Is there an easily available implementation of erf() for Python?

Question

I can implement the error function, erf, myself, but I\'d prefer not to. Is there a python package with no external dependencies that contains an implementation of this func

Answer 1

A pure python implementation can be found in the mpmath module (http://code.google.com/p/mpmath/)

From the doc string:

>>> from mpmath import *
>>> mp.dps = 15
>>> print erf(0)
0.0
>>> print erf(1)
0.842700792949715
>>> print erf(-1)
-0.842700792949715
>>> print erf(inf)
1.0
>>> print erf(-inf)
-1.0

For large real x, \mathrm{erf}(x) approaches 1 very rapidly::

>>> print erf(3)
0.999977909503001
>>> print erf(5)
0.999999999998463

The error function is an odd function::

>>> nprint(chop(taylor(erf, 0, 5)))
[0.0, 1.12838, 0.0, -0.376126, 0.0, 0.112838]

:func:erf implements arbitrary-precision evaluation and supports complex numbers::

>>> mp.dps = 50
>>> print erf(0.5)
0.52049987781304653768274665389196452873645157575796
>>> mp.dps = 25
>>> print erf(1+j)
(1.316151281697947644880271 + 0.1904534692378346862841089j)

Related functions

See also :func:erfc, which is more accurate for large x, and :func:erfi which gives the antiderivative of \exp(t^2).

The Fresnel integrals :func:fresnels and :func:fresnelc are also related to the error function.