Safe Haskell	Safe
Language	Haskell2010

Math.Tools.Median

Synopsis

class Ord m => MedianAlgebra m where
- med :: m -> m -> m -> m
median5 :: MedianAlgebra a => a -> a -> a -> a -> a -> a
median :: Ord a => a -> a -> a -> a
data Interval a = Interval {
- interval_startpoint :: a
- interval_endpoint :: a
}
in_interval :: (Eq a, MedianAlgebra a) => a -> Interval a -> Bool
interval :: (Monad m, MedianAlgebra a) => Interval a -> m a -> m a
median_homomorphism :: MedianAlgebra a => Interval a -> a -> a
andor :: Ord a => (a, a) -> (a, a)
andor' :: Ord a => (a, a) -> (a, a)
andor3 :: Ord a => (a, a, a) -> (a, a, a)

Documentation

class Ord m => MedianAlgebra m where Source #

Rules expected of MedianAlgebra.

From "Knuth: The Art of Computer Programming" section 7.1.1 http://www-cs-faculty.stanford.edu/~uno/taocp.html

"median/majority"

med x x y == x

"median/commutative"

med x y z == med x z y

med x y z == med y z x

med x y z == med z x y

med x y z == med z y x

"median/associative"

med x w (med y w z) == med (med x w y) w z

"median/distributive"

med (med x y z) u v == med x (med y u v) (med z u v)

Methods

med :: m -> m -> m -> m Source #

Instances

Instances details

MedianAlgebra Ordering Source #
Instance details Defined in Math.Tools.Median Methods med :: Ordering -> Ordering -> Ordering -> Ordering Source #
MedianAlgebra Integer Source #
Instance details Defined in Math.Tools.Median Methods med :: Integer -> Integer -> Integer -> Integer Source #
MedianAlgebra Bool Source #
Instance details Defined in Math.Tools.Median Methods med :: Bool -> Bool -> Bool -> Bool Source #
MedianAlgebra Char Source #
Instance details Defined in Math.Tools.Median Methods med :: Char -> Char -> Char -> Char Source #
MedianAlgebra Double Source #
Instance details Defined in Math.Tools.Median Methods med :: Double -> Double -> Double -> Double Source #
MedianAlgebra Float Source #
Instance details Defined in Math.Tools.Median Methods med :: Float -> Float -> Float -> Float Source #
MedianAlgebra Int Source #
Instance details Defined in Math.Tools.Median Methods med :: Int -> Int -> Int -> Int Source #
Integral a => MedianAlgebra (Ratio a) Source #
Instance details Defined in Math.Tools.Median Methods med :: Ratio a -> Ratio a -> Ratio a -> Ratio a Source #
MedianAlgebra a => MedianAlgebra (Vector1 a) Source #
Instance details Defined in Math.Matrix.Vector1 Methods med :: Vector1 a -> Vector1 a -> Vector1 a -> Vector1 a Source #
MedianAlgebra s => MedianAlgebra (Vector2 s) Source #
Instance details Defined in Math.Matrix.Vector2 Methods med :: Vector2 s -> Vector2 s -> Vector2 s -> Vector2 s Source #
MedianAlgebra s => MedianAlgebra (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods med :: Vector3 s -> Vector3 s -> Vector3 s -> Vector3 s Source #
MedianAlgebra s => MedianAlgebra (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods med :: Vector4 s -> Vector4 s -> Vector4 s -> Vector4 s Source #
MedianAlgebra a => MedianAlgebra [a] Source #
Instance details Defined in Math.Tools.Median Methods med :: [a] -> [a] -> [a] -> [a] Source #
(MedianAlgebra a, MedianAlgebra b) => MedianAlgebra (a, b) Source #
Instance details Defined in Math.Tools.Median Methods med :: (a, b) -> (a, b) -> (a, b) -> (a, b) Source #
(MedianAlgebra a, MedianAlgebra b, MedianAlgebra c) => MedianAlgebra (a, b, c) Source #
Instance details Defined in Math.Tools.Median Methods med :: (a, b, c) -> (a, b, c) -> (a, b, c) -> (a, b, c) Source #
(MedianAlgebra a, MedianAlgebra b, MedianAlgebra c, MedianAlgebra d) => MedianAlgebra (a, b, c, d) Source #
Instance details Defined in Math.Tools.Median Methods med :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #
(MedianAlgebra a, MedianAlgebra b, MedianAlgebra c, MedianAlgebra d, MedianAlgebra e) => MedianAlgebra (a, b, c, d, e) Source #
Instance details Defined in Math.Tools.Median Methods med :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

median5 :: MedianAlgebra a => a -> a -> a -> a -> a -> a Source #

median :: Ord a => a -> a -> a -> a Source #

data Interval a Source #

Constructors

Interval
Fields interval_startpoint :: a interval_endpoint :: a

Instances

Instances details

MonadFail Interval Source #
Instance details Defined in Math.Tools.Median Methods fail :: String -> Interval a #
Applicative Interval Source #
Instance details Defined in Math.Tools.Median Methods pure :: a -> Interval a # (<>) :: Interval (a -> b) -> Interval a -> Interval b # liftA2 :: (a -> b -> c) -> Interval a -> Interval b -> Interval c # (>) :: Interval a -> Interval b -> Interval b # (<*) :: Interval a -> Interval b -> Interval a #
Functor Interval Source #
Instance details Defined in Math.Tools.Median Methods fmap :: (a -> b) -> Interval a -> Interval b # (<$) :: a -> Interval b -> Interval a #
Monad Interval Source #
Instance details Defined in Math.Tools.Median Methods (>>=) :: Interval a -> (a -> Interval b) -> Interval b # (>>) :: Interval a -> Interval b -> Interval b # return :: a -> Interval a #
(Num a, Ord a) => Num (Interval a) Source #
Instance details Defined in Math.Tools.Median Methods (+) :: Interval a -> Interval a -> Interval a # (-) :: Interval a -> Interval a -> Interval a # (*) :: Interval a -> Interval a -> Interval a # negate :: Interval a -> Interval a # abs :: Interval a -> Interval a # signum :: Interval a -> Interval a # fromInteger :: Integer -> Interval a #
Show a => Show (Interval a) Source #
Instance details Defined in Math.Tools.Median Methods showsPrec :: Int -> Interval a -> ShowS # show :: Interval a -> String # showList :: [Interval a] -> ShowS #
Num a => InnerProductSpace (Interval a) Source #
Instance details Defined in Math.Tools.Median Methods (%.) :: Interval a -> Interval a -> Scalar (Interval a) Source #
Num a => NormedSpace (Interval a) Source #
Instance details Defined in Math.Tools.Median Methods norm :: Interval a -> Scalar (Interval a) Source # norm_squared :: Interval a -> Scalar (Interval a) Source #
Num a => VectorSpace (Interval a) Source #
Instance details Defined in Math.Tools.Median Associated Types type Scalar (Interval a) Source # Methods vzero :: Interval a Source # vnegate :: Interval a -> Interval a Source # (%+) :: Interval a -> Interval a -> Interval a Source # (%*) :: Scalar (Interval a) -> Interval a -> Interval a Source #
type Scalar (Interval a) Source #
Instance details Defined in Math.Tools.Median type Scalar (Interval a) = a

in_interval :: (Eq a, MedianAlgebra a) => a -> Interval a -> Bool Source #

interval :: (Monad m, MedianAlgebra a) => Interval a -> m a -> m a Source #

median_homomorphism :: MedianAlgebra a => Interval a -> a -> a Source #

andor :: Ord a => (a, a) -> (a, a) Source #

andor is same as (x,y) -> (x && y, x || y), thus the name, except that the type b is more general. Thus if both and and or are combined, sorting of the pair occurs.

andor' :: Ord a => (a, a) -> (a, a) Source #

andor3 :: Ord a => (a, a, a) -> (a, a, a) Source #