Data.LinearMap

Linear maps

Documentation

type :-* u v = MSum (Basis u :->: v)

Linear map, represented as an optional memo-trie from basis to values, where Nothing means the zero map (an optimization).

linear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* v

Function (assumed linear) as linear map.

lapply :: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u)) => (u :-* v) -> u -> v

Apply a linear map to a vector.

atBasis :: (HasTrie a, AdditiveGroup b) => MSum (a :->: b) -> a -> b

Evaluate a linear map on a basis element. I've loosened the type to work around a typing problem in derivAtBasis. atBasis :: (AdditiveGroup v, HasTrie (Basis u)) => (u :-* v) -> Basis u -> v

idL :: (HasBasis u, HasTrie (Basis u)) => u :-* u

(*.*) :: (HasBasis u, HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w) => (v :-* w) -> (u :-* v) -> u :-* w

Compose linear maps

liftMS :: AdditiveGroup a => (a -> b) -> MSum a -> MSum b

liftMS2 :: (AdditiveGroup a, AdditiveGroup b) => (a -> b -> c) -> MSum a -> MSum b -> MSum c

liftMS3 :: (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c) => (a -> b -> c -> d) -> MSum a -> MSum b -> MSum c -> MSum d

liftL :: (Functor f, AdditiveGroup (f a)) => (a -> b) -> MSum (f a) -> MSum (f b)

Apply a linear function to each element of a linear map. liftL f l == linear f *.* l, but works more efficiently.

liftL2 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b)) => (a -> b -> c) -> MSum (f a) -> MSum (f b) -> MSum (f c)

Apply a linear binary function (not to be confused with a bilinear function) to each element of a linear map.

liftL3 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b), AdditiveGroup (f c)) => (a -> b -> c -> d) -> MSum (f a) -> MSum (f b) -> MSum (f c) -> MSum (f d)

Apply a linear ternary function (not to be confused with a trilinear function) to each element of a linear map.