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<h3>Section contents</h3>
<ul>
<li><a class="reference internal" href="#">Welcome to the uncertainties package</a><ul>
<li><a class="reference internal" href="#an-easy-to-use-calculator">An easy-to-use calculator</a></li>
<li><a class="reference internal" href="#available-documentation">Available documentation</a></li>
<li><a class="reference internal" href="#installation-and-download">Installation and download</a><ul>
<li><a class="reference internal" href="#important-note">Important note</a></li>
<li><a class="reference internal" href="#automatic-install-or-upgrade">Automatic install or upgrade</a></li>
<li><a class="reference internal" href="#manual-download-and-install">Manual download and install</a></li>
<li><a class="reference internal" href="#source-code">Source code</a></li>
</ul>
</li>
<li><a class="reference internal" href="#migration-from-version-1-to-version-2">Migration from version 1 to version 2</a></li>
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<div class="section" id="welcome-to-the-uncertainties-package">
<h1>Welcome to the uncertainties package<a class="headerlink" href="#welcome-to-the-uncertainties-package" title="Permalink to this headline">¶</a></h1>
<p>The <a class="reference external" href="http://pypi.python.org/pypi/uncertainties/">uncertainties package</a> is a free, cross-platform program that
<strong>transparently</strong> handles calculations with <strong>numbers with uncertainties</strong>
(like 3.14±0.01). It can also yield the <strong>derivatives</strong> of any
expression.</p>
<p>The <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> package <strong>takes the pain and complexity out</strong>
of uncertainty calculations. Error propagation is not to be feared
anymore!</p>
<p>Calculations of results with uncertainties, or of derivatives, can be
performed either in an <strong>interactive session</strong> (as with a calculator),
or in <strong>programs</strong> written in the <a class="reference external" href="http://python.org/">Python</a> programming language.
Existing calculation code can <strong>run with little or no change</strong>.</p>
<p>Whatever the complexity of a calculation, this package returns its
result with an uncertainty as predicted by linear <a class="reference external" href="http://en.wikipedia.org/wiki/Propagation_of_uncertainty">error propagation
theory</a>. It automatically <a class="reference internal" href="user_guide.html#derivatives"><em>calculates derivatives</em></a>
and uses them for calculating uncertainties. Almost all uncertainty
calculations are performed <strong>analytically</strong>.</p>
<p><strong>Correlations</strong> between variables are automatically handled, which
sets this module apart from many existing error propagation codes.</p>
<p>You may want to check the following related uncertainty calculation
Python packages to see if they better suit your needs: <a class="reference external" href="https://pypi.python.org/pypi/soerp">soerp</a>
(higher-order approximations) and <a class="reference external" href="https://pypi.python.org/pypi/mcerp">mcerp</a> (Monte-Carlo approach).</p>
<div class="section" id="an-easy-to-use-calculator">
<span id="index-0"></span><h2>An easy-to-use calculator<a class="headerlink" href="#an-easy-to-use-calculator" title="Permalink to this headline">¶</a></h2>
<p>Calculations involving <strong>numbers with uncertainties</strong> can be performed
even without knowing anything about the <a class="reference external" href="http://python.org/">Python</a> programming language.
After <a class="reference internal" href="#installing-this-package">installing this package</a> and <a class="reference external" href="http://docs.python.org/tutorial/interpreter.html">invoking the Python interpreter</a>,
calculations with <strong>automatic error propagation</strong> can be performed
<strong>transparently</strong> (i.e., through the usual syntax for mathematical
formulas):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">uncertainties</span> <span class="kn">import</span> <span class="n">ufloat</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">uncertainties.umath</span> <span class="kn">import</span> <span class="o">*</span> <span class="c"># sin(), etc.</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">ufloat</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span> <span class="c"># x = 1+/-0.1</span>
<span class="gp">>>> </span><span class="k">print</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span>
<span class="go">2.00+/-0.20</span>
<span class="gp">>>> </span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">)</span> <span class="c"># In a Python shell, "print" is optional</span>
<span class="go">0.9092974268256817+/-0.08322936730942848</span>
</pre></div>
</div>
<p>Thus, existing calculation code designed for regular numbers can run
with numbers with uncertainties with <a class="reference internal" href="user_guide.html#user-guide"><em>no or little modification</em></a>.</p>
<p id="index-1">Another strength of this package is its correct handling of
<strong>correlations</strong>. For instance, the following quantity is exactly
zero even though <tt class="xref py py-data docutils literal"><span class="pre">x</span></tt> has an uncertainty:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">x</span><span class="o">-</span><span class="n">x</span>
<span class="go">0.0+/-0</span>
</pre></div>
</div>
<p>Many other error propagation codes return the incorrect value 0±0.1414…
because they wrongly assume that the two subtracted quantities are
<em>independent</em> random variables.</p>
<p><strong>Arrays</strong> of numbers with uncertainties are <a class="reference internal" href="user_guide.html#simple-array-use"><em>transparently
handled</em></a> too.</p>
<p><strong>Derivatives</strong> are similarly very <a class="reference internal" href="user_guide.html#derivatives"><em>easy to obtain</em></a>:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="mi">1000</span><span class="p">)</span><span class="o">.</span><span class="n">derivatives</span><span class="p">[</span><span class="n">x</span><span class="p">]</span>
<span class="go">2.0</span>
</pre></div>
</div>
<p>They are calculated with a <a class="reference internal" href="tech_guide.html#differentiation-method"><em>fast method</em></a>.</p>
</div>
<div class="section" id="available-documentation">
<h2>Available documentation<a class="headerlink" href="#available-documentation" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="user_guide.html"><em>User Guide</em></a> details many of the features of this package.</p>
<p>The part <a class="reference internal" href="numpy_guide.html"><em>Uncertainties in arrays</em></a> describes how arrays of numbers with
uncertainties can be created and used.</p>
<p>The <a class="reference internal" href="tech_guide.html"><em>Technical Guide</em></a> gives advanced technical details.</p>
<p>A <tt class="xref download docutils literal"><span class="pre">PDF</span> <span class="pre">version</span></tt>
of the documentation is also available.</p>
<p>Additional information is available through the <a class="reference external" href="http://docs.python.org/library/pydoc.html">pydoc</a> command, which
gives access to many of the documentation strings included in the code.</p>
</div>
<div class="section" id="installation-and-download">
<span id="installing-this-package"></span><span id="index-2"></span><h2>Installation and download<a class="headerlink" href="#installation-and-download" title="Permalink to this headline">¶</a></h2>
<div class="section" id="important-note">
<h3>Important note<a class="headerlink" href="#important-note" title="Permalink to this headline">¶</a></h3>
<p>The installation commands below should be <strong>run in a DOS or Unix
command shell</strong> (<em>not</em> in a Python shell).</p>
<p>Under Windows (version 7 and earlier), a command shell can be obtained
by running <tt class="docutils literal"><span class="pre">cmd.exe</span></tt> (through the Run… menu item from the Start
menu). Under Unix (Linux, Mac OS X,…), a Unix shell is available when
opening a terminal (in Mac OS X, the Terminal program is found in the
Utilities folder, which can be accessed through the Go menu in the
Finder).</p>
</div>
<div class="section" id="automatic-install-or-upgrade">
<h3>Automatic install or upgrade<a class="headerlink" href="#automatic-install-or-upgrade" title="Permalink to this headline">¶</a></h3>
<p>One of the automatic installation or upgrade procedures below might work
on your system, if you have a Python package installer or use certain
Linux distributions.</p>
<p>Under Unix, it may be necessary to prefix the commands below with
<tt class="docutils literal"><span class="pre">sudo</span></tt>, so that the installation program has <strong>sufficient access
rights to the system</strong>.</p>
<p>If you have <a class="reference external" href="http://pip.openplans.org/">pip</a>, you can try to install
the latest version with</p>
<div class="highlight-sh"><div class="highlight"><pre>pip install --upgrade uncertainties
</pre></div>
</div>
<p>If you have <a class="reference external" href="http://pypi.python.org/pypi/setuptools">setuptools</a>, you can try to automatically install or
upgrade this package with</p>
<div class="highlight-sh"><div class="highlight"><pre>easy_install --upgrade uncertainties
</pre></div>
</div>
<p>The <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> package is also available for <strong>Windows</strong>
through the <a class="reference external" href="https://code.google.com/p/pythonxy/">Python(x,y)</a> distribution. It may also be included in
Christoph Gohlke’s Base distribution of <a class="reference external" href="http://www.lfd.uci.edu/~gohlke/pythonlibs/">scientific Python packages</a>.</p>
<p><strong>Mac OS X</strong> users who use the <a class="reference external" href="http://www.macports.org/">MacPorts package manager</a> can install <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> with
<tt class="docutils literal"><span class="pre">sudo</span> <span class="pre">port</span> <span class="pre">install</span> <span class="pre">py**-uncertainties</span></tt>, and upgrade it with <tt class="docutils literal"><span class="pre">sudo</span>
<span class="pre">port</span> <span class="pre">upgrade</span> <span class="pre">py**-uncertainties</span></tt> where <tt class="docutils literal"><span class="pre">**</span></tt> represents the desired
Python version (<tt class="docutils literal"><span class="pre">27</span></tt>, <tt class="docutils literal"><span class="pre">33</span></tt>, etc.).</p>
<p>The <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> package is also available through the
following <strong>Linux</strong> distributions and software platforms: <a class="reference external" href="https://launchpad.net/ubuntu/+source/uncertainties">Ubuntu</a>, <a class="reference external" href="http://pkgs.org/fedora-18/rpm-sphere-i586/python-uncertainties-1.8.dev418-4.1.noarch.rpm.html">Fedora</a>,
<a class="reference external" href="https://build.opensuse.org/package/show?package=python-uncertainties&project=home%3Aocefpaf">openSUSE</a>,
<a class="reference external" href="http://packages.debian.org/search?keywords=python-uncertainties">Debian</a>
and <a class="reference external" href="http://maemo.org/packages/view/python-uncertainties/">Maemo</a>.</p>
</div>
<div class="section" id="manual-download-and-install">
<h3>Manual download and install<a class="headerlink" href="#manual-download-and-install" title="Permalink to this headline">¶</a></h3>
<p>Alternatively, you can simply <a class="reference external" href="http://pypi.python.org/pypi/uncertainties/#downloads">download</a> the package archive from the
Python Package Index (PyPI) and unpack it. The package can then be
installed by <strong>going into the unpacked directory</strong>
(<tt class="file docutils literal"><span class="pre">uncertainties-…</span></tt>), and running the provided <tt class="file docutils literal"><span class="pre">setup.py</span></tt>
program with</p>
<div class="highlight-sh"><div class="highlight"><pre>python setup.py install
</pre></div>
</div>
<p>or, for an installation in the user Python library (no additional access
rights needed):</p>
<div class="highlight-sh"><div class="highlight"><pre>python setup.py install --user
</pre></div>
</div>
<p>or, for an installation in a custom directory <tt class="file docutils literal"><span class="pre">my_directory</span></tt>:</p>
<div class="highlight-sh"><div class="highlight"><pre>python setup.py install --install-lib my_directory
</pre></div>
</div>
<p>or, if additional access rights are needed (Unix):</p>
<div class="highlight-sh"><div class="highlight"><pre>sudo python setup.py install
</pre></div>
</div>
<p>You can also simply <strong>move</strong> the <tt class="file docutils literal"><span class="pre">uncertainties-py*</span></tt> directory
that corresponds best to your version of Python to a location that
Python can import from (directory in which scripts using
<tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> are run, etc.); the chosen
<tt class="file docutils literal"><span class="pre">uncertainties-py*</span></tt> directory should then be renamed
<tt class="file docutils literal"><span class="pre">uncertainties</span></tt>. Python 3 users should then run <tt class="docutils literal"><span class="pre">2to3</span> <span class="pre">-w</span> <span class="pre">.</span></tt>
from inside this directory so as to automatically adapt the code to
Python 3.</p>
</div>
<div class="section" id="source-code">
<h3>Source code<a class="headerlink" href="#source-code" title="Permalink to this headline">¶</a></h3>
<p>The latest, bleeding-edge but working <a class="reference external" href="https://github.com/lebigot/uncertainties/tree/master/uncertainties">code</a>
and <a class="reference external" href="https://github.com/lebigot/uncertainties/tree/master/doc/">documentation source</a> are
available <a class="reference external" href="https://github.com/lebigot/uncertainties/">on GitHub</a>.
The <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> package is written in pure Python and has no
external dependency (the <a class="reference external" href="http://numpy.scipy.org/">NumPy</a> package is optional). It contains
about 7000 lines of code. 75 % of these lines are documentation
strings and comments. The remaining 25 % are split between unit tests
(15 % of the total) and the calculation code proper (10 % of the
total). <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> is thus a <strong>lightweight, portable
package</strong> with abundant documentation and tests.</p>
</div>
</div>
<div class="section" id="migration-from-version-1-to-version-2">
<h2>Migration from version 1 to version 2<a class="headerlink" href="#migration-from-version-1-to-version-2" title="Permalink to this headline">¶</a></h2>
<p>Some <strong>incompatible changes</strong> were introduced in version 2 of
<tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt> (see the <a class="reference external" href="https://pypi.python.org/pypi/uncertainties#version-history">version history</a>). While the version 2
line will support the version 1 syntax for some time, it is
recommended to <strong>update existing programs</strong> as soon as possible. This
can be made easier through the provided <strong>automatic updater</strong>.</p>
<p>The automatic updater works like Python’s <a class="reference external" href="http://docs.python.org/2/library/2to3.html">2to3</a> updater. It can be run
(in a Unix or DOS shell) with:</p>
<div class="highlight-sh"><div class="highlight"><pre>python -m uncertainties.1to2
</pre></div>
</div>
<p>For example, updating a single Python program can be done with</p>
<div class="highlight-sh"><div class="highlight"><pre>python -m uncertainties.1to2 -w example.py
</pre></div>
</div>
<p>All the Python programs contained under a directory <tt class="docutils literal"><span class="pre">Programs</span></tt>
(including in nested sub-directories) can be automatically updated
with</p>
<div class="highlight-sh"><div class="highlight"><pre>python -m uncertainties.1to2 -w Programs
</pre></div>
</div>
<p>Backups are automatically created, unless the <tt class="docutils literal"><span class="pre">-n</span></tt> option is given.</p>
<p>Some <strong>manual adjustments</strong> might be necessary after running the
updater (incorrectly modified lines, untouched obsolete syntax).</p>
<p>While the updater creates backup copies by default, it is generally
useful to <strong>first create a backup</strong> of the modified directory, or
alternatively to use some <a class="reference external" href="http://en.wikipedia.org/wiki/Version_control_system">version control</a>
system. Reviewing the modifications with a <a class="reference external" href="http://en.wikipedia.org/wiki/File_comparison">file comparison tool</a> might also be useful.</p>
</div>
<div class="section" id="what-others-say">
<h2>What others say<a class="headerlink" href="#what-others-say" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li>“<em>Superb,</em>” “<em>wonderful,</em>” “<em>It’s like magic.</em>” (<a class="reference external" href="http://blog.garlicsim.org/post/1266209646/cool-python-module-uncertainties#comment-85154147">Joaquin Abian</a>)</li>
<li>“<em>An awesome python package</em>” (<a class="reference external" href="http://biosport.ucdavis.edu/blog/2010/05/07/uncertainty-analysis">Jason Moore</a>)</li>
<li>“<em>Utterly brilliant</em>” (<a class="reference external" href="http://twitter.com/#!/GeekyJeffrey">Jeffrey Simpson</a>)</li>
<li>“<em>An amazing time saver</em>” (<a class="reference external" href="http://scipyscriptrepo.com/wp/?p=41">Paul Nakroshis</a>)</li>
<li>“<em>Seems to be the gold standard for this kind of thing</em>” (<a class="reference external" href="http://newton.cx/~peter/work/?p=660">Peter Williams</a>)</li>
<li>“<em>This package has a great interface and makes error propagation
something to stop fearing.</em>” (<a class="reference external" href="http://dawes.wordpress.com/2011/01/02/scientific-python/">Dr Dawes</a>)</li>
<li>“<em>uncertainties makes error propagation dead simple.</em>” (<a class="reference external" href="http://readthedocs.org/docs/enrico/en/latest/setup.html">enrico
documentation</a>)</li>
<li>contains “<em>many inspiring ideas</em>” (<a class="reference external" href="https://pypi.python.org/pypi/soerp#acknowledgements">Abraham Lee</a>)</li>
<li>“<em>Those of us working with experimental data or simulation results
will appreciate this.</em>” (<a class="reference external" href="http://khinsen.wordpress.com/2010/07/12/euroscipy-2010/">Konrad Hinsen</a>)</li>
<li>“<em>PyPI’s uncertainties rocks!</em>” (<a class="reference external" href="http://identi.ca/notice/23330742">Siegfried Gevatter</a>)</li>
<li>“<em>A very cool Python module</em>” (<a class="reference external" href="http://blog.garlicsim.org/post/1266209646/cool-python-module-uncertainties">Ram Rachum</a>)</li>
<li>“<em>Holy f*** this would have saved me so much f***ing time last
semester</em>.” (<a class="reference external" href="http://www.reddit.com/r/Python/comments/am84v/now_you_can_do_calculations_with_uncertainties_5/">reddit</a>)</li>
</ul>
</div>
<div class="section" id="future-developments">
<h2>Future developments<a class="headerlink" href="#future-developments" title="Permalink to this headline">¶</a></h2>
<p>Planned future developments include:</p>
<ul class="simple">
<li>support for the units package <a class="reference external" href="https://pypi.python.org/pypi/Pint/">Pint</a>;</li>
<li><a class="reference external" href="http://docs.python.org/library/json.html">JSON</a> support;</li>
<li>increased support for <a class="reference external" href="http://numpy.scipy.org/">NumPy</a>: new linear
algebra methods (eigenvalue and QR decompositions, determinant,…),
more convenient matrix creation, standard deviation of arrays,
automatic wrapping of functions that accept arrays of numbers with
uncertainties, input of arrays with uncertainties as strings (like
in NumPy),…;</li>
<li>addition of new functions from the <tt class="xref py py-mod docutils literal"><span class="pre">math</span></tt> module;</li>
<li>fitting routines that conveniently handle data with uncertainties;</li>
<li>handling of complex numbers with uncertainties;</li>
<li>a re-correlate function that puts correlations back between data
that was saved in separate files;</li>
<li>support for multi-precision numbers with uncertainties;</li>
<li>addition of <tt class="xref py py-attr docutils literal"><span class="pre">real</span></tt> and <tt class="xref py py-attr docutils literal"><span class="pre">imag</span></tt> attributes, for increased
compatibility with existing code (Python numbers have these attributes).</li>
</ul>
<p><strong>Please support the continued development of this program</strong> by using
<a class="reference external" href="https://www.gittip.com/lebigot/">gittip</a> or by <a class="reference external" href="https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=4TK7KNDTEDT4S">donating $10</a> or
more through PayPal (no PayPal account necessary).</p>
</div>
<div class="section" id="contact">
<span id="index-3"></span><h2>Contact<a class="headerlink" href="#contact" title="Permalink to this headline">¶</a></h2>
<p><strong>Feature requests, bug reports, or feedback are much welcome.</strong> They
can be <a class="reference external" href="mailto:eric.lebigot%40normalesup.org">sent</a> to the creator of <tt class="xref py py-mod docutils literal"><span class="pre">uncertainties</span></tt>, <a class="reference external" href="http://linkedin.com/pub/eric-lebigot/22/293/277">Eric O. LEBIGOT
(EOL)</a>.</p>
<div class="figure align-center">
<a class="reference external image-reference" href="http://linkedin.com/pub/eric-lebigot/22/293/277"><img alt="Eric O. LEBIGOT (EOL)" src="_images/eol.jpg" style="width: 64px; height: 64px;" /></a>
</div>
</div>
<div class="section" id="how-to-cite-this-package">
<h2>How to cite this package<a class="headerlink" href="#how-to-cite-this-package" title="Permalink to this headline">¶</a></h2>
<p>If you use this package for a publication (in a journal, on the web,
etc.), please cite it by including as much information as possible
from the following: <em>Uncertainties: a Python package for calculations
with uncertainties</em>, Eric O. LEBIGOT,
<a class="reference external" href="http://pythonhosted.org/uncertainties/">http://pythonhosted.org/uncertainties/</a>. Adding the version
number is optional.</p>
</div>
<div class="section" id="acknowledgments">
<h2>Acknowledgments<a class="headerlink" href="#acknowledgments" title="Permalink to this headline">¶</a></h2>
<p>The author wishes to thank all the people who made generous
<a class="reference external" href="https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=4TK7KNDTEDT4S">donations</a>: they help keep this project alive by providing positive
feedback.</p>
<p>I greatly appreciated getting key technical input from Arnaud
Delobelle, Pierre Cladé, and Sebastian Walter. Patches by Pierre
Cladé, Tim Head, José Sabater Montes, Martijn Pieters, Ram Rachum,
Christoph Deil, and Gabi Davar are gratefully acknowledged.</p>
<p>I would also like to thank users who contributed with feedback and
suggestions, which greatly helped improve this program: Joaquin Abian,
Jason Moore, Martin Lutz, Víctor Terrón, Matt Newville, Matthew Peel,
Don Peterson, Mika Pflueger, Albert Puig, Abraham Lee, Arian Sanusi,
Martin Laloux, Jonathan Whitmore, Federico Vaggi, Marco A. Ferra,
Hernan Grecco, and many others.</p>
<p>I am also grateful to Gabi Davar and Pierre Raybaut for including it
in <a class="reference external" href="https://code.google.com/p/pythonxy/">Python(x,y)</a>, to Christoph Gohlke for including it in his Base
distribution of <a class="reference external" href="http://www.lfd.uci.edu/~gohlke/pythonlibs/">scientific Python packages</a> for Windows, and to the
Mac OS X and Linux distribution maintainers of this package (Jonathan
Stickel, David Paleino, Federico Ceratto, Roberto Colistete Jr, and
Filipe Pires Alvarenga Fernandes).</p>
</div>
<div class="section" id="license">
<span id="index-4"></span><h2>License<a class="headerlink" href="#license" title="Permalink to this headline">¶</a></h2>
<p>This software is released under a <strong>dual license</strong>; one of the
following options can be chosen:</p>
<ol class="arabic simple">
<li>The <a class="reference external" href="http://opensource.org/licenses/BSD-3-Clause">Revised BSD License</a> (© 2010–2013, Eric O. LEBIGOT [EOL]).</li>
<li>Any other license, as long as it is obtained from the creator of
this package.</li>
</ol>
</div>
</div>
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