uncertainties

uncertainties allows calculations such as (2 +/- 0.1)*2 = 4 +/- 0.2 to be performed transparently. Much more complex mathematical expressions involving numbers with uncertainties can also be evaluated directly.

The uncertainties package takes the pain and complexity out of uncertainty calculations.

Detailed information about this package can be found on its main website.

Basic examples

>>> from uncertainties import ufloat

>>> x = ufloat(2, 0.25)
>>> x
2.0+/-0.25

>>> square = x**2  # Transparent calculations
>>> square
4.0+/-1.0
>>> square.nominal_value
4.0
>>> square.std_dev  # Standard deviation
1.0

>>> square - x*x
0.0  # Exactly 0: correlations taken into account

>>> from uncertainties.umath import *  # sin(), etc.
>>> sin(1+x**2)
-0.95892427466313845+/-0.2836621854632263

>>> print (2*x+1000).derivatives[x]  # Automatic calculation of derivatives
2.0

>>> from uncertainties import unumpy  # Array manipulation
>>> random_vars = unumpy.uarray([1, 2], [0.1, 0.2])
>>> print random_vars
[1.0+/-0.1 2.0+/-0.2]
>>> print random_vars.mean()
1.50+/-0.11
>>> print unumpy.cos(random_vars)
[0.540302305868+/-0.0841470984808 -0.416146836547+/-0.181859485365]

Main features

• Transparent calculations with uncertainties: no or little modification of existing code is needed. Similarly, the Python (or IPython) shell can be used as a powerful calculator that handles quantities with uncertainties (print statements are optional, which is convenient).
• Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a non-zero uncertainty for x-x, which is incorrect).
• Almost all mathematical operations are supported, including most functions from the standard math module (sin,...). Comparison operators (>, ==, etc.) are supported too.
• Many fast operations on arrays and matrices of numbers with uncertainties are supported.
• Extensive support for printing numbers with uncertainties (including LaTeX support and pretty-printing).
• Most uncertainty calculations are performed analytically.
• This module also gives access to the derivatives of any mathematical expression (they are used by error propagation theory, and are thus automatically calculated by this module).

Installation or upgrade

Installation instructions are available on the main web site for this package.

Git branches

The release branch is the latest stable release. It should pass the tests.

master* branches in the Github repository are bleeding-edge, and do not necessarily pass the tests. The master branch is the latest, relatively stable versions (while other master* branches are more experimental).

Other branches might be present in the GitHub repository, but they are typically temporary and represent work in progress that does not necessarily run properly yet.

License

This package and its documentation are released under the Revised BSD License.

Voluntary donations

If you find this open-source software useful (e.g. in saving you time or helping you produce something valuable), please consider donating $10 or more.

History

This package was created back around 2009 by Eric O. LEBIGOT.

Ownership of the package was taken over by the lmfit GitHub organization in 2024.