NumHask.Analysis.Metric

Metric classes

Documentation

class Multiplicative a => Signed a where

signum from base is not an operator replicated in numhask, being such a very silly name, and preferred is the much more obvious sign. Compare with Norm where there is a change in codomain

abs a * sign a == a

Generalising this class tends towards size and direction (abs is the size on the one-dim number line of a vector with its tail at zero, and sign is the direction, right?).

Methods

sign :: a -> a

abs :: a -> a

Instances

Signed Double

Defined in NumHask.Analysis.Metric

Methods

sign :: Double -> Double

abs :: Double -> Double

Signed Float

Defined in NumHask.Analysis.Metric

Methods

sign :: Float -> Float

abs :: Float -> Float

Signed Int

Defined in NumHask.Analysis.Metric

Methods

sign :: Int -> Int

abs :: Int -> Int

Signed Int8

Defined in NumHask.Analysis.Metric

Methods

sign :: Int8 -> Int8

abs :: Int8 -> Int8

Signed Int16

Defined in NumHask.Analysis.Metric

Methods

sign :: Int16 -> Int16

abs :: Int16 -> Int16

Signed Int32

Defined in NumHask.Analysis.Metric

Methods

sign :: Int32 -> Int32

abs :: Int32 -> Int32

Signed Int64

Defined in NumHask.Analysis.Metric

Methods

sign :: Int64 -> Int64

abs :: Int64 -> Int64

Signed Integer

Defined in NumHask.Analysis.Metric

Methods

sign :: Integer -> Integer

abs :: Integer -> Integer

Signed Natural

Defined in NumHask.Analysis.Metric

Methods

sign :: Natural -> Natural

abs :: Natural -> Natural

Signed Word

Defined in NumHask.Analysis.Metric

Methods

sign :: Word -> Word

abs :: Word -> Word

Signed Word8

Defined in NumHask.Analysis.Metric

Methods

sign :: Word8 -> Word8

abs :: Word8 -> Word8

Signed Word16

Defined in NumHask.Analysis.Metric

Methods

sign :: Word16 -> Word16

abs :: Word16 -> Word16

Signed Word32

Defined in NumHask.Analysis.Metric

Methods

sign :: Word32 -> Word32

abs :: Word32 -> Word32

Signed Word64

Defined in NumHask.Analysis.Metric

Methods

sign :: Word64 -> Word64

abs :: Word64 -> Word64

GCDConstraints a => Signed (Ratio a)

Defined in NumHask.Data.Rational

Methods

sign :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

Signed a => Signed (Pair a)

Defined in NumHask.Data.Pair

Methods

sign :: Pair a -> Pair a

abs :: Pair a -> Pair a

(Ord a, LowerBoundedField a, UpperBoundedField a, ExpField a) => Signed (LogField a)

Defined in NumHask.Data.LogField

Methods

sign :: LogField a -> LogField a

abs :: LogField a -> LogField a

Signed a => Signed (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

sign :: Wrapped a -> Wrapped a

abs :: Wrapped a -> Wrapped a

Signed a => Signed (Positive a)

Defined in NumHask.Data.Positive

Methods

sign :: Positive a -> Positive a

abs :: Positive a -> Positive a

class (Additive a, Additive b) => Normed a b where

Cab be Normed

norm a >= zero
norm zero == zero

Note that the Normed codomain can be different to the domain.

Methods

norm :: a -> b

Instances

Normed Double Double

Defined in NumHask.Analysis.Metric

Methods

norm :: Double -> Double

Normed Float Float

Defined in NumHask.Analysis.Metric

Methods

norm :: Float -> Float

Normed Int Int

Defined in NumHask.Analysis.Metric

Methods

norm :: Int -> Int

Normed Int8 Int8

Defined in NumHask.Analysis.Metric

Methods

norm :: Int8 -> Int8

Normed Int16 Int16

Defined in NumHask.Analysis.Metric

Methods

norm :: Int16 -> Int16

Normed Int32 Int32

Defined in NumHask.Analysis.Metric

Methods

norm :: Int32 -> Int32

Normed Int64 Int64

Defined in NumHask.Analysis.Metric

Methods

norm :: Int64 -> Int64

Normed Integer Integer

Defined in NumHask.Analysis.Metric

Methods

norm :: Integer -> Integer

Normed Natural Natural

Defined in NumHask.Analysis.Metric

Methods

norm :: Natural -> Natural

Normed Word Word

Defined in NumHask.Analysis.Metric

Methods

norm :: Word -> Word

Normed Word8 Word8

Defined in NumHask.Analysis.Metric

Methods

norm :: Word8 -> Word8

Normed Word16 Word16

Defined in NumHask.Analysis.Metric

Methods

norm :: Word16 -> Word16

Normed Word32 Word32

Defined in NumHask.Analysis.Metric

Methods

norm :: Word32 -> Word32

Normed Word64 Word64

Defined in NumHask.Analysis.Metric

Methods

norm :: Word64 -> Word64

Normed a a => Normed a (Positive a)

Defined in NumHask.Data.Positive

Methods

norm :: a -> Positive a

(ExpField a, Normed a a) => Normed (Complex a) a

Defined in NumHask.Data.Complex

Methods

norm :: Complex a -> a

(ExpField a, Normed a a) => Normed (Pair a) a

Defined in NumHask.Data.Pair

Methods

norm :: Pair a -> a

GCDConstraints a => Normed (Ratio a) (Ratio a)

Defined in NumHask.Data.Rational

Methods

norm :: Ratio a -> Ratio a

Normed a a => Normed (Pair a) (Pair a)

Defined in NumHask.Data.Pair

Methods

norm :: Pair a -> Pair a

Normed a b => Normed (Wrapped a) (Wrapped b)

Defined in NumHask.Data.Wrapped

Methods

norm :: Wrapped a -> Wrapped b

class Metric a b where

distance between numbers using L1 norm

distance a b >= zero
distance a a == zero

Methods

distance :: a -> a -> b

Instances

Metric Double Double

Defined in NumHask.Analysis.Metric

Methods

distance :: Double -> Double -> Double

Metric Float Float

Defined in NumHask.Analysis.Metric

Methods

distance :: Float -> Float -> Float

Metric Int Int

Defined in NumHask.Analysis.Metric

Methods

distance :: Int -> Int -> Int

Metric Int8 Int8

Defined in NumHask.Analysis.Metric

Methods

distance :: Int8 -> Int8 -> Int8

Metric Int16 Int16

Defined in NumHask.Analysis.Metric

Methods

distance :: Int16 -> Int16 -> Int16

Metric Int32 Int32

Defined in NumHask.Analysis.Metric

Methods

distance :: Int32 -> Int32 -> Int32

Metric Int64 Int64

Defined in NumHask.Analysis.Metric

Methods

distance :: Int64 -> Int64 -> Int64

Metric Integer Integer

Defined in NumHask.Analysis.Metric

Methods

distance :: Integer -> Integer -> Integer

Metric Natural Natural

Defined in NumHask.Analysis.Metric

Methods

distance :: Natural -> Natural -> Natural

Metric Word Word

Defined in NumHask.Analysis.Metric

Methods

distance :: Word -> Word -> Word

Metric Word8 Word8

Defined in NumHask.Analysis.Metric

Methods

distance :: Word8 -> Word8 -> Word8

Metric Word16 Word16

Defined in NumHask.Analysis.Metric

Methods

distance :: Word16 -> Word16 -> Word16

Metric Word32 Word32

Defined in NumHask.Analysis.Metric

Methods

distance :: Word32 -> Word32 -> Word32

Metric Word64 Word64

Defined in NumHask.Analysis.Metric

Methods

distance :: Word64 -> Word64 -> Word64

(Subtractive a, Normed a a) => Metric a (Positive a)

Defined in NumHask.Data.Positive

Methods

distance :: a -> a -> Positive a

(Subtractive a, ExpField a, Normed a a) => Metric (Complex a) a

Defined in NumHask.Data.Complex

Methods

distance :: Complex a -> Complex a -> a

(ExpField a, Subtractive a, Normed a a) => Metric (Pair a) a

Defined in NumHask.Data.Pair

Methods

distance :: Pair a -> Pair a -> a

GCDConstraints a => Metric (Ratio a) (Ratio a)

Defined in NumHask.Data.Rational

Methods

distance :: Ratio a -> Ratio a -> Ratio a

(Subtractive a, Normed a a) => Metric (Pair a) (Pair a)

Defined in NumHask.Data.Pair

Methods

distance :: Pair a -> Pair a -> Pair a

Metric a b => Metric (Wrapped a) (Wrapped b)

Defined in NumHask.Data.Wrapped

Methods

distance :: Wrapped a -> Wrapped a -> Wrapped b

class (Eq a, Additive a, Subtractive a, MeetSemiLattice a) => Epsilon a where

Minimal complete definition

Nothing

Methods

epsilon :: a

nearZero :: a -> Bool

aboutEqual :: a -> a -> Bool

Instances

Epsilon Double

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Double

nearZero :: Double -> Bool

aboutEqual :: Double -> Double -> Bool

Epsilon Float

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Float

nearZero :: Float -> Bool

aboutEqual :: Float -> Float -> Bool

Epsilon Int

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Int

nearZero :: Int -> Bool

aboutEqual :: Int -> Int -> Bool

Epsilon Int8

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Int8

nearZero :: Int8 -> Bool

aboutEqual :: Int8 -> Int8 -> Bool

Epsilon Int16

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Int16

nearZero :: Int16 -> Bool

aboutEqual :: Int16 -> Int16 -> Bool

Epsilon Int32

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Int32

nearZero :: Int32 -> Bool

aboutEqual :: Int32 -> Int32 -> Bool

Epsilon Int64

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Int64

nearZero :: Int64 -> Bool

aboutEqual :: Int64 -> Int64 -> Bool

Epsilon Integer

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Integer

nearZero :: Integer -> Bool

aboutEqual :: Integer -> Integer -> Bool

Epsilon Word

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Word

nearZero :: Word -> Bool

aboutEqual :: Word -> Word -> Bool

Epsilon Word8

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Word8

nearZero :: Word8 -> Bool

aboutEqual :: Word8 -> Word8 -> Bool

Epsilon Word16

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Word16

nearZero :: Word16 -> Bool

aboutEqual :: Word16 -> Word16 -> Bool

Epsilon Word32

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Word32

nearZero :: Word32 -> Bool

aboutEqual :: Word32 -> Word32 -> Bool

Epsilon Word64

Defined in NumHask.Analysis.Metric

Methods

epsilon :: Word64

nearZero :: Word64 -> Bool

aboutEqual :: Word64 -> Word64 -> Bool

(Ord a, Signed a, Subtractive a, Epsilon a) => Epsilon (Complex a)

Defined in NumHask.Data.Complex

Methods

epsilon :: Complex a

nearZero :: Complex a -> Bool

aboutEqual :: Complex a -> Complex a -> Bool

(GCDConstraints a, MeetSemiLattice a) => Epsilon (Ratio a)

Defined in NumHask.Data.Rational

Methods

epsilon :: Ratio a

nearZero :: Ratio a -> Bool

aboutEqual :: Ratio a -> Ratio a -> Bool

(Subtractive a, Epsilon a) => Epsilon (Pair a)

Defined in NumHask.Data.Pair

Methods

epsilon :: Pair a

nearZero :: Pair a -> Bool

aboutEqual :: Pair a -> Pair a -> Bool

(Epsilon a, ExpField a, LowerBoundedField a, UpperBoundedField a, Ord a) => Epsilon (LogField a)

Defined in NumHask.Data.LogField

Methods

epsilon :: LogField a

nearZero :: LogField a -> Bool

aboutEqual :: LogField a -> LogField a -> Bool

Epsilon a => Epsilon (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

epsilon :: Wrapped a

nearZero :: Wrapped a -> Bool

aboutEqual :: Wrapped a -> Wrapped a -> Bool

(Epsilon a, Ord a) => Epsilon (Positive a)

Defined in NumHask.Data.Positive

Methods

epsilon :: Positive a

nearZero :: Positive a -> Bool

aboutEqual :: Positive a -> Positive a -> Bool

(~=) :: Epsilon a => a -> a -> Bool infixl 4