units: 's / m' and 's / m' are not convertible

To paraphrase from https://github.com/PlasmaPy/PlasmaPy/issues/587, exceptions like astropy.units.core.UnitConversionError: 's / m' and 's / m' are not convertible (and a few other cases with first, second and third powers of second over meter, curiously) started popping up in our travis tests as seen at https://travis-ci.org/PlasmaPy/PlasmaPy/jobs/466396211 .

For a brief overview, running python setup.py test -d and getting into plasmapy.physics.distribution.Maxwellian_1D:

(Pdb) distFunc
<Quantity 5.91632969e-07 s / m>
(Pdb) p u.s / u.m
Unit("s / m")
(Pdb) p distFunc
<Quantity 5.91632969e-07 s / m>
(Pdb) p distFunc.unit
Unit("s / m")
(Pdb) p distFunc.to(u.s / u.m)
*** astropy.units.core.UnitConversionError: 's / m' and 's / m' are not convertible

I’ve managed to figure out that this is localized to astropy 3.1. As suggested by @astrofrog on slack, I ran git bisect with pytest --doctest-modules $PLASMAPY/plasmapy/physics/distribution.py and I was able to identify the first bad commit as

3a478ca29e86144d6c5a0305dde86169a647ff63 is the first bad commit
commit 3a478ca29e86144d6c5a0305dde86169a647ff63
Author: Marten van Kerkwijk <[e-mail]>
Date:   Thu Jul 12 21:01:28 2018 -0700

    Further short-cuts for single-unit CompositeUnit initialization.

:040000 040000 1ba7cb9440215ab641197f91ef1623ad9bb39378 5c02db4ede9146ec12f84f57a0382f4900777544 M      astropy

I’m currently trying to find out the exact cause of this bug in that commit, but I figured it’s best to submit this issue here before I accidentally close this tab or something.

[mhvk]

OK, here is an astropy-only version (proving it is purely an astropy bug):

import astropy.units as u
v2 = 1*u.m**2/u.s**2
(v2 ** (-1/2)).to(u.s/u.m)
# UnitConversionError: 's / m' and 's / m' are not convertible

[StanczakDominik]

I think I’ve got something. At the end of the problematic Maxwellian_1D function, we have a return distFunc.to(u.s / u.m). In what follows, unit is the unit of distFunc and other is u.s / u.m:

(plasmapy-tests) 18:07:23 dominik: ~/Code/PlasmaPy/PlasmaPy $ pytest --doctest-modules --pdb plasmapy/physics/distribution.py  
=========================================================================== test session starts ============================================================================
platform linux -- Python 3.7.0, pytest-4.0.1, py-1.7.0, pluggy-0.8.0
rootdir: /home/dominik/Code/PlasmaPy/PlasmaPy, inifile: setup.cfg
plugins: remotedata-0.3.1, openfiles-0.3.1, doctestplus-0.2.0, arraydiff-0.2
collected 8 items                                                                                                                                                          

plasmapy/physics/distribution.py F
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> traceback >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
098         \equiv \frac{1}{\sqrt{\pi v_{Th}^2}} e^{-(v - v_{drift})^2 / v_{Th}^2}
099 
100     where :math:`v_{Th} = \sqrt{2 k_B T / m}` is the thermal speed
101 
102     Examples
103     --------
104     >>> from plasmapy.physics import Maxwellian_1D
105     >>> from astropy import units as u
106     >>> v=1*u.m/u.s
107     >>> Maxwellian_1D(v=v, T=30000 * u.K, particle='e', v_drift=0 * u.m / u.s)
UNEXPECTED EXCEPTION: UnitConversionError("'s / m' and 's / m' are not convertible")
Traceback (most recent call last):

  File "/home/dominik/.miniconda3/envs/plasmapy-tests/lib/python3.7/doctest.py", line 1329, in __run
    compileflags, 1), test.globs)

  File "<doctest plasmapy.physics.distribution.Maxwellian_1D[3]>", line 1, in <module>

  File "/home/dominik/Code/PlasmaPy/PlasmaPy/plasmapy/physics/distribution.py", line 142, in Maxwellian_1D
    return distFunc.to(u.s / u.m)

  File "/home/dominik/Code/astropy/astropy/units/quantity.py", line 669, in to
    return self._new_view(self._to_value(unit, equivalencies), unit)

  File "/home/dominik/Code/astropy/astropy/units/quantity.py", line 641, in _to_value
    equivalencies=equivalencies)

  File "/home/dominik/Code/astropy/astropy/units/core.py", line 984, in to
    return self._get_converter(other, equivalencies=equivalencies)(value)

  File "/home/dominik/Code/astropy/astropy/units/core.py", line 915, in _get_converter
    raise exc

  File "/home/dominik/Code/astropy/astropy/units/core.py", line 901, in _get_converter
    self, other, self._normalize_equivalencies(equivalencies))

  File "/home/dominik/Code/astropy/astropy/units/core.py", line 885, in _apply_equivalencies
    unit_str, other_str))

astropy.units.core.UnitConversionError: 's / m' and 's / m' are not convertible

/home/dominik/Code/PlasmaPy/PlasmaPy/plasmapy/physics/distribution.py:107: UnexpectedException
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> entering PDB >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> /home/dominik/Code/astropy/astropy/units/core.py(885)_apply_equivalencies()
-> unit_str, other_str))
(Pdb) p vars(unit)
{'_bases': [Unit("m"), Unit("s")], '_powers': [-1.0, 1.0], '_scale': 1.0, '_decomposed_cache': Unit("s / m")}
(Pdb) p vars(other)
{'_scale': 1.0, '_bases': [Unit("s"), Unit("m")], '_powers': [1, -1], '_decomposed_cache': Unit("s / m")}

So I think this has something to do with that the fact that _powers are floats in one case and ints in another. It may also have to do with the fact that _bases don’t have the same ordering and thus you can’t simply (as I assume this does somewhere… haven’t been able to track it down) cast powers to a common numeric type and check if they agree. They have to be sorted with the same ordering that sorts _bases first.