# The ad package

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 1.1.0

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

## Properties

Versions | 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 |
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Dependencies | array (>=0.2 && <0.4), base (==4.*), comonad (==1.1.*), containers (>=0.2 && <0.5), data-reify (==0.6.*), free (==1.8.*), template-haskell (>=2.4 && <2.6) [details] |

License | BSD3 |

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

Author | Edward Kmett |

Maintainer | ekmett@gmail.com |

Stability | Experimental |

Category | Math |

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

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

Uploaded | Wed Aug 3 05:28:14 UTC 2011 by EdwardKmett |

Distributions | LTSHaskell:4.3.2.1, NixOS:4.3.2.1, Stackage:4.3.2.1, Tumbleweed:4.3.2.1 |

Downloads | 18022 total (125 in the last 30 days) |

Votes | |

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

## Modules

[Index]

## Flags

Name | Description | Default | Type |
---|---|---|---|

templatehaskell24 | Disabled | Automatic |

Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info

## Downloads

- ad-1.2.0.tar.gz [browse] (Cabal source package)
- Package description (included in the package)