Finding local maxima and minima in R - r

Question

I'm trying to create a function to find a "maxima" and "minima". I have the following data:
y
157
144
80
106
124
46
207
188
190
208
143
170
162
178
155
163
162
149
135
160
149
147
133
146
126
120
151
74
122
145
160
155
173
126
172
93
I have tried this function to find "maxima"
localMaxima <- function(x) {
# Use -Inf instead if x is numeric (non-integer)
y <- diff(c(-.Machine$integer.max, x)) > 0L
rle(y)$lengths
y <- cumsum(rle(y)$lengths)
y <- y[seq.int(1L, length(y), 2L)]
if (x[[1]] == x[[2]]) {
y <- y[-1]
}
y
}
maks <- localMaxima(x)
And funtion to find "minima"
localMinima <- function(x) {
# Use -Inf instead if x is numeric (non-integer)
y <- diff(c(.Machine$integer.max, x)) > 0L
rle(y)$lengths
y <- cumsum(rle(y)$lengths)
y <- y[seq.int(1L, length(y), 2L)]
if (x[[1]] == x[[2]]) {
y <- y[-1]
}
y
}
mins <- localMinima(x)
And the result is not 100% right
maks = 1 5 7 10 12 14 16 20 24 27 31 33 35
mins = 3 6 8 11 13 15 19 23 26 28 32 34 36
The result should
maks = 5 7 10 12 14 16 20 24 27 31 33 35
mins = 3 6 8 11 13 15 19 23 26 28 32 34
Finding local maxima and minima in R comes close, but doesn't quite fit.
How can I fix this?
Thanks you very much

Answer 1

You could define two functions like the below which produce the vectors you need:
library(data.table)
#shift lags or leads a vector by a certain amount defined as the second argument
#the default is to lag a vector.
#The rationale behind the below code is that each local minimum's adjucent
#values will be greater than itself. The opposite is true for a local
#maximum. I think this is what you are trying to achieve and one way to do
#it is the following code
maximums <- function(x) which(x - shift(x, 1) > 0 & x - shift(x, 1, type='lead') > 0)
minimums <- function(x) which(x - shift(x, 1) < 0 & x - shift(x, 1, type='lead') < 0)
Output:
> maximums(y)
[1] 5 7 10 12 14 16 20 24 27 31 33 35
> minimums(y)
[1] 3 6 8 11 13 15 19 23 26 28 32 34

Answer 2

this is a function i wrote a while back (and it's more general than you need). it finds peaks in sequential data x, where i define a peak as a local maxima with m points either side of it having lower value than it (so bigger m leads to more stringent criteria for peak finding):
find_peaks <- function (x, m = 3){
shape <- diff(sign(diff(x, na.pad = FALSE)))
pks <- sapply(which(shape < 0), FUN = function(i){
z <- i - m + 1
z <- ifelse(z > 0, z, 1)
w <- i + m + 1
w <- ifelse(w < length(x), w, length(x))
if(all(x[c(z : i, (i + 2) : w)] <= x[i + 1])) return(i + 1) else return(numeric(0))
})
pks <- unlist(pks)
pks
}
so for your case m = 1:
find_peaks(x, m = 1)
#[1] 5 7 10 12 14 16 20 24 27 31 33 35
and for the minima:
find_peaks(-x, m = 1)
#[1] 3 6 8 11 13 15 19 23 26 28 32 34