http://code.activestate.com/recipes/tags/calculus-basic/2016-08-07T22:02:10-07:00ActiveState Code Recipes2016-08-07T22:02:10-07:00Raymond Hettingerhttp://code.activestate.com/recipes/users/178123/http://code.activestate.com/recipes/580610-auto-differentiation/

<p style="color: grey"> Python recipe 580610 by <a href="/recipes/users/178123/">Raymond Hettinger</a> (<a href="/recipes/tags/autodifferentiation/">autodifferentiation</a>, <a href="/recipes/tags/calculus/">calculus</a>, <a href="/recipes/tags/descent/">descent</a>, <a href="/recipes/tags/gradient/">gradient</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/optimization/">optimization</a>, <a href="/recipes/tags/vector/">vector</a>). Revision 5. </p> <p>Directly computes derivatives from ordinary Python functions using auto differentiation. The technique directly computes the desired derivatives to full precision without resorting to symbolic math and without making estimates bases on numerical methods.</p> <p>The module provides a Num class for "dual" numbers that performs both regular floating point math on a value and its derivative at the same time. In addition, the module provides drop-in substitutes for most of the functions in the math module. There are also tools for partial derivatives, directional derivatives, gradients of scalar fields, and the curl and divergence of vector fields.</p>

2010-01-15T06:08:56-08:00Eric-Olivier LE BIGOThttp://code.activestate.com/recipes/users/2672032/http://code.activestate.com/recipes/576721-calculations-with-error-propagation-and-semi-forma/

<p style="color: grey"> Python recipe 576721 by <a href="/recipes/users/2672032/">Eric-Olivier LE BIGOT</a> (<a href="/recipes/tags/calculus/">calculus</a>, <a href="/recipes/tags/error_propagation/">error_propagation</a>, <a href="/recipes/tags/expressions/">expressions</a>, <a href="/recipes/tags/formal_calculations/">formal_calculations</a>, <a href="/recipes/tags/lazy_evaluation/">lazy_evaluation</a>, <a href="/recipes/tags/uncertainties/">uncertainties</a>). Revision 22. </p> <p><strong>Do not use this module</strong>, but use instead the more powerful <a href="http://pypi.python.org/pypi/uncertainties/">uncertainties.py module</a>.</p> <p>Module for performing calculations with error propagation, such as (1 +- 0.1) * 2 = 2 +- 0.2. Mathematical operations (addition, etc.), operations defined in the math module (sin, atan,...) and logical operations (&lt;, &gt;, etc.) can be used.</p> <p>Correlations between parts of an expression are correctly taken into account (for instance, the error on "x-x" is strictly zero).</p> <p>Code written for floats should directly work with the numbers with uncertainty defined here, without much need for modifications.</p> <p>The module also contains a class that represents non-evaluated mathematical expressions. This class is used for performing the differentiation required by the error propagation calculation, but can be used on its own, for manipulating "semi-formal" expressions whose variables can be accessed.</p>