return sum/n
|
|
|
|
n = 10
|
|
|
|
x = np.random.normal(size=n)
|
|
y = np.random.normal(size=n)
|
|
z = x*x*x+y*y +0.5*np.random.normal(size=n)
|
|
covxx = covariance(x,x,n)
|
|
covxy = covariance(x,y,n)
|
|
covxz = covariance(x,z,n)
|
|
covyy = covariance(y,y,n)
|
|
covyz = covariance(y,z,n)
|
|
covzz = covariance(z,z,n)
|
|
|
|
SigmaCov = np.array([ [covxx, covxy, covxz], [covxy, covyy, covyz], [covxz, covyz, covzz]])
|
|
print(SigmaCov)
|
|
|
|
EigValues, EigVectors = np.linalg.eig(SigmaCov)
|
|
# sort eigenvectors and eigenvalues
|
|
permute = EigValues.argsort()
|
|
EigValues = EigValues[permute]
|
|
EigVectors = EigVectors[:,permute]
|
|
print(EigValues)
|
|
print(EigVectors)
|