> > > geometric.mean1 <- function(x) prod(x)^(1/length(x))
> > > geometric.mean2 <- function(x) exp(mean(log(x)))
> > > geometric.mean1(c(-5,-4,4,5))
> > [1] 4.472136
> > > geometric.mean2(c(-5,-4,4,5))
> > [1] NaN
> > Warning message:
> > In log(x) : NaNs produced
> comp.x <- as.complex(c(-5,-4,4,5))
> geometric.mean2(comp.x)
> # [1] 0+4.472136i
Obviously, there's a discrepancy between the answer of geometric.mean1 and
geometric.mean2 with complex inputs. Having thought about it a little
more, I think the problem is with my solution.
The log of a complex number decomposes as log(z) = log(abs(z)) +1i*Arg(z).
When you sum the second components, you need to take the answer modulo
2*pi, since the phase angles wrap around.
Here's an alternative geometric mean function that takes that into
account.
geometric.mean3 <- function(x)
{
a <- mean(log(abs(x)))
b <- 1i/length(x)
c <- sum(Arg(x))%%(2*pi)
exp(a+b*c)
}
geometric.mean3(comp.x)
# [1] 4.472136+0i
Regards,
Richie.
Mathematical Sciences Unit
HSL
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