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 #

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)) #
Generic1 * (V k n) #
Associated Types type Rep1 (V k n) (f :: V k n -> ) :: k -> # Methods from1 :: f a -> Rep1 (V k n) f a # to1 :: Rep1 (V k n) f a -> f 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 # liftA2 :: (a -> b -> c) -> V k n a -> V k n b -> V k n c # (>) :: 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) #
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] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V k n a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [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) #
Dim k n => Hashable1 (V k n) #
Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V k n a -> Int #
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 # liftF2 :: (a -> b -> c) -> V k n a -> V k n b -> V k n c #
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 -> () #
Hashable a => Hashable (V k n a) #
Methods hashWithSalt :: Int -> V k n a -> Int # hash :: V k n a -> Int #
(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 #
(<=) 1 n => Field1 (V Nat n a) (V Nat n a) a a #
Methods _1 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 2 n => Field2 (V Nat n a) (V Nat n a) a a #
Methods _2 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 3 n => Field3 (V Nat n a) (V Nat n a) a a #
Methods _3 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 4 n => Field4 (V Nat n a) (V Nat n a) a a #
Methods _4 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 5 n => Field5 (V Nat n a) (V Nat n a) a a #
Methods _5 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 6 n => Field6 (V Nat n a) (V Nat n a) a a #
Methods _6 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 7 n => Field7 (V Nat n a) (V Nat n a) a a #
Methods _7 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 8 n => Field8 (V Nat n a) (V Nat n a) a a #
Methods _8 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 9 n => Field9 (V Nat n a) (V Nat n a) a a #
Methods _9 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 10 n => Field10 (V Nat n a) (V Nat n a) a a #
Methods _10 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 11 n => Field11 (V Nat n a) (V Nat n a) a a #
Methods _11 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 12 n => Field12 (V Nat n a) (V Nat n a) a a #
Methods _12 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 13 n => Field13 (V Nat n a) (V Nat n a) a a #
Methods _13 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 14 n => Field14 (V Nat n a) (V Nat n a) a a #
Methods _14 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 15 n => Field15 (V Nat n a) (V Nat n a) a a #
Methods _15 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 16 n => Field16 (V Nat n a) (V Nat n a) a a #
Methods _16 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 17 n => Field17 (V Nat n a) (V Nat n a) a a #
Methods _17 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 18 n => Field18 (V Nat n a) (V Nat n a) a a #
Methods _18 :: Lens (V Nat n a) (V Nat n a) a a #
(<=) 19 n => Field19 (V Nat n a) (V Nat n a) a a #
Methods _19 :: Lens (V Nat n a) (V Nat n a) a a #
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-1.20.8-6qbGGpjDPeX4apNvB0Xrr2" 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-1.20.8-6qbGGpjDPeX4apNvB0Xrr2" 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 :: Nat). KnownNat n => Proxy n -> r) -> r #

reifyVectorNat :: forall a r. Vector a -> (forall (n :: Nat). 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 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 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 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 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 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) #