[FIXED] How come using np.linalg.norm introduces unseen numerical inequality but writing it out does not?

Issue

Let's say I have these two variables:

import numpy as np
a = np.array([[ 0,  1, 10,  2,  5]])

b = np.array([[ 0,  1, 18, 15,  5],
              [13,  9, 23,  3, 22],
              [ 2, 10, 17,  4,  8]])

Method 1

m1 = -np.linalg.norm(a[:, np.newaxis, :] - b[np.newaxis, :, :], axis=-1) ** 2 / 2

Method 2

m2 = -np.sum(np.square(a[:, np.newaxis, :] - b[np.newaxis, :, :]), axis=-1) / 2

Both of these outputs look alike (at least according to print()):

array([[-116.5, -346. ,  -73.5]])

But

>>> np.array_equal(m1, m2)
False

What makes it interesting is that defining a literal to check equality leads to:

>>> sanity_check = np.array([[-116.5, -346. ,  -73.5]])
>>> np.array_equal(sanity_check, m1)
False
>>> np.array_equal(sanity_check, m2)
True

How come using the method with np.linalg.norm is the odd one out? If m1 is unequal, how come its print() looks equal?

Solution

There is a tiny amount of numerical error in the actual values:

>>> m1.tolist()
[[-116.49999999999999, -346.0, -73.5]]

>>> m2.tolist()
[[-116.5, -346.0, -73.5]]

This is because:

>>> np.sqrt(8**2 + 13**2)**2
232.99999999999997

>>> 8**2 + 13**2
233

---

NumPy's printoptions controls how many digits are printed. By default, they are:

>>> np.get_printoptions()
{'edgeitems': 3, 'threshold': 1000, 'floatmode': 'maxprec', 'precision': 3, 'suppress': False, 'linewidth': 75, 'nanstr': 'nan', 'infstr': 'inf', 'sign': '-', 'formatter': None, 'legacy': False}

Answered By - Mateen Ulhaq