gen_rand_zonotope.R

#' Generator function for zonotopes
#'
#' This function generates a random \eqn{d}-dimensional zonotope defined by the Minkowski sum of \eqn{m} \eqn{d}-dimensional segments.
#' The function considers \eqn{m} random directions in \eqn{R^d}. There are three strategies to pick the length of each segment: a) it is uniformly sampled from \eqn{[0,100]}, b) it is random from \eqn{\mathcal{N}(50,(50/3)^2)} truncated to \eqn{[0,100]}, c) it is random from \eqn{Exp(1/30)} truncated to \eqn{[0,100]}.
#'
#' @param dimension The dimension of the zonotope.
#' @param nsegments The number of segments that generate the zonotope.
#' @param generator A list that could contain two elements.
#' \describe{
#' \item{distribution}{The distribution to pick the length of each segment from \eqn{[0,100]}: (i) 'uniform', (ii) 'gaussian' or (iii) 'exponential', the default value is 'uniform.}
#' \item{seed}{Optional. A fixed seed for the number generator.}
#' }
#'
#' @return A polytope class representing a zonotope.
#'
#' @examples
#' # generate a 10-dimensional zonotope defined by the Minkowski sum of 20 segments
#' P = gen_rand_zonotope(10, 20)
#' @export
gen_rand_zonotope <- function(dimension, nsegments, generator = list('distribution' = 'uniform')) {

  seed = NULL
  if (!is.null(generator$seed)) {
    seed = generator$seed
  }

  if (is.null(generator$distribution)) {
    kind_gen = 1
  } else if (generator$distribution == 'gaussian') {
    kind_gen = 2
  } else if (generator$distribution == 'exponential') {
    kind_gen = 3
  } else if (generator$distribution == 'uniform'){
    kind_gen = 1
  } else {
    stop("Wrong generator!")
  }

  Mat = poly_gen(kind_gen, FALSE, TRUE, dimension, nsegments, seed)

  # first column is the vector b
  b = Mat[, 1]
  Mat = Mat[, -c(1), drop = FALSE]

  P = Zonotope(G = Mat)

  return(P)
}