On Tuesday, November 4, 2014 9:58:54 PM UTC+1, 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 ? 
>
> I think its the way we treat tolerance which changed, so no real problem 
hidden here .

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 ! 
>
> Sure putting exact values as the centered ones is the best way to go. 

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