linear-1.20.7: Linear Algebra

Linear.Metric

Description

Free metric spaces

Synopsis

# Documentation

class Additive f => Metric f where Source #

Free and sparse inner product/metric spaces.

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


dot :: (Foldable f, 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

signorm :: Floating a => f a -> f a Source #

Convert a non-zero vector to unit vector.

Instances

Normalize a Metric functor to have unit norm. This function does not change the functor if its norm is 0 or 1.
project u v computes the projection of v onto u.