vector-space-0.10.2: Vector & affine spaces, linear maps, and derivatives

Data.LinearMap

Description

Linear maps

Synopsis

# Documentation

data u :-* v Source

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

Instances

 (HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup ((:-*) u v) (HasTrie (Basis u), VectorSpace v) => VectorSpace ((:-*) u v) type Scalar ((:-*) u v) = Scalar v

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

Function (assumed linear) as linear map.

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

Apply a linear map to a vector.

atBasis :: (AdditiveGroup v, HasTrie (Basis u)) => (u :-* v) -> Basis u -> v Source

Evaluate a linear map on a basis element.

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

Identity linear map

(*.*) :: (HasBasis u, HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w) => (v :-* w) -> (u :-* v) -> u :-* w infixr 9 Source

Compose linear maps

inLMap :: (LMap' r s -> LMap' t u) -> (r :-* s) -> t :-* u Source

inLMap2 :: (LMap' r s -> LMap' t u -> LMap' v w) -> (r :-* s) -> (t :-* u) -> v :-* w Source

inLMap3 :: (LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y) -> (r :-* s) -> (t :-* u) -> (v :-* w) -> x :-* y Source

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

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

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

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

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) Source

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) Source

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

firstL :: (HasBasis u, HasBasis u', HasBasis v, HasTrie (Basis u), HasTrie (Basis v), Scalar u ~ Scalar v, Scalar u ~ Scalar u') => (u :-* u') -> (u, v) :-* (u', v) Source