Error Function Erf(z)

Question

This could be a quick one.

I have not been able to find a function for the mathematical "error function" or the "inverse error function" in R. I have not seen a package either.

I am aware I can script this but I thought someone must have made a package for its various approximations by now. Could be poor Googling due to generic terms "error function" ...

Answer 1

These are very closely related to pnorm() and qnorm(): see the last 4 lines of the example code in ?pnorm:

 ## if you want the so-called 'error function'
 erf <- function(x) 2 * pnorm(x * sqrt(2)) - 1
 ## (see Abramowitz and Stegun 29.2.29)
 ## and the so-called 'complementary error function'
 erfc <- function(x) 2 * pnorm(x * sqrt(2), lower = FALSE)
 ## and the inverses
 erfinv <- function (x) qnorm((1 + x)/2)/sqrt(2)
 erfcinv <- function (x) qnorm(x/2, lower = FALSE)/sqrt(2)

If you want to use complex-valued arguments, you need erfz from the pracma package (as commented above by @eipi10). Otherwise, it's not clear whether there's an advantage to using the versions in pracma (the implementations of pnorm() and qnorm() have been very thoroughly tested over a wide range of parameter values ...)

As far as searching goes,

library("sos")
findFn("erf")

seems to work pretty well ...