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

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.