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**: Liittle 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/
Raw data
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"description": "uncertainties\n=============\n\n.. image:: https://readthedocs.org/projects/uncertainties/badge/?version=latest\n :target: https://uncertainties.readthedocs.io/en/latest/?badge=latest\n.. image:: https://img.shields.io/pypi/v/uncertainties.svg\n :target: https://pypi.org/project/uncertainties/\n.. image:: https://pepy.tech/badge/uncertainties/week\n :target: https://pepy.tech/project/uncertainties\n.. image:: https://codecov.io/gh/lmfit/uncertainties/branch/master/graph/badge.svg\n :target: https://codecov.io/gh/lmfit/uncertainties/\n.. image:: https://img.shields.io/github/actions/workflow/status/lmfit/uncertainties/python-package.yml?logo=github%20actions\n :target: https://github.com/lmfit/uncertainties/actions/workflows/python-package.yml\n\nThe ``uncertainties`` package allows calculations with values that have\nuncertaintes, such as (2 +/- 0.1)*2 = 4 +/- 0.2. ``uncertainties`` takes the\npain and complexity out of error propagation and calculations of values with\nuncertainties. For more information, see https://uncertainties.readthedocs.io/\n\nBasic examples\n--------------\n\n.. code-block:: python\n\n >>> from uncertainties import ufloat\n >>> x = ufloat(2, 0.25)\n >>> x\n 2.0+/-0.25\n\n >>> square = x**2\n >>> square\n 4.0+/-1.0\n >>> square.nominal_value\n 4.0\n >>> square.std_dev # Standard deviation\n 1.0\n\n >>> square - x*x\n 0.0 # Exactly 0: correlations taken into account\n\n >>> from uncertainties.umath import sin, cos # and many more.\n >>> sin(1+x**2)\n -0.95892427466313845+/-0.2836621854632263\n\n >>> print (2*x+1000).derivatives[x] # Automatic calculation of derivatives\n 2.0\n\n >>> from uncertainties import unumpy # Array manipulation\n >>> varr = unumpy.uarray([1, 2], [0.1, 0.2])\n >>> print(varr)\n [1.0+/-0.1 2.0+/-0.2]\n >>> print(varr.mean())\n 1.50+/-0.11\n >>> print(unumpy.cos(varr))\n [0.540302305868+/-0.0841470984808 -0.416146836547+/-0.181859485365]\n\nMain features\n-------------\n\n- **Transparent calculations with uncertainties**: Liittle or\n no modification of existing code is needed to convert calculations of floats\n to calculations of values with uncertainties.\n\n- **Correlations** between expressions are correctly taken into\n account. Thus, ``x-x`` is exactly zero.\n\n- **Most mathematical operations** are supported, including most\n functions from the standard math_ module (sin,...). Comparison\n operators (``>``, ``==``, etc.) are supported too.\n\n- Many **fast operations on arrays and matrices** of numbers with\n uncertainties are supported.\n\n- **Extensive support for printing** numbers with uncertainties\n (including LaTeX support and pretty-printing).\n\n- Most uncertainty calculations are performed **analytically**.\n\n- This module also gives access to the **derivatives** of any\n mathematical expression (they are used by `error\n propagation theory`_, and are thus automatically calculated by this\n module).\n\n\nInstallation or upgrade\n-----------------------\n\nTo install `uncertainties`, use::\n\n pip install uncertainties\n\nTo upgrade from an older version, use::\n\n pip install --upgrade uncertainties\n\nFurther details are in the `on-line documentation\n<https://uncertainties.readthedocs.io/en/latest/install.html>`_.\n\n\nGit branches\n------------\n\nThe GitHub ``master`` branch is the latest development version, and is intended\nto be a stable pre-release version. It will be experimental, but should pass\nall tests.. Tagged releases will be available on GitHub, and correspond to the\nreleases to PyPI. The GitHub ``gh-pages`` branch will contain a stable test version\nof the documentation that can be viewed at\n`<https://lmfit.github.io/uncertainties/>`_. Other Github branches should be\ntreated as unstable and in-progress development branches.\n\n\nLicense\n-------\n\nThis package and its documentation are released under the `Revised BSD\nLicense <LICENSE.txt>`_.\n\n\nHistory\n-------\n\n..\n Note from Eric Lebigot: I would like the origin of the package to\n remain documented for its whole life. Thanks!\n\nThis package was created back around 2009 by `Eric O. LEBIGOT <https://github.com/lebigot>`_.\n\nOwnership of the package was taken over by the `lmfit GitHub organization <https://github.com/lmfit>`_ in 2024.\n\n.. _IPython: https://ipython.readthedocs.io/en/stable/\n.. _math: https://docs.python.org/library/math.html\n.. _error propagation theory: https://en.wikipedia.org/wiki/Propagation_of_uncertainty\n.. _main website: https://uncertainties.readthedocs.io/\n",
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