vector-space-0.7.6: Vector & affine spaces, linear maps, and derivatives (requires ghc 6.9 or better)Source codeContentsIndex
Data.LinearMap
Stabilityexperimental
Maintainerconal@conal.net
Description
Linear maps
Synopsis
data u :-* v
linear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* v
lapply :: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u)) => (u :-* v) -> u -> v
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
inLMap :: (LMap' r s -> LMap' t u) -> (r :-* s) -> t :-* u
inLMap2 :: (LMap' r s -> LMap' t u -> LMap' v w) -> (r :-* s) -> (t :-* u) -> v :-* w
inLMap3 :: (LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y) -> (r :-* s) -> (t :-* u) -> (v :-* w) -> x :-* y
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)
liftL2 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b)) => (a -> b -> c) -> MSum (f a) -> MSum (f b) -> MSum (f c)
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)
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)
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).
show/hide Instances
linear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* vSource
Function (assumed linear) as linear map.
lapply :: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u)) => (u :-* v) -> u -> vSource
Apply a linear map to a vector.
atBasis :: (AdditiveGroup v, HasTrie (Basis u)) => (u :-* v) -> Basis u -> vSource
Evaluate a linear map on a basis element.
idL :: (HasBasis u, HasTrie (Basis u)) => u :-* uSource
Identity linear map
(*.*) :: (HasBasis u, HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w) => (v :-* w) -> (u :-* v) -> u :-* wSource
Compose linear maps
inLMap :: (LMap' r s -> LMap' t u) -> (r :-* s) -> t :-* uSource
inLMap2 :: (LMap' r s -> LMap' t u -> LMap' v w) -> (r :-* s) -> (t :-* u) -> v :-* wSource
inLMap3 :: (LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y) -> (r :-* s) -> (t :-* u) -> (v :-* w) -> x :-* ySource
liftMS :: AdditiveGroup a => (a -> b) -> MSum a -> MSum bSource
liftMS2 :: (AdditiveGroup a, AdditiveGroup b) => (a -> b -> c) -> MSum a -> MSum b -> MSum cSource
liftMS3 :: (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c) => (a -> b -> c -> d) -> MSum a -> MSum b -> MSum c -> MSum dSource
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
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