Safe Haskell	Safe-Inferred
Language	Haskell2010

Numeric.Algebra.Normed

Description

Provides the Normed typeclass.

Since: 0.1

Synopsis

class Normed s where
- norm :: s -> s

Documentation

class Normed s where Source #

Defines a "norm" on a given structure. We have the following laws:

Positive definiteness: norm x > 0 for x /= 0, norm 0 = 0.
Subadditivity: norm (x + y) <= norm x + norm y.
Inversion : norm x = norm (-x).

Notice these laws require various algebraic assumptions, from a semigroup up to a group structure. It is expected that types that implement ASemigroup, AMonoid, and AGroup will follow the respective laws.

We do not require any of these typeclasses as constraints as it is possible that we may want to abstract over "positive" types with a type that does not have an additive semigroup instance (consider multiplicative groups).

Since: 0.1

Methods

norm :: s -> s Source #

Since: 0.1

Instances

Instances details

Normed Int16 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Int16 -> Int16 Source #
Normed Int32 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Int32 -> Int32 Source #
Normed Int64 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Int64 -> Int64 Source #
Normed Int8 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Int8 -> Int8 Source #
Normed Word16 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Word16 -> Word16 Source #
Normed Word32 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Word32 -> Word32 Source #
Normed Word64 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Word64 -> Word64 Source #
Normed Word8 Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Word8 -> Word8 Source #
Normed Integer Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Integer -> Integer Source #
Normed Natural Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Natural -> Natural Source #
Normed Double Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Double -> Double Source #
Normed Float Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Float -> Float Source #
Normed Int Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Int -> Int Source #
Normed Word Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Word -> Word Source #
RealFloat a => Normed (Complex a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Complex a -> Complex a Source #
Normed (Ratio Integer) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Ratio Integer -> Ratio Integer Source #
Normed (Ratio Natural) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: Ratio Natural -> Ratio Natural Source #
Normed a => Normed (a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a) -> (a, a) Source #
Normed a => Normed (a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a) -> (a, a, a) Source #
Normed a => Normed (a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a) -> (a, a, a, a) Source #
Normed a => Normed (a, a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a, a) -> (a, a, a, a, a) Source #
Normed a => Normed (a, a, a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a, a, a) -> (a, a, a, a, a, a) Source #
Normed a => Normed (a, a, a, a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a, a, a, a) -> (a, a, a, a, a, a, a) Source #
Normed a => Normed (a, a, a, a, a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a, a, a, a, a) -> (a, a, a, a, a, a, a, a) Source #
Normed a => Normed (a, a, a, a, a, a, a, a, a) Source #	Since: 0.1
Instance details Defined in Numeric.Algebra.Normed Methods norm :: (a, a, a, a, a, a, a, a, a) -> (a, a, a, a, a, a, a, a, a) Source #