Portability | non-portable |
---|---|

Stability | experimental |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | Safe-Inferred |

Free metric spaces

# Documentation

class Applicative f => Metric f whereSource

A free inner product/metric space

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

Compute the inner product of two vectors or (equivalently)
convert a vector `f a`

into a covector `f a -> a`

.

`>>>`

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

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

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

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

Compute the quadrance of the difference

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

Compute the distance between two vectors in a metric space

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

Compute the norm of a vector in a metric space

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

Convert a non-zero vector to unit vector.