R/PaleyII.R

In HadamardR: Hadamard Matrix Generation

#' PaleyII
#'
#' This function create the Hadamard matrix by Paley method 2
#'
#' @param n integer(order of the matrix)
#' @return Hadamard matrix of order n
#' @export
#' @details
#' q=n/2-1, If there is an Hadamard matrix of order h>1, and q = 1 (mod 4) is a prime number,
#' then there exists an Hadamard matrix of order nh.
#'
#' @references
#' Paley, R.E.A.C. (1933). On Orthogonal matrices. J. Combin. Theory, A 57(1), 86-108.
#'
#' @examples
#' PaleyII(12)
#' #      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#'# [1,]    1    1    1    1    1    1    1   -1   -1    -1    -1    -1
#'# [2,]    1    1    1   -1   -1    1   -1    1   -1     1     1    -1
#'# [3,]    1    1    1    1   -1   -1   -1   -1    1    -1     1     1
#'# [4,]    1   -1    1    1    1   -1   -1    1   -1     1    -1     1
#'# [5,]    1   -1   -1    1    1    1   -1    1    1    -1     1    -1
#'# [6,]    1    1   -1   -1    1    1   -1   -1    1     1    -1     1
#'# [7,]    1   -1   -1   -1   -1   -1   -1   -1   -1    -1    -1    -1
#'# [8,]   -1    1   -1    1    1   -1   -1   -1   -1     1     1    -1
#'# [9,]   -1   -1    1   -1    1    1   -1   -1   -1    -1     1     1
#'#[10,]   -1    1   -1    1   -1    1   -1    1   -1    -1    -1     1
#'#[11,]   -1    1    1   -1    1   -1   -1    1    1    -1    -1    -1
#'#[12,]   -1   -1    1    1   -1    1   -1   -1    1     1    -1    -1
#' @examples
#' PaleyII(8)
#' #NULL


PaleyII<-function(n){
  q1<-method1_paleyII(n)
  if(q1!=0){
    h1<-ply1(q1)
    return(h1)
  }

  q2<-method2_paleyII(n)
  if(q2!=0){
    h2<-ply2(q2)
    return(h2)
  }else {
    return(NULL)
  }
}