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Python Welford Algorithm
import math
class Welford(object):
""" Implements Welford's algorithm for computing a running mean
and standard deviation as described at:
http://www.johndcook.com/standard_deviation.html
can take single values or iterables
Properties:
mean - returns the mean
std - returns the std
meanfull- returns the mean and std of the mean
Usage:
>>> foo = Welford()
>>> foo(range(100))
>>> foo
<Welford: 49.5 +- 29.0114919759>
>>> foo([1]*1000)
>>> foo
<Welford: 5.40909090909 +- 16.4437417146>
>>> foo.mean
5.409090909090906
>>> foo.std
16.44374171455467
>>> foo.meanfull
(5.409090909090906, 0.4957974674244838)
"""
def __init__(self,lst=None):
self.k = 0
self.M = 0
self.S = 0
self.__call__(lst)
def update(self,x):
if x is None:
return
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:
self.update(x)
def __call__(self,x):
if hasattr(x,"__iter__"):
self.consume(x)
else:
self.update(x)
@property
def mean(self):
return self.M
@property
def meanfull(self):
return self.mean, self.std/math.sqrt(self.k)
@property
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!

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