NumPy linspace rounding error

Question

Could someone explain this rounding issue with numpy.linspace?

import numpy as np

np.linspace(0, 1, 6) == np.around( np.linspace(0, 1, 6), 10 )
# array([ True,  True,  True, False,  True,  True], dtype=bool)

Here's how I arrived here...

import numpy as np

## Two ways of defining the same thing
A = np.array([ 0., 0.2, 0.4, 0.6, 0.8, 1. ])
B = np.linspace(0, 1, 6)

## A and B appear to be the same
A # array([ 0., 0.2, 0.4, 0.6, 0.8, 1. ])
B # array([ 0., 0.2, 0.4, 0.6, 0.8, 1. ])


## They're not
A == B # array([ True, True, True, False, True, True], dtype=bool)
A - B  # array([ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, -1.11022302e-16, 0.00000000e+00, 0.00000000e+00])


## Gotta round to get my expected result
C = np.round( np.linspace( 0, 1, 6 ), 10 )
C      # array([ 0., 0.2, 0.4, 0.6, 0.8, 1. ])
A == C # array([ True, True, True, True, True, True], dtype=bool)

The way I defined B seems innocent enough . . . is this rounding issue something that can bite us all over the place?

Answer 1

It's not pretty, but its the way floating point is, you are going to have to learn to live with it. This is where your weird result comes from:

>>> a = np.float(1)
>>> a /= 5
>>> a
0.2
>>> a*3
0.6000000000000001

You have np.allclose to help you deal with this kind of stuff, but if you are not disciplined about floating point comparisons then yes, it will bite you over and over again.