# Uncertainties

The uncertainties package is an open source Python library for doing calculations on numbers that have uncertainties (like 3.14±0.01) that are common in many scientific fields. The calculations done with this package will propagate the uncertainties to the result of mathematical calculations. The `uncertainties` package takes the pain and complexity out of uncertainty calculations and error propagation. Here is a quick taste of how to use `uncertainties`:

    >>> from uncertainties import ufloat
    >>> x = ufloat(2, 0.1)   # x = 2+/-0.1
    >>> y = ufloat(3, 0.2)   # y = 3+/-0.2
    >>> print(2*x)
    4.00+/-0.20
    >>> print(x+y)
    5.00+/-0.22
    >>> print(x*y)
    6.0+/-0.5

The `uncertainties` library calculates uncertainties using linear error propagation theory by automatically calculating derivatives and analytically propagating these to the results. Correlations between variables are automatically handled. This library can also yield the derivatives of any expression with respect to the variables that have uncertain values. For other approaches, see soerp (using higher-order terms) and mcerp (using a Monte-Carlo approach).

The source code for the uncertainties package is licensed under the Revised BSD License. This documentation is licensed under the CC-SA-3 License.

# Table of Contents

- Installation and Credits
  - Download and Installation
  - Source code and Development Version
  - Getting Help
  - Credits
  - How to cite this package
  - Acknowledgments
  - License
- User Guide
  - Basic usage
  - Creating Variables: numbers with uncertainties
  - Basic math with uncertain Variables
  - Mathematical operations with uncertain Variables
  - Comparison operators
  - Handling NaNs and infinities
  - Power Function Behavior
  - Automatic correlations
  - Access to the individual sources of uncertainty
  - Covariance and correlation matrices
  - Correlated variables
  - Making custom functions accept numbers with uncertainties
  - Miscellaneous utilities
  - Derivatives
  - Additional information
- Uncertainties and numpy arrays
  - Arrays of uncertainties Variables
  - The unumpy package
  - Storing arrays in text format
  - Additional array functions: unumpy.ulinalg
- Formatting Variables with uncertainties
  - Printing
- Advanced Topics
  - API: Application Programming Interface
  - Special Technical Topics