Create a gist now

Instantly share code, notes, and snippets.

What would you like to do?
Python Welford Algorithm
import math
class Welford(object):
""" Implements Welford's algorithm for computing a running mean
and standard deviation as described at:
can take single values or iterables
mean - returns the mean
std - returns the std
meanfull- returns the mean and std of the mean
>>> foo = Welford()
>>> foo(range(100))
>>> foo
<Welford: 49.5 +- 29.0114919759>
>>> foo([1]*1000)
>>> foo
<Welford: 5.40909090909 +- 16.4437417146>
>>> foo.mean
>>> foo.std
>>> foo.meanfull
(5.409090909090906, 0.4957974674244838)
def __init__(self,lst=None):
self.k = 0
self.M = 0
self.S = 0
def update(self,x):
if x is None:
self.k += 1
newM = self.M + (x - self.M)*1./self.k
newS = self.S + (x - self.M)*(x - newM)
self.M, self.S = newM, newS
def consume(self,lst):
lst = iter(lst)
for x in lst:
def __call__(self,x):
if hasattr(x,"__iter__"):
def mean(self):
return self.M
def meanfull(self):
return self.mean, self.std/math.sqrt(self.k)
def std(self):
if self.k==1:
return 0
return math.sqrt(self.S/(self.k-1))
def __repr__(self):
return "<Welford: {} +- {}>".format(self.mean, self.std)

weak commented Jul 16, 2012

Works great and saved me a bit of time, thanks :)

hamx0r commented Apr 12, 2016

Great gist! moving self.k += 1 until after newM and newS are calculated adds robustness for cases where someone tries to use this with strings or other non-numeric types....the function will then throw an error before incrementing k, thus preserving the accuracy of the data within their Welford instance.

Beautiful! You'd be surprised at how many incorrect versions of Welford are online, thanks!

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment