# R/rhoOpt.R In ktaucenters: Robust Clustering Procedures

#### Documented in derpsiOptpsiOptrhoOpt

```  #' rhoOpt function
#'
#' An implementation of quasi optimal rho functions following reference [1]
#' @param x A real number.
#' @param cc a tunning constant.
#' @return rho(\code{x}/\code{c}\code{c})
#' @examples
#' val= rhoOpt(x=0.5,cc=1)
#' @references  [1] Salibian-Barrera, M., Willems, G., & Zamar, R. (2008).
#' The fast-tau estimator for regression. Journal of Computational and Graphical Statistics, 17(3), 659-682.
#' @export
#'
#'
#'
rhoOpt <- function(x, cc){
tmp <- x^2 / 2 / (3.25*cc^2)
tmp2 <- (1.792 - 0.972 * x^2 / cc^2 + 0.432 * x^4 / cc^4 - 0.052 * x^6 / cc^6 + 0.002 * x^8 / cc^8) / 3.25
tmp[abs(x) > 2*cc] <- tmp2[abs(x) > 2*cc]
tmp[abs(x) > 3*cc] <- 1
tmp
}

#' psiOpt
#' psi function  is the derivative of optimal rho function (see \code{\link{rhoOpt}})
#' @param x A real number.
#' @param cc a tunning constant.
#' @return rho''(\code{x}/ \code{c}\code{c})
#' @examples
#' psiOpt(x=0.5,cc=1)
#' @export
psiOpt <- function(x, cc){
tmp <- x / (3.25*cc^2)
tmp2 <- (-1.944 * x / cc^2 + 1.728 * x^3 / cc^4 - 0.312 * x^5 / cc^6 + 0.016 * x^7 / cc^8) / 3.25
tmp[abs(x) > 2*cc] <- tmp2[abs(x) > 2*cc]
tmp[abs(x) > 3*cc] <- 0
tmp
}

#' derpsiOpt
#' the derivative of the psi function  (see \code{\link{psiOpt}})
#'
#' @param x A real number.
#' @param cc a tunning constant.
#' @return rho'(\code{x} / \code{c}\code{c})
#' @examples
#' psiOpt(x=0.5,cc=1)
#'
#' @export
derpsiOpt<- function(x, cc){
tmp <- rep(1,length(x)) / (3.25*cc^2)
# derivative x^1
# tmp2 <- (-1.944 * x / cc^2 + 1.728 * x^3 / cc^4 - 0.312 * x^5 / cc^6 + 0.016 * x^7 / cc^8) / 3.25
# derivative of expresion above !!
## tmp2 <- (-1.944/ cc^2 + (3*1.728) * x^2 / cc^4 - (5*0.312) * x^4 / cc^6 + (7*0.016) * x^6 / cc^8) / 3.25
tmp2 <- (-1.944/ cc^2 + (5.184) * x^2 / cc^4 - (1.56) * x^4 / cc^6 + ( 0.112) * x^6 / cc^8) / 3.25
tmp[abs(x) > 2*cc] <- tmp2[abs(x) > 2*cc]
tmp[abs(x) > 3*cc] <- 0
tmp
}
```

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ktaucenters documentation built on Aug. 3, 2019, 9:03 a.m.