# ad: Automatic Differentiation

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 1.3

Dependency bump to be compatible with ghc 7.4.1

Changes since 1.2

Compiles with template haskell 2.6, changed interface to comply with the lack of Eq and Show as superclasses of Num in the new GHC.

Changes since 1.1.3

Made primal calculations strict where possible.

Changes since 1.1.0

Introduced a much faster topological sort into the reverse mode AD implementation by Anthony Cowley. This fixes a space leak and a stack overflow problem on very large (>2000 variable) problem sets.

Made bound calculations in reverse mode more strict.

Changes since 1.0.0

Changed the way

`Show`

was derived to comply with changes in instance resolution in ghc >= 7.0 && <= 7.1

Changes since 0.45.0

Converted

`Stream`

to use the external`comonad`

package

Changes since 0.44.5

Added Halley's method

Changes since 0.40.0

Fixed bug fix 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

Versions [faq] | 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 |
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Dependencies | array (>=0.2 && <0.5), base (==4.*), comonad (>=1.1.1.1 && <1.2), containers (>=0.2 && <0.5), data-reify (==0.6.*), free (==2.0.*), template-haskell (>=2.6 && <2.8) [details] |

License | BSD-3-Clause |

Copyright | (c) Edward Kmett 2010-2011, (c) Barak Pearlmutter and Jeffrey Mark Siskind 2008-2009 |

Author | Edward Kmett |

Maintainer | ekmett@gmail.com |

Category | Math |

Home page | http://github.com/ekmett/ad |

Source repo | head: git clone git://github.com/ekmett/ad.git |

Uploaded | by EdwardKmett at Tue Feb 7 11:13:30 UTC 2012 |

Distributions | LTSHaskell:4.3.6, NixOS:4.3.6, Stackage:4.3.6 |

Downloads | 48645 total (1557 in the last 30 days) |

Rating | 2.5 (votes: 3) [estimated by rule of succession] |

Your Rating | |

Status | Docs uploaded by user Build status unknown [no reports yet] |

## Modules

[Index]

## Downloads

- ad-1.3.0.1.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)