| 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.distx y >= 0 - identity of indiscernibles:
forall x y.distx y == 0 <=> x == y - symmetry:
forall x y. dist x y ==disty x - triangle inequality:
forall x y z.distx z <=distx y +disty z
See the Wikipedia article on metric spaces for more details.
- newtype MetricSpace a b = MetricSpace {
- dist :: a -> a -> b
- type ClosedMetricSpace a = MetricSpace a a
- newtype FlippedMetricSpace b a = FlippedMetricSpace (MetricSpace a b)
- type ClosedFlippedMetricSpace a = FlippedMetricSpace a a
- (<->) :: MetricSpace a b -> a -> a -> b
- _FlippedMetricSpace :: Iso (MetricSpace a b) (MetricSpace x y) (FlippedMetricSpace b a) (FlippedMetricSpace y x)
- class SwappedMetricSpace m where
- _SwappedMetricSpace :: Iso (m a b) (m x y) (m a b) (m x y)
- levenshtein :: Integral b => MetricSpace String b
- discrete :: (Eq a, Integral b) => MetricSpace (Vector a) b
- euclidean :: RealFloat a => MetricSpace (Vector a) a
- taxicab :: RealFloat a => MetricSpace (Vector a) a
- hamming :: (Eq a, Integral b) => MetricSpace (Vector a) b
Documentation
>>>import qualified Data.Vector as V
newtype MetricSpace a b
Constructors
| MetricSpace | |
Fields
| |
Instances
| Profunctor MetricSpace | |
| SwappedMetricSpace MetricSpace | |
| Semigroupoid * MetricSpace | |
| Monad (MetricSpace a) | |
| Functor (MetricSpace a) | |
| Applicative (MetricSpace a) | |
| Monoid b => Monoid (MetricSpace a b) | |
| Semigroup b => Semigroup (MetricSpace a b) |
type ClosedMetricSpace a = MetricSpace a a
newtype FlippedMetricSpace b a
Constructors
| FlippedMetricSpace (MetricSpace a b) |
Instances
| SwappedMetricSpace FlippedMetricSpace | |
| Contravariant (FlippedMetricSpace b) | |
| Monoid b => Divisible (FlippedMetricSpace b) |
type ClosedFlippedMetricSpace a = FlippedMetricSpace a a
(<->) :: MetricSpace a b -> a -> a -> b infixl 8
_FlippedMetricSpace :: Iso (MetricSpace a b) (MetricSpace x y) (FlippedMetricSpace b a) (FlippedMetricSpace y x)
class SwappedMetricSpace m where
Minimal complete definition
Nothing
Methods
_SwappedMetricSpace :: Iso (m a b) (m x y) (m a b) (m x y)
levenshtein :: Integral b => MetricSpace String b
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
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
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
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
Hamming distance over n-dimensional Vectors.