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

Instances

data Sparse a Source

We only store partials in sorted order, so the map contained in a partial will only contain partials with equal or greater keys to that of the map in which it was found. This should be key for efficiently computing sparse hessians. there are only (n + k - 1) choose (k - 1) distinct nth partial derivatives of a function with k inputs.

Instances

 (Num a, Bounded a) => Bounded (Sparse a) (Num a, Enum a) => Enum (Sparse a) (Num a, Eq a) => Eq (Sparse a) Floating a => Floating (Sparse a) Fractional a => Fractional (Sparse a) Data a => Data (Sparse a) Source Num a => Num (Sparse a) (Num a, Ord a) => Ord (Sparse a) Real a => Real (Sparse a) RealFloat a => RealFloat (Sparse a) RealFrac a => RealFrac (Sparse a) Show a => Show (Sparse a) Source Erf a => Erf (Sparse a) InvErf a => InvErf (Sparse a) Num a => Mode (Sparse a) Source Num a => Jacobian (Sparse a) Source Num a => Grad (Sparse a) [a] (a, [a]) a Source Num a => Grads (Sparse a) (Cofree [] a) a Source Grads i o a => Grads (Sparse a -> i) (a -> o) a Source Grad i o o' a => Grad (Sparse a -> i) (a -> o) (a -> o') a Source type Scalar (Sparse a) = a Source type D (Sparse a) = Sparse a Source

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

Embed a constant

grad :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f a Source

grad' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f a) Source

grads :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> Cofree f a Source

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f b Source

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f b) Source

# Sparse Jacobians (synonyms)

jacobian :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f a) Source

jacobian' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f a) Source

jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f b) Source

jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f b) Source

jacobians :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (Cofree f a) Source

# Sparse Hessians

hessian :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f (f a) Source

hessian' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f (a, f a)) Source

hessianF :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f (f a)) Source

hessianF' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f (a, f a)) Source