Copyright	(c) Conal Elliott 2008
License	BSD3
Maintainer	conal@conal.net
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.Basis

Description

Basis of a vector space, as an associated type This module requires ghc-6.10 or later

Synopsis

class VectorSpace v => HasBasis v where
- type Basis v :: *
- basisValue :: Basis v -> v
- decompose :: v -> [(Basis v, Scalar v)]
- decompose' :: v -> Basis v -> Scalar v
linearCombo :: VectorSpace v => [(v, Scalar v)] -> v
recompose :: HasBasis v => [(Basis v, Scalar v)] -> v

Documentation

class VectorSpace v => HasBasis v where #

Minimal complete definition

Nothing

Associated Types

type Basis v :: * #

Representation of the canonical basis for v

Methods

basisValue :: Basis v -> v #

Interpret basis rep as a vector

basisValue :: (Generic v, HasBasis (VRep v), Basis (VRep v) ~ Basis v) => Basis v -> v #

Interpret basis rep as a vector

decompose :: v -> [(Basis v, Scalar v)] #

Extract coordinates

decompose :: (Generic v, HasBasis (VRep v), Scalar (VRep v) ~ Scalar v, Basis (VRep v) ~ Basis v) => v -> [(Basis v, Scalar v)] #

Extract coordinates

decompose' :: v -> Basis v -> Scalar v #

Experimental version. More elegant definitions, and friendly to infinite-dimensional vector spaces.

decompose' :: (Generic v, HasBasis (VRep v), Scalar (VRep v) ~ Scalar v, Basis (VRep v) ~ Basis v) => v -> Basis v -> Scalar v #

Experimental version. More elegant definitions, and friendly to infinite-dimensional vector spaces.

Instances

HasBasis Double #
Instance details Defined in Data.Basis Associated Types type Basis Double :: Type # Methods basisValue :: Basis Double -> Double # decompose :: Double -> [(Basis Double, Scalar Double)] # decompose' :: Double -> Basis Double -> Scalar Double #
HasBasis Float #
Instance details Defined in Data.Basis Associated Types type Basis Float :: Type # Methods basisValue :: Basis Float -> Float # decompose :: Float -> [(Basis Float, Scalar Float)] # decompose' :: Float -> Basis Float -> Scalar Float #
HasBasis CFloat #
Instance details Defined in Data.Basis Associated Types type Basis CFloat :: Type # Methods basisValue :: Basis CFloat -> CFloat # decompose :: CFloat -> [(Basis CFloat, Scalar CFloat)] # decompose' :: CFloat -> Basis CFloat -> Scalar CFloat #
HasBasis CDouble #
Instance details Defined in Data.Basis Associated Types type Basis CDouble :: Type # Methods basisValue :: Basis CDouble -> CDouble # decompose :: CDouble -> [(Basis CDouble, Scalar CDouble)] # decompose' :: CDouble -> Basis CDouble -> Scalar CDouble #
Integral a => HasBasis (Ratio a) #
Instance details Defined in Data.Basis Associated Types type Basis (Ratio a) :: Type # Methods basisValue :: Basis (Ratio a) -> Ratio a # decompose :: Ratio a -> [(Basis (Ratio a), Scalar (Ratio a))] # decompose' :: Ratio a -> Basis (Ratio a) -> Scalar (Ratio a) #
(HasBasis u, s ~ Scalar u, HasBasis v, s ~ Scalar v) => HasBasis (u, v) #
Instance details Defined in Data.Basis Associated Types type Basis (u, v) :: Type # Methods basisValue :: Basis (u, v) -> (u, v) # decompose :: (u, v) -> [(Basis (u, v), Scalar (u, v))] # decompose' :: (u, v) -> Basis (u, v) -> Scalar (u, v) #
HasBasis a => HasBasis (Rec0 a s) #
Instance details Defined in Data.Basis Associated Types type Basis (Rec0 a s) :: Type # Methods basisValue :: Basis (Rec0 a s) -> Rec0 a s # decompose :: Rec0 a s -> [(Basis (Rec0 a s), Scalar (Rec0 a s))] # decompose' :: Rec0 a s -> Basis (Rec0 a s) -> Scalar (Rec0 a s) #
(HasBasis u, s ~ Scalar u, HasBasis v, s ~ Scalar v, HasBasis w, s ~ Scalar w) => HasBasis (u, v, w) #
Instance details Defined in Data.Basis Associated Types type Basis (u, v, w) :: Type # Methods basisValue :: Basis (u, v, w) -> (u, v, w) # decompose :: (u, v, w) -> [(Basis (u, v, w), Scalar (u, v, w))] # decompose' :: (u, v, w) -> Basis (u, v, w) -> Scalar (u, v, w) #
(HasBasis (f p), HasBasis (g p), Scalar (f p) ~ Scalar (g p)) => HasBasis ((f :*: g) p) #
Instance details Defined in Data.Basis Associated Types type Basis ((f :: g) p) :: Type # Methods basisValue :: Basis ((f :: g) p) -> (f :: g) p # decompose :: (f :: g) p -> [(Basis ((f :: g) p), Scalar ((f :: g) p))] # decompose' :: (f :: g) p -> Basis ((f :: g) p) -> Scalar ((f :*: g) p) #
HasBasis (f p) => HasBasis (M1 i c f p) #
Instance details Defined in Data.Basis Associated Types type Basis (M1 i c f p) :: Type # Methods basisValue :: Basis (M1 i c f p) -> M1 i c f p # decompose :: M1 i c f p -> [(Basis (M1 i c f p), Scalar (M1 i c f p))] # decompose' :: M1 i c f p -> Basis (M1 i c f p) -> Scalar (M1 i c f p) #

linearCombo :: VectorSpace v => [(v, Scalar v)] -> v #

Linear combination of vectors

recompose :: HasBasis v => [(Basis v, Scalar v)] -> v #