Linear.Trace

Simple matrix operation for low-dimensional primitives.

Documentation

class Functor m => Trace m where

Methods

trace :: Num a => m (m a) -> a

Compute the trace of a matrix

>>> trace (V2 (V2 a b) (V2 c d))
a + d

trace :: (Foldable m, Num a) => m (m a) -> a

Compute the trace of a matrix

>>> trace (V2 (V2 a b) (V2 c d))
a + d

diagonal :: m (m a) -> m a

Compute the diagonal of a matrix

>>> diagonal (V2 (V2 a b) (V2 c d))
V2 a d

diagonal :: Monad m => m (m a) -> m a

Compute the diagonal of a matrix

>>> diagonal (V2 (V2 a b) (V2 c d))
V2 a d

Instances

Trace Complex

Methods

trace :: Num a => Complex (Complex a) -> a

diagonal :: Complex (Complex a) -> Complex a

Trace IntMap

Methods

trace :: Num a => IntMap (IntMap a) -> a

diagonal :: IntMap (IntMap a) -> IntMap a

Trace V0

Methods

trace :: Num a => V0 (V0 a) -> a

diagonal :: V0 (V0 a) -> V0 a

Trace V1

Methods

trace :: Num a => V1 (V1 a) -> a

diagonal :: V1 (V1 a) -> V1 a

Trace V2

Methods

trace :: Num a => V2 (V2 a) -> a

diagonal :: V2 (V2 a) -> V2 a

Trace V3

Methods

trace :: Num a => V3 (V3 a) -> a

diagonal :: V3 (V3 a) -> V3 a

Trace V4

Methods

trace :: Num a => V4 (V4 a) -> a

diagonal :: V4 (V4 a) -> V4 a

Trace Plucker

Methods

trace :: Num a => Plucker (Plucker a) -> a

diagonal :: Plucker (Plucker a) -> Plucker a

Trace Quaternion

Methods

trace :: Num a => Quaternion (Quaternion a) -> a

diagonal :: Quaternion (Quaternion a) -> Quaternion a

Ord k => Trace (Map k)

Methods

trace :: Num a => Map k (Map k a) -> a

diagonal :: Map k (Map k a) -> Map k a

(Eq k, Hashable k) => Trace (HashMap k)

Methods

trace :: Num a => HashMap k (HashMap k a) -> a

diagonal :: HashMap k (HashMap k a) -> HashMap k a

Dim k n => Trace (V k n)

Methods

trace :: Num a => V k n (V k n a) -> a

diagonal :: V k n (V k n a) -> V k n a

(Trace f, Trace g) => Trace (Product * f g)

Methods

trace :: Num a => Product * f g (Product * f g a) -> a

diagonal :: Product * f g (Product * f g a) -> Product * f g a

(Distributive g, Trace g, Trace f) => Trace (Compose * * g f)

Methods

trace :: Num a => Compose * * g f (Compose * * g f a) -> a

diagonal :: Compose * * g f (Compose * * g f a) -> Compose * * g f a