R help - Mar 2008 - rounding in calculation

dear all,

I report a problem very simple, that I does non know how to handle.

look at the following code:
> a = rep(16.256, 5)
> sum(a[1:5]^2) - (sum(a[1:5])^2/5)
[1] 2.273737e-13

as you can see i retrieve a non 0 value, when i am expected to. what can I
do?
> sessionInfo()
R version 2.6.2 (2008-02-08)
i386-pc-mingw32

locale:
LC_COLLATE=Italian_Italy.1252;LC_CTYPE=Italian_Italy.1252;LC_MONETARY=Italian_Italy.1252;LC_NUMERIC=C;LC_TIME=Italian_Italy.1252

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached):
[1] rcompgen_0.1-17

	[[alternative HTML version deleted]]

Read R FAQ 7.31 ?

http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

Gabor

On Fri, Mar 21, 2008 at 04:17:28PM +0100, John Lande
wrote:
> dear all,
> 
> I report a problem very simple, that I does non know how to handle.
> 
> look at the following code:
> 
> > a = rep(16.256, 5)
> > sum(a[1:5]^2) - (sum(a[1:5])^2/5)
> [1] 2.273737e-13
> 
> as you can see i retrieve a non 0 value, when i am expected to. what can I
> do?
> 
> > sessionInfo()
> R version 2.6.2 (2008-02-08)
> i386-pc-mingw32
> 
> locale:
>
LC_COLLATE=Italian_Italy.1252;LC_CTYPE=Italian_Italy.1252;LC_MONETARY=Italian_Italy.1252;LC_NUMERIC=C;LC_TIME=Italian_Italy.1252
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
> 
> loaded via a namespace (and not attached):
> [1] rcompgen_0.1-17
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-- 
Csardi Gabor <csardi at rmki.kfki.hu>    UNIL DGM

On Fri, 21 Mar 2008, John Lande wrote:
> dear all,
>
> I report a problem very simple, that I does non know how to handle.
>
> look at the following code:
>
>> a = rep(16.256, 5)
>> sum(a[1:5]^2) - (sum(a[1:5])^2/5)
> [1] 2.273737e-13
>
> as you can see i retrieve a non 0 value, when i am expected to. what can I
> do?
Use mean() when you want a mean:
> sum(a[1:5]^2) - 5*mean(a[1:5])^2
[1] 0

Your number is not exactly representable so some rounding error would be 
acceptable, but there are more accurate ways to do this, e.g.

sum((a-mean(a))^2)

or make use of var(), which is written by someone knowledgable about these 
things.
>
>> sessionInfo()
> R version 2.6.2 (2008-02-08)
> i386-pc-mingw32
>
> locale:
>
LC_COLLATE=Italian_Italy.1252;LC_CTYPE=Italian_Italy.1252;LC_MONETARY=Italian_Italy.1252;LC_NUMERIC=C;LC_TIME=Italian_Italy.1252
>
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
>
> loaded via a namespace (and not attached):
> [1] rcompgen_0.1-17
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595