Copyright	(c) Conal Elliott 2008
License	BSD3
Maintainer	conal@conal.net
Stability	experimental
Safe Haskell	Safe-Inferred
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 Source #

Minimal complete definition

Nothing

Associated Types

type Basis v :: * Source #

Representation of the canonical basis for v

type Basis v = Basis (VRep v)

Methods

basisValue :: Basis v -> v Source #

Interpret basis rep as a vector

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

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

Extract coordinates

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

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

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

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

Instances

Instances details

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

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

Linear combination of vectors

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