| Copyright | (c) Edward Kmett 2010-2014 |
|---|---|
| License | BSD3 |
| Maintainer | ekmett@gmail.com |
| Stability | experimental |
| Portability | GHC only |
| Safe Haskell | None |
| Language | Haskell2010 |
Numeric.AD.Rank1.Tower
Description
Higher order derivatives via a "dual number tower".
- data Tower a
- auto :: Mode t => Scalar t -> t
- taylor :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a]
- taylor0 :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a]
- maclaurin :: Fractional a => (Tower a -> Tower a) -> a -> [a]
- maclaurin0 :: Fractional a => (Tower a -> Tower a) -> a -> [a]
- diff :: Num a => (Tower a -> Tower a) -> a -> a
- diff' :: Num a => (Tower a -> Tower a) -> a -> (a, a)
- diffs :: Num a => (Tower a -> Tower a) -> a -> [a]
- diffs0 :: Num a => (Tower a -> Tower a) -> a -> [a]
- diffsF :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a]
- diffs0F :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a]
- du :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> a
- du' :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> (a, a)
- dus :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a]
- dus0 :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a]
- duF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g a
- duF' :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g (a, a)
- dusF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a]
- dus0F :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a]
Documentation
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 |
Taylor Series
taylor :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a] Source
taylor0 :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a] Source
Maclaurin Series
maclaurin :: Fractional a => (Tower a -> Tower a) -> a -> [a] Source
maclaurin0 :: Fractional a => (Tower a -> Tower a) -> a -> [a] Source