ad: Automatic Differentiation

[ bsd3, library, math ] [ Propose Tags ]

Forward-, reverse- and mixed- mode automatic differentiation combinators with a common API.

Type-level "branding" is used to both prevent the end user from confusing infinitesimals and to limit unsafe access to the implementation details of each Mode.

Each mode has a separate module full of combinators.

  • Numeric.AD.Mode.Forward provides basic forward-mode AD. It is good for computing simple derivatives.

  • Numeric.AD.Mode.Reverse uses benign side-effects to compute reverse-mode AD. It is good for computing gradients in one pass.

  • Numeric.AD.Mode.Sparse computes a sparse forward-mode AD tower. It is good for higher derivatives or large numbers of outputs.

  • Numeric.AD.Mode.Tower computes a dense forward-mode AD tower useful for higher derivatives of single input functions.

  • Numeric.AD.Mode.Mixed computes using whichever mode or combination thereof is suitable to each individual combinator. This mode is the default, re-exported by Numeric.AD

While not every mode can provide all operations, the following basic operations are supported, modified as appropriate by the suffixes below:

  • grad computes the gradient (partial derivatives) of a function at a point.

  • jacobian computes the Jacobian matrix of a function at a point.

  • diff computes the derivative of a function at a point.

  • du computes a directional derivative of a function at a point.

  • hessian computes the Hessian matrix (matrix of second partial derivatives) of a function at a point.

The following suffixes alter the meanings of the functions above as follows:

  • ' -- also return the answer

  • With lets the user supply a function to blend the input with the output

  • F is a version of the base function lifted to return a Traversable (or Functor) result

  • s means the function returns all higher derivatives in a list or f-branching Stream

  • T means the result is transposed with respect to the traditional formulation.

  • 0 means that the resulting derivative list is padded with 0s at the end.

Changes since 0.40.0

  • Bug fix in the derivative calculated for (/) :: (Mode s, Fractional a) => AD s a

  • Improved documentation

  • Regularized naming conventions

  • Exposed Id, probe, and lower methods via Numeric.AD.Types

  • Removed monadic combinators

  • Retuned the Mixed mode jacobian calculations to only require a Functor-based result.

  • Added unsafe variadic vgrad, vgrad', and vgrads combinators

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Versions [RSS] 0.12, 0.13, 0.15, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.27, 0.28, 0.30.0, 0.31.0, 0.32.0, 0.33.0, 0.40, 0.40.1, 0.44.0, 0.44.1, 0.44.2, 0.44.3, 0.44.4, 0.45.0, 0.46.0, 0.46.1, 0.46.2, 0.47.0, 1.0.0, 1.0.1, 1.0.2, 1.0.3, 1.0.4, 1.0.5, 1.0.6, 1.1.0, 1.1.0.1, 1.1.1, 1.1.3, 1.2.0, 1.2.0.1, 1.2.0.2, 1.3, 1.3.0.1, 1.3.1, 1.4, 1.5, 1.5.0.1, 1.5.0.2, 3.0, 3.0.1, 3.1.1, 3.1.2, 3.1.3, 3.1.4, 3.2, 3.2.1, 3.2.2, 3.3.0.1, 3.3.1, 3.3.1.1, 3.4, 4.0, 4.0.0.1, 4.1, 4.2, 4.2.0.1, 4.2.1, 4.2.1.1, 4.2.2, 4.2.3, 4.2.4, 4.3, 4.3.1, 4.3.2, 4.3.2.1, 4.3.3, 4.3.4, 4.3.5, 4.3.6, 4.4, 4.4.1, 4.5, 4.5.1, 4.5.2
Dependencies array (>=0.2 && <0.4), base (>=4 && <5), containers (>=0.2 && <0.4), data-reify (>=0.5 && <0.6), template-haskell (>=2.4 && <2.5) [details]
License BSD-3-Clause
Copyright (c) Edward Kmett 2010, (c) Barak Pearlmutter and Jeffrey Mark Siskind 2008-2009
Author Edward Kmett
Maintainer ekmett@gmail.com
Category Math
Home page http://comonad.com/reader/
Uploaded by EdwardKmett at 2010-06-12T07:32:18Z
Distributions LTSHaskell:4.5.2, NixOS:4.5.2, Stackage:4.5.2
Downloads 79520 total (142 in the last 30 days)
Rating 2.5 (votes: 4) [estimated by Bayesian average]
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