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.Quaternion

Description

Quaternions

Synopsis

Documentation

data Quaternion a Source #

Quaternions

Constructors

Quaternion !a !(V3 a)

Instances

Monad Quaternion Source #
Methods (>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # (>>) :: Quaternion a -> Quaternion b -> Quaternion b # return :: a -> Quaternion a # fail :: String -> Quaternion a #
Functor Quaternion Source #
Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
MonadFix Quaternion Source #
Methods mfix :: (a -> Quaternion a) -> Quaternion a #
Applicative Quaternion Source #
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 Source #
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 Source #
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 Source #
Associated Types type Rep1 (Quaternion :: * -> ) :: -> * # Methods from1 :: Quaternion a -> Rep1 Quaternion a # to1 :: Rep1 Quaternion a -> Quaternion a #
Distributive Quaternion Source #
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 Source #
Associated Types type Rep (Quaternion :: * -> ) :: # Methods tabulate :: (Rep Quaternion -> a) -> Quaternion a # index :: Quaternion a -> Rep Quaternion -> a #
Eq1 Quaternion Source #
Methods liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool #
Ord1 Quaternion Source #
Methods liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering #
Read1 Quaternion Source #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Quaternion a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Quaternion a] #
Show1 Quaternion Source #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quaternion a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quaternion a] -> ShowS #
MonadZip Quaternion Source #
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 Source #
Methods serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m () # deserializeWith :: MonadGet m => m a -> m (Quaternion a) #
Apply Quaternion Source #
Methods (<.>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # (.>) :: Quaternion a -> Quaternion b -> Quaternion b # (<.) :: Quaternion a -> Quaternion b -> Quaternion a #
Bind Quaternion Source #
Methods (>>-) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b # join :: Quaternion (Quaternion a) -> Quaternion a #
Additive Quaternion Source #
Methods zero :: Num a => Quaternion a Source # (^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a Source # (^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a Source # lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a Source # liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a Source # liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c Source #
Metric Quaternion Source #
Methods dot :: Num a => Quaternion a -> Quaternion a -> a Source # quadrance :: Num a => Quaternion a -> a Source # qd :: Num a => Quaternion a -> Quaternion a -> a Source # distance :: Floating a => Quaternion a -> Quaternion a -> a Source # norm :: Floating a => Quaternion a -> a Source # signorm :: Floating a => Quaternion a -> Quaternion a Source #
Finite Quaternion Source #
Associated Types type Size (Quaternion :: * -> *) :: Nat Source # Methods toV :: Quaternion a -> V Nat (Size Quaternion) a Source # fromV :: V Nat (Size Quaternion) a -> Quaternion a Source #
Hamiltonian Quaternion Source #
Methods _j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a) Source #
Complicated Quaternion Source #
Methods _e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source #
Trace Quaternion Source #
Methods trace :: Num a => Quaternion (Quaternion a) -> a Source # diagonal :: Quaternion (Quaternion a) -> Quaternion a Source #
Affine Quaternion Source #
Associated Types type Diff (Quaternion :: * -> ) :: -> * Source # Methods (.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a Source # (.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a Source # (.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a Source #
Unbox a => Vector Vector (Quaternion a) Source #
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) Source #
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)) #
(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source #
Methods comult :: (E Quaternion -> r) -> E Quaternion -> E Quaternion -> r Source # counital :: (E Quaternion -> r) -> r Source #
(Num r, TrivialConjugate r) => Algebra r (E Quaternion) Source #
Methods mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r Source # unital :: r -> E Quaternion -> r Source #
Eq a => Eq (Quaternion a) Source #
Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
RealFloat a => Floating (Quaternion a) Source #
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) Source #
Methods (/) :: Quaternion a -> Quaternion a -> Quaternion a # recip :: Quaternion a -> Quaternion a # fromRational :: Rational -> Quaternion a #
Data a => Data (Quaternion a) Source #
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) Source #
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) Source #
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) Source #
Methods readsPrec :: Int -> ReadS (Quaternion a) # readList :: ReadS [Quaternion a] # readPrec :: ReadPrec (Quaternion a) # readListPrec :: ReadPrec [Quaternion a] #
Show a => Show (Quaternion a) Source #
Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Ix a => Ix (Quaternion a) Source #
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) Source #
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) Source #
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) Source #
Methods put :: Quaternion a -> Put # get :: Get (Quaternion a) # putList :: [Quaternion a] -> Put #
Serial a => Serial (Quaternion a) Source #
Methods serialize :: MonadPut m => Quaternion a -> m () # deserialize :: MonadGet m => m (Quaternion a) #
Serialize a => Serialize (Quaternion a) Source #
Methods put :: Putter (Quaternion a) # get :: Get (Quaternion a) #
NFData a => NFData (Quaternion a) Source #
Methods rnf :: Quaternion a -> () #
Hashable a => Hashable (Quaternion a) Source #
Methods hashWithSalt :: Int -> Quaternion a -> Int # hash :: Quaternion a -> Int #
Unbox a => Unbox (Quaternion a) Source #

Ixed (Quaternion a) Source #
Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source #
Methods nearZero :: Quaternion a -> Bool Source #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a) Source #
Methods conjugate :: Quaternion a -> Quaternion a Source #
FunctorWithIndex (E Quaternion) Quaternion Source #
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 Source #
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 Source #
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 Source #
Methods each :: Traversal (Quaternion a) (Quaternion b) a b #
type Rep1 Quaternion Source #
type Rep1 Quaternion = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.6-7GMSraBBXwf75Iqz3D0i5l" 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 Source #
type Rep Quaternion = E Quaternion
type Size Quaternion Source #
type Size Quaternion = 4
type Diff Quaternion Source #
type Diff Quaternion = Quaternion
data MVector s (Quaternion a) Source #
data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)
type Rep (Quaternion a) Source #
type Rep (Quaternion a) = D1 (MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.6-7GMSraBBXwf75Iqz3D0i5l" 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)))))
data Vector (Quaternion a) Source #
data Vector (Quaternion a) = V_Quaternion !Int (Vector a)
type Index (Quaternion a) Source #
type Index (Quaternion a) = E Quaternion
type IxValue (Quaternion a) Source #
type IxValue (Quaternion a) = a

class Complicated t where Source #

A vector space that includes the basis elements _e and _i

Methods

_e, _i :: Lens' (t a) a Source #

Instances

Complicated Complex Source #
Methods _e :: Functor f => (a -> f a) -> Complex a -> f (Complex a) Source # _i :: Functor f => (a -> f a) -> Complex a -> f (Complex a) Source #
Complicated Quaternion Source #
Methods _e :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _i :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source #

class Complicated t => Hamiltonian t where Source #

A vector space that includes the basis elements _e, _i, _j and _k

Methods

_j, _k :: Lens' (t a) a Source #

_ijk :: Lens' (t a) (V3 a) Source #

Instances

Hamiltonian Quaternion Source #
Methods _j :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _k :: Functor f => (a -> f a) -> Quaternion a -> f (Quaternion a) Source # _ijk :: Functor f => (V3 a -> f (V3 a)) -> Quaternion a -> f (Quaternion a) Source #