Welcome to AutoUncertainties’s documentation!

Static Badge GitHub Release python JOSS Paper

AutoUncertainties is a package that makes handling linear uncertainty propagation for scientific applications straightforward and automatic using auto-differentiation.

For instructions on how to install AutoUncertainties, see Getting Started.

Supported Features

Usage

Quick Reference

Statement of Need

AutoUncertainties is a Python package for uncertainty propagation of independent random variables. It provides a drop-in mechanism to add uncertainty information to Python scalar and NumPy array objects. It implements manual propagation rules for the Python dunder math methods, and uses automatic differentiation via JAX to propagate uncertainties for most NumPy methods applied to both scalar and NumPy array variables. In doing so, it eliminates the need for carrying around additional uncertainty variables or for implementing custom propagation rules for any NumPy operator with a gradient rule implemented by JAX. In most cases, it requires minimal modification to existing code—typically only when uncertainties are attached to central values.

One of the most important aspects of AutoUncertainties is its seamless support for NumPy:

Example
>>> import numpy as np
>>> from auto_uncertainties import Uncertainty
>>> vals = np.array([0.5, 0.75])
>>> errs = np.array([0.05, 0.3])
>>> u = Uncertainty(vals, errs)
>>> print(np.cos(u))
[0.877583 +/- 0.0239713, 0.731689 +/- 0.204492]

This is in contrast to the uncertainties package, which would have required the use of unumpy, a module containing several hand-implemented analogs of the true NumPy functions.

Current Limitations and Future Work

Dependent Random Variables

To simplify operations on Uncertainty objects, AutoUncertainties assumes all variables are independent. This means that, in the case where the programmer assumes dependence between two or more Uncertainty objects, unexpected and counter-intuitive behavior may arise during uncertainty propagation. This is a common pitfall when working with Uncertainty objects, especially since the package will not prevent you from manipulating variables in a manner that implies dependence.

  • Subtracting Equivalent Uncertainties

    Subtracting an Uncertainty from itself will not result in a standard deviation of zero.

    Example
    >>> x = Uncertainty(5.0, 0.5)
>>> x - x
0 +/- 0.707107

  • Mean Error Propagation

    When multiplying a vector by a scalar Uncertainty object, each component of the resulting vector is assumed to be a multivariate normal distribution with no covariance, which may not be the desired behavior. For instance, taking the mean of such a vector will return an Uncertainty object with an unexpectedly small standard deviation.

    Example
    >>> u = Uncertainty(5.0, 0.5)
>>> arr = np.ones(10) * 10
>>> np.mean(u * arr)
50 +/- 1.58114, rather than 50 +/- 5 as expected

    To obtain the uncertainty corresponding to the case where each element of the array is fully correlated, two workaround techniques can be used:

    1. Separate the central value from the relative error, multiply the vector by the central value, take the mean of the resulting vector, and then multiply by the previously stored relative error.

      Example
      >>> u = Uncertainty(5.0, 0.5)
>>> scale_error = Uncertainty(1, u.relative)  # collect relative error
>>> scale_value = u.value                     # collect central value

>>> arr = np.ones(10) * 10
>>> np.mean(scale_value * arr) * scale_error
50 +/- 5

    2. Take the mean of the vector, and then multiply by the Uncertainty:

      >>> u = Uncertainty(5.0, 0.5)
>>> arr = np.ones(10) * 10
>>> u * np.mean(arr)
50 +/- 5

These workarounds are nevertheless cumbersome, and cause AutoUncertainties to fall somewhat short of the original goals of automated error propagation. In principle, this could be addressed by storing a full computational graph of the result of chained operations, similar to what is done in uncertainties. However, the complexity of such a system places it out of scope for AutoUncertainties at this time.

It should be noted that, in cases where random variables have covariance that lies somewhere between fully correlated and fully independent, calculations like those described above would be more complex. To accurately propagate uncertainty, one would need to specify individual correlations between each variable, and adjust the computation as necessary. This is also currently out of scope for AutoUncertainties.

Inspirations

The class structure of Uncertainty, and the NumPy ufunc implementation is heavily inspired by the excellent package Pint.

Indices and Tables

Contents:

API Reference