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

[Charles R Harris]

On Wed, Mar 16, 2016 at 6:41 PM, Charles R Harris <charlesr.harris at gmail.com
> wrote:

>
>
> 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>
>
>
Note that this might be an indication that the result of the calculation
has an intrinsically large error bar.

Chuck
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