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

Documentation

class VectorSpace v => HasBasis v where #

Minimal complete definition

basisValue, decompose, decompose'

Associated Types

type Basis v :: * #

Representation of the canonical basis for v

Methods

basisValue :: Basis v -> v #

Interpret basis rep as a vector

decompose :: 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.

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 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) #

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

Linear combination of vectors

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