### Subversion checkout URL

You can clone with
or
.
Barak's Forward Automatic Differentiation

Fetching latest commit…

Cannot retrieve the latest commit at this time

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

Maintainer : bjorn.buckwalter@gmail.com
Stability  : experimental
Portability: GHC only?

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.

employed in this library see:
<http://www.bcl.hamilton.ie/~barak/papers/ifl2005.pdf>

Installation
============
To install:
cabal install

Or:

Examples
========
Define an example function 'f':

> 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
=======
Barak A. Pearlmutter <barak@cs.nuim.ie> &
Jeffrey Mark Siskind <qobi@purdue.edu>

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