R/randomBeta.R

In evolvability: Calculation of Evolvability Parameters

#' Generating selection gradients/vectors in random directions.
#'
#' \code{randomBeta} generates unit length vectors (selection gradients)
#' uniformly distributed in a k-dimensional hypersphere.
#'
#' @param n Number of selection gradients/vectors.
#' @param k Number of dimensions.
#' @details \code{randomBeta} exploits the spherical symmetry of a multidimensional
#' Gaussian density function. Each element of each vector is randomly sampled
#' from a univariate Gaussian distribution with zero mean and unit variance. The
#' vector is then divided by its norm to standardize it to unit length.
#' @return \code{randomBeta} returns a matrix where the vectors are stacked column
#' wise.
#' @author Geir H. Bolstad
#' @examples
#' # Two vectors of dimension 3:
#' randomBeta(n = 2, k = 3)
#' @importFrom stats rnorm
#' @export
randomBeta <- function(n = 1, k = 2) {
  X <- matrix(rnorm(n * k), ncol = n)
  X <- t(t(X) / sqrt(colSums(X^2)))
  rownames(X) <- paste("dim", 1:k, sep = "")
  X
}