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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" ...
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The property erf (−z) = −erf z means that the error function is an odd function.
An error function is defined by the integral. (1) and it occurs frequently in engineering problems; e.g., in heat conduction problems. The error function represents the area under the Gaussian function from t = 0 to t = x, so that erf ∞ = 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 ...
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