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.Square

Description

An example instance of the algebraic classes: square matrices.

Synopsis

newtype Matrix (n :: Nat) a = Square (Matrix n n a)
matrix :: forall (n :: Nat) a. (KnownNat n, AdditiveMonoid a) => [[a]] -> Matrix n a
diagonal :: forall (n :: Nat) a. (KnownNat n, AdditiveMonoid a) => a -> Matrix n a
transpose :: forall (n :: Nat) a. KnownNat n => Matrix n a -> Matrix n a
determinant :: forall (n :: Nat) a. (KnownNat n, Ring a) => Matrix n a -> a
adjugate :: forall (n :: Nat) a. (KnownNat n, Ring a) => Matrix n a -> Matrix n a
apply :: forall a (n :: Nat). Semiring a => Matrix n a -> Vector n a -> Vector n a

Documentation

newtype Matrix (n :: Nat) a Source #

Square nxn matrices

Constructors

Square (Matrix n n a)

Instances

Instances details

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

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

Construct a square matrix from a list of row values.

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

Square matrix with x's along the diagonal

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

Transpose of a square matrix

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

Determinant of a square matrix

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

Adjugate of a square matrix, satisfying

m * adjugate m = diagonal (determinant m)

Caution: The implementation used here is very inefficient, and also not a numerically stable method for matrix inversion.

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

Multiply a vector by a square matrix.