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#' Generalized log transform data.
#'
#' \code{generalized_log} transforms specified observation variables using \eqn{x = log( (x + sqrt(x ^ 2 + offset ^ 2 )) / 2 )}.
#'
#' @param population tbl with grouping (metadata) and observation variables.
#' @param variables character vector specifying observation variables.
#' @param offset optional offset parameter for the transformation.
#'
#' @return transformed data of the same class as \code{population}.
#'
#' @examples
#' population <- tibble::tibble(
#' Metadata_Well = c("A01", "A02", "B01", "B02"),
#' Intensity_DNA = c(8, 20, 12, 32)
#' )
#' variables <- c("Intensity_DNA")
#' generalized_log(population, variables)
#' @importFrom magrittr %>%
#' @importFrom magrittr %<>%
#' @importFrom rlang :=
#' @export
generalized_log <- function(population, variables, offset = 1) {
offset <- rlang::enquo(offset)
for (variable in variables) {
x <- rlang::sym(variable)
population %<>%
dplyr::mutate(!!x :=
log(((!!x) + ((!!x)^2 + (!!offset)^2)^0.5) / 2))
}
population
}
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