Copyright | (C) 2012-2015 Edward Kmett |
---|---|
License | BSD-style (see the file LICENSE) |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Stability | experimental |
Portability | non-portable |
Safe Haskell | Trustworthy |
Language | Haskell98 |
Free metric spaces
Documentation
class Additive f => Metric f where #
Free and sparse inner product/metric spaces.
dot :: Num a => f a -> f a -> a #
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 #
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 #
Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.
qd :: Num a => f a -> f a -> a #
Compute the quadrance of the difference
distance :: Floating a => f a -> f a -> a #
Compute the distance between two vectors in a metric space
norm :: Floating a => f a -> a #
Compute the norm of a vector in a metric space
signorm :: Floating a => f a -> f a #
Convert a non-zero vector to unit vector.
Metric [] # | |
Metric Maybe # | |
Metric Identity # | |
Metric ZipList # | |
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) # | |
project :: (Metric v, Fractional a) => v a -> v a -> v a #
project u v
computes the projection of v
onto u
.