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.

The script below

Requirements:

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

**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.

Thank you for illustrating how to use my uncertainties package with arrays! The code looks good to me.

ReplyDeleteI would like to mention that the final errors errz actually depend on x and y too: errz = f(x, errx, y, erry) would be more appropriate.

One can also write the simpler "from uncertainties import unumpy". :)

Dear Eric,

DeleteYour package is very useful. I have been using it lately a lot in my work!

Thanks for pointing that out.

Cheers.

Great post.

ReplyDeleteWhat if the errors are correlated ?

Great post.

ReplyDeleteWhat if the errors are correlated ?

Correlations are automatically and transparently taken into account (see http://pythonhosted.org/uncertainties/ for more information). For example, x-x is strictly equal to zero, even if x has an uncertainty.

ReplyDeleteI just found out about the uncertainties package via this blog (via Google, of course) and could not be happier post-installation. As an astronomy PhD student, I feel that error propagation directs too much of my time towards the nitty gritty and away from doing the exciting parts of science. THANK YOU.

ReplyDeleteGlad this is helpful! Cheers

Deleteexcellent blog and really useful for me to cross-check my monte-carlo error propagator, cheers!

ReplyDelete