Linear.V

n-D Vectors

Documentation

newtype V n a

Constructors

V

Fields

• toVector :: Vector a

Instances

FunctorWithIndex Int (V k n)

Methods

imap :: (Int -> a -> b) -> V k n a -> V k n b

imapped :: (Indexable Int p, Settable f) => p a (f b) -> V k n a -> f (V k n b)

FoldableWithIndex Int (V k n)

Methods

ifoldMap :: Monoid m => (Int -> a -> m) -> V k n a -> m

ifolded :: (Indexable Int p, Contravariant f, Applicative f) => p a (f a) -> V k n a -> f (V k n a)

ifoldr :: (Int -> a -> b -> b) -> b -> V k n a -> b

ifoldl :: (Int -> b -> a -> b) -> b -> V k n a -> b

ifoldr' :: (Int -> a -> b -> b) -> b -> V k n a -> b

ifoldl' :: (Int -> b -> a -> b) -> b -> V k n a -> b

TraversableWithIndex Int (V k n)

Methods

itraverse :: Applicative f => (Int -> a -> f b) -> V k n a -> f (V k n b)

itraversed :: (Indexable Int p, Applicative f) => p a (f b) -> V k n a -> f (V k n b)

(Dim k n, Unbox a) => Vector Vector (V k n a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V k n a) -> m (Vector (V k n a))

basicUnsafeThaw :: PrimMonad m => Vector (V k n a) -> m (Mutable Vector (PrimState m) (V k n a))

basicLength :: Vector (V k n a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (V k n a) -> Vector (V k n a)

basicUnsafeIndexM :: Monad m => Vector (V k n a) -> Int -> m (V k n a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V k n a) -> Vector (V k n a) -> m ()

elemseq :: Vector (V k n a) -> V k n a -> b -> b

(Dim k n, Unbox a) => MVector MVector (V k n a)

Methods

basicLength :: MVector s (V k n a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (V k n a) -> MVector s (V k n a)

basicOverlaps :: MVector s (V k n a) -> MVector s (V k n a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V k n a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (V k n a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> V k n a -> m (MVector (PrimState m) (V k n a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V k n a) -> Int -> m (V k n a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V k n a) -> Int -> V k n a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (V k n a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (V k n a) -> V k n a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V k n a) -> MVector (PrimState m) (V k n a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V k n a) -> MVector (PrimState m) (V k n a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V k n a) -> Int -> m (MVector (PrimState m) (V k n a))

Dim k n => Dim * (V k n a)

Methods

reflectDim :: p n -> Int

Dim k n => Monad (V k n)

Methods

(>>=) :: V k n a -> (a -> V k n b) -> V k n b

(>>) :: V k n a -> V k n b -> V k n b

return :: a -> V k n a

fail :: String -> V k n a

Functor (V k n)

Methods

fmap :: (a -> b) -> V k n a -> V k n b

(<$) :: a -> V k n b -> V k n a

Dim k n => MonadFix (V k n)

Methods

mfix :: (a -> V k n a) -> V k n a

Dim k n => Applicative (V k n)

Methods

pure :: a -> V k n a

(<*>) :: V k n (a -> b) -> V k n a -> V k n b

(*>) :: V k n a -> V k n b -> V k n b

(<*) :: V k n a -> V k n b -> V k n a

Foldable (V k n)

Methods

fold :: Monoid m => V k n m -> m

foldMap :: Monoid m => (a -> m) -> V k n a -> m

foldr :: (a -> b -> b) -> b -> V k n a -> b

foldr' :: (a -> b -> b) -> b -> V k n a -> b

foldl :: (b -> a -> b) -> b -> V k n a -> b

foldl' :: (b -> a -> b) -> b -> V k n a -> b

foldr1 :: (a -> a -> a) -> V k n a -> a

foldl1 :: (a -> a -> a) -> V k n a -> a

toList :: V k n a -> [a]

null :: V k n a -> Bool

length :: V k n a -> Int

elem :: Eq a => a -> V k n a -> Bool

maximum :: Ord a => V k n a -> a

minimum :: Ord a => V k n a -> a

sum :: Num a => V k n a -> a

product :: Num a => V k n a -> a

Traversable (V k n)

Methods

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

sequenceA :: Applicative f => V k n (f a) -> f (V k n a)

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

sequence :: Monad m => V k n (m a) -> m (V k n a)

Generic1 (V k n)

Associated Types

type Rep1 (V k n :: * -> *) :: * -> *

Methods

from1 :: V k n a -> Rep1 (V k n) a

to1 :: Rep1 (V k n) a -> V k n a

Dim k n => Distributive (V k n)

Methods

distribute :: Functor f => f (V k n a) -> V k n (f a)

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

distributeM :: Monad m => m (V k n a) -> V k n (m a)

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

Dim k n => Representable (V k n)

Associated Types

type Rep (V k n :: * -> *) :: *

Methods

tabulate :: (Rep (V k n) -> a) -> V k n a

index :: V k n a -> Rep (V k n) -> a

Eq1 (V k n)

Methods

liftEq :: (a -> b -> Bool) -> V k n a -> V k n b -> Bool

Ord1 (V k n)

Methods

liftCompare :: (a -> b -> Ordering) -> V k n a -> V k n b -> Ordering

Dim k n => Read1 (V k n)

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V k n a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V k n a]

Show1 (V k n)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V k n a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V k n a] -> ShowS

Dim k n => MonadZip (V k n)

Methods

mzip :: V k n a -> V k n b -> V k n (a, b)

mzipWith :: (a -> b -> c) -> V k n a -> V k n b -> V k n c

munzip :: V k n (a, b) -> (V k n a, V k n b)

Dim k n => Serial1 (V k n)

Methods

serializeWith :: MonadPut m => (a -> m ()) -> V k n a -> m ()

deserializeWith :: MonadGet m => m a -> m (V k n a)

Apply (V k n)

Methods

(<.>) :: V k n (a -> b) -> V k n a -> V k n b

(.>) :: V k n a -> V k n b -> V k n b

(<.) :: V k n a -> V k n b -> V k n a

Bind (V k n)

Methods

(>>-) :: V k n a -> (a -> V k n b) -> V k n b

join :: V k n (V k n a) -> V k n a

Dim k n => Additive (V k n)

Methods

zero :: Num a => V k n a

(^+^) :: Num a => V k n a -> V k n a -> V k n a

(^-^) :: Num a => V k n a -> V k n a -> V k n a

lerp :: Num a => a -> V k n a -> V k n a -> V k n a

liftU2 :: (a -> a -> a) -> V k n a -> V k n a -> V k n a

liftI2 :: (a -> b -> c) -> V k n a -> V k n b -> V k n c

Dim k n => Metric (V k n)

Methods

dot :: Num a => V k n a -> V k n a -> a

quadrance :: Num a => V k n a -> a

qd :: Num a => V k n a -> V k n a -> a

distance :: Floating a => V k n a -> V k n a -> a

norm :: Floating a => V k n a -> a

signorm :: Floating a => V k n a -> V k n a

Finite (V Nat n)

Associated Types

type Size (V Nat n :: * -> *) :: Nat

Methods

toV :: V Nat n a -> V Nat (Size (V Nat n)) a

fromV :: V Nat (Size (V Nat n)) a -> V Nat n a

Dim k n => Trace (V k n)

Methods

trace :: Num a => V k n (V k n a) -> a

diagonal :: V k n (V k n a) -> V k n a

Dim * n => Affine (V * n)

Associated Types

type Diff (V * n :: * -> *) :: * -> *

Methods

(.-.) :: Num a => V * n a -> V * n a -> Diff (V * n) a

(.+^) :: Num a => V * n a -> Diff (V * n) a -> V * n a

(.-^) :: Num a => V * n a -> Diff (V * n) a -> V * n a

(Bounded a, Dim k n) => Bounded (V k n a)

Methods

minBound :: V k n a

maxBound :: V k n a

Eq a => Eq (V k n a)

Methods

(==) :: V k n a -> V k n a -> Bool

(/=) :: V k n a -> V k n a -> Bool

(Dim k n, Floating a) => Floating (V k n a)

Methods

pi :: V k n a

exp :: V k n a -> V k n a

log :: V k n a -> V k n a

sqrt :: V k n a -> V k n a

(**) :: V k n a -> V k n a -> V k n a

logBase :: V k n a -> V k n a -> V k n a

sin :: V k n a -> V k n a

cos :: V k n a -> V k n a

tan :: V k n a -> V k n a

asin :: V k n a -> V k n a

acos :: V k n a -> V k n a

atan :: V k n a -> V k n a

sinh :: V k n a -> V k n a

cosh :: V k n a -> V k n a

tanh :: V k n a -> V k n a

asinh :: V k n a -> V k n a

acosh :: V k n a -> V k n a

atanh :: V k n a -> V k n a

log1p :: V k n a -> V k n a

expm1 :: V k n a -> V k n a

log1pexp :: V k n a -> V k n a

log1mexp :: V k n a -> V k n a

(Dim k n, Fractional a) => Fractional (V k n a)

Methods

(/) :: V k n a -> V k n a -> V k n a

recip :: V k n a -> V k n a

fromRational :: Rational -> V k n a

(Typeable (* -> *) (V k n), Typeable * (V k n a), Dim k n, Data a) => Data (V k n a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V k n a -> c (V k n a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V k n a)

toConstr :: V k n a -> Constr

dataTypeOf :: V k n a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (V k n a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V k n a))

gmapT :: (forall b. Data b => b -> b) -> V k n a -> V k n a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V k n a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V k n a -> r

gmapQ :: (forall d. Data d => d -> u) -> V k n a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> V k n a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> V k n a -> m (V k n a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V k n a -> m (V k n a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V k n a -> m (V k n a)

(Dim k n, Num a) => Num (V k n a)

Methods

(+) :: V k n a -> V k n a -> V k n a

(-) :: V k n a -> V k n a -> V k n a

(*) :: V k n a -> V k n a -> V k n a

negate :: V k n a -> V k n a

abs :: V k n a -> V k n a

signum :: V k n a -> V k n a

fromInteger :: Integer -> V k n a

Ord a => Ord (V k n a)

Methods

compare :: V k n a -> V k n a -> Ordering

(<) :: V k n a -> V k n a -> Bool

(<=) :: V k n a -> V k n a -> Bool

(>) :: V k n a -> V k n a -> Bool

(>=) :: V k n a -> V k n a -> Bool

max :: V k n a -> V k n a -> V k n a

min :: V k n a -> V k n a -> V k n a

Read a => Read (V k n a)

Methods

readsPrec :: Int -> ReadS (V k n a)

readList :: ReadS [V k n a]

readPrec :: ReadPrec (V k n a)

readListPrec :: ReadPrec [V k n a]

Show a => Show (V k n a)

Methods

showsPrec :: Int -> V k n a -> ShowS

show :: V k n a -> String

showList :: [V k n a] -> ShowS

Generic (V k n a)

Associated Types

type Rep (V k n a) :: * -> *

Methods

from :: V k n a -> Rep (V k n a) x

to :: Rep (V k n a) x -> V k n a

(Dim k n, Storable a) => Storable (V k n a)

Methods

sizeOf :: V k n a -> Int

alignment :: V k n a -> Int

peekElemOff :: Ptr (V k n a) -> Int -> IO (V k n a)

pokeElemOff :: Ptr (V k n a) -> Int -> V k n a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (V k n a)

pokeByteOff :: Ptr b -> Int -> V k n a -> IO ()

peek :: Ptr (V k n a) -> IO (V k n a)

poke :: Ptr (V k n a) -> V k n a -> IO ()

(Dim k n, Binary a) => Binary (V k n a)

Methods

put :: V k n a -> Put

get :: Get (V k n a)

putList :: [V k n a] -> Put

(Dim k n, Serial a) => Serial (V k n a)

Methods

serialize :: MonadPut m => V k n a -> m ()

deserialize :: MonadGet m => m (V k n a)

(Dim k n, Serialize a) => Serialize (V k n a)

Methods

put :: Putter (V k n a)

get :: Get (V k n a)

NFData a => NFData (V k n a)

Methods

rnf :: V k n a -> ()

(Dim k n, Unbox a) => Unbox (V k n a)

Ixed (V k n a)

Methods

ix :: Index (V k n a) -> Traversal' (V k n a) (IxValue (V k n a))

(Dim k n, Epsilon a) => Epsilon (V k n a)

Methods

nearZero :: V k n a -> Bool

Each (V k n a) (V k n b) a b

Methods

each :: Traversal (V k n a) (V k n b) a b

data MVector s (V k n a)

data MVector s (V k n a) = MV_VN !Int !(MVector s a)

type Rep1 (V k n)

type Rep1 (V k n) = D1 (MetaData "V" "Linear.V" "linear-1.20.7-5lThnmKUFiyAbTBcmo6MON" True) (C1 (MetaCons "V" PrefixI True) (S1 (MetaSel (Just Symbol "toVector") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Vector)))

type Rep (V k n)

type Rep (V k n) = Int

type Size (V Nat n)

type Size (V Nat n) = n

type Diff (V * n)

type Diff (V * n) = V * n

type Rep (V k n a)

type Rep (V k n a) = D1 (MetaData "V" "Linear.V" "linear-1.20.7-5lThnmKUFiyAbTBcmo6MON" True) (C1 (MetaCons "V" PrefixI True) (S1 (MetaSel (Just Symbol "toVector") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector a))))

data Vector (V k n a)

data Vector (V k n a) = V_VN !Int !(Vector a)

type Index (V k n a)

type Index (V k n a) = Int

type IxValue (V k n a)

type IxValue (V k n a) = a

int :: Int -> TypeQ

This can be used to generate a template haskell splice for a type level version of a given int.

This does not use GHC TypeLits, instead it generates a numeric type by hand similar to the ones used in the "Functional Pearl: Implicit Configurations" paper by Oleg Kiselyov and Chung-Chieh Shan.

instance Num (Q Exp) provided in this package allows writing $(3) instead of $(int 3). Sometimes the two will produce the same representation (if compiled without the -DUSE_TYPE_LITS preprocessor directive).

dim :: forall n a. Dim n => V n a -> Int

class Dim n where

Minimal complete definition

reflectDim

Methods

reflectDim :: p n -> Int

Instances

KnownNat n => Dim Nat n

Methods

reflectDim :: p n -> Int

Dim k n => Dim * (V k n a)

Methods

reflectDim :: p n -> Int

reifyDim :: Int -> (forall n. Dim n => Proxy n -> r) -> r

reifyVector :: forall a r. Vector a -> (forall n. Dim n => V n a -> r) -> r

reifyDimNat :: Int -> (forall n. KnownNat n => Proxy n -> r) -> r

reifyVectorNat :: forall a r. Vector a -> (forall n. KnownNat n => V n a -> r) -> r

fromVector :: forall n a. Dim n => Vector a -> Maybe (V n a)

class Finite v where

Minimal complete definition

fromV

Associated Types

type Size (v :: * -> *) :: Nat

Methods

toV :: v a -> V (Size v) a

toV :: Foldable v => v a -> V (Size v) a

fromV :: V (Size v) a -> v a

Instances

Finite Complex

Associated Types

type Size (Complex :: * -> *) :: Nat

Methods

toV :: Complex a -> V Nat (Size Complex) a

fromV :: V Nat (Size Complex) a -> Complex a

Finite V0

Associated Types

type Size (V0 :: * -> *) :: Nat

Methods

toV :: V0 a -> V Nat (Size V0) a

fromV :: V Nat (Size V0) a -> V0 a

Finite V1

Associated Types

type Size (V1 :: * -> *) :: Nat

Methods

toV :: V1 a -> V Nat (Size V1) a

fromV :: V Nat (Size V1) a -> V1 a

Finite V2

Associated Types

type Size (V2 :: * -> *) :: Nat

Methods

toV :: V2 a -> V Nat (Size V2) a

fromV :: V Nat (Size V2) a -> V2 a

Finite V3

Associated Types

type Size (V3 :: * -> *) :: Nat

Methods

toV :: V3 a -> V Nat (Size V3) a

fromV :: V Nat (Size V3) a -> V3 a

Finite V4

Associated Types

type Size (V4 :: * -> *) :: Nat

Methods

toV :: V4 a -> V Nat (Size V4) a

fromV :: V Nat (Size V4) a -> V4 a

Finite Plucker

Associated Types

type Size (Plucker :: * -> *) :: Nat

Methods

toV :: Plucker a -> V Nat (Size Plucker) a

fromV :: V Nat (Size Plucker) a -> Plucker a

Finite Quaternion

Associated Types

type Size (Quaternion :: * -> *) :: Nat

Methods

toV :: Quaternion a -> V Nat (Size Quaternion) a

fromV :: V Nat (Size Quaternion) a -> Quaternion a

Finite f => Finite (Point f)

Associated Types

type Size (Point f :: * -> *) :: Nat

Methods

toV :: Point f a -> V Nat (Size (Point f)) a

fromV :: V Nat (Size (Point f)) a -> Point f a

Finite (V Nat n)

Associated Types

type Size (V Nat n :: * -> *) :: Nat

Methods

toV :: V Nat n a -> V Nat (Size (V Nat n)) a

fromV :: V Nat (Size (V Nat n)) a -> V Nat n a

_V :: (Finite u, Finite v) => Iso (V (Size u) a) (V (Size v) b) (u a) (v b)

_V' :: Finite v => Iso (V (Size v) a) (V (Size v) b) (v a) (v b)