ghc-ad

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.

          

---

License: BSD-3-Clause
URL: https://hackage.haskell.org/package/ad