NumHask.Vector

Two classes are supplied:

• A Vector class, with fixed-length n, where shape is held at the type level.
• A SomeVector class, with fixed-length, where shape is held at the value level.

Documentation

newtype Vector n a

A one-dimensional array where shape is specified at the type level The main purpose of this, beyond safe-typing, is to supply the Representable instance with an initial object. A boxed Vector is used under the hood.

Constructors

Vector

Fields

• toVec :: Vector a

Instances

Functor (Vector n)

Methods

fmap :: (a -> b) -> Vector n a -> Vector n b

(<$) :: a -> Vector n b -> Vector n a

KnownNat n => Applicative (Vector n)

Methods

pure :: a -> Vector n a

(<*>) :: Vector n (a -> b) -> Vector n a -> Vector n b

(*>) :: Vector n a -> Vector n b -> Vector n b

(<*) :: Vector n a -> Vector n b -> Vector n a

Foldable (Vector n)

Methods

fold :: Monoid m => Vector n m -> 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

Traversable (Vector n)

Methods

traverse :: Applicative f => (a -> f b) -> Vector n a -> f (Vector n b)

sequenceA :: Applicative f => Vector n (f a) -> f (Vector n a)

mapM :: Monad m => (a -> m b) -> Vector n a -> m (Vector n b)

sequence :: Monad m => Vector n (m a) -> m (Vector n a)

KnownNat n => Distributive (Vector n)

Methods

distribute :: Functor f => f (Vector n a) -> Vector n (f a)

collect :: Functor f => (a -> Vector n b) -> f a -> Vector n (f b)

distributeM :: Monad m => m (Vector n a) -> Vector n (m a)

collectM :: Monad m => (a -> Vector n b) -> m a -> Vector n (m b)

KnownNat n => Representable (Vector n)

Associated Types

type Rep (Vector n :: * -> *) :: *

Methods

tabulate :: (Rep (Vector n) -> a) -> Vector n a

index :: Vector n a -> Rep (Vector n) -> a

Eq1 (Vector n)

Methods

liftEq :: (a -> b -> Bool) -> Vector n a -> Vector n b -> Bool

KnownNat n => HasShape (Vector n)

Associated Types

type Shape (Vector n :: * -> *) :: *

Methods

shape :: Vector n a -> Shape (Vector n)

(Semiring a, KnownNat n) => Hilbert (Vector n) a

Methods

(<.>) :: Vector n a -> Vector n a -> a

(KnownNat n, AdditiveUnital a) => IsList (Vector n a)

pads with zeros if needed

Associated Types

type Item (Vector n a) :: *

Methods

fromList :: [Item (Vector n a)] -> Vector n a

fromListN :: Int -> [Item (Vector n a)] -> Vector n a

toList :: Vector n a -> [Item (Vector n a)]

Eq a => Eq (Vector n a)

Methods

(==) :: Vector n a -> Vector n a -> Bool

(/=) :: Vector n a -> Vector n a -> Bool

(Show a, KnownNat n) => Show (Vector n a)

Methods

showsPrec :: Int -> Vector n a -> ShowS

show :: Vector n a -> String

showList :: [Vector n a] -> ShowS

(KnownNat n, Arbitrary a, AdditiveUnital a) => Arbitrary (Vector n a)

Methods

arbitrary :: Gen (Vector n a)

shrink :: Vector n a -> [Vector n a]

(KnownNat n, AdditiveGroup a) => AdditiveGroup (Vector n a)

Methods

(-) :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, Additive a) => Additive (Vector n a)

Methods

(+) :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, AdditiveInvertible a) => AdditiveInvertible (Vector n a)

Methods

negate :: Vector n a -> Vector n a

(KnownNat n, AdditiveCommutative a) => AdditiveCommutative (Vector n a)

(KnownNat n, AdditiveAssociative a) => AdditiveAssociative (Vector n a)

(KnownNat n, AdditiveUnital a) => AdditiveUnital (Vector n a)

Methods

zero :: Vector n a

(KnownNat n, AdditiveMagma a) => AdditiveMagma (Vector n a)

Methods

plus :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, MultiplicativeGroup a) => MultiplicativeGroup (Vector n a)

Methods

(/) :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, Multiplicative a) => Multiplicative (Vector n a)

Methods

(*) :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, MultiplicativeInvertible a) => MultiplicativeInvertible (Vector n a)

Methods

recip :: Vector n a -> Vector n a

(KnownNat n, MultiplicativeCommutative a) => MultiplicativeCommutative (Vector n a)

(KnownNat n, MultiplicativeAssociative a) => MultiplicativeAssociative (Vector n a)

(KnownNat n, MultiplicativeUnital a) => MultiplicativeUnital (Vector n a)

Methods

one :: Vector n a

(KnownNat n, MultiplicativeMagma a) => MultiplicativeMagma (Vector n a)

Methods

times :: Vector n a -> Vector n a -> Vector n a

(KnownNat n, MultiplicativeMagma a, Additive a) => Distribution (Vector n a)

(KnownNat n, CRing a) => CRing (Vector n a)

(KnownNat n, Ring a) => Ring (Vector n a)

(KnownNat n, Semiring a) => Semiring (Vector n a)

(KnownNat n, BoundedField a) => BoundedField (Vector n a)

Methods

maxBound :: Vector n a

minBound :: Vector n a

nan :: Vector n a

isNaN :: Vector n a -> Bool

(KnownNat n, ExpField a) => ExpField (Vector n a)

Methods

exp :: Vector n a -> Vector n a

log :: Vector n a -> Vector n a

logBase :: Vector n a -> Vector n a -> Vector n a

(**) :: Vector n a -> Vector n a -> Vector n a

sqrt :: Vector n a -> Vector n a

(KnownNat n, Field a) => Field (Vector n a)

(KnownNat n, Epsilon a) => Epsilon (Vector n a)

Methods

nearZero :: Vector n a -> Bool

aboutEqual :: Vector n a -> Vector n a -> Bool

positive :: Vector n a -> Bool

veryPositive :: Vector n a -> Bool

veryNegative :: Vector n a -> Bool

(KnownNat n, Signed a) => Signed (Vector n a)

Methods

sign :: Vector n a -> Vector n a

abs :: Vector n a -> Vector n a

(KnownNat n, Integral a) => Integral (Vector n a)

Methods

div :: Vector n a -> Vector n a -> Vector n a

mod :: Vector n a -> Vector n a -> Vector n a

divMod :: Vector n a -> Vector n a -> (Vector n a, Vector n a)

(KnownNat n, ExpField a) => Metric (Vector n a) a

Methods

distance :: Vector n a -> Vector n a -> a

ExpField a => Normed (Vector n a) a

Methods

size :: Vector n a -> a

type Rep (Vector n)

type Rep (Vector n) = Int

type Shape (Vector n)

type Shape (Vector n) = Int

type Item (Vector n a)

type Item (Vector n a) = a

data SomeVector a

a one-dimensional array where shape is specified at the value level

Constructors

SomeVector Int (Vector a)

Instances

Functor SomeVector

Methods

fmap :: (a -> b) -> SomeVector a -> SomeVector b

(<$) :: a -> SomeVector b -> SomeVector a

Foldable SomeVector

Methods

fold :: Monoid m => SomeVector m -> m

foldMap :: Monoid m => (a -> m) -> SomeVector a -> m

foldr :: (a -> b -> b) -> b -> SomeVector a -> b

foldr' :: (a -> b -> b) -> b -> SomeVector a -> b

foldl :: (b -> a -> b) -> b -> SomeVector a -> b

foldl' :: (b -> a -> b) -> b -> SomeVector a -> b

foldr1 :: (a -> a -> a) -> SomeVector a -> a

foldl1 :: (a -> a -> a) -> SomeVector a -> a

toList :: SomeVector a -> [a]

null :: SomeVector a -> Bool

length :: SomeVector a -> Int

elem :: Eq a => a -> SomeVector a -> Bool

maximum :: Ord a => SomeVector a -> a

minimum :: Ord a => SomeVector a -> a

sum :: Num a => SomeVector a -> a

product :: Num a => SomeVector a -> a

HasShape SomeVector

Associated Types

type Shape (SomeVector :: * -> *) :: *

Methods

shape :: SomeVector a -> Shape SomeVector

IsList (SomeVector a)

Associated Types

type Item (SomeVector a) :: *

Methods

fromList :: [Item (SomeVector a)] -> SomeVector a

fromListN :: Int -> [Item (SomeVector a)] -> SomeVector a

toList :: SomeVector a -> [Item (SomeVector a)]

Eq a => Eq (SomeVector a)

Methods

(==) :: SomeVector a -> SomeVector a -> Bool

(/=) :: SomeVector a -> SomeVector a -> Bool

Ord a => Ord (SomeVector a)

Methods

compare :: SomeVector a -> SomeVector a -> Ordering

(<) :: SomeVector a -> SomeVector a -> Bool

(<=) :: SomeVector a -> SomeVector a -> Bool

(>) :: SomeVector a -> SomeVector a -> Bool

(>=) :: SomeVector a -> SomeVector a -> Bool

max :: SomeVector a -> SomeVector a -> SomeVector a

min :: SomeVector a -> SomeVector a -> SomeVector a

Show a => Show (SomeVector a)

Methods

showsPrec :: Int -> SomeVector a -> ShowS

show :: SomeVector a -> String

showList :: [SomeVector a] -> ShowS

Arbitrary a => Arbitrary (SomeVector a)

Methods

arbitrary :: Gen (SomeVector a)

shrink :: SomeVector a -> [SomeVector a]

type Shape SomeVector

type Shape SomeVector = Int

type Item (SomeVector a)

type Item (SomeVector a) = a

Conversion

someVector :: KnownNat r => Vector (r :: Nat) a -> SomeVector a

convert from a Vector to a SomeVector

unsafeToVector :: SomeVector a -> Vector (r :: Nat) a

convert from a SomeVector to a Vector with no shape check

toVector :: forall a r. KnownNat r => SomeVector a -> Maybe (Vector (r :: Nat) a)

convert from a SomeVector to a Vector, checking shape

Arbitrary

newtype ShapeV

ShapeV is used to generate sensible lengths for arbitrary instances of SomeVector and SomeMatrix

Constructors

ShapeV

Fields

• unshapeV :: Int

Instances

Arbitrary ShapeV

Methods

arbitrary :: Gen ShapeV

shrink :: ShapeV -> [ShapeV]