R/epsilon.R

In calculus: High Dimensional Numerical and Symbolic Calculus

#' Levi-Civita Symbol
#' 
#' Computes the Levi-Civita totally antisymmetric tensor.
#' 
#' @param n number of dimensions.
#' 
#' @return \code{array} representing the Levi-Civita symbol.
#' 
#' @examples 
#' ### Levi-Civita symbol in 2 dimensions
#' epsilon(2)
#' 
#' ### Levi-Civita symbol in 3 dimensions
#' epsilon(3)
#' 
#' @family tensor algebra
#' 
#' @references 
#' Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. \doi{10.18637/jss.v104.i05}
#' 
#' @export
#'
epsilon <- function(n){
  
  mu <- as.matrix(expand.grid(lapply(1:n, function(i) 1:n)))
  
  eps <- cpp_parity(x = mu, y = matrix(1:n, nrow = 1))
  
  return(array(eps, dim = rep(n,n)))
  
}