Python Numpy array equality failure

Question

Why does this fail? I create an array, create a new variable with that array minus a value from within the array, and then compare the array to a value that appears to be in the array. So why does the equality test fail?

import numpy as np
import platform
print platform.python_version()
print np.__version__ 
x = np.arange( -1,1,0.1 )
new_x = x - x[5]
print new_x
print new_x == -0.2

outputs:

2.7.9
1.9.2
[-0.5 -0.4 -0.3 -0.2 -0.1  0.  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.   1.1  1.2  1.3  1.4]
[False False False False False False False False False False False False False False False False False False False False]

EDIT: Using np.round() causes the comparison to behave as expected; the question now is, why am I being presented with rounded numbers when I print the array? In my experience python will usually print scientific notation or just a bunch of decimal places when the numbers are not exact.

Shockingly, I have been programming in python scientifically for 6 years and never seen this! It feels like a noob question but I really don't understand why what's printed is rounded.

I just tested, and np.linspace() behaves the same way. I am assuming this is a precision thing but it would be nice to know exactly why it's happening. — Brian Hayden
– Brian Hayden, Commented Jul 5, 2015 at 0:52
I don't know the answer as to why, but it seems due to floating point precision. — Scott
– Scott, Commented Jul 5, 2015 at 0:56
It looks like by default, numpy will round to 8 digits when printing: docs.scipy.org/doc/numpy/reference/generated/… — Brian Hayden
– Brian Hayden, Commented Jul 5, 2015 at 1:07
stackoverflow.com/questions/5595425/… has some usefule ideas... particularly np.isclose(x[12], 0.2, rtol=1e-05, atol=1e-08, equal_nan=False) a bit of overkill for two numbers but useful otherwise Scott ... do a search using "Floating point representation" to find out why with examples — user1121588
– user1121588, Commented Jul 5, 2015 at 1:19

Community · Accepted Answer · 2017-05-23 11:51:14Z

3

As you suspect, the strange behavior is due to small precision errors that occur during the floating point calculations. To see the differences, you can convert the floats into a hexadecimal form using float.hex():

>>> new_x[3].hex()
'-0x1.9999999999998p-3'
>>> (-0.2).hex()
'-0x1.999999999999ap-3'

Notice that they are, in fact, two different floating point numbers. The "rounding" only occurs while printing, and is in fact something that Python itself does by default. The basic idea is that there are two forms of string representations for Python objects (including floats): str and repr. Whereas repr should return an "authentic", reproducible string representation, str should optimize for human-readability - and part of that includes "rounding", to hide small precision errors. Notice:

>>> repr(new_x[3])
'-0.19999999999999996'
>>> repr(-0.2)
'-0.2'

For floats, you can simulate an equality check using numpy.isclose(), like so:

>>> print numpy.isclose(new_x, -0.2)
[False False False  True False False False False False False False False
 False False False False False False False False]

edited May 23, 2017 at 11:51

CommunityBot

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answered Jul 5, 2015 at 1:27

voithos

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2 Comments

Scott Over a year ago

When calling repr(new_x) each value within the numpy array is rounded. Seems inconsistent. Any idea why this was chosen over an array where each value is the full repr value?

voithos Over a year ago

@Scott: Hmm, that is odd. Unfortunately, I don't know why this is the case. You can always submit a ticket about it.

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