R/BIB.R

Defines functions BIB

Documented in BIB

#' Balanced Incomplete binary Blocks Designs
#'
#' Gives the configuration of a Balanced Incomplete binary Blocks
#' Designs (BIBD) using a projective geometry on a Galois Field of order 2 GF(2).
#'
#' @usage BIB(m)
#' @param m Dimension of the projective geometry defined on GF(2)
#' @return A LIST of:
#' \enumerate{
#'  \item \code{V }{Number of treatments in the BIBD.}
#'  \item \code{B }{Number of blocks of the BIBD.}
#'  \item \code{R }{Repetition of each treatment.}
#'  \item \code{K }{Size of each block.}
#'  \item \code{BIB }{The configuration of the BIBD.}
#' }
#' @author Mohamed Laib, Abla Boudraa and Zebida Gheribi-Aoulmi
#' @references D. Dugué Traité de statistique théorique et appliquée, Masson et Cie, 1958.
#' @examples
#'
#' m<-4
#' X<-BIB(m)   #BIB from PG(4,2)
#'
#' @export
BIB <-function(m){
  p=2
  lin<-(p^(m+1))
  coll<-m+1
  prg<-matrix(nrow=lin, ncol=coll)
  for (j in 1:coll ) {prg[,j]<-c(rep(0,lin/(p^j)),rep(1,lin/(p^j)))}
  prg<-prg[-1,]
  t<-dim(prg)[1]
  f<-dim(prg)[2]
  fill<-function(i,mat) {x<-c();m<-c();w<-which(mat[i,]==1)
for (j in 1:t) {
for (k in w) {x<-c(x,prg[j,k])}
if (sum(x)%%2==0) {m<-c(m,j)}
x<-c()}
m}
  k<-(t-1)/2;bie<-matrix(nrow=t, ncol=k)
  for (i in 1:t) {bie[i,]<-fill(i,prg)}
  v <- sort(unique(as.vector(bie)))
  V<-length(v)
  T<-bie[1,1]
  R<-length(which(T==bie))
  B<-dim(bie)[1]
  K<-dim(bie)[2]
return(list(V=V,B=B,R=R,K=K,BIB=bie))}

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PGM2 documentation built on May 29, 2017, 11:56 a.m.