name: ad version: 0.47.0 license: BSD3 license-File: LICENSE 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 homepage: http://github.com/ekmett/ad synopsis: Automatic Differentiation description: 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 0.45.0 . * 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 build-type: Simple build-depends: base >= 4 && < 5, data-reify >= 0.6 && < 0.7, containers >= 0.2 && < 0.5, template-haskell >= 2.4 && < 2.5, array >= 0.2 && < 0.4, comonad >= 0.9 && < 0.10, streams >= 0.5 && < 0.6 exposed-modules: Numeric.AD Numeric.AD.Classes Numeric.AD.Types Numeric.AD.Newton Numeric.AD.Halley Numeric.AD.Internal.Classes Numeric.AD.Internal.Combinators Numeric.AD.Internal.Forward Numeric.AD.Internal.Tower Numeric.AD.Internal.Reverse Numeric.AD.Internal.Sparse Numeric.AD.Internal.Dense Numeric.AD.Internal.Composition Numeric.AD.Mode.Directed Numeric.AD.Mode.Forward Numeric.AD.Mode.Mixed Numeric.AD.Mode.Reverse Numeric.AD.Mode.Tower Numeric.AD.Mode.Sparse other-modules: Numeric.AD.Internal.Types Numeric.AD.Internal.Tensors Numeric.AD.Internal.Identity Extra-Source-Files: TODO GHC-Options: -Wall -fspec-constr -fdicts-cheap -O2