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#' Forms the labelled candidate set of treatments
#'
#' This function forms the candidate set of treatments from the factors' levels,
#' adds labels, with optional spherical transformation of the coordinates.
#' @param Levels Levels of each factor.
#' @param K Number of factors.
#' @param Hypercube Indicates if the experimental region is a hypercube ('TRUE') or spherical ('FALSE').
#' @return Matrix of candidate set of treatments, with treatment labels contained in the first column.
#' @export
#' @examples
#'
#' # Candidate treatment set for five 3-level factors
#'
#' K<-5; Levels <- rep(list(1:3),K);
#' candidate_trt_set(Levels, K)
candidate_trt_set <- function(Levels, K, Hypercube = TRUE)
{
cand <- as.matrix(expand.grid(Levels))
candl <- cbind(label(cand, Levels, K), cand) # creating a column of treatment labels
cand.trt <- cbind(candl[,1], apply(as.matrix(candl[,-1]), 2, Transform)) # rescaling the factors' values to [-1, 1]
if (!Hypercube) {cand.trt<-as.matrix(spheric(cand.trt, K))} # spheric coords
return (cand.trt)
}
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