[Numpy-discussion] `allclose` vs `assert_allclose`

[Nathaniel Smith]

On Thu, Jul 17, 2014 at 9:07 PM,  <josef.pktd at gmail.com> wrote:
> On Wed, Jul 16, 2014 at 9:52 AM, Nathaniel Smith <njs at pobox.com> wrote:
>> What you say makes sense to me, and loosening the default tolerances won't
>> break any existing tests. (And I'm not too worried about people who were
>> counting on getting 1e-7 instead of 1e-5 or whatever... if it matters that
>> much to you exactly what tolerance you test, you should be setting the
>> tolerance explicitly!) I vote that unless someone comes up with some
>> terrible objection in the next few days then you should submit a PR :-)
>
> If you mean by this to add atol=1e-8 as default, then I'm against it.
>
> At least it will change the meaning of many of our tests in statsmodels.
>
> I'm using rtol to check for correct 1e-15 or 1e-30, which would be
> completely swamped if you change the default atol=0.
> Adding atol=0 to all assert_allclose that currently use only rtol is a lot
> of work.
> I think I almost never use a default rtol, but I often leave atol at the
> default = 0.
>
> If we have zeros, then I don't think it's too much work to decide whether
> this should be atol=1e-20, or 1e-8.

This is a compelling use-case, but there are also lots of compelling
usecases that want some non-zero atol (i.e., comparing stuff to 0).
Saying that allclose is for one of those use cases and assert_allclose
is for the other is... not a very felicitious API design, I think. So
we really should do *something*.

Are there really any cases where you want non-zero atol= that don't
involve comparing something against a 'desired' value of zero? It's a
little wacky, but I'm wondering if we ought to change the rule (for
all versions of allclose) to

if desired == 0:
    tol = atol
else:
    tol = rtol * desired

In particular, means that np.allclose(x, 1e-30) would reject x values
of 0 or 2e-30, but np.allclose(x, 0) will accept x == 1e-30 or 2e-30.

-n

-- 
Nathaniel J. Smith
Postdoctoral researcher - Informatics - University of Edinburgh
http://vorpus.org