[R] Beyond double-precision?

[spencerg]

Dear Berwin:  Thanks for the elegant correction.  Spencer
Berwin A Turlach wrote:
> 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)
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>
>