Fisher's Z Transform

Fisher.Z <- function(x, inverse = FALSE)
{
    ## Purpose: Fisher's Z Transform (application to correlation confidence interval)
    ## Arguments:
    ##   x: a positive numeric vector
    ##   inverse: if TRUE, do the inverse transform. 
    ## Return: a transformed (or back-transformed) vector
    ## Author: Feiming Chen
    ## ________________________________________________

    if (inverse) {
        y <- tanh(x)
        ## equivalent to the following:
        ## e <- exp(2 * x)
        ## y <- (e - 1) / (e + 1)
    } else {
        y <- atanh(x)
        ## equivalent to the following:
        ## y <- 1/2 * log((1 + x) / (1 - x))
    }
    y
}
if (F) {                                # Unit Test
    Fisher.Z(0.8)                       # 1.0986
    Fisher.Z(1.2, inverse = TRUE)       # 0.83365

    x <- rbeta(10, 1, 1)                # simulate correlations
    Fisher.Z(x)
    Fisher.Z(x, inverse = TRUE)
    all.equal(x, Fisher.Z(Fisher.Z(x), inverse = TRUE)) # TRUE
}