# File name: FindARS.txt
# Find the change points (shift to area restricted search)
# x = a trip data file (e.g. TID###.RData) with latitude
#     and longitude as the 2nd and 3rd columns and the 
#     date/time as the first column. 
# thresh = the window for finding local max/min
# Algorithm based on 
#    Knell, A. (2011) Identifying Behavioural Changes in
#        Movement Path Data. Unpublished doctoral dissertation,
#        Department of Mathematical Sciences, University of Essex.
#    Knell A, Codling E (2012) Classifying area-restricted
#        search (ARS) using a partial sum approach. 
#        Theoretical Ecology 5: 325-339.
# 
FindARS <- function(x, thresh=900){
    # Missing values for distance indicate a time gap
    # in the original data (missing seconds of data).
    # Replace missing values with distance/time (seconds) to
    # provide an estimate of the speed over the gap.
    miss <- which(is.na(x$Dist))
    if (length(miss)>0){
		require(geosphere)
        distH <- distHaversine(x[miss,3:2], x[miss-1, 3:2])
        distT <- difftime(x[miss,1], x[miss-1, 1])
        x$Dist[miss] <- distH/as.numeric(distT)
    }
    # Cumulative sum of centered data (C-tau)
    ZDist <- cumsum(scale(x$Dist, scale=FALSE))
    # count increases until threshhold is reached
	count <- 1
	# idx stores index of candidate Max/Min
    idx <- 1
	# ZOpt stores current candidate for Max/Min
    ZOpt <- ZDist[1]
	# opttbl is a data.frame containing the results
    opttbl <- data.frame()
    # Are we looking for a min or a max at the start?
    if (ZDist[1] < median(ZDist[2:120])) {
        sg <- "Max"
    } else {sg <- "Min"
    }
    # Use sg to switch between Max/Min
    i <- 1
    while (i < length(ZDist)) {
        i <- i + 1
		# Is next value greater (Max) or less (Min)
        if(sg=="Min"){
            test <- (ZOpt > ZDist[i])
        } else {
            test <- (ZOpt < ZDist[i])
        }
		# If so, replace ZOpt
        if (test) {
            ZOpt <- ZDist[i]
            idx <- i
            count <- 1
		# if not, continue
        } else {
            count <- count + 1
        }
		# if threshhold reached, copy current Max/Min
		# and set i back to idx so that we start from the
		# last Max/Min
        if (count > thresh) {
            count <- 0
            opttbl <- rbind(opttbl, data.frame(idx, ZOpt, sg))
            i <- idx
            if (sg=="Min") {
                sg <- "Max"
            } else {
                sg <- "Min"
            }
        }
    }
	# Once at the end of the array, add the current Max/Min
	# and return the data.table
    return(rbind(opttbl, data.frame(idx, ZOpt, sg)))
}