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#' Circular Averaging based on Vector Averaging
#'
#' \code{circular.averaging} calculates the average direction (0 - 360) given a
#' vector of directions.\cr\cr \code{vector.averaging} calculates the average
#' distance and direction given a vector of directions and a vector of
#' distances.
#'
#' functions return NA if the average distance or direction is not valid...
#' e.g., when averaging directions of 0 & 180 degrees, the result could
#' theoretically be 90 or 270 but is practically neither.
#'
#' @param direction a vector of directions given in degrees (0 - 360) if
#' \code{deg}==TRUE or in radians if \code{deg}==FALSE
#' @param distance a vector of distances associated with each direction
#' @param deg a boolean object defining if \code{direction} is in degrees
#' (TRUE) or radians (FALSE)
#' @return \code{circular.averaging} returns the average direction while
#' \code{vector.averaging} returns a list with 2 elements distance & direction
#' @author Jeremy VanDerWal \email{jjvanderwal@@gmail.com} & Lorena Falconi
#' \email{lorefalconi@@gmail.com}
#' @examples
#'
#' #EXAMPLE circular.averaging
#' circular.averaging(c(0,90,180,270)) #result is NA
#' circular.averaging(c(70,82,96,110,119,259))
#'
#' #EXAMPLE vector.averaging
#' vector.averaging(c(10,20,70,78,108), distance=10)
#' vector.averaging(c(159,220,258,273,310),distance=runif(5))
#'
#' @export
circular.averaging = function(direction,deg=TRUE) {
n=length(direction) #get the length of direction vector
out = vector.averaging(direction=direction,distance=rep(1,n),deg=deg)
return(out$direction)
}
#' @rdname circular.averaging
#' @export
vector.averaging = function(direction,distance,deg=TRUE) {
if (deg) direction = direction*pi/180 #convert to radians
n=length(direction) #get the length of direction vector
if (any(is.na(direction))) { #ensure no NA data
warning('NAs in data'); pos = which(is.na(direction)); direction = direction[-pos]; distance = distance[-pos]
} else {
sinr <- sum(sin(direction))
cosr <- sum(cos(direction))
if (sqrt((sinr^2 + cosr^2))/n > .Machine$double.eps) {
Ve = sum(distance*sin(direction))/n
Vn = sum(distance*cos(direction))/n
UV = sqrt(Ve^2 + Vn^2)
AV1 = atan(Ve/Vn)
AV2 = atan2(sinr, cosr)
#perform some checks and correct when output in wrong quadrant
AV = NULL
if (abs(AV1-AV2) <= .Machine$double.eps) { #if both methods of determining directions are reporting the same values
if (AV1>0) AV = AV1
if (AV1<0) AV = 2 * pi + AV1
} else { #case when they are different values... add necessary values of pi
if (AV1>0) AV = AV1 + pi
if (AV1<0) AV = AV2
}
if (is.null(AV)) {
return(list(distance=NA,direction=NA))
} else {
if (deg) AV = AV * 180 / pi #convert back to degrees
return(list(distance=UV,direction=AV))
}
} else {
return(list(distance=NA,direction=NA))
}
}
}
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