# [R] Fast R implementation of Gini mean difference

Andrew C. Ward s195404 at student.uq.edu.au
Thu Apr 24 06:23:51 CEST 2003

```Thank you to Deepayan Sarkar and Berwin Turlach for reminding me of
the outer() function. A quick comparison shows outer() to be more than
10 times faster than the nested for() loop. The memory does blow out a
bit (ran out of memory with a vector of 10000 elements), but it would
be rare for me to calculate a mean difference for that many. Thanks
again!

Regards,

Andrew C. Ward

CAPE Centre
Department of Chemical Engineering
The University of Queensland
Brisbane Qld 4072 Australia
andreww at cheque.uq.edu.au

Quoting Deepayan Sarkar <deepayan at stat.wisc.edu>:

>
> You can avoid the for loops with outer, but that will use more
> memory.
>
> gmd <-
>    function(x, w) 0.5 * sqrt(pi) * sum(w * abs(outer(x, x, "-")))
> /
>        ((length(x)-1)*sum(w))
>
>
> On Wednesday 23 April 2003 10:17 pm, Andrew C. Ward wrote:
> > I have written the following function to calculate the weighted
> mean
> > difference for univariate data (see
> > http://www.xycoon.com/gini_mean_difference.htm for a related
> > formula). Unsurprisingly, the function is slow (compared to sd or
> > for long vectors. I wonder if there's a way to make the function
> > faster, short of creating an external C function. Thanks very
> much
> >
> >
> > gmd <- function(x, w) { # x=data vector, w=weights vector
> >    n <- length(x)
> >    tmp <- 0
> >    for (i in 1:n) {
> >       for (j in 1:n) {
> >          tmp <- tmp + w[i]*abs(x[i]-x[j])
> >       }
> >    }
> >    retval <- 0.5*sqrt(pi)*tmp/((n-1)*sum(w))
> > }
> >
> > gmd(rnorm(100))
> >
> >
> >
> > Regards,
> >
> > Andrew C. Ward
> >
> > CAPE Centre
> > Department of Chemical Engineering
> > The University of Queensland
> > Brisbane Qld 4072 Australia
> > andreww at cheque.uq.edu.au
> >
> > ______________________________________________
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> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>
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>

```