ad
Version 4.5 revision 0 uploaded by ryanglscott.
Package meta
- 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. It generates a Wengert list (linear tape) usingData.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 answerWith
lets the user supply a function to blend the input with the outputF
is a version of the base function lifted to return a Traversable (or Functor) results
means the function returns all higher derivatives in a list or f-branching StreamT
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
- Author
- Edward Kmett
- Bug reports
- http://github.com/ekmett/ad/issues
- Category
- Math
- Copyright
- (c) Edward Kmett 2010-2021, (c) Barak Pearlmutter and Jeffrey Mark Siskind 2008-2009
- Homepage
- http://github.com/ekmett/ad
- Maintainer
- ekmett@gmail.com
- Package URL
- n/a
- Stability
- Experimental