Fast, transparent calculations of first and second-order automatic differentiation
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``ad`` Package Documentation

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The ``ad`` package allows you to **easily** and **transparently** perform 
**first and second-order automatic differentiation**. Advanced math 
involving trigonometric, logarithmic, hyperbolic, etc. functions can also 
be evaluated directly using the ``admath`` sub-module. 

**All base numeric types are supported** (``int``, ``float``, ``complex``, 
etc.). This package is designed so that the underlying numeric types will 
interact with each other *as they normally do* when performing any 
calculations. Thus, this package acts more like a "wrapper" that simply helps 
keep track of derivatives while **maintaining the original functionality** of 
the numeric calculations.

From the Wikipedia entry on `Automatic differentiation`_ (AD):

    "AD exploits the fact that every computer program, no matter how 
    complicated, executes a sequence of elementary arithmetic operations 
    (addition, subtraction, multiplication, division, etc.) and elementary 
    functions (exp, log, sin, cos, etc.). By applying the chain rule 
    repeatedly to these operations, derivatives of arbitrary order can be 
    computed automatically, and accurate to working precision."

See the `package documentation`_ for details and examples.

Main Features

- **Transparent calculations with derivatives: no or little 
  modification of existing code** is needed, including when using
  the `Numpy`_ module.

- **Almost all mathematical operations** are supported, including
  functions from the standard math_ module (sin, cos, exp, erf, 
  etc.) and cmath_ module (phase, polar, etc.) with additional convenience 
  trigonometric, hyperbolic, and logarithmic functions (csc, acoth, ln, etc.).
  Comparison operators follow the **same rules as the underlying numeric 

- **Real and complex** arithmetic handled seamlessly. Treat objects as you
  normally would using the `math`_ and `cmath`_ functions, but with their new 
  ``admath`` counterparts.
- **Automatic gradient and hessian function generator** for optimization 
  studies using `scipy.optimize`_ routines with ``gh(your_func_here)``.

- **Compatible Linear Algebra Routines** in the ``ad.linalg`` submodule, 
  similar to those found in NumPy's ``linalg`` submodule, that are not 
  dependent on LAPACK. There are currently:
  a. Decompositions
     1. ``chol``: Cholesky Decomposition
     2. ``lu``: LU Decomposition
     3. ``qr``: QR Decomposition
  b. Solving equations and inverting matrices
     1. ``solve``: General solver for linear systems of equations
     2. ``lstsq``: Least-squares solver for linear systems of equations
     3. ``inv``: Solve for the (multiplicative) inverse of a matrix


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 install`` from the command-line.
2. Simply copy the unzipped ``ad-XYZ`` 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 command-line.
4. If ``pip`` is installed, run ``pip install --upgrade ad`` from the 

5. Download the *bleeding-edge* version on GitHub_


Please send **feature requests, bug reports, or feedback** to 
`Abraham Lee`_.


The author expresses his thanks to :

- `Eric O. LEBIGOT (EOL)`_, author of the `uncertainties`_ package, for providing 
  code insight and inspiration
- Stephen Marks, professor at Pomona College, for useful feedback concerning 
  the interface with optimization routines in ``scipy.optimize``.
- Wendell Smith, for updating testing functionality and numerous other useful
  function updates
- Jonathan Terhorst, for catching a bug that made derivatives of logarithmic
  functions (base != e) give the wrong answers.
- GitHub user ``fhgd`` for catching a mis-calculation in ``admath.atan2``

.. _NumPy:
.. _math:
.. _cmath:
.. _Automatic differentiation:
.. _Eric O. LEBIGOT (EOL):
.. _uncertainties:
.. _scipy.optimize:
.. _Abraham Lee:
.. _package documentation:
.. _GitHub: