R/signed_log.R

In MyKo101/mutils: Various utility functions to make data processing smoother

#' @name signed_log
#'
#' @title
#' Calculates the signed log of a value
#'
#' @description
#' The signed logarithm allows a pseudo-logarithmic re-scaling to
#' be performed on data that is both positive and negativeis. It defined as:
#'
#' \deqn{ \textrm{signed_log}_b(x) = \textrm{sign}(x)\log_b(|x| + 1)}
#'
#'
#' @param x
#' a numeric vector.
#'
#' @param base
#' a positive number
#'
#' @export
#'
#' @examples
#' x <- seq(-10, 10, 0.01)
#' y <- signed_log(x)
#'
#' plot(x, y, type = "l")
#'
#' x0 <- unsigned_log(y)
#'
#' plot(y, x0, type = "l")
#'
#' plot(x, x0, type = "l")
signed_log <- function(x, base = exp(1)) {
  if (is.complex(x) || is.complex(base)) {
    stop("unimplemented for complex numbers")
  }
  log(abs(x) + 1, base = base) * sign(x)
}

#' @rdname signed_log
#' @export

unsigned_log <- function(x, base = exp(1)) {
  if (is.complex(x) || is.complex(base)) {
    stop("unimplemented for complex numbers")
  }
  sign(x) * (exp(log(base) * abs(x)) - 1)
}