Safe Haskell	None
Language	Haskell2010

Numeric.Algebra.MetricSpace

Description

Provides the MetricSpace typeclass.

Since: 0.1

Synopsis

class MetricSpace s where
- diffR :: s -> s -> Double
diffℝ :: MetricSpace a => a -> a -> Double

Documentation

class MetricSpace s where Source #

Defines a metric space. A metric is a function \(d : M \times M \to \mathbb{R}\) s.t. for all \(x, y, z \in M\):

\(d(x, x) = 0\)
Positivity: If \(x \ne y\), then \(d(x, y) > 0\)
Symmetry: \(d(x, y) = d(y, x)\)
Triangle equality: \(d(x, z) \le d(x, y) + d(y, z) \)

Since: 0.1

Methods

diffR :: s -> s -> Double Source #

Since: 0.1

Instances

Instances details

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

diffℝ :: MetricSpace a => a -> a -> Double Source #

Unicode alias for diffR, with U+211D.

Since: 0.1