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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

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.
```
Marco
```