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	Safe
Language	Haskell98

Linear.Trace

Description

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 #