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	Haskell2010

Linear.Trace

Description

Simple matrix operation for low-dimensional primitives.

Synopsis

class Functor m => Trace m where
- trace :: Num a => m (m a) -> a
- diagonal :: m (m a) -> m a
frobenius :: (Num a, Foldable f, Additive f, Additive g, Distributive g, Trace g) => f (g a) -> a

Documentation

class Functor m => Trace m where Source #

Minimal complete definition

Nothing

Methods

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

Compute the trace of a matrix

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

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

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

Compute the diagonal of a matrix

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

default diagonal :: Monad m => m (m a) -> m a Source #

Instances

Instances details

Trace Complex Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Complex (Complex a) -> a Source # diagonal :: Complex (Complex a) -> Complex a Source #
Trace IntMap Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => IntMap (IntMap a) -> a Source # diagonal :: IntMap (IntMap a) -> IntMap a Source #
Trace Plucker Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Plucker (Plucker a) -> a Source # diagonal :: Plucker (Plucker a) -> Plucker a Source #
Trace Quaternion Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Quaternion (Quaternion a) -> a Source # diagonal :: Quaternion (Quaternion a) -> Quaternion a Source #
Trace V0 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V0 (V0 a) -> a Source # diagonal :: V0 (V0 a) -> V0 a Source #
Trace V1 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V1 (V1 a) -> a Source # diagonal :: V1 (V1 a) -> V1 a Source #
Trace V2 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V2 (V2 a) -> a Source # diagonal :: V2 (V2 a) -> V2 a Source #
Trace V3 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a Source # diagonal :: V3 (V3 a) -> V3 a Source #
Trace V4 Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V4 (V4 a) -> a Source # diagonal :: V4 (V4 a) -> V4 a Source #
Ord k => Trace (Map k) Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Map k (Map k a) -> a Source # diagonal :: Map k (Map k a) -> Map k a Source #
(Eq k, Hashable k) => Trace (HashMap k) Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => HashMap k (HashMap k a) -> a Source # diagonal :: HashMap k (HashMap k a) -> HashMap k a Source #
Dim n => Trace (V n) Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => V n (V n a) -> a Source # diagonal :: V n (V n a) -> V n a Source #
(Trace f, Trace g) => Trace (Product f g) Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Product f g (Product f g a) -> a Source # diagonal :: Product f g (Product f g a) -> Product f g a Source #
(Distributive g, Trace g, Trace f) => Trace (Compose g f) Source #
Instance details Defined in Linear.Trace Methods trace :: Num a => Compose g f (Compose g f a) -> a Source # diagonal :: Compose g f (Compose g f a) -> Compose g f a Source #

frobenius :: (Num a, Foldable f, Additive f, Additive g, Distributive g, Trace g) => f (g a) -> a Source #

Compute the Frobenius norm of a matrix.