Copyright	(C) 2015 Ricky Elrod, Tony Morris
License	BSD2 (see LICENSE file)
Maintainer	Ricky Elrod <ricky@elrod.me>
Stability	provisional
Portability	lens
Safe Haskell	None
Language	Haskell2010

Math.MetricSpace

Description

A MetricSpace is a set together with a notion of distance between elements. Distance is computed by a function dist which has the following four laws:

non-negative: forall x y. dist x y >= 0
identity of indiscernibles: forall x y. dist x y == 0 <=> x == y
symmetry: forall x y. dist x y == dist y x
triangle inequality: forall x y z. dist x z <= dist x y + dist y z

See the Wikipedia article on metric spaces for more details.

Synopsis

Documentation

>>> import qualified Data.Vector as V

newtype MetricSpace a b Source

Constructors

MetricSpace
Fields dist :: a -> a -> b

Instances

Profunctor MetricSpace Source
SwappedMetricSpace MetricSpace Source
Semigroupoid * MetricSpace Source
Monad (MetricSpace a) Source
Functor (MetricSpace a) Source
Applicative (MetricSpace a) Source
Monoid b => Monoid (MetricSpace a b) Source
Semigroup b => Semigroup (MetricSpace a b) Source

type ClosedMetricSpace a = MetricSpace a a Source

newtype FlippedMetricSpace b a Source

Constructors

FlippedMetricSpace (MetricSpace a b)

Instances

SwappedMetricSpace FlippedMetricSpace Source
Contravariant (FlippedMetricSpace b) Source
Monoid b => Divisible (FlippedMetricSpace b) Source

type ClosedFlippedMetricSpace a = FlippedMetricSpace a a Source

(<->) :: MetricSpace a b -> a -> a -> b infixl 8 Source

_FlippedMetricSpace :: Iso (MetricSpace a b) (MetricSpace x y) (FlippedMetricSpace b a) (FlippedMetricSpace y x) Source

class SwappedMetricSpace m where Source

Minimal complete definition

Nothing

Methods

_SwappedMetricSpace :: Iso (m a b) (m x y) (m a b) (m x y) Source

Instances

SwappedMetricSpace FlippedMetricSpace Source
SwappedMetricSpace MetricSpace Source

levenshtein :: Integral b => MetricSpace String b Source

Levenshtein distance between Strings.

>>> dist levenshtein "foo" "bar"
3

>>> dist levenshtein "hi" "ha"
1

>>> dist levenshtein "ff" "ff"
0

discrete :: (Eq a, Integral b) => MetricSpace (Vector a) b Source

Discrete distance over n-dimensional Vectors.

>>> dist discrete (V.fromList [3,4]) (V.fromList [3,4])
0

>>> dist discrete (V.fromList [1,49]) (V.fromList [3,-94])
1

euclidean :: RealFloat a => MetricSpace (Vector a) a Source

Euclidean distance over n-dimensional Vectors.

>>> dist euclidean (V.fromList [3,4]) (V.fromList [3,4])
0.0

>>> dist euclidean (V.fromList [1,49]) (V.fromList [3,-94])
143.01398533010678

taxicab :: RealFloat a => MetricSpace (Vector a) a Source

Taxicab distance over n-dimensional Vectors.

>>> dist taxicab (V.fromList [3,4]) (V.fromList [3,4])
0.0

>>> dist taxicab (V.fromList [1,49]) (V.fromList [3,-94])
145.0

hamming :: (Eq a, Integral b) => MetricSpace (Vector a) b Source

Hamming distance over n-dimensional Vectors.