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## Re: Study about accuracy of statistical software, incl. Octave

 From: Jaroslav Hajek Subject: Re: Study about accuracy of statistical software, incl. Octave Date: Tue, 24 Mar 2009 20:28:41 +0100

```On Tue, Mar 24, 2009 at 7:46 PM, Marco Caliari <address@hidden> wrote:
> On Tue, 24 Mar 2009, Jaroslav Hajek wrote:
>
>> On Tue, Mar 24, 2009 at 7:03 PM, Marco Caliari <address@hidden>
>> wrote:
>>>>
>>>> And Marco Caliari writes:
>>>>>
>>>>> The other deficiencies are much harder to fix. I will give a look.
>>>>
>>>> std() could be fixed relatively easily by calling the BLAS's
>>>> routines (SNRM2, DNRM2, SCNRM2, DZNRM2) rather than relying on
>>>> sqrt (sumsq (...)).  The half drop in precision is a typical
>>>> failure mode for implementations that don't scale.  I suspect
>>>> that fixing std() may fix corrcoef and help anova.
>>>
>>> Dear Jason,
>>>
>>> I already tried with a .m implementation of dnrm2, without any
>>> improvement.
>>> For interested people, the sample vector is
>>>
>>> v=[10000000.2,repmat([10000000.1,10000000.3],1,500)];
>>>
>>> whose exact mean is 10000000.2 and exact standard deviation 0.1.
>>>
>>> Best regards,
>>>
>>> Marco
>>>
>>
>> What do you mean by "exact mean" here? I don't think any of the three
>> numbers are exactly representable in IEEE floating-point. It would be
>> better to choose numbers that have an exact representation, such as
>> 1e7 + 0.25, 1e7 + 0.5, 1.7 + 0.75 or such. Otherwise, you can't avoid
>> introducing errors just by writing these numbers.
>
> I agree with you, Jaroslav. On the other hand, in the paper it is written
> that R can compute the standard deviation with 15 correct digits.
> Actually, Octave can compute the mean with 14 correct digits and with 15
> correct digits with the patch I sent. The standard deviation with 8 correct
> digits.
>

But what is the correct answer? Just writing those numbers into Octave
introduces an error ~ 3e-17. I *don't* expect the "correct" answer is
1e7 + 0.2. You can't expect Octave to guess your actual numbers.

--
RNDr. Jaroslav Hajek
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz

```