# An algorithm to find local extrema in a vector

May 3, 2009
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I spend some time looking for an algorithm to find local extrema in a vector (time series). The solution I used is to “walk” through the vector by step larger than 1, in order to retain only one value even when the values are very noisy (see the picture at the end of the post).

It goes like this :

```findpeaks <- function(vec,bw=1,x.coo=c(1:length(vec)))
{
pos.x.max <- NULL
pos.y.max <- NULL
pos.x.min <- NULL
pos.y.min <- NULL 	for(i in 1:(length(vec)-1)) 	{ 		if((i+1+bw)>length(vec)){
sup.stop <- length(vec)}else{sup.stop <- i+1+bw
}
if((i-bw)<1){inf.stop <- 1}else{inf.stop <- i-bw}
subset.sup <- vec[(i+1):sup.stop]
subset.inf <- vec[inf.stop:(i-1)]

is.max   <- sum(subset.inf > vec[i]) == 0
is.nomin <- sum(subset.sup > vec[i]) == 0

no.max   <- sum(subset.inf > vec[i]) == length(subset.inf)
no.nomin <- sum(subset.sup > vec[i]) == length(subset.sup)

if(is.max & is.nomin){
pos.x.max <- c(pos.x.max,x.coo[i])
pos.y.max <- c(pos.y.max,vec[i])
}
if(no.max & no.nomin){
pos.x.min <- c(pos.x.min,x.coo[i])
pos.y.min <- c(pos.y.min,vec[i])
}
}
return(list(pos.x.max,pos.y.max,pos.x.min,pos.y.min))
}```

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