Data.Array.Accelerate.Linear.Metric

Free metric spaces

Documentation

>>> :set -XPatternSynonyms
>>> import Data.Array.Accelerate.Linear.V2 ( pattern V2_ )
>>> import Linear.V2

class Metric f => Metric f where

Free and sparse inner product/metric spaces.

Minimal complete definition

Nothing

Methods

dot :: forall a. (Num a, Box f a) => Exp (f a) -> Exp (f a) -> Exp a

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

>>> (V2_ 1 2 :: Exp (V2 Int)) `dot` (V2_ 3 4 :: Exp (V2 Int))
11

quadrance :: forall a. (Num a, Box f a) => Exp (f a) -> Exp a

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

qd :: forall a. (Num a, Box f a) => Exp (f a) -> Exp (f a) -> Exp a

Compute the quadrance of the difference

distance :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp (f a) -> Exp a

Compute the distance between two vectors in a metric space

norm :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp a

Compute the norm of a vector in a metric space

signorm :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp (f a)

Convert a non-zero vector to unit vector.

Instances

Metric Plucker

Defined in Data.Array.Accelerate.Linear.Plucker

Methods

dot :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

quadrance :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp a

qd :: (Num a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

distance :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp a

norm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp a

signorm :: (Floating a, Box Plucker a) => Exp (Plucker a) -> Exp (Plucker a)

Metric Quaternion

Defined in Data.Array.Accelerate.Linear.Quaternion

Methods

dot :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a

quadrance :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp a

qd :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a

distance :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a

norm :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp a

signorm :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a)

Metric V0

Defined in Data.Array.Accelerate.Linear.V0

Methods

dot :: (Num a, Box V0 a) => Exp (V0 a) -> Exp (V0 a) -> Exp a

quadrance :: (Num a, Box V0 a) => Exp (V0 a) -> Exp a

qd :: (Num a, Box V0 a) => Exp (V0 a) -> Exp (V0 a) -> Exp a

distance :: (Floating a, Box V0 a) => Exp (V0 a) -> Exp (V0 a) -> Exp a

norm :: (Floating a, Box V0 a) => Exp (V0 a) -> Exp a

signorm :: (Floating a, Box V0 a) => Exp (V0 a) -> Exp (V0 a)

Metric V4

Defined in Data.Array.Accelerate.Linear.V4

Methods

dot :: (Num a, Box V4 a) => Exp (V4 a) -> Exp (V4 a) -> Exp a

quadrance :: (Num a, Box V4 a) => Exp (V4 a) -> Exp a

qd :: (Num a, Box V4 a) => Exp (V4 a) -> Exp (V4 a) -> Exp a

distance :: (Floating a, Box V4 a) => Exp (V4 a) -> Exp (V4 a) -> Exp a

norm :: (Floating a, Box V4 a) => Exp (V4 a) -> Exp a

signorm :: (Floating a, Box V4 a) => Exp (V4 a) -> Exp (V4 a)

Metric V3

Defined in Data.Array.Accelerate.Linear.V3

Methods

dot :: (Num a, Box V3 a) => Exp (V3 a) -> Exp (V3 a) -> Exp a

quadrance :: (Num a, Box V3 a) => Exp (V3 a) -> Exp a

qd :: (Num a, Box V3 a) => Exp (V3 a) -> Exp (V3 a) -> Exp a

distance :: (Floating a, Box V3 a) => Exp (V3 a) -> Exp (V3 a) -> Exp a

norm :: (Floating a, Box V3 a) => Exp (V3 a) -> Exp a

signorm :: (Floating a, Box V3 a) => Exp (V3 a) -> Exp (V3 a)

Metric V2

Defined in Data.Array.Accelerate.Linear.V2

Methods

dot :: (Num a, Box V2 a) => Exp (V2 a) -> Exp (V2 a) -> Exp a

quadrance :: (Num a, Box V2 a) => Exp (V2 a) -> Exp a

qd :: (Num a, Box V2 a) => Exp (V2 a) -> Exp (V2 a) -> Exp a

distance :: (Floating a, Box V2 a) => Exp (V2 a) -> Exp (V2 a) -> Exp a

norm :: (Floating a, Box V2 a) => Exp (V2 a) -> Exp a

signorm :: (Floating a, Box V2 a) => Exp (V2 a) -> Exp (V2 a)

Metric V1

Defined in Data.Array.Accelerate.Linear.V1

Methods

dot :: (Num a, Box V1 a) => Exp (V1 a) -> Exp (V1 a) -> Exp a

quadrance :: (Num a, Box V1 a) => Exp (V1 a) -> Exp a

qd :: (Num a, Box V1 a) => Exp (V1 a) -> Exp (V1 a) -> Exp a

distance :: (Floating a, Box V1 a) => Exp (V1 a) -> Exp (V1 a) -> Exp a

norm :: (Floating a, Box V1 a) => Exp (V1 a) -> Exp a

signorm :: (Floating a, Box V1 a) => Exp (V1 a) -> Exp (V1 a)

type IsMetric f a = (Metric f, Box f a)

normalize :: (Elt (f a), Floating a, IsMetric f a, Epsilon a) => Exp (f a) -> Exp (f a)

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

project :: forall f a. (Floating a, IsMetric f a) => Exp (f a) -> Exp (f a) -> Exp (f a)

project u v computes the projection of v onto u.