Copyright	(c) Edward Kmett 2010-2015
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Rank1.Tower

Contents

Taylor Series
Maclaurin Series
Derivatives
Directional Derivatives

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

(Num a, Bounded a) => Bounded (Tower a)
(Num a, Enum a) => Enum (Tower a)
(Num a, Eq a) => Eq (Tower a)
Floating a => Floating (Tower a)
Fractional a => Fractional (Tower a)
Data a => Data (Tower a)
Num a => Num (Tower a)
(Num a, Ord a) => Ord (Tower a)
Real a => Real (Tower a)
RealFloat a => RealFloat (Tower a)
RealFrac a => RealFrac (Tower a)
Show a => Show (Tower a)
Erf a => Erf (Tower a)
InvErf a => InvErf (Tower a)
Num a => Mode (Tower a)
Num a => Jacobian (Tower a)
Typeable (* -> *) Tower
type Scalar (Tower a) = a
type D (Tower a) = Tower a

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