uncertainties
=============

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The ``uncertainties`` package allows calculations with values that have
uncertaintes, such as (2 +/- 0.1)*2 = 4 +/- 0.2.  ``uncertainties`` takes the
pain and complexity out of error propagation and calculations of values with
uncertainties.  For more information, see https://uncertainties.readthedocs.io/

Basic examples
--------------

.. code-block:: python

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

    >>> square = x**2
    >>> 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, cos  # and many more.
    >>> 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
    >>> varr = unumpy.uarray([1, 2], [0.1, 0.2])
    >>> print(varr)
    [1.0+/-0.1 2.0+/-0.2]
    >>> print(varr.mean())
    1.50+/-0.11
    >>> print(unumpy.cos(varr))
    [0.540302305868+/-0.0841470984808 -0.416146836547+/-0.181859485365]

Main features
-------------

- **Transparent calculations with uncertainties**: Little or
  no modification of existing code is needed to convert calculations of floats
  to calculations of values with uncertainties.

- **Correlations** between expressions are correctly taken into
  account.  Thus, ``x-x`` is exactly zero.

- **Most  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
-----------------------

To install `uncertainties`, use::

     pip install uncertainties

To upgrade from an older version, use::

     pip install --upgrade uncertainties

Further details are in the `on-line documentation
<https://uncertainties.readthedocs.io/en/latest/install.html>`_.


Git branches
------------

The GitHub ``master`` branch is the latest development version, and is intended
to be a stable pre-release version. It will be experimental, but should pass
all tests..  Tagged releases will be available on GitHub, and correspond to the
releases to PyPI.  The GitHub ``gh-pages`` branch will contain a stable test version
of the documentation that can be viewed at
`<https://lmfit.github.io/uncertainties/>`_.  Other Github branches should be
treated as unstable and in-progress development branches.


License
-------

This package and its documentation are released under the `Revised BSD
License <LICENSE.txt>`_.


History
-------

..
   Note from Eric Lebigot: I would like the origin of the package to
   remain documented for its whole life. Thanks!

This package was created back around 2009 by `Eric O. LEBIGOT <https://github.com/lebigot>`_.

Ownership of the package was taken over by the `lmfit GitHub organization <https://github.com/lmfit>`_ in 2024.

.. _IPython: https://ipython.readthedocs.io/en/stable/
.. _math: https://docs.python.org/library/math.html
.. _error propagation theory: https://en.wikipedia.org/wiki/Propagation_of_uncertainty
.. _main website: https://uncertainties.readthedocs.io/
