peakwindow {cardidates}

Identify Peaks in Time Series

Description

This function identifies peaks in time series and helps to identify the time window of the first maximum according to given rules.

Usage

peakwindow(x, y = NULL, xstart = 0, xmax = max(x), minpeak = 0.1, mincut = 0.382)

Arguments

x, y

the x (in day of year) and y coordinates of a set of points. Alternatively, a single argument x can be provided.

xstart

x value (e.g. time of ice-out) before the maximum value of the searched peak (this is a “weak” limit),

xmax

maximum of the end of the searched peak (this is a “hard” maximum,

minpeak

minimum value of the total maximum which is regarded as peak,

mincut

minimum relative height of a pit compared to the lower of the two neighbouring maxima at which these maxima are regarded as separate peaks (default value is derived from golden section).

Details

This is a heuristic peak detection algorithm. It can be used for two related purposes, (i) to identify all relevant peaks within a time-series and (ii) to identify the time window which belongs to one single peak (smd = specified mass development, e.g. spring maximum in phytoplankton time series).

Value

A list with the following elements:

peaks

a data frame with the characteristics (index, xleft, x, xright and y) of all identified peaks,

data

the original data set (x, y),

smd.max.index

index of the maximum value of the “specified” peak,

smd.max.x

x-value of the maximum of the “specified” peak,

smd.indices

indices (data window) of all data belonging to the “specified” peak,

smd.x

x-values (time window) of all data belonging to the “specified” peak,

smd.y

corresponding y-values of all data belonging to the “specified” peak,

peakid

vector with peak-id-numbers for all data.

See Also

weibull4, weibull6, fitweibull, CDW plot.cardiPeakwindow cardidates

Examples

## generate test data with 3 peaks
set.seed(123)
x <- seq(0, 360, length = 20)
y <- abs(rnorm(20, mean = 1, sd = 0.1))
y[5:10] <- c(2, 4, 7, 3, 4, 2)
y <- c(y, 0.8 * y, 1.2 * y)
x <- seq(0, 360, along = y)
y[6] <- y[7]   # test case with 2 neighbouring equal points

## plot the test data
plot(x, y, type="b")

## identify the "spring mass development"
peaks <- peakwindow(x, y)
ind <- peaks$smd.indices
lines(x[ind], y[ind], col="red", lwd=2)

## now fit the cardinal dates
fit <- fitweibull6(peaks$smd.x, peaks$smd.y)
CDW(fit)
plot(fit)

## some more options ...
peaks <- peakwindow(x, y, xstart=150, mincut = 0.455)
ind <- peaks$smd.indices
lines(x[ind], y[ind], col = "blue")
points(x, y, col = peaks$peakid +1, pch = 16) # all peaks

## work with indices only
peaks <- peakwindow(y)

## test case with disturbed sinus
x<- 1:100
y <- sin(x/5) +1.5 + rnorm(x, sd = 0.2)
peaks <- peakwindow(x, y)
plot(x, y, type = "l", ylim = c(0, 3))
points(x, y, col = peaks$peakid + 2, pch = 16)

## test case: only one peak
yy <- c(1:10, 11:1)
peakwindow(yy)

## error handling test case: no turnpoints
# yy <- rep(1, length(x))
# peakwindow(x, yy)