linear-1.20.9: Linear Algebra
Copyright(C) 2012-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellTrustworthy
LanguageHaskell98

Linear.Quaternion

Description

Quaternions

Synopsis

Documentation

data Quaternion a Source #

Quaternions

Constructors

Quaternion !a !(V3 a) 

Instances

Instances details
Monad Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

(>>=) :: Quaternion a -> (a -> Quaternion b) -> Quaternion b

(>>) :: Quaternion a -> Quaternion b -> Quaternion b

return :: a -> Quaternion a

Functor Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

fmap :: (a -> b) -> Quaternion a -> Quaternion b #

(<$) :: a -> Quaternion b -> Quaternion a #

MonadFix Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

mfix :: (a -> Quaternion a) -> Quaternion a

Applicative Quaternion Source # 
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 Source # 
Instance details

Defined in Linear.Quaternion

Methods

fold :: Monoid m => Quaternion m -> m

foldMap :: Monoid m => (a -> m) -> Quaternion a -> 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 # 
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)

Distributive Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

distribute :: Functor f => f (Quaternion a) -> Quaternion (f a) Source #

collect :: Functor f => (a -> Quaternion b) -> f a -> Quaternion (f b) Source #

distributeM :: Monad m => m (Quaternion a) -> Quaternion (m a) Source #

collectM :: Monad m => (a -> Quaternion b) -> m a -> Quaternion (m b) Source #

Representable Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Associated Types

type Rep Quaternion Source #

Show1 Quaternion Source # 
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

Read1 Quaternion Source # 
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]

Ord1 Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

liftCompare :: (a -> b -> Ordering) -> Quaternion a -> Quaternion b -> Ordering

Eq1 Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

liftEq :: (a -> b -> Bool) -> Quaternion a -> Quaternion b -> Bool

MonadZip Quaternion Source # 
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 Source # 
Instance details

Defined in Linear.Quaternion

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Quaternion a -> m () Source #

deserializeWith :: MonadGet m => m a -> m (Quaternion a) Source #

Hashable1 Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Quaternion a -> Int Source #

Apply Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Bind Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Additive Quaternion Source # 
Instance details

Defined in Linear.Quaternion

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 # 
Instance details

Defined in Linear.Quaternion

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 # 
Instance details

Defined in Linear.Quaternion

Associated Types

type Size Quaternion :: Nat Source #

Hamiltonian Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Complicated Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

_e :: Lens' (Quaternion a) a Source #

_i :: Lens' (Quaternion a) a Source #

Trace Quaternion Source # 
Instance details

Defined in Linear.Trace

Affine Quaternion Source # 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Quaternion :: Type -> Type 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 # 
Instance details

Defined in Linear.Quaternion

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> m (Vector (Quaternion a)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (Quaternion a) -> m (Mutable Vector (PrimState m) (Quaternion a)) Source #

basicLength :: Vector (Quaternion a) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a) Source #

basicUnsafeIndexM :: Monad m => Vector (Quaternion a) -> Int -> m (Quaternion a) Source #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> Vector (Quaternion a) -> m () Source #

elemseq :: Vector (Quaternion a) -> Quaternion a -> b -> b Source #

Unbox a => MVector MVector (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

basicLength :: MVector s (Quaternion a) -> Int Source #

basicUnsafeSlice :: Int -> Int -> MVector s (Quaternion a) -> MVector s (Quaternion a) Source #

basicOverlaps :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> Bool Source #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Quaternion a)) Source #

basicInitialize :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () Source #

basicUnsafeReplicate :: PrimMonad m => Int -> Quaternion a -> m (MVector (PrimState m) (Quaternion a)) Source #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (Quaternion a) Source #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> Quaternion a -> m () Source #

basicClear :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () Source #

basicSet :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Quaternion a -> m () Source #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () Source #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () Source #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (MVector (PrimState m) (Quaternion a)) Source #

(Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) Source # 
Instance details

Defined in Linear.Algebra

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 # 
Instance details

Defined in Linear.Algebra

Methods

mult :: (E Quaternion -> E Quaternion -> r) -> E Quaternion -> r Source #

unital :: r -> E Quaternion -> r Source #

Eq a => Eq (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

(==) :: Quaternion a -> Quaternion a -> Bool

(/=) :: Quaternion a -> Quaternion a -> Bool

RealFloat a => Floating (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

RealFloat a => Fractional (Quaternion a) Source # 
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) Source # 
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 :: forall r r'. (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 # 
Instance details

Defined in Linear.Quaternion

Ord a => Ord (Quaternion a) Source # 
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) Source # 
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) Source # 
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) Source # 
Instance details

Defined in Linear.Quaternion

Generic (Quaternion a) Source # 
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

Lift a => Lift (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

lift :: Quaternion a -> Q Exp

Storable a => Storable (Quaternion a) Source # 
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 ()

Serial a => Serial (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

serialize :: MonadPut m => Quaternion a -> m () Source #

deserialize :: MonadGet m => m (Quaternion a) Source #

Serialize a => Serialize (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Hashable a => Hashable (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

hashWithSalt :: Int -> Quaternion a -> Int Source #

hash :: Quaternion a -> Int Source #

Unbox a => Unbox (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Ixed (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Binary a => Binary (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

put :: Quaternion a -> Put

get :: Get (Quaternion a)

putList :: [Quaternion a] -> Put

NFData a => NFData (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

rnf :: Quaternion a -> ()

(Conjugate a, RealFloat a) => Conjugate (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

(RealFloat a, Epsilon a) => Epsilon (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

Methods

nearZero :: Quaternion a -> Bool Source #

Generic1 Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Associated Types

type Rep1 Quaternion :: k -> Type

Methods

from1 :: forall (a :: k). Quaternion a -> Rep1 Quaternion a

to1 :: forall (a :: k). Rep1 Quaternion a -> Quaternion a

FunctorWithIndex (E Quaternion) Quaternion Source # 
Instance details

Defined in Linear.Quaternion

FoldableWithIndex (E Quaternion) Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m Source #

ifolded :: IndexedFold (E Quaternion) (Quaternion a) a Source #

ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b Source #

ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b Source #

ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b Source #

ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b Source #

TraversableWithIndex (E Quaternion) Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) Source #

itraversed :: IndexedTraversal (E Quaternion) (Quaternion a) (Quaternion b) a b Source #

Each (Quaternion a) (Quaternion b) a b Source # 
Instance details

Defined in Linear.Quaternion

Methods

each :: Traversal (Quaternion a) (Quaternion b) a b Source #

Field1 (Quaternion a) (Quaternion a) a a Source # 
Instance details

Defined in Linear.Quaternion

Methods

_1 :: Lens (Quaternion a) (Quaternion a) a a Source #

Field2 (Quaternion a) (Quaternion a) a a Source # 
Instance details

Defined in Linear.Quaternion

Methods

_2 :: Lens (Quaternion a) (Quaternion a) a a Source #

Field3 (Quaternion a) (Quaternion a) a a Source # 
Instance details

Defined in Linear.Quaternion

Methods

_3 :: Lens (Quaternion a) (Quaternion a) a a Source #

Field4 (Quaternion a) (Quaternion a) a a Source # 
Instance details

Defined in Linear.Quaternion

Methods

_4 :: Lens (Quaternion a) (Quaternion a) a a Source #

type Rep Quaternion Source # 
Instance details

Defined in Linear.Quaternion

type Size Quaternion Source # 
Instance details

Defined in Linear.Quaternion

type Size Quaternion = 4
type Diff Quaternion Source # 
Instance details

Defined in Linear.Affine

data MVector s (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)
type Rep (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

type Rep (Quaternion a) = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.9-RPUBINYq384VPzdgkhYOj" '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))))
data Vector (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

data Vector (Quaternion a) = V_Quaternion !Int (Vector a)
type Index (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

type IxValue (Quaternion a) Source # 
Instance details

Defined in Linear.Quaternion

type IxValue (Quaternion a) = a
type Rep1 Quaternion Source # 
Instance details

Defined in Linear.Quaternion

type Rep1 Quaternion = D1 ('MetaData "Quaternion" "Linear.Quaternion" "linear-1.20.9-RPUBINYq384VPzdgkhYOj" '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)))

class Complicated t where Source #

A vector space that includes the basis elements _e and _i

Methods

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

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

Instances

Instances details
Complicated Complex Source # 
Instance details

Defined in Linear.Quaternion

Methods

_e :: Lens' (Complex a) a Source #

_i :: Lens' (Complex a) a Source #

Complicated Quaternion Source # 
Instance details

Defined in Linear.Quaternion

Methods

_e :: Lens' (Quaternion a) a Source #

_i :: Lens' (Quaternion a) a Source #

class Complicated t => Hamiltonian t where Source #

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

Methods

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

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

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

Instances

Instances details
Hamiltonian Quaternion Source # 
Instance details

Defined in Linear.Quaternion

ee :: Complicated t => E t Source #

ei :: Complicated t => E t Source #

ej :: Hamiltonian t => E t Source #

ek :: Hamiltonian t => E t Source #

slerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a Source #

Spherical linear interpolation between two quaternions.

asinq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

asin with a specified branch cut.

acosq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

acos with a specified branch cut.

atanq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

atan with a specified branch cut.

asinhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

asinh with a specified branch cut.

acoshq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

acosh with a specified branch cut.

atanhq :: RealFloat a => Quaternion a -> Quaternion a -> Quaternion a Source #

atanh with a specified branch cut.

absi :: Floating a => Quaternion a -> a Source #

norm of the imaginary component

pow :: RealFloat a => Quaternion a -> a -> Quaternion a Source #

raise a Quaternion to a scalar power

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

Apply a rotation to a vector.

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

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