# R/FSD.R In FSMUMI: Imputation of Time Series Based on Fuzzy Logic

#### Documented in compute.fsd

```#' @title Fraction of Standard Deviation (FSD)
#' @author Thi-Thu-Hong Phan, Andre Bigand, Emilie Poisson-Caillault
#' @description Compute the Fraction of Standard Deviation (FSD) of two univariate signals Y (imputed values) and X (true values).
#' @details
#' This function returns the FSD value between two univariate signals.
#' FSD value approaches zero means that a better performance method for the imputation task.
#' Y and X must have the same length, conversely an error will be appeared.
#' In both input vectors, NA will be exluded with a warning diplayed.
#' @param Y vector of imputed values
#' @param X vector of true values
#' @param verbose if TRUE, print advice about the quality of the model
#' @importFrom stats sd
#' @examples
#' data(dataFSMUMI)
#' X <- dataFSMUMI[, 1] ; Y <- dataFSMUMI[, 2]
#' compute.fsd(Y,X)
#' compute.fsd(Y,X, verbose = TRUE)
#'
#' # By definition, if true and imputed values are equal and constant,
#' # FSD = 0.
#' X <- rep(runif(1), 10)
#' Y <- X
#' compute.fsd(Y,X)
#'
#' # However, if true and imputed values are constant but different,
#' # FSD is not calculable. An error is displayed.
#' \dontrun{
#' X <- rep(runif(1), 10);Y <- rep(runif(1), 10)
#' compute.fsd(Y,X)}

compute.fsd <- function(Y, X, verbose=F){

if(length(Y)!=length(X)){stop("Input vectors are of different length !!!")}

lengthNAX <- sum(is.na(X)) # Number of NA values
if(lengthNAX > 0){warning(paste("Vector of true values contains ", lengthNAX, " NA !!! NA excluded", sep = ""))}
lengthNAY <- sum(is.na(Y)) # Number of NA values
if(lengthNAY > 0){warning(paste("Vector of imputed values contains ", lengthNAY, " NA !!! NA excluded", sep = ""))}

sd1=sd(Y, na.rm = T)
sd2=sd(X, na.rm = T)

if(sd1==sd2){
if(mean(X, na.rm = T)==mean(Y, na.rm = T)){
warning("Vectors of true and imputed values are constant and equal !!! By definition FSD=0")
FS <- 0
if(verbose){print("acceptable model")}
}
else{
stop("Impossible to compute FSD: vectors of true and imputed values are constant but different !!!")
}
out <- FS
return(out)
}
else{
FS <- 2*abs((sd1-sd2)/(sd1+sd2))
if(verbose){
if(abs(FS)<0.5) {print("acceptable model");
}else{print("non acceptable FS");}
}
out <- FS
return(out)
}
}
```

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FSMUMI documentation built on May 2, 2019, 12:40 p.m.