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Automatic Differentiation

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* http://comonad.com/haskell/monoids/dist/doc/html/monoids/Data-Ring-Module-AutomaticDifferentiation.html

Revision as of 21:26, 12 May 2011

Automatic Differentiation roughly means that a numerical value is equipped with a derivative part, which is updated accordingly on every function application. Let the number x0 be equipped with the derivative x1: \langle x_0,x_1 \rangle. For example the sinus is defined as:

  • \sin\langle x_0,x_1 \rangle = \langle \sin x_0, x_1\cdot\cos x_0\rangle

You see, that's just estimating errors as in physics. However, it becomes more interesting for vector functions.

Implementations:

1 Power Series

You may count arithmetic with power series also as Automatic Differentiation, since this means just working with all derivatives simultaneously.

Implementation with Haskell 98 type classes: http://code.haskell.org/~thielema/htam/src/PowerSeries/Taylor.hs

With advanced type classes in Numeric Prelude: http://hackage.haskell.org/packages/archive/numeric-prelude/0.0.5/doc/html/MathObj-PowerSeries.html

2 See also