Is there an easily available implementation of erf() for Python?
Solution 1:
Since v.2.7. the standard math module contains erf function. This should be the easiest way.
http://docs.python.org/2/library/math.html#math.erf
Solution 2:
I recommend SciPy for numerical functions in Python, but if you want something with no dependencies, here is a function with an error error is less than 1.5 * 10-7 for all inputs.
def erf(x):
# save the sign of x
sign = 1 if x >= 0 else -1
x = abs(x)
# constants
a1 = 0.254829592
a2 = -0.284496736
a3 = 1.421413741
a4 = -1.453152027
a5 = 1.061405429
p = 0.3275911
# A&S formula 7.1.26
t = 1.0/(1.0 + p*x)
y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
return sign*y # erf(-x) = -erf(x)
The algorithm comes from Handbook of Mathematical Functions, formula 7.1.26.