How to easily do error propagation with Python

You can easily do error propagation using the uncertainties package in Python, without having to estimate analytically the propagated error or doing Monte Carlo simulations.

Example: Suppose you have two arrays x and y which have associated uncertainties errx and erry. Using x and y, you calculate some function z = f(x, y) which can be arbitrarily complicated (but can be expressed in an analytical form) and you want to estimate the resulting uncertainty errz in z from errx and erry.

The script below

• defines the arrays x, y, errx and erry using numpy
• defines a function z=log10(x+y^2) for illustration purposes
• demonstrates how to invoke 'uncertainties' in order to estimate the uncertainty in z from errx and erry (i.e., errz = f(errx, erry) )

Requirements:

• Numpy, Scipy
• method random_normal
• uncertainties package

 import uncertainties as unc  
 import uncertainties.unumpy as unumpy  
 import numpy  
 import nemmen  
   
 # Defines x and y  
 x=numpy.linspace(0,10,50)  
 y=numpy.linspace(15,20,50)  
   
 # Defines the error arrays, values follow a normal distribution  
 # (method random_normal defined in http://astropython.blogspot.com/2012/04/how-to-generate-array-of-random-numbers.html)  
 errx=nemmen.random_normal(0.1,0.2,50);     errx=numpy.abs(errx)  
 erry=nemmen.random_normal(0.3,0.2,50);     erry=numpy.abs(erry)  
   
 # Defines special arrays holding the values *and* errors  
 x=unumpy.uarray(( x, errx ))  
 y=unumpy.uarray(( y, erry ))  
   
 """  
 Now any operation that you carry on xerr and yerr will   
 automatically propagate the associated errors, as long  
 as you use the methods provided with uncertainties.unumpy  
 instead of using the numpy methods.  
   
 Let's for instance define z as   
 z = log10(x+y**2)  
 and estimate errz.  
 """  
 z=unumpy.log10(x+y**2)  
   
 # Print the propagated error errz  
 errz=unumpy.std_devs(z)  
 print errz  

Update Oct. 23rd 2014: code snippet available on github.