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#' Frobenius norm
#'
#' @aliases frobenius_norm
#'
#' @description
#' Computes the Frobenius norm.
#'
#' @usage
#' frobenius_norm(m)
#'
#' @param m Data matrix with the residuals. This matrix has
#' the same dimensions as the original data matrix.
#'
#' @details
#' Residuals are vectors. If there are p variables (columns),
#' for every observation there is a residual that there is
#' a p-dimensional vector. If there are n observations, the
#' residuals are an n times p matrix.
#'
#' @return
#' Real number.
#'
#' @author
#' Guillermo Vinue, Irene Epifanio
#'
#' @references
#' Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in
#' R, 2009. \emph{Journal of Statistical Software} \bold{30(8)}, 1-23,
#' \url{https://doi.org/10.18637/jss.v030.i08}
#'
#' Vinue, G., Epifanio, I., and Alemany, S.,Archetypoids: a new approach to
#' define representative archetypal data, 2015.
#' \emph{Computational Statistics and Data Analysis} \bold{87}, 102-115,
#' \url{https://doi.org/10.1016/j.csda.2015.01.018}
#'
#' Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017.
#' \emph{Journal of Statistical Software} \bold{77(6)}, 1-39,
#' \url{https://doi.org/10.18637/jss.v077.i06}
#
#' @examples
#' mat <- matrix(1:4, nrow = 2)
#' frobenius_norm(mat)
#'
#' @export
frobenius_norm <- function(m) {
return(sum(apply(m, 2, int_prod_mat)))
}
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