Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Berwin A Turlach
> Sent: Saturday, May 09, 2009 10:18 AM
> To: spencerg
> Cc: r-help at r-project.org; joaks1
> Subject: Re: [R] Beyond double-precision?
>
> G'day all,
>
> On Sat, 09 May 2009 08:01:40 -0700
> spencerg <spencer.graves at prodsyse.com> wrote:
>
> > The harmonic mean is exp(mean(logs)). Therefore, log(harmonic
> > mean) = mean(logs).
> >
> > Does this make sense?
>
> I think you are talking here about the geometric mean and not the
> harmonic mean. :)
>
> The harmonic mean is a bit more complicated. If x_i are positive
> values, then the harmonic mean is
>
> H= n / (1/x_1 + 1/x_2 + ... + 1/x_n)
>
> so
>
> log(H) = log(n) - log( 1/x_1 + 1/x_2 + ... + 1/x_n)
>
> now log(1/x_i) = -log(x_i) so if log(x_i) is available, the logarithm
> of the individual terms are easily calculated. But we need to
> calculate the logarithm of a sum from the logarithms of the individual
> terms.
>
> At the C level R's API has the function logspace_add for such tasks, so
> it would be easy to do this at the C level. But one could also
> implement the equivalent of the C routine using R commands. The way to
> calculate log(x+y) from lx=log(x) and ly=log(y) according to
> logspace_add is:
>
> max(lx,ly) + log1p(exp(-abs(lx-ly)))
>
> So the following function may be helpful:
>
> logadd <- function(x){
> logspace_add <- function(lx, ly)
> max(lx, ly) + log1p(exp(-abs(lx-ly)))
>
> len_x <- length(x)
> if(len_x > 1){
> res <- logspace_add(x[1], x[2])
> if( len_x > 2 ){
> for(i in 3:len_x)
> res <- logspace_add(res, x[i])
> }
> }else{
> res <- x
> }
> res
> }
>
> R> set.seed(1)
> R> x <- runif(50)
> R> lx <- log(x)
> R> log(1/mean(1/x)) ## logarithm of harmonic mean
> [1] -1.600885
> R> log(length(x)) - logadd(-lx)
> [1] -1.600885
>
> Cheers,
>
> Berwin
>
> =========================== Full address =============================
> Berwin A Turlach Tel.: +65 6515 4416 (secr)
> Dept of Statistics and Applied Probability +65 6515 6650 (self)
> Faculty of Science FAX : +65 6872 3919
> National University of Singapore
> 6 Science Drive 2, Blk S16, Level 7 e-mail: statba at nus.edu.sg
> Singapore 117546 http://www.stat.nus.edu.sg/~statba
>
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