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.Sparse

Contents

Sparse Gradients
Variadic Gradients
Higher-Order Gradients
Variadic Higher-Order Gradients
Sparse Jacobians (synonyms)
Sparse Hessians

Description

Higher order derivatives via a "dual number tower".

Synopsis

Documentation

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 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)
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)
Erf a => Erf (Sparse a)
InvErf a => InvErf (Sparse a)
Num a => Mode (Sparse a)
Num a => Jacobian (Sparse a)
Num a => Grad (Sparse a) [a] (a, [a]) a
Num a => Grads (Sparse a) (Cofree [] a) a
Typeable (* -> *) Sparse
Grads i o a => Grads (Sparse a -> i) (a -> o) a
Grad i o o' a => Grad (Sparse a -> i) (a -> o) (a -> o') a
type Scalar (Sparse a) = a
type D (Sparse a) = Sparse a

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

Embed a constant

Sparse Gradients

grad :: (Traversable f, Num a) => (f (Sparse a) -> Sparse a) -> f a -> f a Source

grad' :: (Traversable f, Num a) => (f (Sparse a) -> Sparse a) -> f a -> (a, f a) Source

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (f (Sparse a) -> Sparse a) -> f a -> f b Source

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

Variadic Gradients

Variadic combinators for variadic mixed-mode automatic differentiation.

Unfortunately, variadicity comes at the expense of being able to use quantification to avoid sensitivity confusion, so be careful when counting the number of auto calls you use when taking the gradient of a function that takes gradients!

class Num a => Grad i o o' a | i -> a o o', o -> a i o', o' -> a i o Source

Minimal complete definition

pack, unpack, unpack'

Instances

Num a => Grad (Sparse a) [a] (a, [a]) a
Grad i o o' a => Grad (Sparse a -> i) (a -> o) (a -> o') a

vgrad :: Grad i o o' a => i -> o Source

Higher-Order Gradients

grads :: (Traversable f, Num a) => (f (Sparse a) -> Sparse a) -> f a -> Cofree f a Source

Variadic Higher-Order Gradients

class Num a => Grads i o a | i -> a o, o -> a i Source

Minimal complete definition

packs, unpacks

Instances

Num a => Grads (Sparse a) (Cofree [] a) a
Grads i o a => Grads (Sparse a -> i) (a -> o) a

vgrads :: Grads i o a => i -> o Source

Sparse Jacobians (synonyms)

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

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

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

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

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

Sparse Hessians

hessian :: (Traversable f, Num a) => (f (Sparse a) -> Sparse a) -> f a -> f (f a) Source

hessian' :: (Traversable f, Num a) => (f (Sparse a) -> Sparse a) -> f a -> (a, f (a, f a)) Source

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

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