linear-1.20.1: Linear Algebra

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

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

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 :: (Floating a, Metric f, Epsilon a) => f a -> f a 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`.