Copyright	2014 Edward Kmett Charles Durham [2015..2020] Trevor L. McDonell
License	BSD-style (see the file LICENSE)
Maintainer	Trevor L. McDonell <trevor.mcdonell@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Array.Accelerate.Linear.Quaternion

Contents

Orphan instances

Description

Quaternions

Synopsis

data Quaternion a = Quaternion !a !(V3 a)
pattern Quaternion_ :: Elt a => Exp a -> Exp (V3 a) -> Exp (Quaternion a)
slerp :: RealFloat a => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a -> Exp (Quaternion a)
asinq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
acosq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
atanq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
asinhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
acoshq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
atanhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
absi :: Floating a => Exp (Quaternion a) -> Exp a
pow :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp a -> Exp (Quaternion a)
rotate :: forall a. (Conjugate (Exp a), RealFloat a) => Exp (Quaternion a) -> Exp (V3 a) -> Exp (V3 a)
axisAngle :: (Epsilon a, Floating a) => Exp (V3 a) -> Exp a -> Exp (Quaternion a)

Documentation

data Quaternion a #

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.Quaternion Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
MonadFix Quaternion
Instance details Defined in Linear.Quaternion Methods mfix :: (a -> Quaternion a) -> Quaternion a #
Applicative Quaternion
Instance details Defined in Linear.Quaternion Methods pure :: a -> Quaternion a # (<>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # liftA2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c # (>) :: Quaternion a -> Quaternion b -> Quaternion b # (<*) :: Quaternion a -> Quaternion b -> Quaternion a #
Foldable Quaternion
Instance details Defined in Linear.Quaternion Methods fold :: Monoid m => Quaternion m -> m # foldMap :: Monoid m => (a -> m) -> Quaternion a -> m # foldr :: (a -> b -> b) -> b -> Quaternion a -> b # foldr' :: (a -> b -> b) -> b -> Quaternion a -> b # foldl :: (b -> a -> b) -> b -> Quaternion a -> b # foldl' :: (b -> a -> b) -> b -> Quaternion a -> b # foldr1 :: (a -> a -> a) -> Quaternion a -> a # foldl1 :: (a -> a -> a) -> Quaternion a -> a # toList :: Quaternion a -> [a] # null :: Quaternion a -> Bool # length :: Quaternion a -> Int # elem :: Eq a => a -> Quaternion a -> Bool # maximum :: Ord a => Quaternion a -> a # minimum :: Ord a => Quaternion a -> a # sum :: Num a => Quaternion a -> a # product :: Num a => Quaternion a -> a #
Traversable Quaternion
Instance details Defined in Linear.Quaternion Methods traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b) # sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a) # mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b) # sequence :: Monad m => Quaternion (m a) -> m (Quaternion a) #
Functor Quaternion Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods fmap :: (Elt a, Elt b, Elt (Quaternion a), Elt (Quaternion b)) => (Exp a -> Exp b) -> Exp (Quaternion a) -> Exp (Quaternion b) # (<$) :: (Elt a, Elt b, Elt (Quaternion a), Elt (Quaternion b)) => Exp a -> Exp (Quaternion b) -> Exp (Quaternion a) #
Distributive Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.Quaternion Associated Types type Rep Quaternion :: Type # Methods tabulate :: (Rep Quaternion -> a) -> Quaternion a # index :: Quaternion a -> Rep Quaternion -> a #
Eq1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool #
Ord1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering #
Read1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Quaternion a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Quaternion a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Quaternion a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Quaternion a] #
Show1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS #
MonadZip Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.Quaternion Methods serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m () # deserializeWith :: MonadGet m => m a -> m (Quaternion a) #
Hashable1 Quaternion
Instance details Defined in Linear.Quaternion Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Quaternion a -> Int #
Apply Quaternion
Instance details Defined in Linear.Quaternion Methods (<.>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # (.>) :: Quaternion a -> Quaternion b -> Quaternion b # (<.) :: Quaternion a -> Quaternion b -> Quaternion a # liftF2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Trace Quaternion
Instance details Defined in Linear.Trace Methods trace :: Num a => Quaternion (Quaternion a) -> a # diagonal :: Quaternion (Quaternion a) -> Quaternion a #
Complicated Quaternion
Instance details Defined in Linear.Quaternion Methods _e :: Lens' (Quaternion a) a # _i :: Lens' (Quaternion a) a #
Hamiltonian Quaternion
Instance details Defined in Linear.Quaternion Methods _j :: Lens' (Quaternion a) a # _k :: Lens' (Quaternion a) a # _ijk :: Lens' (Quaternion a) (V3 a) #
R4 Quaternion
Instance details Defined in Linear.Quaternion Methods _w :: Lens' (Quaternion a) a # _xyzw :: Lens' (Quaternion a) (V4 a) #
R3 Quaternion
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a # _xyz :: Lens' (Quaternion a) (V3 a) #
R2 Quaternion
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a # _xy :: Lens' (Quaternion a) (V2 a) #
R1 Quaternion
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a #
Finite Quaternion
Instance details Defined in Linear.Quaternion Associated Types type Size Quaternion :: Nat # Methods toV :: Quaternion a -> V (Size Quaternion) a # fromV :: V (Size Quaternion) a -> Quaternion a #
Metric Quaternion
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Bind Quaternion
Instance details Defined in Linear.Quaternion Methods (>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # join :: Quaternion (Quaternion a) -> Quaternion a #
Additive Quaternion Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion 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 #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion 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 #
Trace Quaternion Source #
Instance details Defined in Data.Array.Accelerate.Linear.Trace 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 #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Associated Types type Plain (Quaternion a) :: Type # Methods lift :: Quaternion a -> Exp (Plain (Quaternion a)) #
Elt a => Unlift Exp (Quaternion (Exp a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods unlift :: Exp (Plain (Quaternion (Exp a))) -> Quaternion (Exp a) #
Unbox a => Vector Vector (Quaternion a)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
(RealFloat a, Elt (Complex a)) => Floating (Exp (Quaternion a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods pi :: Exp (Quaternion a) # exp :: Exp (Quaternion a) -> Exp (Quaternion a) # log :: Exp (Quaternion a) -> Exp (Quaternion a) # sqrt :: Exp (Quaternion a) -> Exp (Quaternion a) # (**) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # logBase :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # sin :: Exp (Quaternion a) -> Exp (Quaternion a) # cos :: Exp (Quaternion a) -> Exp (Quaternion a) # tan :: Exp (Quaternion a) -> Exp (Quaternion a) # asin :: Exp (Quaternion a) -> Exp (Quaternion a) # acos :: Exp (Quaternion a) -> Exp (Quaternion a) # atan :: Exp (Quaternion a) -> Exp (Quaternion a) # sinh :: Exp (Quaternion a) -> Exp (Quaternion a) # cosh :: Exp (Quaternion a) -> Exp (Quaternion a) # tanh :: Exp (Quaternion a) -> Exp (Quaternion a) # asinh :: Exp (Quaternion a) -> Exp (Quaternion a) # acosh :: Exp (Quaternion a) -> Exp (Quaternion a) # atanh :: Exp (Quaternion a) -> Exp (Quaternion a) # log1p :: Exp (Quaternion a) -> Exp (Quaternion a) # expm1 :: Exp (Quaternion a) -> Exp (Quaternion a) # log1pexp :: Exp (Quaternion a) -> Exp (Quaternion a) # log1mexp :: Exp (Quaternion a) -> Exp (Quaternion a) #
RealFloat a => Floating (Quaternion a)
Instance details Defined in Linear.Quaternion 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 (Exp (Quaternion a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods (/) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # recip :: Exp (Quaternion a) -> Exp (Quaternion a) # fromRational :: Rational -> Exp (Quaternion a) #
RealFloat a => Fractional (Quaternion a)
Instance details Defined in Linear.Quaternion Methods (/) :: Quaternion a -> Quaternion a -> Quaternion a # recip :: Quaternion a -> Quaternion a # fromRational :: Rational -> Quaternion a #
Data a => Data (Quaternion a)
Instance details Defined in Linear.Quaternion 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 (Exp (Quaternion a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods (+) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # (-) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # (*) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # negate :: Exp (Quaternion a) -> Exp (Quaternion a) # abs :: Exp (Quaternion a) -> Exp (Quaternion a) # signum :: Exp (Quaternion a) -> Exp (Quaternion a) # fromInteger :: Integer -> Exp (Quaternion a) #
RealFloat a => Num (Quaternion a)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion Methods readsPrec :: Int -> ReadS (Quaternion a) # readList :: ReadS [Quaternion a] # readPrec :: ReadPrec (Quaternion a) # readListPrec :: ReadPrec [Quaternion a] #
Show a => Show (Quaternion a)
Instance details Defined in Linear.Quaternion Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Ix a => Ix (Quaternion a)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion Associated Types type Rep (Quaternion a) :: Type -> Type # Methods from :: Quaternion a -> Rep (Quaternion a) x # to :: Rep (Quaternion a) x -> Quaternion a #
Semigroup a => Semigroup (Quaternion a)
Instance details Defined in Linear.Quaternion Methods (<>) :: Quaternion a -> Quaternion a -> Quaternion a # sconcat :: NonEmpty (Quaternion a) -> Quaternion a # stimes :: Integral b => b -> Quaternion a -> Quaternion a #
Monoid a => Monoid (Quaternion a)
Instance details Defined in Linear.Quaternion Methods mempty :: Quaternion a # mappend :: Quaternion a -> Quaternion a -> Quaternion a # mconcat :: [Quaternion a] -> Quaternion a #
Lift a => Lift (Quaternion a)
Instance details Defined in Linear.Quaternion Methods lift :: Quaternion a -> Q Exp #
Ord a => Ord (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods (<) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (>) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (<=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (>=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # min :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # max :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # compare :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Ordering #
Eq a => Eq (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods (==) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (/=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool #
Elt a => Elt (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Associated Types type EltR (Quaternion a) :: Type Methods eltR :: TypeR (EltR (Quaternion a)) tagsR :: [TagR (EltR (Quaternion a))] fromElt :: Quaternion a -> EltR (Quaternion a) toElt :: EltR (Quaternion a) -> Quaternion a
Storable a => Storable (Quaternion a)
Instance details Defined in Linear.Quaternion 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)
Instance details Defined in Linear.Quaternion Methods put :: Quaternion a -> Put # get :: Get (Quaternion a) # putList :: [Quaternion a] -> Put #
Serial a => Serial (Quaternion a)
Instance details Defined in Linear.Quaternion Methods serialize :: MonadPut m => Quaternion a -> m () # deserialize :: MonadGet m => m (Quaternion a) #
Serialize a => Serialize (Quaternion a)
Instance details Defined in Linear.Quaternion Methods put :: Putter (Quaternion a) # get :: Get (Quaternion a) #
NFData a => NFData (Quaternion a)
Instance details Defined in Linear.Quaternion Methods rnf :: Quaternion a -> () #
Hashable a => Hashable (Quaternion a)
Instance details Defined in Linear.Quaternion Methods hashWithSalt :: Int -> Quaternion a -> Int # hash :: Quaternion a -> Int #
Unbox a => Unbox (Quaternion a)
Instance details Defined in Linear.Quaternion
Ixed (Quaternion a)
Instance details Defined in Linear.Quaternion Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a)
Instance details Defined in Linear.Quaternion Methods nearZero :: Quaternion a -> Bool #
(RealFloat a, Conjugate (Exp a)) => Conjugate (Exp (Quaternion a)) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods conjugate :: Exp (Quaternion a) -> Exp (Quaternion a) #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a)
Instance details Defined in Linear.Quaternion Methods conjugate :: Quaternion a -> Quaternion a #
Random a => Random (Quaternion a)
Instance details Defined in Linear.Quaternion Methods randomR :: RandomGen g => (Quaternion a, Quaternion a) -> g -> (Quaternion a, g) # random :: RandomGen g => g -> (Quaternion a, g) # randomRs :: RandomGen g => (Quaternion a, Quaternion a) -> g -> [Quaternion a] # randoms :: RandomGen g => g -> [Quaternion a] # randomRIO :: (Quaternion a, Quaternion a) -> IO (Quaternion a) # randomIO :: IO (Quaternion a) #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods nearZero :: Exp (Quaternion a) -> Exp Bool Source #
Generic1 Quaternion
Instance details Defined in Linear.Quaternion Associated Types type Rep1 Quaternion :: k -> Type # Methods from1 :: Quaternion a -> Rep1 Quaternion a # to1 :: Rep1 Quaternion a -> Quaternion a #
FunctorWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b # imapped :: IndexedSetter (E Quaternion) (Quaternion a) (Quaternion b) a b #
FoldableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # ifolded :: IndexedFold (E Quaternion) (Quaternion a) 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
Instance details Defined in Linear.Quaternion Methods itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) # itraversed :: IndexedTraversal (E Quaternion) (Quaternion a) (Quaternion b) a b #
Each (Quaternion a) (Quaternion b) a b
Instance details Defined in Linear.Quaternion Methods each :: Traversal (Quaternion a) (Quaternion b) a b #
Field1 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _1 :: Lens (Quaternion a) (Quaternion a) a a #
Field2 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _2 :: Lens (Quaternion a) (Quaternion a) a a #
Field3 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _3 :: Lens (Quaternion a) (Quaternion a) a a #
Field4 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _4 :: Lens (Quaternion a) (Quaternion a) a a #
(Elt a, Elt b) => Each (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion Methods each :: Traversal (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) #
type Rep Quaternion
Instance details Defined in Linear.Quaternion type Rep Quaternion = E Quaternion
type Size Quaternion
Instance details Defined in Linear.Quaternion type Size Quaternion = 4
data MVector s (Quaternion a)
Instance details Defined in Linear.Quaternion data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)
type Rep (Quaternion a)
Instance details Defined in Linear.Quaternion type Rep (Quaternion a) = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.21.1-GSRtap511Ww6RirKx1xviJ" False) (C1 (MetaCons "Quaternion" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec0 (V3 a))))
type EltR (Quaternion a)
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion type EltR (Quaternion a) = GEltR () (Rep (Quaternion a))
type Plain (Quaternion a) Source #
Instance details Defined in Data.Array.Accelerate.Linear.Quaternion type Plain (Quaternion a) = Quaternion (Plain a)
data Vector (Quaternion a)
Instance details Defined in Linear.Quaternion data Vector (Quaternion a) = V_Quaternion !Int (Vector a)
type Index (Quaternion a)
Instance details Defined in Linear.Quaternion type Index (Quaternion a) = E Quaternion
type IxValue (Quaternion a)
Instance details Defined in Linear.Quaternion type IxValue (Quaternion a) = a
type Rep1 Quaternion
Instance details Defined in Linear.Quaternion type Rep1 Quaternion = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.21.1-GSRtap511Ww6RirKx1xviJ" False) (C1 (MetaCons "Quaternion" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec1 V3)))

pattern Quaternion_ :: Elt a => Exp a -> Exp (V3 a) -> Exp (Quaternion a) Source #

slerp :: RealFloat a => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a -> Exp (Quaternion a) Source #

Spherical linear interpolation between two quaternions

asinq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

asin with a specified branch cut

acosq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

acos with a specified branch cut

atanq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

atan with a specified branch cut

asinhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

asinh with a specified branch cut

acoshq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

acosh with a specified branch cut

atanhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) Source #

atanh with a specified branch cut

absi :: Floating a => Exp (Quaternion a) -> Exp a Source #

norm of the imaginary component

pow :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp a -> Exp (Quaternion a) Source #

raise a Quaternion to a scalar power

rotate :: forall a. (Conjugate (Exp a), RealFloat a) => Exp (Quaternion a) -> Exp (V3 a) -> Exp (V3 a) Source #

Apply a rotation to a vector

axisAngle :: (Epsilon a, Floating a) => Exp (V3 a) -> Exp a -> Exp (Quaternion a) Source #

axisAngle axis theta builds a Quaternion representing a rotation of theta radians about axis.

Orphan instances

Functor Quaternion Source #
Instance details Methods fmap :: (Elt a, Elt b, Elt (Quaternion a), Elt (Quaternion b)) => (Exp a -> Exp b) -> Exp (Quaternion a) -> Exp (Quaternion b) # (<$) :: (Elt a, Elt b, Elt (Quaternion a), Elt (Quaternion b)) => Exp a -> Exp (Quaternion b) -> Exp (Quaternion a) #
Additive Quaternion Source #
Instance details 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 #
Instance details 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 #
(Lift Exp a, Elt (Plain a)) => Lift Exp (Quaternion a) Source #
Instance details Associated Types type Plain (Quaternion a) :: Type # Methods lift :: Quaternion a -> Exp (Plain (Quaternion a)) #
Elt a => Unlift Exp (Quaternion (Exp a)) Source #
Instance details Methods unlift :: Exp (Plain (Quaternion (Exp a))) -> Quaternion (Exp a) #
(RealFloat a, Elt (Complex a)) => Floating (Exp (Quaternion a)) Source #
Instance details Methods pi :: Exp (Quaternion a) # exp :: Exp (Quaternion a) -> Exp (Quaternion a) # log :: Exp (Quaternion a) -> Exp (Quaternion a) # sqrt :: Exp (Quaternion a) -> Exp (Quaternion a) # (**) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # logBase :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # sin :: Exp (Quaternion a) -> Exp (Quaternion a) # cos :: Exp (Quaternion a) -> Exp (Quaternion a) # tan :: Exp (Quaternion a) -> Exp (Quaternion a) # asin :: Exp (Quaternion a) -> Exp (Quaternion a) # acos :: Exp (Quaternion a) -> Exp (Quaternion a) # atan :: Exp (Quaternion a) -> Exp (Quaternion a) # sinh :: Exp (Quaternion a) -> Exp (Quaternion a) # cosh :: Exp (Quaternion a) -> Exp (Quaternion a) # tanh :: Exp (Quaternion a) -> Exp (Quaternion a) # asinh :: Exp (Quaternion a) -> Exp (Quaternion a) # acosh :: Exp (Quaternion a) -> Exp (Quaternion a) # atanh :: Exp (Quaternion a) -> Exp (Quaternion a) # log1p :: Exp (Quaternion a) -> Exp (Quaternion a) # expm1 :: Exp (Quaternion a) -> Exp (Quaternion a) # log1pexp :: Exp (Quaternion a) -> Exp (Quaternion a) # log1mexp :: Exp (Quaternion a) -> Exp (Quaternion a) #
RealFloat a => Fractional (Exp (Quaternion a)) Source #
Instance details Methods (/) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # recip :: Exp (Quaternion a) -> Exp (Quaternion a) # fromRational :: Rational -> Exp (Quaternion a) #
RealFloat a => Num (Exp (Quaternion a)) Source #
Instance details Methods (+) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # (-) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # (*) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # negate :: Exp (Quaternion a) -> Exp (Quaternion a) # abs :: Exp (Quaternion a) -> Exp (Quaternion a) # signum :: Exp (Quaternion a) -> Exp (Quaternion a) # fromInteger :: Integer -> Exp (Quaternion a) #
Ord a => Ord (Quaternion a) Source #
Instance details Methods (<) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (>) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (<=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (>=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # min :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # max :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a) # compare :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Ordering #
Eq a => Eq (Quaternion a) Source #
Instance details Methods (==) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool # (/=) :: Exp (Quaternion a) -> Exp (Quaternion a) -> Exp Bool #
Elt a => Elt (Quaternion a) Source #
Instance details Associated Types type EltR (Quaternion a) :: Type Methods eltR :: TypeR (EltR (Quaternion a)) tagsR :: [TagR (EltR (Quaternion a))] fromElt :: Quaternion a -> EltR (Quaternion a) toElt :: EltR (Quaternion a) -> Quaternion a
(RealFloat a, Conjugate (Exp a)) => Conjugate (Exp (Quaternion a)) Source #
Instance details Methods conjugate :: Exp (Quaternion a) -> Exp (Quaternion a) #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source #
Instance details Methods nearZero :: Exp (Quaternion a) -> Exp Bool Source #
(Elt a, Elt b) => Each (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) Source #
Instance details Methods each :: Traversal (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) #