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.Vector

Description

An example instance of the algebraic classes: vectors.

Synopsis

data Vector (n :: Nat) a
vector :: forall (n :: Nat) a. (KnownNat n, AdditiveMonoid a) => [a] -> Vector n a
unsafeVector :: forall a (n :: Nat). [a] -> Vector n a
coordinates :: forall (n :: Nat) a. Vector n a -> [a]
dot :: forall a (n :: Nat). Semiring a => Vector n a -> Vector n a -> a
sqnorm :: forall a (n :: Nat). Semiring a => Vector n a -> a

Documentation

data Vector (n :: Nat) a Source #

Vectors on n elements

Instances

Instances details

Foldable (Vector n) Source #
Instance details Defined in Data.YAP.Vector Methods fold :: Monoid m => Vector n m -> m # foldMap :: Monoid m => (a -> m) -> Vector n a -> m # foldMap' :: Monoid m => (a -> m) -> Vector n a -> m # foldr :: (a -> b -> b) -> b -> Vector n a -> b # foldr' :: (a -> b -> b) -> b -> Vector n a -> b # foldl :: (b -> a -> b) -> b -> Vector n a -> b # foldl' :: (b -> a -> b) -> b -> Vector n a -> b # foldr1 :: (a -> a -> a) -> Vector n a -> a # foldl1 :: (a -> a -> a) -> Vector n a -> a # toList :: Vector n a -> [a] # null :: Vector n a -> Bool # length :: Vector n a -> Int # elem :: Eq a => a -> Vector n a -> Bool # maximum :: Ord a => Vector n a -> a # minimum :: Ord a => Vector n a -> a # sum :: Num a => Vector n a -> a # product :: Num a => Vector n a -> a #
KnownNat n => Applicative (Vector n) Source #
Instance details Defined in Data.YAP.Vector Methods pure :: a -> Vector n a # (<>) :: Vector n (a -> b) -> Vector n a -> Vector n b # liftA2 :: (a -> b -> c) -> Vector n a -> Vector n b -> Vector n c # (>) :: Vector n a -> Vector n b -> Vector n b # (<*) :: Vector n a -> Vector n b -> Vector n a #
Functor (Vector n) Source #
Instance details Defined in Data.YAP.Vector Methods fmap :: (a -> b) -> Vector n a -> Vector n b # (<$) :: a -> Vector n b -> Vector n a #
Show a => Show (Vector n a) Source #
Instance details Defined in Data.YAP.Vector Methods showsPrec :: Int -> Vector n a -> ShowS # show :: Vector n a -> String # showList :: [Vector n a] -> ShowS #
Eq a => Eq (Vector n a) Source #
Instance details Defined in Data.YAP.Vector Methods (==) :: Vector n a -> Vector n a -> Bool # (/=) :: Vector n a -> Vector n a -> Bool #
Ord a => Ord (Vector n a) Source #
Instance details Defined in Data.YAP.Vector Methods compare :: Vector n a -> Vector n a -> Ordering # (<) :: Vector n a -> Vector n a -> Bool # (<=) :: Vector n a -> Vector n a -> Bool # (>) :: Vector n a -> Vector n a -> Bool # (>=) :: Vector n a -> Vector n a -> Bool # max :: Vector n a -> Vector n a -> Vector n a # min :: Vector n a -> Vector n a -> Vector n a #
(KnownNat n, AbelianGroup a) => AbelianGroup (Vector n a) Source #
Instance details Defined in Data.YAP.Vector Methods (-) :: Vector n a -> Vector n a -> Vector n a # negate :: Vector n a -> Vector n a # gtimes :: (AbelianGroup b, ToInteger b) => b -> Vector n a -> Vector n a #
(KnownNat n, AdditiveMonoid a) => AdditiveMonoid (Vector n a) Source #
Instance details Defined in Data.YAP.Vector Methods (+) :: Vector n a -> Vector n a -> Vector n a # zero :: Vector n a # atimes :: ToInteger b => b -> Vector n a -> Vector n a #

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

Construct a vector from a list of coordinates, trimming or padding with zeros to obtain the required length.

unsafeVector :: forall a (n :: Nat). [a] -> Vector n a Source #

Construct a vector from a list of coordinates: valid only if the list has length n.

coordinates :: forall (n :: Nat) a. Vector n a -> [a] Source #

The coordinates of a vector

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

Dot product of two vectors.

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

Squared norm of a vector.