QuiRk in numpy - All normalized elements get assigned to 0 in QR decomposition using reflectors

Question

All the normalized elements in the array get set to 0.

I am attempting to create a reflector for an array. When I normalize all the elements in the array by the first element (x[1:] /= x[0], x[0] = 1) in Python, I just get all zeros and a 1 in the first element.

import numpy as np
#project x via householder
u = np.array([9,4,1,3,1])
x = np.array([3,4,1,3,1])

for i in range(1,len(u)):
  u[i] /= u[0]
u[0] = 1

The result should look like this (u = [1, 4/9, 1/9, 3/9, 1/9])

Answer 1

When we define a numpy array, we are able to define it's type by specifying dtype in np.array.

import numpy as np
#project x via householder
u = np.array([9,4,1,3,1], dtype = np.float64)

for i in range(1,len(u)):
  u[i] /= u[0]
u[0] = 1
print(u)

gives us

[1.         0.44444444 0.11111111 0.33333333 0.11111111]