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 exampl

Answer 1

Finding local maxima and minima for a not so easy sequence e.g. 1 0 1 1 2 0 1 1 0 1 1 1 0 1 I would give their positions at (1), 5, 7.5, 11 and (14) for maxima and 2, 6, 9, 13 for minima.

#Position                1 1 1 1 1
#      1 2 3 4 5 6 7 8 9 0 1 2 3 4
x <- c(1,0,1,1,2,0,1,1,0,1,1,1,0,1) #Frequency
#      p v     p v  p  v   p   v p  p..Peak, v..Valey

peakPosition <- function(x, inclBorders=TRUE) {
  if(inclBorders) {y <- c(min(x), x, min(x))
  } else {y <- c(x[1], x)}
  y <- data.frame(x=sign(diff(y)), i=1:(length(y)-1))
  y <- y[y$x!=0,]
  idx <- diff(y$x)<0
  (y$i[c(idx,F)] + y$i[c(F,idx)] - 1)/2
}

#Find Peaks
peakPosition(x)
#1.0  5.0  7.5 11.0 14.0

#Find Valeys
peakPosition(-x)
#2  6  9 13

peakPosition(c(1,2,3,2,1,1,2,1)) #3 7