Copyright : 2008-2009, Barak A. Pearlmutter and Jeffrey Mark Siskind

License : BSD3

Maintainer : bjorn.buckwalter@gmail.com

Stability : experimental

Portability: GHC only?

Forward Automatic Differentiation via overloading to perform

nonstandard interpretation that replaces original numeric type with

corresponding generalized dual number type.

Each invocation of the differentiation function introduces a

distinct perturbation, which requires a distinct dual number type.

In order to prevent these from being confused, tagging, called

branding in the Haskell community, is used. This seems to prevent

perturbation confusion, although it would be nice to have an actual

proof of this. The technique does require adding invocations of

lift at appropriate places when nesting is present.

For more information on perturbation confusion and the solution

employed in this library see:

<http://www.bcl.hamilton.ie/~barak/papers/ifl2005.pdf>

<http://thread.gmane.org/gmane.comp.lang.haskell.cafe/22308/>

Installation

============

To install:

cabal install

Or:

runhaskell Setup.lhs configure

runhaskell Setup.lhs build

runhaskell Setup.lhs install

Examples

========

Define an example function 'f':

> import Numeric.FAD

> f x = 6 - 5 * x + x ^ 2 -- Our example function

Basic usage of the differentiation operator:

> y = f 2 -- f(2) = 0

> y' = diff f 2 -- First derivative f'(2) = -1

> y'' = diff (diff f) 2 -- Second derivative f''(2) = 2

List of derivatives:

> ys = take 3 $ diffs f 2 -- [0, -1, 2]

Example optimization method; find a zero using Newton's method:

> y_newton1 = zeroNewton f 0 -- converges to first zero at 2.0.

> y_newton2 = zeroNewton f 10 -- converges to second zero at 3.0.

Credits

=======

Authors: Copyright 2008,

Barak A. Pearlmutter <barak@cs.nuim.ie> &

Jeffrey Mark Siskind <qobi@purdue.edu>

Work started as stripped-down version of higher-order tower code

published by Jerzy Karczmarczuk <jerzy.karczmarczuk@info.unicaen.fr>

which used a non-standard standard prelude.

Initial perturbation-confusing code is a modified version of

<http://cdsmith.wordpress.com/2007/11/29/some-playing-with-derivatives/>

Tag trick, called "branding" in the Haskell community, from

Bjorn Buckwalter <bjorn.buckwalter@gmail.com>

<http://thread.gmane.org/gmane.comp.lang.haskell.cafe/22308/>