vector-space-0.2.0: Vector & affine spaces, plus derivatives Source code Contents Index

Data.LinearMap Stability experimental Maintainer conal@conal.net

Description

Linear maps

Synopsis

class VectorSpace a s => LMapDom a s | a -> s where data :-* a :: * -> * lapply :: VectorSpace b s => (a :-* b) -> a -> b linear :: (a -> b) -> a :-* b inL :: (LMapDom c s, VectorSpace b s', LMapDom a s') => ((a -> b) -> c -> d) -> (a :-* b) -> c :-* d inL2 :: (LMapDom c s, VectorSpace b s', LMapDom a s', LMapDom e s, VectorSpace d s) => ((a -> b) -> (c -> d) -> e -> f) -> (a :-* b) -> (c :-* d) -> e :-* f inL3 :: (LMapDom a s, VectorSpace b s, VectorSpace f s, LMapDom p s, LMapDom c s', VectorSpace d s', LMapDom e s) => ((a -> b) -> (c -> d) -> (e -> f) -> p -> q) -> (a :-* b) -> (c :-* d) -> (e :-* f) -> p :-* q linearK :: LMapDom a s => (a -> b) -> (b -> c) -> a :-* c (.*) :: (VectorSpace c s, LMapDom b s, LMapDom a s) => (b :-* c) -> (a :-* b) -> a :-* c pureL :: LMapDom a s => b -> a :-* b (<$>*) :: (LMapDom a s, VectorSpace b s) => (b -> c) -> (a :-* b) -> a :-* c liftL2 :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace d s) => (b -> c -> d) -> (a :-* b) -> (a :-* c) -> a :-* d liftL3 :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace d s, VectorSpace e s) => (b -> c -> d -> e) -> (a :-* b) -> (a :-* c) -> (a :-* d) -> a :-* e idL :: LMapDom a s => a :-* a

Documentation

class VectorSpace a s => LMapDom a s | a -> s where Source

Domain of a linear map. Associated Types data :-* a :: * -> * Source Linear map type Methods lapply :: VectorSpace b s => (a :-* b) -> a -> b Source Linear map as function linear :: (a -> b) -> a :-* b Source Function (assumed linear) as linear map. Instances LMapDom Double Double LMapDom Float Float LMapDom u s => LMapDom (Vector2 u) s (LMapDom a s, LMapDom b s) => LMapDom ((,) a b) s (LMapDom a s, LMapDom b s, LMapDom c s) => LMapDom ((,,) a b c) s

inL :: (LMapDom c s, VectorSpace b s', LMapDom a s') => ((a -> b) -> c -> d) -> (a :-* b) -> c :-* d Source

Transform a linear map by transforming a linear function.

inL2 :: (LMapDom c s, VectorSpace b s', LMapDom a s', LMapDom e s, VectorSpace d s) => ((a -> b) -> (c -> d) -> e -> f) -> (a :-* b) -> (c :-* d) -> e :-* f Source

Transform a linear maps by transforming linear functions.

inL3 :: (LMapDom a s, VectorSpace b s, VectorSpace f s, LMapDom p s, LMapDom c s', VectorSpace d s', LMapDom e s) => ((a -> b) -> (c -> d) -> (e -> f) -> p -> q) -> (a :-* b) -> (c :-* d) -> (e :-* f) -> p :-* q Source

Transform a linear maps by transforming linear functions.

linearK :: LMapDom a s => (a -> b) -> (b -> c) -> a :-* c Source

Convenience function for linear definitions. Both functions are assumed linear.

(.*) :: (VectorSpace c s, LMapDom b s, LMapDom a s) => (b :-* c) -> (a :-* b) -> a :-* c Source

Compose linear maps

pureL :: LMapDom a s => b -> a :-* b Source

Constant value as a linear map

(<$>*) :: (LMapDom a s, VectorSpace b s) => (b -> c) -> (a :-* b) -> a :-* c Source

Map a linear function over a linear map.

liftL2 :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace d s) => (b -> c -> d) -> (a :-* b) -> (a :-* c) -> a :-* d Source

Apply a linear binary function over linear maps.

liftL3 :: (LMapDom a s, VectorSpace b s, VectorSpace c s, VectorSpace d s, VectorSpace e s) => (b -> c -> d -> e) -> (a :-* b) -> (a :-* c) -> (a :-* d) -> a :-* e Source

Apply a linear ternary function over linear maps.

idL :: LMapDom a s => a :-* a Source

Identity linear map

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