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#' Generate all incomplete rankings of k elements out of n complete elements
#'
#' This function generates all the possible incomplete rankings of
#' k elements out of n complete elements. E.g. c(1, 2, NA) is an
#' incomplete ranking out with 2 non-missing elements of 3 elements
#'
#' @param n number of complete elements
#' @param k number of non-missing elements in the incomplete ranking
#' @return a matrix each of whose column is a possible incomplete ranking
#' @export
#' @author Li Qinglong <liqinglong0830@@163.com>
#' @examples
#' incomplete.rankings(5, 3)
incomplete.rankings <- function(n, k)
{
if (n < k)
{
stop("n should be larger than k!")
}
output_mat = matrix(NA, ncol = factorial(n) / factorial(n - k), nrow = n)
u = t(generate.perms(k))
ind = generate.combs(n, k)
len = dim(u)[2]
head = 1
for (i in seq(dim(ind)[2]))
{
tail = head + len - 1
output_mat[ind[, i], head:tail] = u
head = tail + 1
}
return(output_mat)
}
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