#' Return apportioned vector according to Dean's Method - allows for zeros
#'
#' @param x A named vector.
#' @param n Number of apportioned units to sum to
#' @param k The incrementing interval used to search for divisors
#' @return A named vector of length \code{x} containing apportioned integers summing to \code{n}.
#' @examples
#' majs <- c(100, 154, 0, 22, 5)
#' names(majs) <- c("English", "History", "Swahili", "French", "Aeronautics")
#' dean0(majs,10)
#' @section References:
#' http://www.maa.org/publications/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-deans-method-of-apportionment
#' @section Further details:
#' Method suggested in 1920s by James Dean, professsor of astronomy and mathematics at Dartmouth and University of Vermont.
#' @export
dean0 <- function(x, n=100, k=1){
divisor <- (sum(x)/n)
seats <- dean2(x, divisor)
if(sum(seats)==n) {return(seats)}
if(sum(seats) != n) {
#set up vector of possible divisors
myd1 <- rev(seq(0,divisor, by=k))
myd2 <- seq(divisor, divisor+(length(myd1)*k), by=k)
#account for potential of unequal vector sizes prior to rbind
shortest <- min(length(myd1), length(myd2))
myd2 <- head(myd2, shortest)
myd1 <- head(myd1, shortest)
mydivisors <- c(rbind(myd1, myd2))
#find divisor
j<-1
while(TRUE) {
if(j == length(mydivisors))
stop("have not found an appropriate divisor - try adjusting 'k'")
tmp <- dean2(x, mydivisors[j])
if(sum(tmp) == n)
break
j = j + 1
}
res <- dean2(x, mydivisors[j])
return(res)
}
}
harmon1 = function(x){2 / ( (1/x[1]) + (1/x[2]) )}
dean2<-function(x,divi){
quotas <- x / divi
lwqt <- floor(quotas)
upqt <- ceiling(quotas)
harmons <- apply(cbind(lwqt, upqt), 1, harmon1)
seats <- ifelse(quotas > harmons, upqt, lwqt)
return(seats)
}
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