ad 1.0.1
Fast, transparent, calculations of first and secondorder automatic differentiation package
Latest Version: 1.3.2
Overview========
The ``ad`` package allows you to **easily** and **transparently** perform
**first and secondorder automatic differentiation**. Advanced math
involving trigonometric, logarithmic, hyperbolic, etc. functions can also
be evaluated directly using the ``admath`` submodule.
`Automatic differentiation`_ is different from numerical and symbolic
differentiation in that it uses prior knowledge of how derivatives
are calculated, `but that's the part you don't need to worry about
while using this package`. They are then transmitted through subsequent
calculations (using the generalized `chain rule`_).
Basic examples
==============
::
>>> from ad import AD
>>> x = AD(2.0)
>>> x
ADV(2.0)
>>> square = x**2
>>> square
ADF(4.0)
>>> square.d(x) # get the first derivative wrt x
4.0
>>> square.d2(x) # get the second derivative wrt x
2.0
>>> from ad.admath import * # sin, cos, log, exp, sqrt, etc.
>>> sin(1 + x**2)
ADF(0.958924274663)
>>> print (2*x + 1000).d() # no inputs shows dict of all derivatives
{ADV(2.0): 2.0}
>>> y = AD(3, tag='y') # tags are useful for tracking original variables
>>> y
y(3.0)
>>> y.d(x) # returns zero if the derivative doesn't exist
0.0
>>> z = x*y**2
>>> z
ADF(18.0)
>>> z.gradient([x, y]) # show the gradient in the order given
[9.0, 12.0]
>>> z.d2c(x, y) # second crossderivatives, order doesn't matter > (x,y) or (y,x)
6.0
>>> z.hessian([x, y])
[[0.0, 6.0], [6.0, 4.0]]
>>> import numpy as np # most numpy functions work out of the box
>>> arr = np.array(AD([1, 2, 3])) # multiple input support
>>> arr.sum()
ADF(6.0)
>>> arr.max()
ADV(3.0)
>>> arr.mean()
ADF(2.0)
>>> arr.var() # array variance
ADF(0.666666666667)
>>> sqrt(arr) # vectorized operations supported with ad operators
array([ADF(1.0), ADF(1.41421356237), ADF(1.73205080757)], dtype=object)
Main Features
=============
 **Transparent calculations with derivatives: no or little
modification of existing code** is needed, including when using
the `Numpy`_ module. The only function (that I have tested, and I
certainly haven't tested most of them) that doesn't work right
out of the box is ``numpy.std`` since it internally calls its
builtin ``sqrt`` function. Two alternatives exist to work around
this: 1) use ``**0.5`` or 2) using the ``admath.sqrt``
operator.
 **Almost all mathematical operations** are supported, including
functions from the standard `math`_ module (sin, cos, exp, erf,
etc.) with additional convenience trigonometric, hyperbolic,
and logarithmic functions (csc, acoth, ln, etc.). Comparison
operators follow the same rules as ``float`` types.
 Nearly all derivative calculations are performed **analytically**
(only the ``gamma`` and ``lgamma`` functions use a highaccuracy
finite difference formula).
Installation
============
You have several easy, convenient options to install the ``ad`` package
(administrative privileges may be required)
1. Download the package files below, unzip to any directory, and run
``python setup.py install`` from the commandline
2. Simply copy the unzipped ``adXYZ`` directory to any other location
that python can find it and rename it ``ad``
3. If ``setuptools`` is installed, run ``easy_install upgrade ad``
from the commandline
4. If ``pip`` is installed, run ``pip upgrade ad`` from the commandline
Contact
=======
Please send **feature requests, bug reports, or feedback** to
`Abraham Lee`_.
Version History
===============
Main changes:
 1.0.1: Smashed some vectorization bugs
 1.0: Initial release. Nearly full differentiation support for all
`math`_ module functions.
.. _NumPy: http://numpy.scipy.org/
.. _math: http://docs.python.org/library/math.html
.. _Automatic differentiation: http://en.wikipedia.org/wiki/Automatic_differentiation
.. _chain rule: http://en.wikipedia.org/wiki/Chain_rule
.. _Abraham Lee: mailto:tisimst@gmail.com
File  Type  Py Version  Uploaded on  Size  

ad1.0.1.tar.gz (md5)  Source  20130628  13KB  
ad1.0.1.zip (md5)  Source  20130628  16KB  
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 Author: Abraham Lee
 Documentation: ad package documentation
 Home Page: http://pypi.python.org/pypi/ad
 Keywords: automatic differentiation,first order,second order,derivative
 License: BSD License

Categories
 Development Status :: 5  Production/Stable
 Intended Audience :: Education
 Intended Audience :: Science/Research
 License :: OSI Approved :: BSD License
 Operating System :: OS Independent
 Programming Language :: Python
 Programming Language :: Python :: 2.6
 Programming Language :: Python :: 2.7
 Programming Language :: Python :: 3.0
 Programming Language :: Python :: 3.1
 Programming Language :: Python :: 3.2
 Programming Language :: Python :: 3.3
 Topic :: Education
 Topic :: Scientific/Engineering
 Topic :: Scientific/Engineering :: Mathematics
 Topic :: Scientific/Engineering :: Physics
 Topic :: Software Development
 Topic :: Software Development :: Libraries
 Topic :: Software Development :: Libraries :: Python Modules
 Topic :: Utilities
 Package Index Owner: tisimst.myopenid.com
 DOAP record: ad1.0.1.xml