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

From: Marco Caliari
Subject: Re: Study about accuracy of statistical software, incl. Octave
Date: Tue, 24 Mar 2009 19:46:32 +0100 (CET)
User-agent: Alpine 1.00 (DEB 882 2007-12-20)

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


whose exact mean is 10000000.2 and exact standard deviation 0.1.

Best regards,


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.


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