NumHask.Algebra.Module

Algebra

Module

class (Representable m, Additive a) => AdditiveModule m a where

AdditiveModule

Methods

(.+) :: m a -> a -> m a infixl 6

(+.) :: a -> m a -> m a infixl 6

Instances

(Representable r, Additive a) => AdditiveModule r a

Methods

(.+) :: r a -> a -> r a

(+.) :: a -> r a -> r a

class (Representable m, AdditiveGroup a) => AdditiveGroupModule m a where

AdditiveGroupModule

Methods

(.-) :: m a -> a -> m a infixl 6

(-.) :: a -> m a -> m a infixl 6

Instances

(Representable r, AdditiveGroup a) => AdditiveGroupModule r a

Methods

(.-) :: r a -> a -> r a

(-.) :: a -> r a -> r a

class (Representable m, Multiplicative a) => MultiplicativeModule m a where

MultiplicativeModule

Methods

(.*) :: m a -> a -> m a infixl 7

(*.) :: a -> m a -> m a infixl 7

Instances

(Representable r, Multiplicative a) => MultiplicativeModule r a

Methods

(.*) :: r a -> a -> r a

(*.) :: a -> r a -> r a

class (Representable m, MultiplicativeGroup a) => MultiplicativeGroupModule m a where

MultiplicativeGroupModule

Methods

(./) :: m a -> a -> m a infixl 7

(/.) :: a -> m a -> m a infixl 7

Instances

(Representable r, MultiplicativeGroup a) => MultiplicativeGroupModule r a

Methods

(./) :: r a -> a -> r a

(/.) :: a -> r a -> r a

Tensoring

class (Representable m, ExpField a, Normed (m a) a) => Banach m a where

Banach

Methods

normalize :: m a -> m a

Instances

(Normed (r a) a, ExpField a, Representable r) => Banach r a

Methods

normalize :: r a -> r a

class Additive (m a) => Hilbert m a where

Hilbert

Minimal complete definition

(<.>)

Methods

(<.>) :: m a -> m a -> a infix 8

Instances

(Additive (r a), Foldable r, Representable r, CRing a) => Hilbert r a

Methods

(<.>) :: r a -> r a -> a

type family (a :: k1) >< (b :: k2) :: * infix 8

tensorial tomfoolery

Instances

type (><) * * (r a) b

type (><) * * (r a) b

type (><) * * Double Double

type (><) * * Double Double = Double

type (><) * * Float Float

type (><) * * Float Float = Float

type (><) * * Int Int

type (><) * * Int Int = Int

type (><) * * Integer Integer

type (><) * * Integer Integer = Integer

class TensorProduct a where

TensorAlgebra

Minimal complete definition

(><), timesleft, timesright

Methods

(><) :: a -> a -> a >< a infix 8

timesleft :: a -> (a >< a) -> a

timesright :: (a >< a) -> a -> a

Instances

(AdditiveGroup (r a), Foldable r, Representable r, CRing a) => TensorProduct (r a)

Methods

(><) :: r a -> r a -> (* >< *) (r a) (r a)

timesleft :: r a -> (* >< *) (r a) (r a) -> r a

timesright :: (* >< *) (r a) (r a) -> r a -> r a