Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell98

Linear.Metric

Description

Free metric spaces

Synopsis

Documentation

class Additive f => Metric f where Source

Free and sparse inner product/metric spaces.

Minimal complete definition

Nothing

Methods

dot :: Num a => f a -> f a -> a Source

Compute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.

>>> V2 1 2 `dot` V2 3 4
11

quadrance :: Num a => f a -> a Source

Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

qd :: Num a => f a -> f a -> a Source

Compute the quadrance of the difference

distance :: Floating a => f a -> f a -> a Source

Compute the distance between two vectors in a metric space

norm :: Floating a => f a -> a Source

Compute the norm of a vector in a metric space

Convert a non-zero vector to unit vector.

Instances

Metric []
Metric ZipList
Metric Maybe
Metric Identity
Metric IntMap
Metric Vector
Metric V0
Metric V1
Metric V2
Metric V3
Metric V4
Metric Plucker
Metric Quaternion
Ord k => Metric (Map k)
(Hashable k, Eq k) => Metric (HashMap k)
Metric f => Metric (Point f)
Dim k n => Metric (V k n)

Normalize a Metric functor to have unit norm. This function does not change the functor if its norm is 0 or 1.

project :: (Metric v, Fractional a) => v a -> v a -> v a Source

project u v computes the projection of v onto u.