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#' @title FA2
#' @author Camille Dezecache, Hong T. T. Phan, Emilie Poisson-Caillault
#' @description Estimates the FA2 of two univariate signals Y (imputed values) and X (true values).
#' @details
#' This function returns the value of FA2 of two vectors corresponding to univariate signals X (true values) and Y (imputed values).
#' This FA2 corresponds to the percentage of pairs of values (\eqn{x_{i}, y_{i}}) satisfying the condition \eqn{0,5 <= (Y_{i}/X_{i}) <= 2}.
#' The closer FA2 is to 1, the more accurate is the imputation model.
#' Both vectors Y and X must be of equal length, on the contrary an error will be displayed.
#' In both input vectors, eventual 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
#' @examples
#' data(dataDTWBI)
#' X <- dataDTWBI[, 1] ; Y <- dataDTWBI[, 2]
#' compute.fa2(Y,X)
#' compute.fa2(Y,X, verbose = TRUE)
#'
#' # By definition, if pairs of true and imputed values are zero,
#' # FA2 corresponding to this pair of values equals 1.
#' X[1] <- 0
#' Y[1] <- 0
#' compute.fa2(Y,X)
compute.fa2<-function(Y, X,verbose=F){
Xtemp <- X
Ytemp <- Y
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 = ""))}
Xtemp <- X[which(!is.na(X)&!is.na(Y))] # Removing NA
Ytemp <- Y[which(!is.na(X)&!is.na(Y))] # Removing NA
id0XY <- which(X==0&Y==0) # Identify pairs of XY values equal to 0
Xtemp[id0XY] <- 1
Ytemp[id0XY] <- 1
ratio <- (Ytemp/Xtemp)
fraction <- ratio[ratio>=0.5 & ratio<=2]
FA2 <- length(fraction)/length(ratio)
if (verbose){
if(FA2>0.8) {print("good model")
}else{print("important number of different points")}
}
out<-FA2
return(out)
}
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