It could. But in this case looking at the 1e-15 tolerance I think that
we are just hitting numerical noise because the specification for double
doesn't insure that those last decimals are exact. And even if it
was for a single computation we could be hit by rounding error if there is
a number of computations involved. I think on a number of those the people
who wrote the test were too decimal happy without looking at whether or
not the last ones made any sense in the first place.
The last batch is probably triggered by the ATLAS update to 3.10.2.
In sage-on-gentoo I use openblas and it causes one other doctest to
fail at ~1e-18 level
sage -t --long /usr/share/sage/src/sage/matrix/matrix_double_dense.pyx
**********************************************************************
File "/usr/share/sage/src/sage/matrix/matrix_double_dense.pyx", line 1856, in
sage.matrix.matrix_double_dense.Matrix_double_dense.solve_left
Failed example:
x = A.solve_left(b); x.zero_at(1e-18) # fix noisy zeroes
Expected:
(0.666666666..., 0.0, 0.333333333...)
Got:
(0.6666666666666666, 7.50150692314295e-18, 0.3333333333333332)
**********************************************************************
That test looks if something is 0 up to 1e-18 and I have a result smaller
than 1e-17. Where do you put the bar? And the difference here is in blas
implementation.
At that kind of tolerance, unless you have algorithm that use gmp/mpfr/mpc
and are geared towards high accuracy you see nothing. It is mainly looking
at decimals that are already numerical noise as if they were actually
correct.
Francois
On Tue, 04 Nov 2014 21:58:53 Thierry wrote:
> Hi,
>
> all those numerical noise appearing suddenly, couldn't that mean that
> some numerical algorithm became less stable/accurate somewhere in the
> code ?
>
> If it turns out to be the case, we should thank doctests for the
> discovery, not asking them to shut up by enlarging the tolerance !
>
> Also, in the case where the error is just "going the other way", we
> should not enlarge the tolerence, but instead have an exact expected
> result in the doctest. For example, (see #17291):
>
> On Tue, Nov 04, 2014 at 05:15:29PM +0000, John Cremona wrote:
> > File "src/sage/tests/french_book/linsolve_doctest.py", line 51, in
> > sage.tests.french_book.linsolve_doctest
> >
> > Failed example:
> > x = A\b; x # rel tol 1e-15
> >
> > Expected:
> > (-0.20000000000000018, 0.9000000000000001)
> >
> > Got:
> > (-0.19999999999999987, 0.8999999999999999)
> >
> > Tolerance exceeded in 1 of 2:
> > -0.20000000000000018 vs -0.19999999999999987, tolerance 2e-15 >
> > 1e-15
>
> We should expect (-0.2, 0.9) with the previous tolerance instead of
> enlarging the tolerance (therefore weakening the doctest) with an
> inexact expected result, since the errors are of the same magnitude but
> not the same direction.
>
> The same holds for, for example (see #17278):
>
> On 04/11/2014 14:16, John Cremona wrote:> It's a long time since I have
>
> > File "src/sage/matrix/matrix_double_dense.pyx", line 87, in
> > sage.matrix.matrix_double_dense.
> > Matrix_double_dense
> >
> > Failed example:
> > m^(-1)
> >
> > Expected:
> > [-1.9999999999999996 0.9999999999999998]
> > [ 1.4999999999999998 -0.4999999999999999]
> >
> > Got:
> > [-2.0 1.0]
> > [ 1.5 -0.5]
>
> Enlagring the tolerance for catching the correct result instead of
> taking this correct result as the centered expectation looks like an odd
> fix !
>
> Ciao,
> Thierry
>
> On Tue, Nov 04, 2014 at 05:15:29PM +0000, John Cremona wrote:
> > On 4 November 2014 15:42, Volker Braun <[email protected]> wrote:
> > > Do you get any failures with #17278?
> >
> > 2 pass, 1 still fails:
> >
> > File "src/sage/tests/french_book/linsolve_doctest.py", line 51, in
> > sage.tests.french_book.linsolve_doctest
> >
> > Failed example:
> > x = A\b; x # rel tol 1e-15
> >
> > Expected:
> > (-0.20000000000000018, 0.9000000000000001)
> >
> > Got:
> > (-0.19999999999999987, 0.8999999999999999)
> >
> > Tolerance exceeded in 1 of 2:
> > -0.20000000000000018 vs -0.19999999999999987, tolerance 2e-15 > 1e-15
> >
> > John
> >
> > > On Tuesday, November 4, 2014 1:58:34 PM UTC, Jean-Pierre Flori wrote:
> > >> On Tuesday, November 4, 2014 2:16:43 PM UTC+1, John Cremona wrote:
> > >>> It's a long time since I have done a "make ptestlong" and not had
> > >>> several test failures. I have done "make distclean" first and have
> > >>> pulled the latest develop branch (commit
> > >>> 8b95db32005c62e289d6698e8233218d5fda0f60) but see this:
> > >>>
> > >>> sage -t --long src/sage/matrix/matrix_double_dense.pyx # 1 doctest
> > >>> failed
> > >>> sage -t --long src/sage/tests/french_book/linsolve_doctest.py # 1
> > >>> doctest failed
> > >>> sage -t --long src/sage/matrix/matrix_real_double_dense.pyx # 1
> > >>> doctest
> > >>> failed
> > >>> sage -t --long src/sage/crypto/mq/sr.py # Timed out
> > >>>
> > >>> where I think the first three are the usual suspects (for me). The
> > >>> last one was ok on a retry. The others are
> > >>>
> > >>> File "src/sage/matrix/matrix_double_dense.pyx", line 87, in
> > >>> sage.matrix.matrix_double_dense.
> > >>> Matrix_double_dense
> > >>>
> > >>> Failed example:
> > >>> m^(-1)
> > >>>
> > >>> Expected:
> > >>> [-1.9999999999999996 0.9999999999999998]
> > >>> [ 1.4999999999999998 -0.4999999999999999]
> > >>>
> > >>> Got:
> > >>> [-2.0 1.0]
> > >>> [ 1.5 -0.5]
> > >>>
> > >>> File "src/sage/tests/french_book/linsolve_doctest.py", line 51, in
> > >>> sage.tests.french_book.li
> > >>> nsolve_doctest
> > >>>
> > >>> Failed example:
> > >>> x = A\b; x # rel tol 1e-15
> > >>>
> > >>> Expected:
> > >>> (-0.20000000000000018, 0.9000000000000001)
> > >>>
> > >>> Got:
> > >>> (-0.19999999999999987, 0.8999999999999999)
> > >>>
> > >>> Tolerance exceeded in 1 of 2:
> > >>> -0.20000000000000018 vs -0.19999999999999987, tolerance 2e-15 >
> > >>> 1e-15
> > >>>
> > >>> File "src/sage/matrix/matrix_real_double_dense.pyx", line 61, in
> > >>> sage.matrix.matrix_real_dou
> > >>> ble_dense.Matrix_real_double_dense
> > >>>
> > >>> Failed example:
> > >>> n = m^(-1); n
> > >>>
> > >>> Expected:
> > >>> [-1.9999999999999996 0.9999999999999998]
> > >>> [ 1.4999999999999998 -0.4999999999999999]
> > >>>
> > >>> Got:
> > >>> [-2.0 1.0]
> > >>> [ 1.5 -0.5]
> > >>>
> > >>> which I am sure have been mentioned before, but I also thought they
> > >>> had been fixed?
> > >>
> > >> Were this specific ones mentonied?
> > >> I know some were fixed in #17063, some in #17126, some in #17238 ...
> > >> And with all of these merged, everything was fine with 6.4..rc0, but
> > >> now I
> > >> get new failing ones with 6.4.rc1 :)
> > >
> > > --
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