erfInverse¶

Evaluates the real inverse error function $erf^{-1}(x)$ .

Synopsis¶

erfInverse (x)

Required Arguments¶

float x (Input): Point at which the inverse error function is to be evaluated. It must be between −1 and 1.

Return Value¶

The value of the inverse error function $erf^{-1}(x)$ .

Description¶

The inverse error function $erf^{-1}(x)$ is such that $x=erf(y)$ , where

$\mathrm{erf}(y) = \frac{2}{\sqrt{\pi}} \int_0^y e^{-t^2} dt$

The inverse error function is defined only for $-1<x<1$ .

Figure 9.10 — Plot of $erf^{-1}(x)$

Example¶

Evaluate the inverse error function at $x=1/2$ .

from __future__ import print_function
from numpy import *
from pyimsl.math.erfInverse import erfInverse

x = 0.5
ans = erfInverse(x)
print("Inverse erf(%f) = %f" % (x, ans))

Output¶

Inverse erf(0.500000) = 0.476936

Warning Errors¶

IMSL_LARGE_ABS_ARG_WARN The answer is less accurate than half precision because $|x|$ large.

Fatal Errors¶

IMSL_REAL_OUT_OF_RANGE The inverse error function is defined only for −1 < x < 1.