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 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

Modules

[Last Documentation]

Downloads

• ad-1.0.1.tar.gz [browse] (Cabal source package)
• Package description (revised from the package)

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Maintainer's Corner

Package maintainers

• EdwardKmett, EricMertens, ryanglscott

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