[Haskell] Re: [Haskell-cafe] ANNOUNCE: fad 1.0 -- Forward Automatic
Differentiation library
Edward Kmett
ekmett at gmail.com
Fri Apr 3 10:26:26 EDT 2009
Very nice to have!
FYI- there is at least one more quantification-based automatic
differentiation implementation in Hackage:
http://comonad.com/haskell/monoids/dist/doc/html/monoids/Data-Ring-Module-AutomaticDifferentiation.html
My implementation is/was focused upon use with monoids and other
more-limited-than-Num classes and only included the equivalent of your
'lift' and 'diffUU' operations, however.
-Edward Kmett
On Thu, Apr 2, 2009 at 10:28 PM, Bjorn Buckwalter <
bjorn.buckwalter at gmail.com> wrote:
> I'm pleased to announce the initial release of the Haskell fad
> library, developed by Barak A. Pearlmutter and Jeffrey Mark Siskind.
> Fad provides Forward Automatic Differentiation (AD) for functions
> polymorphic over instances of 'Num'. There have been many Haskell
> implementations of forward AD, with varying levels of completeness,
> published in papers and blog posts[1], but alarmingly few of these
> have made it into hackage -- to date Conal Elliot's vector-spaces[2]
> package is the only one I am aware of.
>
> Fad is an attempt to make as comprehensive and usable a forward AD
> package as is possible in Haskell. However, correctness is given
> priority over ease of use, and this is in my opinion the defining
> quality of fad. Specifically, Fad leverages Haskell's expressive
> type system to tackle the problem of _perturbation confusion_,
> brought to light in Pearlmutter and Siskind's 2005 paper "Perturbation
> Confusion and Referential Transparency"[3]. Fad prevents perturbation
> confusion by employing type-level "branding" as proposed by myself
> in a 2007 post to haskell-cafe[4]. To the best of our knowledge all
> other forward AD implementations in Haskell are susceptible to
> perturbation confusion.
>
> As this library has been in the works for quite some time it is
> worth noting that it hasn't benefited from Conal's ground-breaking
> work[5] in the area. Once we wrap our heads around his beautiful
> constructs perhaps we'll be able to borrow some tricks from him.
>
> As mentioned already, fad was developed primarily by Barak A.
> Pearlmutter and Jeffrey Mark Siskind. My own contribution has been
> providing Haskell infrastructure support and wrapping up loose ends
> in order to get the library into a releasable state. Many thanks
> to Barak and Jeffrey for permitting me to release fad under the BSD
> license.
>
> Fad resides on GitHub[6] and hackage[7] and is only a "cabal install
> fad" away! What follows is Fad's README, refer to the haddocks for
> detailed documentation.
>
> Thanks,
> Bjorn Buckwalter
>
>
> [1] http://www.haskell.org/haskellwiki/Functional_differentiation
> [2] http://www.haskell.org/haskellwiki/Vector-space
> [3]: http://www.bcl.hamilton.ie/~qobi/nesting/papers/ifl2005.pdf
> [4]: http://thread.gmane.org/gmane.comp.lang.haskell.cafe/22308/
> [5]: http://conal.net/papers/beautiful-differentiation/
> [6] http://github.com/bjornbm/fad/
> [7] http://hackage.haskell.org/cgi-bin/hackage-scripts/package/fad
>
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> Copyright : 2008-2009, Barak A. Pearlmutter and Jeffrey Mark Siskind
> License : BSD3
>
> Maintainer : bjorn.buckwalter at 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 at cs.nuim.ie> &
> Jeffrey Mark Siskind <qobi at purdue.edu>
>
> Work started as stripped-down version of higher-order tower code
> published by Jerzy Karczmarczuk <jerzy.karczmarczuk at 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 at gmail.com>
> <http://thread.gmane.org/gmane.comp.lang.haskell.cafe/22308/>
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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>
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