Numeric.AD.Mode.Sparse

Higher order derivatives via a "dual number tower".

Sparse Gradients

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

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

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

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

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

Sparse Jacobians (synonyms)

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

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

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

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

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

Sparse Hessians

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

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

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

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

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