[SciPy-Dev] Slight change in lstsq accuracy for 0.17 - expected?

[Charles R Harris]

On Wed, Mar 16, 2016 at 6:05 PM, Matthew Brett <matthew.brett at gmail.com>
wrote:

> Hi,
>
> On Sun, Mar 13, 2016 at 3:43 AM, Ralf Gommers <ralf.gommers at gmail.com>
> wrote:
> >
> >
> > On Sat, Mar 12, 2016 at 6:16 AM, Matthew Brett <matthew.brett at gmail.com>
> > wrote:
> >>
> >> Hi,
> >>
> >> I just noticed that our (neuroimaging) test suite fails for scipy
> 0.17.0:
> >>
> >> https://travis-ci.org/matthew-brett/nipy/jobs/115471563
> >>
> >> This turns out to be due to small changes in the result of
> >> `scipy.linalg.lstsq` between 0.16.1 and 0.17.0 - on the same platform
> >> - the travis Ubuntu in this case.
> >>
> >> Is that expected?   I haven't investigated deeply, but I believe the
> >> 0.16.1 result (back into the depths of time) is slightly more
> >> accurate.  Is that possible?
> >
> >
> > That's very well possible, because we changed the underlying LAPACK
> routine
> > that's used:
> >
> https://github.com/scipy/scipy/blob/master/doc/release/0.17.0-notes.rst#scipy-linalg-improvements
> .
> > This PR also had some lstsq precision issues, so could be useful:
> > https://github.com/scipy/scipy/pull/5550
> >
> > What is the accuracy difference in your case?
>
> Damn - I thought you might ask me that!
>
> The test where it showed up comes from some calculations on a simple
> regression problem.
>
> The regression model is $y = X B + e$, with ordinary least squares fit
> given by $B = X^+ y$ where $X^+$ is the pseudoinverse of matrix X.
>
> For my particular X, $\Sigma e^2$ (SSE) is smaller using scipy 0.16
> pinv, compared to scipy 0.17 pinv:
>
> # SSE using high-precision sympy pinv
> 72.0232781366615313
> # SSE using scipy 0.16 pinv
> 72.0232781366625261
> # SSE using scipy 0.17 pinv
> 72.0232781390480170
>

That difference looks pretty big, looks almost like a cutoff effect. What
is the matrix X, in particular, what is its condition number or singular
values? Might also be interesting to see residuals for the different
functions.

<snip>

Chuck
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