svd_homework.py

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

# 1. Generate 100 points x uniformly distributed between 0 and 1, and let y = 2+3x+ζ,
#    where ζ is a Gaussian random variable with a standard deviation of 0.5. Use an
#    SVD to fit y = a + bx to this data set, finding a and b.

import numpy as np

# x is uniformly distributed
x = np.random.random(100)

for i in x:
  # zeta is gaussian with sd = 0.5
  zeta = np.random.normal(0, 0.5)
  y = 2 + 3*x + zeta

array = np.array([y])

U,s,V = np.linalg.svd(array)
#
print("U:")
print(U.shape)
print(U)
print("s: ")
print(s.shape)
print(s)
print("V: ")
print(V.shape)
print(V)

pinv_svd = np.dot(np.dot(V.T,np.linalg.inv(np.diag(s))),U.T)

# ValueError: matrices are not aligned