#' @name matrix_k
#' @aliases matrix_k
#' @title k Matrix
#' @description Gives k matrix
#'
#' @param n Number of columns
#'
#' @return Matrix
#'
#' @author
#' \enumerate{
#' \item Muhammad Yaseen (\email{myaseen208@gmail.com})
#' }
#'
#' @references
#' Crossa, J., Perez-Elizalde, S., Jarquin, D., Cotes, J.M., Viele, K., Liu, G., and Cornelius, P.L. (2011)
#' Bayesian Estimation of the Additive Main Effects and Multiplicative Interaction Model
#' \emph{Crop Science}, \strong{51}, 1458–1469.
#' (\href{https://dl.sciencesocieties.org/publications/cs/abstracts/51/4/1458?access=0&view=pdf}{doi: 10.2135/cropsci2010.06.0343})
#'
#' @export
matrix_k <- function(n){
UseMethod("matrix_k")
}
#' @export
#' @rdname matrix_k
matrix_k.default <- function(n){
m <- matrix(0, nrow = (n-1), ncol = n)
long <- sqrt((n - (0:(n-2)) - 1) * (n - (0:(n-2))))
diag(m) <- (n - (0:(n-2)) - 1)
m[upper.tri(m)] <- -1
m / long[row(m)]
}
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