Copyright (c) Edward Kmett 2010-2015 BSD3 ekmett@gmail.com experimental GHC only None Haskell2010

Description

Higher order derivatives via a "dual number tower".

Synopsis

# Documentation

data Tower a Source #

Tower is an AD Mode that calculates a tangent tower by forward AD, and provides fast diffsUU, diffsUF

Instances

auto :: Mode t => Scalar t -> t Source #

Embed a constant

# Taylor Series

taylor :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a] Source #

taylor f x compute the Taylor series of f around x.

taylor0 :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a] Source #

taylor0 f x compute the Taylor series of f around x, zero-padded.

# Maclaurin Series

maclaurin :: Fractional a => (Tower a -> Tower a) -> a -> [a] Source #

maclaurin f compute the Maclaurin series of f

maclaurin0 :: Fractional a => (Tower a -> Tower a) -> a -> [a] Source #

maclaurin f compute the Maclaurin series of f, zero-padded

# Derivatives

diff :: Num a => (Tower a -> Tower a) -> a -> a Source #

Compute the first derivative of a function (a -> a)

diff' :: Num a => (Tower a -> Tower a) -> a -> (a, a) Source #

Compute the answer and first derivative of a function (a -> a)

diffs :: Num a => (Tower a -> Tower a) -> a -> [a] Source #

Compute the answer and all derivatives of a function (a -> a)

diffs0 :: Num a => (Tower a -> Tower a) -> a -> [a] Source #

Compute the zero-padded derivatives of a function (a -> a)

diffsF :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a] Source #

Compute the answer and all derivatives of a function (a -> f a)

diffs0F :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a] Source #

Compute the zero-padded derivatives of a function (a -> f a)

# Directional Derivatives

du :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> a Source #

Compute a directional derivative of a function (f a -> a)

du' :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> (a, a) Source #

Compute the answer and a directional derivative of a function (f a -> a)

dus :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a] Source #

Given a function (f a -> a), and a tower of derivatives, compute the corresponding directional derivatives.

dus0 :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a] Source #

Given a function (f a -> a), and a tower of derivatives, compute the corresponding directional derivatives, zero-padded

duF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g a Source #

Compute a directional derivative of a function (f a -> g a)

duF' :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g (a, a) Source #

Compute the answer and a directional derivative of a function (f a -> g a)

dusF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a] Source #

Given a function (f a -> g a), and a tower of derivatives, compute the corresponding directional derivatives

dus0F :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a] Source #

Given a function (f a -> g a), and a tower of derivatives, compute the corresponding directional derivatives, zero-padded