Skip to content

Instantly share code, notes, and snippets.

Created March 21, 2012 19:29
Show Gist options
  • Save alexalemi/2151722 to your computer and use it in GitHub Desktop.
Save alexalemi/2151722 to your computer and use it in GitHub Desktop.
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)
Copy link

ghost commented Jul 16, 2012

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

Copy link

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.

Copy link

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

Copy link

gerardsimons commented Feb 27, 2020

Nice code! One minor thing: not sure if returning an std of 0 is appropriate in the case of k=1 though as this is confusing when k != 0 but std = 0?

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