Data.Basis

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

Documentation

class VectorSpace v => HasBasis v where

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

Associated Types

type Basis Double :: *

Methods

basisValue :: Basis Double -> Double

decompose :: Double -> [(Basis Double, Scalar Double)]

decompose' :: Double -> Basis Double -> Scalar Double

HasBasis Float

Associated Types

type Basis Float :: *

Methods

basisValue :: Basis Float -> Float

decompose :: Float -> [(Basis Float, Scalar Float)]

decompose' :: Float -> Basis Float -> Scalar Float

HasBasis CFloat

Associated Types

type Basis CFloat :: *

Methods

basisValue :: Basis CFloat -> CFloat

decompose :: CFloat -> [(Basis CFloat, Scalar CFloat)]

decompose' :: CFloat -> Basis CFloat -> Scalar CFloat

HasBasis CDouble

Associated Types

type Basis CDouble :: *

Methods

basisValue :: Basis CDouble -> CDouble

decompose :: CDouble -> [(Basis CDouble, Scalar CDouble)]

decompose' :: CDouble -> Basis CDouble -> Scalar CDouble

Integral a => HasBasis (Ratio a)

Associated Types

type Basis (Ratio a) :: *

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)

Associated Types

type Basis (u, v) :: *

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)

Associated Types

type Basis (Rec0 * a s) :: *

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)

Associated Types

type Basis (u, v, w) :: *

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)

Associated Types

type Basis ((* :*: f) g p) :: *

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)

Associated Types

type Basis (M1 * i c f p) :: *

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