# `kcuts` cuts variable `x` into `centers` categories with k-means.
kcuts <- function(x, centers)
{
  km <- kmeans(x = x, centers = centers)
  cuts <- unlist(lapply(order(km$centers), function(clustId) {
    min(x[km$cluster == clustId]) }))
  cuts <- c(cuts, max(x))
}

# ventilate modality `mod` of categorical var `cat` of dataframe `dat`
# into the remaining modalities according to their relative frequencies.
ventilate <- function(cat, mod)
{
  if (mod == "NA") isna <- TRUE else isna <- FALSE
  tab <- table(cat)
  if (isna)
  {
    sup_i <- which(is.na(cat))
    sup_n <- length(sup_i)
    act_mod <- tab
  }
  else
  {
    sup_i <- which(cat == mod)
    sup_n <- tab[mod]
    act_mod <- tab[! names(tab) %in% mod]
  }
  prob <- act_mod / sum(act_mod)
  smpl <- sample(names(prob), size = sup_n, replace = TRUE, prob = prob)
  r <- list(sup_mod = mod,
            sup_n = sup_n,
            sup_i = sup_i,
            smpl = smpl)
  return(r)
}