Numeric.AD.Mode.Sparse

Higher order derivatives via a "dual number tower".

Sparse Gradients

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

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

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

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

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

Sparse Jacobians (synonyms)

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

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

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

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

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

Sparse Hessians

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

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

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

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

Unsafe gradients

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

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

Exposed Types

module Numeric.AD.Types

class Lifted t => Mode t where

Methods

lift :: Num a => a -> t a

Embed a constant

(<+>) :: Num a => t a -> t a -> t a

Vector sum

(*^) :: Num a => a -> t a -> t a

Scalar-vector multiplication

(^*) :: Num a => t a -> a -> t a

Vector-scalar multiplication

(^/) :: Fractional a => t a -> a -> t a

Scalar division

zero :: Num a => t a

 'zero' = 'lift' 0

Instances

Mode Id

Lifted Forward => Mode Forward

Lifted Tower => Mode Tower

Lifted Reverse => Mode Reverse

Lifted Sparse => Mode Sparse

Mode f => Mode (AD f)

(Traversable f, Lifted (Dense f)) => Mode (Dense f)

(Mode f, Mode g) => Mode (ComposeMode f g)

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

Instances

Num a => Grad (AD Sparse a) [a] (a, [a]) a

Grad i o o' a => Grad (AD Sparse a -> i) (a -> o) (a -> o') a

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

Instances

Grads i o a => Grads (AD Sparse a -> i) (a -> o) a

Num a => Grads (AD Sparse a) (Cofree [] a) a