r - Finding local maxima and minima

Question

I'm looking for a computationally efficient way to find local maxima/minima for a large list of numbers in R. Hopefully without for loops...

For example, if I have a datafile like 1 2 3 2 1 1 2 1, I want the function to return 3 and 7, which are the positions of the local maxima.

Answer 1

diff(diff(x)) (or diff(x,differences=2): thanks to @ZheyuanLi) essentially computes the discrete analogue of the second derivative, so should be negative at local maxima. The +1 below takes care of the fact that the result of diff is shorter than the input vector.

edit: added @Tommy's correction for cases where delta-x is not 1...

tt <- c(1,2,3,2,1, 1, 2, 1)
which(diff(sign(diff(tt)))==-2)+1

My suggestion above ( http://statweb.stanford.edu/~tibs/PPC/Rdist/ ) is intended for the case where the data are noisier.