Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell98

Linear.V

Description

n-D Vectors

Synopsis

Documentation

newtype V n a Source

Constructors

V
Fields toVector :: Vector a

Instances

FunctorWithIndex Int (V k n) Source
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) Source
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) Source
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) Source
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) Source
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) Source
Methods reflectDim :: p (V k n a) -> Int Source
Dim k n => Monad (V k n) Source
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) Source
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) Source
Methods mfix :: (a -> V k n a) -> V k n a
Dim k n => Applicative (V k n) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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
Dim k n => MonadZip (V k n) Source
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) Source
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) Source
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) Source
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 => Eq1 (V k n) Source
Methods eq1 :: Eq a => V k n a -> V k n a -> Bool
Dim k n => Ord1 (V k n) Source
Methods compare1 :: Ord a => V k n a -> V k n a -> Ordering
Dim k n => Read1 (V k n) Source
Methods readsPrec1 :: Read a => Int -> ReadS (V k n a)
Dim k n => Show1 (V k n) Source
Methods showsPrec1 :: Show a => Int -> V k n a -> ShowS
Dim k n => Additive (V k n) Source
Methods zero :: Num a => V k n a Source (^+^) :: Num a => V k n a -> V k n a -> V k n a Source (^-^) :: Num a => V k n a -> V k n a -> V k n a Source lerp :: Num a => a -> V k n a -> V k n a -> V k n a Source liftU2 :: (a -> a -> a) -> V k n a -> V k n a -> V k n a Source liftI2 :: (a -> b -> c) -> V k n a -> V k n b -> V k n c Source
Dim k n => Metric (V k n) Source
Methods dot :: Num a => V k n a -> V k n a -> a Source quadrance :: Num a => V k n a -> a Source qd :: Num a => V k n a -> V k n a -> a Source distance :: Floating a => V k n a -> V k n a -> a Source norm :: Floating a => V k n a -> a Source signorm :: Floating a => V k n a -> V k n a Source
Dim * n => Trace (V * n) Source
Methods trace :: Num a => V * n (V * n a) -> a Source diagonal :: V * n (V * n a) -> V * n a Source
Dim * n => Affine (V * n) Source
Associated Types type Diff (V * n :: * -> ) :: -> * Source Methods (.-.) :: Num a => V * n a -> V * n a -> Diff (V * n) a Source (.+^) :: Num a => V * n a -> Diff (V * n) a -> V * n a Source (.-^) :: Num a => V * n a -> Diff (V * n) a -> V * n a Source
(Bounded a, Dim k n) => Bounded (V k n a) Source
Methods minBound :: V k n a maxBound :: V k n a
Eq a => Eq (V k n a) Source
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) Source
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
(Dim k n, Fractional a) => Fractional (V k n a) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
Methods put :: V k n a -> Put get :: Get (V k n a)
(Dim k n, Serial a) => Serial (V k n a) Source
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) Source
Methods put :: Putter (V k n a) get :: Get (V k n a)
NFData a => NFData (V k n a) Source
Methods rnf :: V k n a -> ()
(Dim k n, Unbox a) => Unbox (V k n a) Source

Ixed (V k n a) Source
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) Source
Methods nearZero :: V k n a -> Bool Source
Each (V k n a) (V k n b) a b Source
Methods each :: Traversal (V k n a) (V k n b) a b
data MVector s (V k n a) = MV_VN !Int !(MVector s a) Source
type Rep1 (V k n) Source
type Rep (V k n) = Int Source
type Diff (V * n) = V * n Source
type Rep (V k n a) Source
data Vector (V k n a) = V_VN !Int !(Vector a) Source
type Index (V k n a) = Int Source
type IxValue (V k n a) = a Source

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 Source

class Dim n where Source

Methods

reflectDim :: p n -> Int Source

Instances

KnownNat n => Dim Nat n Source
Methods reflectDim :: p n -> Int Source
Dim k n => Dim * (V k n a) Source
Methods reflectDim :: p (V k n a) -> Int Source

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

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

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

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

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