Copyright	(c) Ross Paterson 2023
License	BSD-style (see the file LICENSE)
Maintainer	[email protected]
Stability	provisional
Portability	type-level literals
Safe Haskell	None
Language	Haskell2010

Data.YAP.Matrix

Description

An example instance of the algebraic classes: matrices.

Synopsis

data Matrix (m :: Nat) (n :: Nat) a
matrix :: forall (m :: Nat) (n :: Nat) a. (KnownNat m, KnownNat n, AdditiveMonoid a) => [[a]] -> Matrix m n a
rows :: forall (m :: Nat) (n :: Nat) a. Matrix m n a -> [[a]]
multiply :: forall (p :: Nat) a (m :: Nat) (n :: Nat). (KnownNat p, Semiring a) => Matrix m n a -> Matrix n p a -> Matrix m p a
transpose :: forall (m :: Nat) (n :: Nat) a. (KnownNat m, KnownNat n) => Matrix m n a -> Matrix n m a
apply :: forall a (m :: Nat) (n :: Nat). Semiring a => Matrix m n a -> Vector n a -> Vector m a

Documentation

data Matrix (m :: Nat) (n :: Nat) a Source #

Matrix with m rows and n columns

Instances

Instances details

(KnownNat m, KnownNat n) => Applicative (Matrix m n) Source #
Instance details Defined in Data.YAP.Matrix Methods pure :: a -> Matrix m n a # (<>) :: Matrix m n (a -> b) -> Matrix m n a -> Matrix m n b # liftA2 :: (a -> b -> c) -> Matrix m n a -> Matrix m n b -> Matrix m n c # (>) :: Matrix m n a -> Matrix m n b -> Matrix m n b # (<*) :: Matrix m n a -> Matrix m n b -> Matrix m n a #
Functor (Matrix m n) Source #
Instance details Defined in Data.YAP.Matrix Methods fmap :: (a -> b) -> Matrix m n a -> Matrix m n b # (<$) :: a -> Matrix m n b -> Matrix m n a #
Show a => Show (Matrix m n a) Source #
Instance details Defined in Data.YAP.Matrix Methods showsPrec :: Int -> Matrix m n a -> ShowS # show :: Matrix m n a -> String # showList :: [Matrix m n a] -> ShowS #
Eq a => Eq (Matrix m n a) Source #
Instance details Defined in Data.YAP.Matrix Methods (==) :: Matrix m n a -> Matrix m n a -> Bool # (/=) :: Matrix m n a -> Matrix m n a -> Bool #
Ord a => Ord (Matrix m n a) Source #
Instance details Defined in Data.YAP.Matrix Methods compare :: Matrix m n a -> Matrix m n a -> Ordering # (<) :: Matrix m n a -> Matrix m n a -> Bool # (<=) :: Matrix m n a -> Matrix m n a -> Bool # (>) :: Matrix m n a -> Matrix m n a -> Bool # (>=) :: Matrix m n a -> Matrix m n a -> Bool # max :: Matrix m n a -> Matrix m n a -> Matrix m n a # min :: Matrix m n a -> Matrix m n a -> Matrix m n a #
(KnownNat m, KnownNat n, AbelianGroup a) => AbelianGroup (Matrix m n a) Source #
Instance details Defined in Data.YAP.Matrix Methods (-) :: Matrix m n a -> Matrix m n a -> Matrix m n a # negate :: Matrix m n a -> Matrix m n a # gtimes :: (AbelianGroup b, ToInteger b) => b -> Matrix m n a -> Matrix m n a #
(KnownNat m, KnownNat n, AdditiveMonoid a) => AdditiveMonoid (Matrix m n a) Source #
Instance details Defined in Data.YAP.Matrix Methods (+) :: Matrix m n a -> Matrix m n a -> Matrix m n a # zero :: Matrix m n a # atimes :: ToInteger b => b -> Matrix m n a -> Matrix m n a #

matrix :: forall (m :: Nat) (n :: Nat) a. (KnownNat m, KnownNat n, AdditiveMonoid a) => [[a]] -> Matrix m n a Source #

Construct a matrix from a list of row values.

rows :: forall (m :: Nat) (n :: Nat) a. Matrix m n a -> [[a]] Source #

The rows of a matrix

multiply :: forall (p :: Nat) a (m :: Nat) (n :: Nat). (KnownNat p, Semiring a) => Matrix m n a -> Matrix n p a -> Matrix m p a Source #

Multiply matrices

transpose :: forall (m :: Nat) (n :: Nat) a. (KnownNat m, KnownNat n) => Matrix m n a -> Matrix n m a Source #

Transpose of a matrix

apply :: forall a (m :: Nat) (n :: Nat). Semiring a => Matrix m n a -> Vector n a -> Vector m a Source #

Multiply a vector by a matrix.