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## ==============================================================================
## author :Ghislain Vieilledent, Jeanne Clément
## email :ghislain.vieilledent@cirad.fr, jeanne.clement16@laposte.net
## web :https://ecology.ghislainv.fr
## license :GPLv3
## ==============================================================================
#'@name logit
#'@aliases logit
#'@title Generalized logit function
#'@description Compute generalized logit function.
#' @param x value(s) to be transformed
#' @param min Lower end of logit interval
#' @param max Upper end of logit interval
#' @details The generalized logit function takes values on \eqn{[min, max]} and transforms them to span \eqn{[ -\infty, +\infty ]}{[-Inf,+Inf]} it is defined as:
#' \deqn{y = log(\frac{p}{(1-p)})}{y = log(p/(1-p))}
#' \deqn{where}
#'\deqn{p=\frac{(x-min)}{(max-min)}}{p=(x-min)/(max-min)}
#' @return y Transformed value(s).
#'@author{Gregory R. Warnes <greg@warnes.net>}
#' @examples x <- seq(0,10, by=0.25)
#' xt <- jSDM::logit(x, min=0, max=10)
#' cbind(x,xt)
#' y <- jSDM::inv_logit(xt, min=0, max=10)
#' cbind(x,xt,y)
#' @keywords math logistic logit
#' @export
logit <- function(x, min=0, max=1)
{
p <- (x-min)/(max-min)
log(p/(1-p))
}
#'@name inv_logit
#'@aliases inv_logit
#'@title Generalized inverse logit function
#'@description Compute generalized inverse logit function.
#' @param x value(s) to be transformed
#' @param min Lower end of logit interval
#' @param max Upper end of logit interval
#' @details The generalized inverse logit function takes values on [-Inf,Inf] and transforms them to span [min, max] :
#' \deqn{y = p' (max-min) + min}{y = p * (max-min) + min}
#' \deqn{where}
#'\deqn{p =\frac{exp(x)}{(1+exp(x))}}{p =exp(x)/(1+exp(x))}
#' @return y Transformed value(s).
#'@author{Gregory R. Warnes <greg@warnes.net>}
#' @examples x <- seq(0,10, by=0.25)
#' xt <- jSDM::logit(x, min=0, max=10)
#' cbind(x,xt)
#' y <- jSDM::inv_logit(xt, min=0, max=10)
#' cbind(x,xt,y)
#' @keywords math logistic logit
#' @export
inv_logit <- function(x, min=0, max=1)
{
p <- exp(x)/(1+exp(x))
p <- ifelse( is.na(p) & !is.na(x), 1, p ) # fix problems with +Inf
p * (max-min) + min
}
# End
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