R devel - Sep 2021 - Question about quantile fuzz and GPL license

On 9/14/21 9:22 AM, Abel AOUN wrote:
> Hello,
> 
> I'm currently working on Python numpy package to develop linear
interpolation methods for quantiles.
> Currently, numpy only support the type 7 of Hyndman & Fan and I did the
implementation for the 8 other methods to do as much as R ::quantile.
> 
> As you may guess, I was inspired by R implementation as well as other
sources, which lead to my questions:
> 
> About fuzz (see first reference below for the source code),
> fuzz <- 4 * .Machine $ double.eps
> I think I understand why the machine epsilon is used to correct some edge
cases where the float comparisons would fail.
> However I don't get why epsilon is multiplied by 4 instead of simply
using epsilon.
> Is there someone who can explain this 4 ?
No, but doing a bit of archaeology

https://github.com/wch/r-source/blame/trunk/src/library/stats/R/quantile.R

   give the commit message for these lines as "add (modified) version of 
quantile.default from Rob Hyndman (17 years ago)".  This commit was made 
by Brian Ripley.

   However, the code from Rob Hyndman here:

https://stat.ethz.ch/pipermail/r-devel/2004-July/030204.html

   does **not** have the lines with the fuzz.  So my guess would be that 
Brian Ripley is the author of that particular bit of code.

   I can't say, myself, what the logic behind 4 * .Machine$double.eps is ...

> 
> About licence,
> Numpy is under license BSD and R is on GPL.
> The only thing I really cherry picked and rewrote for numpy is the fuzz
part.
> I'm quite new to open source development. We are wondering if doing
this breaks the license GPL and if I can credit the original authors.
> Plus, I'm not quite sure this is the right place to ask this, if not,
sorry for the noise.
> The relevant discussion on numpy PR is here: [
https://github.com/numpy/numpy/pull/19857#discussion_r706019184 |
https://github.com/numpy/numpy/pull/19857#discussion_r706019184 ]
> 
> 
> Thank you for your time.
> 
> Regards,
> Abel Aoun
> 
> 
> References:
> The source code for R::quantile (fuzz is at line 82) [
https://github.com/wch/r-source/blob/79298c499218846d14500255efd622b5021c10ec/src/library/stats/R/quantile.R
|
https://github.com/wch/r-source/blob/79298c499218846d14500255efd622b5021c10ec/src/library/stats/R/quantile.R
] [ https://github.com/numpy/numpy/pull/19857 ]
> R doc for quantile : [
https://www.rdocumentation.org/packages/stats/versions/3.5.0/topics/quantile |
https://www.rdocumentation.org/packages/stats/versions/3.5.0/topics/quantile ]
> The ongoing PR on numpy: [ https://github.com/numpy/numpy/pull/19857 |
https://github.com/numpy/numpy/pull/19857 ]
> 
> 
> 
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> 
> ______________________________________________
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> https://stat.ethz.ch/mailman/listinfo/r-devel
> 
-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
Graduate chair, Mathematics & Statistics

On 9/14/21 9:22 AM, Abel AOUN wrote:
> However I don't get why epsilon is multiplied by 4 instead of simply
using epsilon.
> Is there someone who can explain this 4 ?
.Machine$double.eps is the "precision" of floating point values for
values close to 1.0 (between 0.5 and 2.0).

Using fuzz = .Machine$double.eps would have no effect if nppm is greater than or
equal to 2.
Using fuzz = 4 * .Machine$double.eps can fix rounding errors for nppm < 8;
for greater nppm, it has no effect.

Indeed:
2 + .Machine$double.eps == 2
8+ 4*.Machine$double.eps == 8

Since nppm is approximatively equal to the quantile multiplied by the sample
size, it can be much greater than 2 or 8.

Maybe the rounding errors are only problematic for small nppm; or only that case
is taken in account.

Moreover, if rounding errors are cumulative, they can be much greater than the
precision of the floating point value. I do not know how this constant was
chosen and what the use-cases were.

--
Sincerely
Andre GILLIBERT


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