# Leibniz's notation for computing the curvic length on Asymptotic Model
#
# Leibniz's notation for computing the curvic length on Asymptotic Model
#
# expression : sqrt(1+(-((R0 - Asym) * (exp(-exp(lrc) * input) *
# exp(lrc))))^2)
#
# @param input numeric vector of data values
# @param parms numeric vector, parameters with given names: "Asym", "lrc",
# "R0"
# @seealso \code{\link{SSasymp}}
# @references Jose Pinheiro and Douglas Bates
# @keywords math
# @examples
#
# x <- seq(0.1,1,length=20)
# parms <- c(Asym = 0.1, lrc = 0.2, R0 = 0.3)
# integrate(function(x) { dsdx_asymp(input = x, parms = parms ) }, lower = 0,
# upper = 0.5)
#
#' @importFrom stats integrate
dsdx_asymp <- function(input, parms) {
.value <-
sqrt(1 + (-((parms["R0"] - parms["Asym"]) * (
exp(-exp(parms["lrc"]) * input) * exp(parms["lrc"])
))) ^ 2)
.value
}
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