[R] Beyond double-precision?

[Berwin A Turlach]

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

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Berwin A Turlach                            Tel.: +65 6515 4416 (secr)
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