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

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

HasBasis Float

HasBasis CFloat

HasBasis CDouble

Integral a => HasBasis (Ratio a)

(HasBasis u, (~) * s (Scalar u), HasBasis v, (~) * s (Scalar v)) => HasBasis (u, v)

(HasBasis u, (~) * s (Scalar u), HasBasis v, (~) * s (Scalar v), HasBasis w, (~) * s (Scalar w)) => HasBasis (u, v, w)

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

Linear combination of vectors

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