Copyright	2014 Edward Kmett Charles Durham 2015 Trevor L. McDonell
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell98

Data.Array.Accelerate.Linear.Quaternion

Contents

Orphan instances

Description

Quaternions

Synopsis

Documentation

data Quaternion a :: * -> * #

Quaternions

Constructors

Quaternion ~a ~(V3 a)

Instances

Monad Quaternion
Methods (>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # (>>) :: Quaternion a -> Quaternion b -> Quaternion b # return :: a -> Quaternion a # fail :: String -> Quaternion a #
Functor Quaternion
Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
MonadFix Quaternion
Methods mfix :: (a -> Quaternion a) -> Quaternion a #
Applicative Quaternion
Methods pure :: a -> Quaternion a # (<>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # (>) :: Quaternion a -> Quaternion b -> Quaternion b # (<*) :: Quaternion a -> Quaternion b -> Quaternion a #
Foldable Quaternion
Methods fold :: Monoid m => Quaternion m -> m # foldMap :: Monoid m => (a -> m) -> Quaternion a -> m # foldr :: (a -> b -> b) -> b -> Quaternion a -> b # foldr' :: (a -> b -> b) -> b -> Quaternion a -> b # foldl :: (b -> a -> b) -> b -> Quaternion a -> b # foldl' :: (b -> a -> b) -> b -> Quaternion a -> b # foldr1 :: (a -> a -> a) -> Quaternion a -> a # foldl1 :: (a -> a -> a) -> Quaternion a -> a # toList :: Quaternion a -> [a] # null :: Quaternion a -> Bool # length :: Quaternion a -> Int # elem :: Eq a => a -> Quaternion a -> Bool # maximum :: Ord a => Quaternion a -> a # minimum :: Ord a => Quaternion a -> a # sum :: Num a => Quaternion a -> a # product :: Num a => Quaternion a -> a #
Traversable Quaternion
Methods traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b) # sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a) # mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b) # sequence :: Monad m => Quaternion (m a) -> m (Quaternion a) #
Generic1 Quaternion
Associated Types type Rep1 (Quaternion :: * -> ) :: -> * # Methods from1 :: Quaternion a -> Rep1 Quaternion a # to1 :: Rep1 Quaternion a -> Quaternion a #
Distributive Quaternion
Methods distribute :: Functor f => f (Quaternion a) -> Quaternion (f a) # collect :: Functor f => (a -> Quaternion b) -> f a -> Quaternion (f b) # distributeM :: Monad m => m (Quaternion a) -> Quaternion (m a) # collectM :: Monad m => (a -> Quaternion b) -> m a -> Quaternion (m b) #
Representable Quaternion
Associated Types type Rep (Quaternion :: * -> ) :: # Methods tabulate :: (Rep Quaternion -> a) -> Quaternion a # index :: Quaternion a -> Rep Quaternion -> a #
Eq1 Quaternion
Methods liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool #
Ord1 Quaternion
Methods liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering #
Read1 Quaternion
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Quaternion a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Quaternion a] #
Show1 Quaternion
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS #
MonadZip Quaternion
Methods mzip :: Quaternion a -> Quaternion b -> Quaternion (a, b) # mzipWith :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c # munzip :: Quaternion (a, b) -> (Quaternion a, Quaternion b) #
Serial1 Quaternion
Methods serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m () # deserializeWith :: MonadGet m => m a -> m (Quaternion a) #
Trace Quaternion
Methods trace :: Num a => Quaternion (Quaternion a) -> a # diagonal :: Quaternion (Quaternion a) -> Quaternion a #
Complicated Quaternion
Methods _e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) # _i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) #
Hamiltonian Quaternion
Methods _j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) # _k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) # _ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a) #
Metric Quaternion
Methods dot :: Num a => Quaternion a -> Quaternion a -> a # quadrance :: Num a => Quaternion a -> a # qd :: Num a => Quaternion a -> Quaternion a -> a # distance :: Floating a => Quaternion a -> Quaternion a -> a # norm :: Floating a => Quaternion a -> a # signorm :: Floating a => Quaternion a -> Quaternion a #
Additive Quaternion
Methods zero :: Num a => Quaternion a # (^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # (^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a # liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a # liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Apply Quaternion
Methods (<.>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # (.>) :: Quaternion a -> Quaternion b -> Quaternion b # (<.) :: Quaternion a -> Quaternion b -> Quaternion a #
Bind Quaternion
Methods (>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # join :: Quaternion (Quaternion a) -> Quaternion a #
Trace Quaternion Source #
Methods trace :: (Num a, Box2 Quaternion Quaternion a) => Exp (Quaternion (Quaternion a)) -> Exp a Source # diagonal :: Box2 Quaternion Quaternion a => Exp (Quaternion (Quaternion a)) -> Exp (Quaternion a) Source #
Unbox a => Vector Vector (Quaternion a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> m (Vector (Quaternion a)) # basicUnsafeThaw :: PrimMonad m => Vector (Quaternion a) -> m (Mutable Vector (PrimState m) (Quaternion a)) # basicLength :: Vector (Quaternion a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a) # basicUnsafeIndexM :: Monad m => Vector (Quaternion a) -> Int -> m (Quaternion a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> Vector (Quaternion a) -> m () # elemseq :: Vector (Quaternion a) -> Quaternion a -> b -> b #
Unbox a => MVector MVector (Quaternion a)
Methods basicLength :: MVector s (Quaternion a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Quaternion a) -> MVector s (Quaternion a) # basicOverlaps :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Quaternion a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Quaternion a -> m (MVector (PrimState m) (Quaternion a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (Quaternion a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> Quaternion a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Quaternion a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (MVector (PrimState m) (Quaternion a)) #
Eq a => Eq (Quaternion a)
Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
RealFloat a => Floating (Quaternion a)
Methods pi :: Quaternion a # exp :: Quaternion a -> Quaternion a # log :: Quaternion a -> Quaternion a # sqrt :: Quaternion a -> Quaternion a # (**) :: Quaternion a -> Quaternion a -> Quaternion a # logBase :: Quaternion a -> Quaternion a -> Quaternion a # sin :: Quaternion a -> Quaternion a # cos :: Quaternion a -> Quaternion a # tan :: Quaternion a -> Quaternion a # asin :: Quaternion a -> Quaternion a # acos :: Quaternion a -> Quaternion a # atan :: Quaternion a -> Quaternion a # sinh :: Quaternion a -> Quaternion a # cosh :: Quaternion a -> Quaternion a # tanh :: Quaternion a -> Quaternion a # asinh :: Quaternion a -> Quaternion a # acosh :: Quaternion a -> Quaternion a # atanh :: Quaternion a -> Quaternion a # log1p :: Quaternion a -> Quaternion a # expm1 :: Quaternion a -> Quaternion a # log1pexp :: Quaternion a -> Quaternion a # log1mexp :: Quaternion a -> Quaternion a #
RealFloat a => Fractional (Quaternion a)
Methods (/) :: Quaternion a -> Quaternion a -> Quaternion a # recip :: Quaternion a -> Quaternion a # fromRational :: Rational -> Quaternion a #
Data a => Data (Quaternion a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Quaternion a -> c (Quaternion a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Quaternion a) # toConstr :: Quaternion a -> Constr # dataTypeOf :: Quaternion a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Quaternion a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Quaternion a)) # gmapT :: (forall b. Data b => b -> b) -> Quaternion a -> Quaternion a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Quaternion a -> r # gmapQ :: (forall d. Data d => d -> u) -> Quaternion a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Quaternion a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Quaternion a -> m (Quaternion a) #
RealFloat a => Num (Quaternion a)
Methods (+) :: Quaternion a -> Quaternion a -> Quaternion a # (-) :: Quaternion a -> Quaternion a -> Quaternion a # (*) :: Quaternion a -> Quaternion a -> Quaternion a # negate :: Quaternion a -> Quaternion a # abs :: Quaternion a -> Quaternion a # signum :: Quaternion a -> Quaternion a # fromInteger :: Integer -> Quaternion a #
Ord a => Ord (Quaternion a)
Methods compare :: Quaternion a -> Quaternion a -> Ordering # (<) :: Quaternion a -> Quaternion a -> Bool # (<=) :: Quaternion a -> Quaternion a -> Bool # (>) :: Quaternion a -> Quaternion a -> Bool # (>=) :: Quaternion a -> Quaternion a -> Bool # max :: Quaternion a -> Quaternion a -> Quaternion a # min :: Quaternion a -> Quaternion a -> Quaternion a #
Read a => Read (Quaternion a)
Methods readsPrec :: Int -> ReadS (Quaternion a) # readList :: ReadS [Quaternion a] # readPrec :: ReadPrec (Quaternion a) # readListPrec :: ReadPrec [Quaternion a] #
Show a => Show (Quaternion a)
Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Ix a => Ix (Quaternion a)
Methods range :: (Quaternion a, Quaternion a) -> [Quaternion a] # index :: (Quaternion a, Quaternion a) -> Quaternion a -> Int # unsafeIndex :: (Quaternion a, Quaternion a) -> Quaternion a -> Int inRange :: (Quaternion a, Quaternion a) -> Quaternion a -> Bool # rangeSize :: (Quaternion a, Quaternion a) -> Int # unsafeRangeSize :: (Quaternion a, Quaternion a) -> Int
Generic (Quaternion a)
Associated Types type Rep (Quaternion a) :: * -> * # Methods from :: Quaternion a -> Rep (Quaternion a) x # to :: Rep (Quaternion a) x -> Quaternion a #
Storable a => Storable (Quaternion a)
Methods sizeOf :: Quaternion a -> Int # alignment :: Quaternion a -> Int # peekElemOff :: Ptr (Quaternion a) -> Int -> IO (Quaternion a) # pokeElemOff :: Ptr (Quaternion a) -> Int -> Quaternion a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Quaternion a) # pokeByteOff :: Ptr b -> Int -> Quaternion a -> IO () # peek :: Ptr (Quaternion a) -> IO (Quaternion a) # poke :: Ptr (Quaternion a) -> Quaternion a -> IO () #
Binary a => Binary (Quaternion a)
Methods put :: Quaternion a -> Put # get :: Get (Quaternion a) # putList :: [Quaternion a] -> Put #
Serial a => Serial (Quaternion a)
Methods serialize :: MonadPut m => Quaternion a -> m () # deserialize :: MonadGet m => m (Quaternion a) #
Serialize a => Serialize (Quaternion a)
Methods put :: Putter (Quaternion a) # get :: Get (Quaternion a) #
NFData a => NFData (Quaternion a)
Methods rnf :: Quaternion a -> () #
Hashable a => Hashable (Quaternion a)
Methods hashWithSalt :: Int -> Quaternion a -> Int # hash :: Quaternion a -> Int #
Unbox a => Unbox (Quaternion a)

Ixed (Quaternion a)
Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)
Methods conjugate :: Quaternion a -> Quaternion a #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)
Methods nearZero :: Quaternion a -> Bool #
FunctorWithIndex (E Quaternion) Quaternion
Methods imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b # imapped :: (Indexable (E Quaternion) p, Settable f) => p a (f b) -> Quaternion a -> f (Quaternion b) #
FoldableWithIndex (E Quaternion) Quaternion
Methods ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # ifolded :: (Indexable (E Quaternion) p, Contravariant f, Applicative f) => p a (f a) -> Quaternion a -> f (Quaternion a) # ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b # ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b #
TraversableWithIndex (E Quaternion) Quaternion
Methods itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) # itraversed :: (Indexable (E Quaternion) p, Applicative f) => p a (f b) -> Quaternion a -> f (Quaternion b) #
Each (Quaternion a) (Quaternion b) a b
Methods each :: Traversal (Quaternion a) (Quaternion b) a b #
type Rep1 Quaternion
type Rep1 Quaternion = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.5-CEAsJizrl7jL0iAxtpGqYP" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec1 V3))))
type Rep Quaternion
type Rep Quaternion = E Quaternion
data MVector s (Quaternion a)
data MVector s (Quaternion a) = MV_Quaternion ~Int (MVector s a)
type Rep (Quaternion a)
type Rep (Quaternion a) = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.5-CEAsJizrl7jL0iAxtpGqYP" False) (C1 (MetaCons "Quaternion" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) SourceUnpack SourceStrict DecidedUnpack) (Rec0 (V3 a)))))
type EltRepr (Quaternion a)
type EltRepr (Quaternion a) = EltRepr (a, a, a, a)
type ProdRepr (Quaternion a)
type ProdRepr (Quaternion a) = ProdRepr (a, a, a, a)
type Plain (Quaternion a) #
type Plain (Quaternion a) = Quaternion (Plain a)
data Vector (Quaternion a)
data Vector (Quaternion a) = V_Quaternion ~Int (Vector a)
type Index (Quaternion a)
type Index (Quaternion a) = E Quaternion
type IxValue (Quaternion a)
type IxValue (Quaternion a) = a

Orphan instances

Additive Quaternion Source #
Methods zero :: (Elt (Quaternion a), Num a) => Exp (Quaternion a) Source # (^+^) :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source # (^-^) :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source # lerp :: (Num a, Box Quaternion a) => Exp a -> Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #
Metric Quaternion Source #
Methods dot :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a Source # quadrance :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp a Source # qd :: (Num a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a Source # distance :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a Source # norm :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp a Source # signorm :: (Floating a, Box Quaternion a) => Exp (Quaternion a) -> Exp (Quaternion a) Source #
cst a => IsProduct cst (Quaternion a) Source #
Associated Types type ProdRepr (Quaternion a) :: * Methods fromProd :: proxy cst -> Quaternion a -> ProdRepr (Quaternion a) toProd :: proxy cst -> ProdRepr (Quaternion a) -> Quaternion a prod :: proxy cst -> Quaternion a -> ProdR cst (ProdRepr (Quaternion a))
(Lift Exp a, Elt (Plain a)) => Lift Exp (Quaternion a) Source #
Associated Types type Plain (Quaternion a) :: * # Methods lift :: Quaternion a -> Exp (Plain (Quaternion a)) #
Elt a => Unlift Exp (Quaternion (Exp a)) Source #
Methods unlift :: Exp (Plain (Quaternion (Exp a))) -> Quaternion (Exp a) #
Elt a => Elt (Quaternion a) Source #
Methods eltType :: Quaternion a -> TupleType (EltRepr (Quaternion a)) fromElt :: Quaternion a -> EltRepr (Quaternion a) toElt :: EltRepr (Quaternion a) -> Quaternion a
(Elt a, Elt b) => Each (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) Source #
Methods each :: Traversal (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) #