ad-4.2.1.1: Automatic Differentiation

Safe Haskell None Haskell2010

Numeric.AD.Internal.Sparse

Synopsis

# Documentation

newtype Index Source

Constructors

 Index (IntMap Int)

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.

Constructors

 Sparse !a (IntMap (Sparse a)) Zero

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

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

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

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

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

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

skeleton :: Traversable f => f a -> f Int Source

spartial :: Num a => [Int] -> Sparse a -> Maybe a Source

partial :: Num a => [Int] -> Sparse a -> a Source

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

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

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

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

Methods

pack :: i -> [Sparse a] -> Sparse a Source

unpack :: ([a] -> [a]) -> o Source

unpack' :: ([a] -> (a, [a])) -> o' Source

Instances

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

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

Methods

packs :: i -> [Sparse a] -> Sparse a Source

unpacks :: ([a] -> Cofree [] a) -> o Source

Instances

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