# 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. It generates a Wengert list (linear tape) using`Data.Reflection`

.`Numeric.AD.Mode.Kahn`

uses benign side-effects to compute reverse-mode AD. It is good for computing gradients in one pass. It generates a tree-like tape that needs to be topologically sorted in the end.`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`

computes using whichever mode or combination thereof is suitable to each individual combinator.

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.`NoEq`

means that an infinite list of converging values is returned rather than truncating the list when they become constant

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Versions [RSS] [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, 4.4, 4.4.1, 4.5 |
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Change log | CHANGELOG.markdown |

Dependencies | adjunctions (>=4.4 && <5), array (>=0.4 && <0.6), base (>=4.9 && <5), comonad (>=4 && <6), containers (>=0.5 && <0.7), data-reify (==0.6.*), erf (==2.0.*), free (>=4.6.1 && <6), nats (>=0.1.2 && <2), reflection (>=1.4 && <3), semigroups (>=0.16 && <1), tagged (>=0.7 && <1), transformers (>=0.5.2.0 && <0.6) [details] |

License | BSD-3-Clause |

Copyright | (c) Edward Kmett 2010-2021, (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 |

Bug tracker | http://github.com/ekmett/ad/issues |

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

Uploaded | by ryanglscott at 2021-11-07T13:45:52Z |

Distributions | LTSHaskell:4.4.1, NixOS:4.4.1, Stackage:4.4.1 |

Downloads | 77534 total (2128 in the last 30 days) |

Rating | 2.5 (votes: 4) [estimated by Bayesian average] |

Your Rating | |

Status | Docs available [build log] Last success reported on 2021-11-07 [all 1 reports] |

## Modules

[Index] [Quick Jump]

*Numeric*- Numeric.AD
- Numeric.AD.Double
*Halley**Internal*- Numeric.AD.Jacobian
- Numeric.AD.Jet
- Numeric.AD.Mode
- Numeric.AD.Newton
*Rank1*

- Numeric.AD

## Manual Flags

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

herbie | Disabled | |

ffi | Disabled |

## Automatic Flags

Name | Description | Default |
---|

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

## Downloads

- ad-4.5.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)