erfc

Evaluates the real complementary error function erfc(x).

Synopsis

erfc (x)

Required Arguments

float x (Input)

Point at which the complementary error function is to be evaluated.

Return Value

The value of the complementary error function erfc(x).

Description

The complementary error function erfc(x) is defined to be

$$\mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2} dt$$

The argument x must not be so large that the result underflows. Approximately, x should be less than

$$\left[-\ln(\sqrt{\pi}s)\right]^{1/2}$$

where s is the smallest representable floating-point number.

Figure 9.9 — Plot of erfc(x)

Example

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

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

x = 0.5
ans = erfc(x)
print("erfc(%f) = %f" % (x, ans))

Output

erfc(0.500000) = 0.479500

Alert Errors

IMSL_LARGE_ARG_UNDERFLOW

The argument x is so large that the result underflows.