Copyright | 2014 Edward Kmett Charles Durham 2015 Trevor L. McDonell |
---|---|
License | BSD-style (see the file LICENSE) |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Stability | experimental |
Portability | non-portable |
Safe Haskell | None |
Language | Haskell98 |
Free metric spaces
Documentation
class Metric f => Metric f where Source #
Free and sparse inner product/metric spaces.
dot :: forall a. (Num a, Box f a) => Exp (f a) -> Exp (f a) -> Exp 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 :: forall a. (Num a, Box f a) => Exp (f a) -> Exp a Source #
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 Source #
Compute the quadrance
of the difference
distance :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp (f a) -> Exp a Source #
Compute the distance between two vectors in a metric space
norm :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp a Source #
Compute the norm of a vector in a metric space
signorm :: forall a. (Floating a, Box f a) => Exp (f a) -> Exp (f a) Source #
Convert a non-zero vector to unit vector.